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University of Southern California Dissertations and Theses
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Ultrafast dynamics of excited state intra- and intermolecular proton transfer in nitrogen containing photobases
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Ultrafast dynamics of excited state intra- and intermolecular proton transfer in nitrogen containing photobases
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Content
Ultrafast Dynamics of Excited State Intra-
and Intermolecular Proton Transfer in
Nitrogen Containing Photobases
by
Eric William Driscoll
A Dissertation Presented to the
Faculty of The USC Graduate School
University of Southern California
In Partial Fulllment of the
Requirements for the Degree
Doctor of Philosophy
(Chemistry)
August 2017
Copyright 2017 Eric William Driscoll
ii
Acknowledgments
I am thankful to have gotten the opportunity to work with a wide variety of talented individuals
during the course of my graduate studies. You have all played a role in the research presented
here, either directly through scientic discussion and collaboration, or indirectly via support and
friendship. These acknowledgments are an attempt to verbalize the gratitude that I feel towards
all of you.
First, I must thank my advisor, Jahan, who's endless source of patience and compassion has been
crucial to my success. When Shayne and I decided to join the lab in 2012, neither of us knew much
of anything about lasers or optics having come from a chemistry background. Jahan very patiently
helped us over the large learning curve of joining an ultrafast spectroscopy group. His knowledge
of scientic concepts and commitment to teaching them with as little jargon as possible are well
known and speak for themselves. What I wish to highlight here instead is his profound ability
for humility and compassion. I always felt that he placed a high priority on his students' physical
and emotional well-being, as well as our long-term professional success. Such a supportive work
environment is unfortunately not actively encouraged in graduate programs, but instead is highly
dependent on the moral character and emotional intelligence of the advisor. Jahan recognizes the
value in a healthy work environment and for that I will say thank you once more.
Similarly, it has been a pleasure to work alongside my group members. I value our unwritten
policy on openness to asking for help from each other and hope that it continues into future
generations. I will also sincerely miss our tangential, philosophical conversations that tend to crop
up on Friday afternoons. They are analogous to stimulated emission, where one member will think
iii
iv ACKNOWLEDGMENTS
aloud spontaneously, and an avalanche of ideas and opinions from everyone else follows.
The friends that I've made on the west coast are a truly remarkable, eclectic, and often times
eccentric, bunch of people. There are too many of you to name names so I'll just list, in no
particular order, some of my most cherished memories that you've helped to create: long bike rides,
rock climbing indoors and outside, music shows and festivals, hiking and camping in places that
are too hot and in places that are too cold, the most international Thanksgiving dinner I've ever
had, jumping out of airplanes, all those deep one-on-one conversations, and all those beers we've
shared. Finding a sense of community here has been wonderfully fun and enlightening. Thank you.
Finally, I owe many thanks to my family, who have provided me with an upbringing that allowed
me to succeed academically. They have always been encouraging in my pursuit of knowledge, even
when it means moving away from home and only being able to visit during the holidays.
Eric Driscoll
June 2017
Los Angeles, CA
Table of Contents
Acknowledgments iii
List of Figures ix
List of Tables xxi
1 Introduction 1
1.1 Proton Transfer Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Investigation of Model Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Excited State Proton Transfer in a Model System 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Transient Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 Steady State Absorption and Emission Spectra . . . . . . . . . . . . . . . . . 11
2.3.2 Diol Transient Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.3 Solvent Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.4 Ethoxy-ol Transient Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 Electronic Structure Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.2 Stokes Shift Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.4 Absence of Wavepackets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Supporting Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.1 Chirp Correction and Blank Spectra . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.2 Transient Absorption Fit Residuals and Fourier Transforms . . . . . . . . . . 25
2.7 Relative Time Constants and Kinetic Isotope Eect . . . . . . . . . . . . . . . . . . 29
2.7.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.7.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
v
vi TABLE OF CONTENTS
2.7.3 Transient Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Photobase Thermodynamics 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Electronic Singlet States of Quinoline . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 F orster cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Hammett Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5 Limit of Photobasicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6 Deviation of Quinoline's State Energies . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.7 ICT and Analogy to Photoacids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.8 Triplet States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.10 Experimental Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10.2 Steady State Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10.3 F orster cycle Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.10.4 Computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.11 Supplemental Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.11.1 The F orster cycle and its approximations . . . . . . . . . . . . . . . . . . . . 52
3.11.2 Choosing a set of Hammett parameters . . . . . . . . . . . . . . . . . . . . . 53
3.11.3 Charge Density Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.11.4 Photoacid-like behavior of MeOQ . . . . . . . . . . . . . . . . . . . . . . . . . 56
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Photobase Kinetics 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Experimental Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.2 Steady State Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.3 Transient Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.1 Identication of Transient Chemical Species . . . . . . . . . . . . . . . . . . . 66
4.3.2 5-methoxyquinoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.3 Quinoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3.4 5-chloro and 5-bromoquinoline . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3.5 5-cyanoquinoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.6 5-aminoquinoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.7 Electronic States in Quinoline and Quinolinium Ion . . . . . . . . . . . . . . 76
4.3.8 Observed Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5 Supporting Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.1 Absorption, Emission, and Transient Absorption Spectra by Compound . . . 81
4.5.2 UV Absorption Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.5.3 Auxiliary Ultrafast Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
TABLE OF CONTENTS vii
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5 Pump-Probe Transient Absorption 115
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.3 TA with Balanced Detection of Broadband Probe . . . . . . . . . . . . . . . . . . . . 119
5.3.1 White Light Supercontinuum Generation . . . . . . . . . . . . . . . . . . . . 124
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6 Singular Value Decomposition of Spectroscopic Data 127
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2 Minimal example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.3 Addition of noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.4 Rank approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.5 Singular values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.6 Image Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.7 Simulated Spectroscopic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.8 Orthogonal Basis Spectra Versus Species Associated Spectra . . . . . . . . . . . . . . 145
6.9 Rotation of Basis Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.10 Rotation In 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.11 Extraction of Dynamics from SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.12 Generalization to Other Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.13 Potential Pit Falls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
A MATLAB Code 159
A.1 dechirp.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
A.2 defaultGraphingOptions.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
A.3 TAt.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
A.4 svdplots.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
A.5 svdrank.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
B Trigger Circuit Diagram 173
viii TABLE OF CONTENTS
List of Figures
1.1 Examples of molecules that experience a change in protonation state upon absorp-
tion of light. Fragments highlighted in red become more acidic upon excitation,
while fragments in blue become more alkaline. Left: the excited state intramolecular
proton transfer molecule (chapter 2) has connected photoacidic and photobasic frag-
ments. Center: the well known photoacid 1-napthol shows tunability in its excited
state pKa via charge donation and withdrawal by a substituent in the 5 position.
?
.
Right: quinoline, a photobase, shows tunability of its singlet excited states via sub-
stitution similar to 1-naphthol (chapter 3). However, its ultrafast dynamics are more
complicated and involve intersystem crossing to triplet states depending on the sub-
stituent R (chapter 4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Chemical species discussed in this paper, denoted with \E" for enol and \K" for keto.
(top) The three possible tautomers of the diol molecule and a schematic showing
their interconversion in the ground and excited states. Three possible mechanisms
for relaxation are shown in color: single proton transfer (red), stepwise double proton
transfer (blue), and concerted proton transfer (green). (bottom) The two possible
tautomers of the ethoxy substituted molecule (ethoxy-ol) and their interconversion. . 9
ix
x LIST OF FIGURES
2.2 TA of the diol in methanol. (a) Steady state absorption (blue) and emission (red)
spectra of the diol in methanol. Pump (dashed blue) and probe (dashed red) pulse
spectra. (b) 1,3-Bis(imino)isoindole diol, shown in the enol-enol tautomer as it exists
in the electronic ground state. (c) Visible pump-white light probe TA over 4 ps. (d)
A temporal slice of transient absorption along the dashed line in (c) through = 650
nm. The stimulated emission shows single exponential behavior. The solvent shows
some TA features at short times (dashed blue line and Figure 2 in SI) which are not
interpreted or tted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 TA of the ethoxy-ol in methanol. (a) Steady state absorption (blue) and emission
(red) spectra of the ethoxy-ol in methanol. Pump (dashed blue) and probe (dashed
red) pulse spectra. (b) Ethoxy substituted isoindole, shown in the enol tautomer.
(c) Visible pump-white light probe TA over 4 ps. (d) A temporal slice of transient
absorption along the dashed line in (c) through = 650 nm. . . . . . . . . . . . . . 16
2.4 Cartoon of the diol potential energy surface resulting from stepwise proton transfer
events. The blue arrow shows optical excitation of the EE tautomer, while the red
arrows show possible emission from EK* and KK* tautomers. Although this diagram
is meant to be qualitative, the spacing between levels and heights of the barriers are
drawn based on calculations by Su
?
. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Frontier molecular orbitals of the diol and ethoxy-ol in the EE and E tautomers.
TD-DFT calculations suggest that the S
0
!S
1
excitation is primarily between the
HOMOs and LUMOs. Upon optical excitation electron density shifts from around
the benzene and hydroxyl groups towards the pyrrole and pyridine groups in both
compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
LIST OF FIGURES xi
2.6 Cross correlation of pump and probe in a 0.5 mm sapphire plate. (a) Nonresonant
response from sapphire ts well to a second order polynomial (dashed blue line).
Fit parameters: a = -0.0034
fs
2
nm
2
, b = 5.34
fs
nm
. (b) Chirp corrected version of
the nonresonant signal. The instrument resolution is approximately 200 fs for each
spectral component. This t was applied to all sample and blank spectra so that
temporal evolution of many spectral components could be compared at the same time. 24
2.7 Transient response of methanol in a quartz
ow cell. . . . . . . . . . . . . . . . . . . 24
2.8 (a) Time trace of the diol in methanol (Figure 2D reproduced here). (b) Residual
of exponential t in (a). (c) Time trace of the ethoxy-ol in methanol (Figure 3D
reproduced here). (d) Residual of exponential t in (c). . . . . . . . . . . . . . . . . 25
2.9 (a) Time trace of the diol in methanol with small step size (5 fs), probed in the
uorescence band at 625 nm. A gaussian window function (green line) is multiplied
by the data (blue line) to remove the oscillations present in the coherent spike, which
are not from nuclear motion. (b) Fourier amplitudes of the raw (blue line) and
windowed (red line) data. No single frequency is dominant. . . . . . . . . . . . . . . 26
2.10 (a) Time trace of the diol in chloroform with small step size (2 fs), probed in the
uorescence band at 600 nm. (b) Fourier transforming reveals a dominant mode
at 332 cm
-1
which is due to chloroform. A gaussian window function (green line)
is multiplied by the complex Fourier transform to lter out the oscillation due to
chloroform. (c) Inverse Fourier transforming returns a time trace without oscillations.
(d) The residual of the exponential t in (c) is plotted. . . . . . . . . . . . . . . . . . 27
2.11 (a) Time trace of the diol in cyclohexane with 10 fs step size, probed in the
u-
orescence band at 600 nm. (b) Fourier amplitude shows no dominant modes. (c)
Residual of the exponential t in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.12 Cartoon diagram of the molecular seesaw eect. The diol (left) contains two equiva-
lent hydrogen bonds which compete with each other. The ethoxy-ol (right) contains
a single hydrogen bond, allowing the geometry to relax to a decreased N-H bond
distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
xii LIST OF FIGURES
2.13 Depiction of the molecular seesaw eect. Optimized geometries for the ESIPT re-
actant for the diol (top panel) and the ethoxy-ol (bottom panel) are shown from
calculations at the B3LYP/ TZVP level of theory. ESIPT distances are shown in
blue and given in angstroms, and the CCC bond angles are shown in black. As
illustrated at right, removing one of the hydrogen bonds, as in the ethoxy-ol, elim-
inates the competition of the two hydrogen bonds and thus shortens the remaining
hydrogen bond. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.14 The coherent spike due to the interaction between the pump and probe in pure
acetonitrile and the sample holder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.15 Transient absorption of the diol in acetonitrile. (left) Single exponential t of the
population dynamics retrieved by SVD. (right) . . . . . . . . . . . . . . . . . . . . . 34
2.16 Transient absorption of the diol-D in acetonitrile. (left) Single exponential t of the
population dynamics retrieved by SVD. (right) . . . . . . . . . . . . . . . . . . . . . 34
2.17 Transient absorption of the ethoxy-ol in acetonitrile. (left) Single exponential t of
the population dynamics retrieved by SVD. (right) . . . . . . . . . . . . . . . . . . . 35
2.18 Transient absorption of the ethoxy-ol-D in acetonitrile. (left) Single exponential t
of the population dynamics retrieved by SVD. (right) . . . . . . . . . . . . . . . . . . 35
3.1 (a) The structure of 5-substituted quinoline. (b) Normalized absorption (solid) and
emission (dashed) spectra of 5-bromoquinoline in basic (blue) and acidic (red) aque-
ous solutions. The approximate origin band energies of the two lowest lying singlet
states are annotated. The
1
L
b
origin is observed as a sharp feature, while the
1
L
a
origin is estimated by averaging absorption and emission maxima. For all other com-
pounds in this study, the spectra can be found in the SI. (c) Depiction of the F orster
cycle as it applies to quinolines. The excited state equilibrium is between the two
lowest lying singlet states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
LIST OF FIGURES xiii
3.2 The dependence of
1
L
a
and
1
L
b
states for protonated and deprotonated forms on the
Hammett parameter of the substituents. Straight lines are approximate ts (with
the exclusion of unsubstituted quinoline as described in the text). The lowest excited
state is
1
L
A
(RQH
+
) throughout the range of the study. The excited state G
for
protonation is far more favorable than the ground state G, giving rise to photobasic-
ity. Hammett values for which the
1
L
a
and
1
L
b
states becomes possibly degenerate,
are indicated by the vertical dashed line. The dierence G = G
G, de-
termining pK
a
seems to rapidly diminish upon crossing the point of degeneracy of
the
1
L
a
state for the deprotonated form. . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Ground and excited state pK
a
of 5-substituted quinolines versus Hammett
p
pa-
rameter. Lines of linear t are shown in solid. The two central ndings of our work
are the linear dependence of the excited state pK
a
on
p
and its larger slope
5. 48
3.4 Calculated Mulliken charge on the heterocyclic nitrogen in 5-substituted quinolines
when in the ground state (o), excited state (x), protonated (red), and deprotonated
(blue) as a function of experimentally measured pK
a
. . . . . . . . . . . . . . . . . . 55
3.5 Comparison of the in
uence of the substituent groups on photoacidity and photoba-
sicity. Electron density dierence maps show the S
1
electron density minus the S
0
electron density. Green (red) indicates an increase (decrease) in density upon exci-
tation. Electron donating (withdrawing) groups are shown to enhance photobasicity
(photoacidity). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6 Excitation spectra of 5-methoxyquinoline in acidic aqueous solution shows two dis-
tinct species corresponding to the protonated and deprotonated forms. A solvent
Raman peak is labeled with \R". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.7 Excitation dependent emission in excess acid suggests photoacid-like behavior. Ex-
citing the higher lying
1
L
b
state releases the proton to form the neutral MeOQ*
species. A solvent Raman peak is labeled with \R". . . . . . . . . . . . . . . . . . . 58
xiv LIST OF FIGURES
4.1 5-methoxyquinoline transient absorption in water. (A) TA spectra at pH 3.0 (solid),
steady state
uorescence in acidic water displayed inverted and scaled (dashed); (B)
TA spectra at pH 7.0 (solid), steady state
uorescence in methanol displayed inverted
and scaled (dashed). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Quinoline transient absorption in water. (A) TA spectra at pH 2.4 (solid), steady
state
uorescence in acidic water displayed inverted and scaled (dashed); (B) TA
spectra at pH 7.0. As explained in the text, these TA spectra are evidence for
rapid triplet formation, which is consistent with the lack of steady state
uorescence.
Triplet-triplet absorption energies used to construct the state diagram in Figure 4.6
are marked withy and *. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Halogenated quinoline transient absorption in water. (A) 5-chloroquinoline TA at
pH 1.8 (solid), steady state
uorescence in acidic water displayed inverted and scaled
(dashed); (B) 5-chloroquinoline TA at pH 5.3. (C) 5-bromoquinoline TA at pH
1.9 (solid), steady state
uorescence in acidic water displayed inverted and scaled
(dashed); (D) 5-bromoquinoline TA at pH 5.3. The sharp feature at 570 nm is an
artifact from pump scatter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 5-cyanoquinoline transient absorption in water at pH 1.2 (A); pH 7.0 (B); . . . . . . 73
4.5 5-aminoquinoline transient absorption at pH 3.4 (A); pH 8.2 at early times (B); and
pH 8.2 at late times (C); Transient spectra of acidic and basic solutions at long time
delays. (D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.6 Approximate singlet (blue) and triplet (red) state ordering in quinoline and quino-
linium ion in water. Degenerate levels are drawn with slight displacement for clarity.
Proposed mechanisms for
uorescence of quinolinium (left) and triplet photobasicity
of quinoline (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.7 Absorption spectra (left) and titration curve (right) for 5-aminoquinoline in aqueous
solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.8 UV absorption spectrum of 5-aminoquinoline under acidic (red) and basic (blue)
conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
LIST OF FIGURES xv
4.9 Emission spectra of 5-aminoquinoline in aqueous solution. . . . . . . . . . . . . . . . 82
4.10 Transient absorption of 5-aminoquinoline at pH 3.4. . . . . . . . . . . . . . . . . . . 83
4.11 Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) =ae
(x=tau)
+c; Coecients (with 95% condence bounds): a =
-0.3632 (-0.3831, -0.3432); c = 0.09813 (0.07681, 0.1195); tau = 36.15 (29.91, 42.39);
Goodness of t: SSE: 0.05554; R-square: 0.9396; Adjusted R-square: 0.9383; RMSE:
0.02418. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.12 Transient absorption of 5-aminoquinoline at pH 8.2. . . . . . . . . . . . . . . . . . . 85
4.13 Population dynamics of rst component obtained from singular value decomposition
of TA data. Fitting equation: f(x) =ae
(x=tau)
+c; Coecients (with 95% con-
dence bounds): a = -0.2837 (-0.2911, -0.2763); c = -0.01002 (-0.01352, -0.006514); tau
= 40.92 (38.53, 43.31); Goodness of t: SSE: 0.007521; R-square: 0.9856; Adjusted
R-square: 0.9853; RMSE: 0.008805. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.14 Population dynamics of second component obtained from singular value decomposi-
tion of TA data. Fitting equation: f(x) =a1e
(x=tau1)
+a2e
(x=41)
+c; Coecients
(with 95% condence bounds): a1 = -1.719 (-2.739, -0.6982); a2 = 1.393 (0.3303,
2.455); c = -0.01268 (-0.03476, 0.009393); tau1 = 26.82 (19.51, 34.12); Goodness of
t: SSE: 0.1807; R-square: 0.7877; Adjusted R-square: 0.7811; RMSE: 0.04338. . . . 87
4.15 Transient absorption of 5-aminoquinoline in acidic and basic solutions at long time
delays (left); Transient absorption of 5-aminoquinoline at a negative delay (probe hits
rst) and the
uorescence spectrum of 5-methoxyquinoline inverted for comparison
(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.16 Absorption spectra (left) and titration curve (right) for 5-methoxyquinoline in aque-
ous solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.17 UV absorption spectrum of 5-methoxyquinoline under acidic (red) and basic (blue)
conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.18 Emission spectra of 5-methoxyquinoline in various solvents.
ex
= 340 nm . . . . . . 90
4.19 Transient absorption of 5-methoxyquinoline at pH 3.0. . . . . . . . . . . . . . . . . . 90
xvi LIST OF FIGURES
4.20 Transient absorption of 5-methoxyquinoline at pH 7.0. . . . . . . . . . . . . . . . . . 91
4.21 Transient absorption spectra of 5-methoxyquinoline decomposed into Gaussian func-
tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.22 Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) =ae
(x=tau)
+c; a = 0.3839 (0.3777, 0.3901); c = -0.0758 (-0.07938,
-0.07222); tau = 23.29 (22.37, 24.21); Goodness of t: SSE: 0.005699; R-square:
0.9942; Adjusted R-square: 0.994; RMSE: 0.007705. . . . . . . . . . . . . . . . . . . 92
4.23 Absorption spectra (left) and titration curve (right) for quinoline in aqueous solution. 93
4.24 UV absorption spectrum of quinoline under acidic (red) and basic (blue) conditions. 93
4.25 Emission spectra of quinoline in two solvents. . . . . . . . . . . . . . . . . . . . . . . 94
4.26 Transient absorption of quinoline at pH 2.4. . . . . . . . . . . . . . . . . . . . . . . . 94
4.27 Transient absorption of quinoline at pH 7.0. . . . . . . . . . . . . . . . . . . . . . . . 95
4.28 Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) =ae
(x=tau)
+c; a = -0.3884 (-0.3942, -0.3826); c = 0.1312 (0.1263,
0.136); tau = 28.43 (27.19, 29.67); Goodness of t: SSE: 0.004946; R-square: 0.9949;
Adjusted R-square: 0.9948; RMSE: 0.007373. . . . . . . . . . . . . . . . . . . . . . . 96
4.29 Absorption spectra (left) and titration curve (right) for 5-chloroquinoline in aqueous
solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.30 UV absorption spectrum of 5-chloroquinoline under acidic (red) and basic (blue)
conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.31 Emission spectra of 5-chloroquinoline in various solvents. . . . . . . . . . . . . . . . . 98
4.32 Transient absorption of 5-chloroquinoline at pH 1.9 . . . . . . . . . . . . . . . . . . . 98
4.33 Transient absorption of 5-chloroquinoline at pH 5.3 . . . . . . . . . . . . . . . . . . . 99
4.34 Absorption spectra (left) and titration curve (right) for 5-bromoquinoline in aqueous
solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.35 UV absorption spectrum of 5-bromoquinoline under acidic (red) and basic (blue)
conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.36 Emission spectra of 5-bromoquinoline in acidic and basic aqueous solution. . . . . . 101
LIST OF FIGURES xvii
4.37 Transient absorption of 5-bromoquinoline at pH 1.9 . . . . . . . . . . . . . . . . . . . 101
4.38 Transient absorption of 5-bromoquinoline at pH 5.3 . . . . . . . . . . . . . . . . . . . 102
4.39 Absorption spectra (left) and titration curve (right) for 5-cyanoyquinoline in aqueous
solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.40 UV absorption spectrum of 5-cyanoquinoline under acidic (red) and basic (blue)
conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.41 Emission spectrum of 5-cyanoquinoline in acidic solution. . . . . . . . . . . . . . . . 104
4.42 Transient absorption of 5-cyanoquinoline at pH 1.2 . . . . . . . . . . . . . . . . . . . 104
4.43 Transient absorption of 5-cyanoquinoline at pH 5.3 . . . . . . . . . . . . . . . . . . . 105
4.44 Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) =ae
(x=tau)
+c; a = -0.3942 (-0.4039, -0.3845); c = 0.07762 (0.07321,
0.08203); tau = 39.82 (37.67, 41.97); Goodness of t: SSE: 0.01258; R-square: 0.9874;
Adjusted R-square: 0.9872; RMSE: 0.01139. . . . . . . . . . . . . . . . . . . . . . . . 106
4.45 Maximum absorption energy of the
1
(n,
) transition of free base and protonated
quinolines as a function of Hammett parameter,
p
. Strong electron donating sub-
stituends (negative
p
) red shifts the state energy. Protonation also red shifts this
energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.46 Cross correlation of 287 nm pump pulse and CaF
2
white light continuum in water. . 108
4.47 Cross correlation of 310 nm pump pulse and CaF
2
white light continuum in water. . 109
4.48 Cross correlation of 333 nm pump pulse and CaF
2
white light continuum in water. . 110
4.49 Transient absorption power dependence of 5-aminoquinoline. . . . . . . . . . . . . . 111
4.50 Transient absorption power dependence of 5-methoxyquinoline. . . . . . . . . . . . . 111
4.51 Transient absorption power dependence of 5-bromoquinoline. . . . . . . . . . . . . . 112
4.52 Transient absorption power dependence of 5-cyanoquinoline. . . . . . . . . . . . . . . 112
xviii LIST OF FIGURES
5.1 A transient absorption experiment done in pump-probe geometry. Top: A sample (S)
will have some absorption cross section. A white light probe is transmitted through
the sample and it's intensity detected with a spectrometer. Bottom: A pump pulse
prepares the molecules in a sample in an excited state. This pumped sample (S*())
is now a function of time. Another probe pulse is transmitted through the sample at
some specied delay, . The transmitted intensity is detected with a spectrometer. . 117
5.2 Transient absorption signal calculation. Top: The intensities of the pump on and
pump o cases shown in gure 5.1. See text for description of GSB, SE, and ESA.
Bottom: The log of the ratios of the intensities shown in the top gure are plotted.
Typically, because TA signals are small, this optical density is multiplied by 1000
and plotted in mOD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.3 A traditional pump-probe transient absorption experiment. Pump and probe pulse
trains with an optical chopper dividing the repetition rate of the pump. The intensity
of the probe when unpumped (I
u
) is compared to the intensity of the probe when
pumped (I
p
). The dierence absorption is typically small and multiplied by 10
3
to
be shown in units of optical density 10
3
(mOD). . . . . . . . . . . . . . . . . . . . . 119
5.4 Top: White light continuum spectrum generated in water. Bottom left: Transient
spectrum of 1000 pulse pair averages of the WLC spectrum with the pump o.
Bottom right: Another example. Although one may expect the spectral
uctuations
to be random certain features appear even after a large number of averages. A broad
peak on the blue side and high frequency oscillations on the red side are often seen. 120
5.5 In a balanced detection scheme the probe is split into sample and reference arms.
The reference is slightly misaligned so it never feels the in
uence of the pump. Al-
ternatively it may be delayed in time to achieve this. The reference pulse pair only
contains instability of the probe (i.e. the transient spectra shown in gure 5.4), while
the sample contains the instability and the pump induced TA. The averaging scheme
shown subtracts the instability terms leaving only the real TA. Bonus points: why
is the re
ected portion of the beam splitter the sample arm? . . . . . . . . . . . . . . 121
LIST OF FIGURES xix
5.7 Intensity pattern on the CCD array when collecting both sample and reference in
image mode. Check to see that each beam remain within the top of bottom half
and does not bleed into the other. Notice how each intensity pattern is slanted
towards the center at the right hand side of the array (red side of spectrum). This is
unavoidable in this alignment scheme. These are water white light pulses, spectrum
shown in gure 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.6 Alignment of sample and reference beams through sample and into a monochromator
for detection. All focusing optics are shown as lenses for the purpose of clarity. Most
are in fact curved mirrors. The y dimension is normal to the surface of the table, z
is along the direction of beam propagation, x is orthogonal to y and z. . . . . . . . . 122
5.8 Setup of optical hardware. Using this three chopper scheme it's possible to set the
pump/probe phase incorrectly. Check it with a photodiode and oscilloscope to be
sure. Adjust the phase of the choppers if necessary. . . . . . . . . . . . . . . . . . . . 123
5.9 Setup of electrical hardware. SDG delays do not have to be 1 and 2 specically. . . . 123
6.1 Dimensional analysis of data decomposition by SVD. Top: When the SVD algorithm
is applied to a data matrix,D, three matrices are returned such thatD =USV
y
. U
andV contains information about the column space and row space ofD, respectively.
S is a diagonal matrix which contains the singular values. Bottom: An example data
set can be constructed by multiplying a set of spectra and decay proles, where
each row/column represents features of a chemical species. Some numerical work
and often times assumptions are needed to turn SVD (top decomposition) into a
chemically insightful form (bottom decomposition). . . . . . . . . . . . . . . . . . . . 132
6.2 The rst column of U contains information about the dynamics of the data set. It
is an orthonormal basis vector of U, which by itself is not chemically meaningful.
However, it can also be expressed as a linear combination of the decay proles we
dened earlier. This is demonstrated by tting the orthonormal vector with a sum
of exponential functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
xx LIST OF FIGURES
6.3 A Gaussian function centered at 400 nm that shifts linearly to 500 nm in 1000 fs.
Noise is added at 10% of the maximum value. This is a simple simulation of how
excited state relaxation may manifest in transient spectroscopy. . . . . . . . . . . . . 153
6.4 The singular values obtained from SVD of the above data, expressed a percent of the
rst singular value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.5 The rst three columns of the U matrix obtained from SVD . . . . . . . . . . . . . 154
6.6 The rst three columns of the V matrix obtained from SVD . . . . . . . . . . . . . 155
B.1 Logic and connection diagram of circuit that triggers the Pixis camera. \Arduino"
is a digital output pin on an Arduino microcontroller that is controlled with the
LabVIEW ArduinoSendEdges.vi program. \Trig In" is usually the output of an
optical chopper control box. \SDG In" is one of the delays from the signal delay
generator. \Trig Out" is sent to the Ext Sync on the Pixis camera. The AND and
OR gates perform their corresponding logic operations on their inputs as one may
expect. The JK chips set to \
ip-
op" mode are less well known, but simply change
their output state (either from 0 to 1 or vice versa) when a rising edge is detected on
the input. A red indicator LED is placed such that when the gate is open the LED
is illuminated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
List of Tables
2.1 Experimental and calculated Stokes shifts for various ESIPT species. . . . . . . . . . 14
2.2 Calculated and Measured Proton Transfer Times, , of the Diol and the Ethoxy-ol
and Respective Relative Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Calculated and Measured KIE of the Diol and the Ethoxy-ol, as Well as the Respec-
tive Relative Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Proton transfer time constants in femtoseconds measured in acetonitrile. For com-
parison transfer times from ref
?
measured in other solvents are given. . . . . . . . . 33
3.1 Approximate origin band transition energies, pK
a
, and pK
a
for the set of 5-R-
quinolines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Hammett parameters and thermodynamic measurements . . . . . . . . . . . . . . . . 54
3.3 Reaction constants and correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1 Ultrafast dynamics of 5-substituted quinolines in their base and cationic forms or-
dered by Hammett
p
parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Approximate energy levels of quinoline and quinolinium ion in water . . . . . . . . . 78
xxi
xxii LIST OF TABLES
Chapter 1
Introduction
1.1 Proton Transfer Reactions
The concept of an acid-base reaction is one of the most fundamental and important constructs in
the eld of chemistry. Under the Brnsted-Lowry denition an acid is a proton donor, and a base
is a proton acceptor.
1
When proton donors and acceptors are located on the same molecule the
acid-base reaction is referred to as tautomerization. The ubiquity of proton transfer reactions in
nature is not understated. Protons play major roles in photosynthesis
2,3
, medicine
4
, our sense of
sour taste
5
, and nitrogen xation
6
.
As our society moves towards a more sustainable energy economy, we seek methods for the genera-
tion of chemical fuels, such as hydrogen gas, methanol, and methane, that do not rely on fossilized
carbon. Production of these fuels from readily available feedstocks like water and carbon dioxide will
be energy storing, endothermic reactions. An abundant, carbon neutral, option for providing this
thermodynamic drive is solar radiation. In addition to being thermodynamically unfavorable, solar
fuel generation involves redox reactions that require the reorganization of multiple electrons and
protons. Plants and certain bacteria have developed the molecular machinery necessary to manipu-
late these charge carriers in a process referred to as proton coupled electron transfer (PCET).
2,3,7{9
Signicant scientic eort has been made to create articial photosynthetic
10
systems which, rather
1
2 CHAPTER 1. INTRODUCTION
than producing sugars as is done in plants, produce fuels such as hydrogen
11
and hydrocarbons.
12
1.2 Investigation of Model Systems
The complex nature of PCET calls for the investigation of simpler systems that couple the absorp-
tion of light into proton motion. In the research presented here, we examine two model systems
which undergo reversible, excited state proton transfer: a bis(imino)isoindole diol and substituted
quinoline photobase. Unlike a photocatalyst, no stable chemical fuel product is produced. The
purpose is to rst discover and distill the essential features of molecular systems that lead to the
coupling of light absorption into proton transfer.
The rst system studied is a model exited state intramolecular proton transfer (ESIPT) molecule
presented in chapter 2. This system is interesting because it contains two equivalent protonation
sites, thus making it a potential model of a process involving multi-proton transfer. However, while
it appears to poised to undergo double proton transfer, it in fact only undergoes single proton
transfer. The reasoning behind this behavior was further elucidated by a collaborated with Ralph
Welsch and Tom Miller, dubbed the \seesaw" eect.
The results from the ESIPT study prompted us to think about excited state proton transfer in
terms of acidic functional groups becoming more acidic and basic functional groups becoming more
basic as a result of the charge redistribution upon light absorption.
Molecules which undergo a pK
a
change in an electronically excited state are said to be photoacidic
(pK
a
< pK
a
) or photobasic (pK
a
> pK
a
). In the literature are numerous examples of pho-
toacids.
14{18
In the case of solution phase photoacids, the proton acceptor is often the solvent
molecule, typically water. It was surprising to learn that the logical counterpart of photoacids,
photobases, were substantially less studied in the literature
19{21
. While several examples of photo-
bases do exist, they have not found utility in the types of research applications that photoacids have
been used for.
22{24
In order to encourage the use of photobases for pOH jump experiments and po-
tentially as functional elements of photocatalysts we have investigated some of their photophysical
properties.
1.3. EXPERIMENTAL METHODS 3
Figure 1.1: Examples of molecules that experience a change in protonation state upon absorption
of light. Fragments highlighted in red become more acidic upon excitation, while fragments in blue
become more alkaline. Left: the excited state intramolecular proton transfer molecule (chapter 2)
has connected photoacidic and photobasic fragments. Center: the well known photoacid 1-napthol
shows tunability in its excited state pKa via charge donation and withdrawal by a substituent in
the 5 position.
13
. Right: quinoline, a photobase, shows tunability of its singlet excited states via
substitution similar to 1-naphthol (chapter 3). However, its ultrafast dynamics are more compli-
cated and involve intersystem crossing to triplet states depending on the substituent R (chapter
4).
In chapter 3 we explore the limits of pK
a
tunability in substituted quinoline photobases. We found
that the singlet excited state energies could be tuned in a predictable way, similar to the 1-naphthol
photoacid family. Chapter 4 details the picosecond dynamics associated with quinoline photobases.
We found that there were multiple relaxation pathways possible, most of which do not undergo
singlet state proton transfer. This is in stark contrast to the 1-naphthol family of structurally
similar photoacids, which all undergo singlet state proton transfer. The inclusion of a heterocyclic
nitrogen, a fundamentally important feature in a photobase, causes a triplet state to emerge at a
similar energy to S
1
. These nearly degenerate states makes the rate of intersystem cross highly
sensitive to substitution.
1.3 Experimental Methods
The primary experimental technique used in these studies is a pump-probe style transient absorp-
tion. Throughout the development of our lab this apparatus has had several improvements and
4 CHAPTER 1. INTRODUCTION
expansions built into it. Specically, the way white light is generated for use as a probe pulse
and the broadband balanced detection scheme that I developed. The experimental details of these
components are described in chapter 5.
I have utilized the numerical algorithm known as singular value decomposition (SVD) extensively in
my research. I feel that its utility in data analysis rivals even that of the gloried Fourier transform.
Chapter 6 is a tutorial style account of how SVD may be applied to the workup of time-resolved
spectroscopic data. Additionally , some of the MATLAB code that I have employed in my research,
for doing SVD and otherwise, is included in the appendix. The circuit diagram I designed that
triggers the camera is also included in the appendix.
REFERENCES 5
References
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[3] Klauss, A.; Haumann, M.; Dau, H. Proceedings of the National Academy of Sciences 2012,
109, 16035{16040.
[4] Avdeef, A. Current topics in medicinal chemistry 2001, 1, 277{351.
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Chick, W. S.; Hill-Eubanks, D. C.; Nelson, M. T.; Kinnamon, S. C.; Liman, E. R. Proceedings
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[6] Kim, J.; Rees, D. C. Biochemistry 1994, 33, 389{397, PMID: 8286368.
[7] Reece, S. Y.; Nocera, D. G. Annual Review of Biochemistry 2009, 78, 673{699.
[8] Weinberg, D. R.; Gagliardi, C. J.; Hull, J. F.; Murphy, C. F.; Kent, C. A.; Westlake, B. C.;
Paul, A.; Ess, D. H.; McCaerty, D. G.; Meyer, T. J. Chemical Reviews 2012, 112, 4016{4093,
PMID: 22702235.
[9] Hammes-Schier, S. Journal of the American Chemical Society 2015, 137, 8860{8871, PMID:
26110700.
[10] Qu, Y.; Duan, X. Chem. Soc. Rev. 2013, 42, 2568{2580.
[11] Esswein, A. J.; Nocera, D. G.; Esswein, A. J.; Nocera, D. G. Chem. Rev. 2007, 107, 4022{4047.
[12] White, J. L.; Baruch, M. F.; Pander, J. E.; Hu, Y.; Fortmeyer, I. C.; Park, J. E.; Zhang, T.;
Liao, K.; Gu, J.; Yan, Y.; Shaw, T. W.; Abelev, E.; Bocarsly, A. B. Chemical Reviews 2015,
115, 12888{12935.
[13] Premont-Schwarz, M.; Barak, T.; Pines, D.; Nibbering, E. T. J.; Pines, E. J. Phys. Chem. B
2013, 117, 4594{4603.
[14] Arnaut, L. G.; Formosinho, S. J. J. Photochem. Photobiol., A 1993, 75, 1{20.
[15] Ireland, J. F.; Wyatt, P. A. H. Advances in Physical Organic Chemistry 1976, 12, 131{221.
[16] Pines, D.; Nibbering, E. T. J.; Pines, E. Israel Journal of Chemistry 2015, 55, 1240{1251.
[17] Solntsev, K. M.; Sullivant, E. N.; Tolbert, L. M.; Ashkenazi, S.; Leiderman, P.; Huppert, D.
Journal of the American Chemical Society 2004, 126, 12701{12708.
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6 REFERENCES
[20] Favaro, G.; Mazzucato, U.; Masetti, F. The Journal of Physical Chemistry 1973, 77, 601{604.
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Small, E. W. Biophysical journal 2000, 78, 405{415.
[23] Dempsey, J. L.; Winkler, J. R.; Gray, H. B. J. Am. Chem. Soc. 2010, 132, 16774{16776.
[24] Haghighat, S.; Ostresh, S.; Dawlaty, J. M. The journal of physical chemistry. B 2016, 120,
1002{07.
Chapter 2
Excited State Proton Transfer in a
Model System
2.1 Introduction
Coupling of electron and proton motion is of central importance in a wide range of chemical phe-
nomena, including natural and articial light harvesting
2{7
, enzymatic reactions
8,9
, and synthetic
organic chemistry
10
. In many proton-requiring redox reactions it is hypothesized that concerted
transfer of electron and proton occurs through lower reaction barriers compared to step-wise trans-
fer. A challenge in contemporary chemical dynamics is to measure, explain, and ultimately control
such correlated motion of charges in the excited states
11,12
.
Photocatalytic redox reactions that are relevant for energy conversion and solar light harvesting
often involve transfer of several electrons and protons. For example photocatalytic oxidation of
water requires removal of four electrons and four protons from two water molecules, making its
mechanisms challenging to understand and study. To elucidate such correlated motion of electrons
and protons it is necessary to resort to simpler model systems. Photoacids
13,14
and molecules with
Excited State Intramolecular Proton Transfer (ESIPT)
15
capability serve this purpose and have
7
8 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
been known for decades. In these systems, optical excitation, often of a conjugated electronic sys-
tem, renders an attached phenolic group acidic. While in the excited state, the phenolic proton
is transferred either to another molecule or to a proton acceptor within the same the molecule
16
.
The dynamics of such processes have been extensively studied with ultrafast time-resolution both
experimentally and theoretically
17{19
. In particular, questions such as double proton transfer
20{25
,
involvement of intramolecular vibrational degrees of freedom
24,26{29
, the role of impulsively excited
vibrations in transferring the proton, and the role of skeletal versus direct -OH vibrations
26,30
, have
been debated. The origin of photoacidity is electronic charge redistribution in the excited state,
which in
uences the motion of protons. The details of such coupling between electrons and protons
remains an area of active study
13,27
. For example, whether the proton motion is a consequence,
rather than a cause of electronic charge redistribution has been debated
13,30,31
. Apart from serv-
ing as model systems for ultrafast proton transfer, photoacids and ESIPT molecules have several
applications including optical pH-jump agents
32,33
, laser dyes
34
,
uorescent probes
35
, molecular
photoswitches
36
, photostabilizers, high energy radiation detectors, and white light emitting single
molecules
37
, which are either envisaged or realized. A complete review of such systems is beyond
the capacity of this introduction.
Here, we study two derivatives, shown in Figure 2.1, of a recently synthesized 1,3-bis(imino)isoindole
motif with ESIPT capability
38
. A distinct feature of 1,3-bis(2-pyridylimino)-4,7-dihydroxyisoindole,
which will be referred to as the \diol" derivative, is the existence of two equivalent transferable pro-
tons. The current study of this molecule has three main goals. First, we report the measured time-
scale of proton transfer in the excited state using ultrafast broad-band pump-probe spectroscopy
and compare the dynamics to smaller ESIPT molecules. Second, to nd out whether one or both
of the protons transfer in the excited state we compare the proton transfer dynamics between the
diol and 1,3-bis(2-pyridylimino)-4-ethoxy-7-hydroxyisoindole, referred to as the \ethoxy-ol", which
only has one proton available for transfer. Finally, we show computational results to correlate the
intramolecular redistribution of electronic charge density with the motion of protons. We will chart
out a path for further theoretical and experimental investigations, with emphasis on understanding
the coupling between electronic charge redistribution and proton motion.
2.1. INTRODUCTION 9
Figure 2.1: Chemical species discussed in this paper, denoted with \E" for enol and \K" for
keto. (top) The three possible tautomers of the diol molecule and a schematic showing their
interconversion in the ground and excited states. Three possible mechanisms for relaxation are
shown in color: single proton transfer (red), stepwise double proton transfer (blue), and concerted
proton transfer (green). (bottom) The two possible tautomers of the ethoxy substituted molecule
(ethoxy-ol) and their interconversion.
10 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
2.2 Methods
2.2.1 Materials
Materials The compounds 1,3-bis(2-pyridylimino)-4,7-dihydroxyisoindole and 1,3-bis(2-
pyridylimino)-4-ethoxy-7-hydroxyisoindole were prepared via the procedures in reference 38.
Solutions of approximately 2 mM were prepared in methanol, dichloromethane, and hexane.
2.2.2 Transient Absorption
Transient Absorption A pump pulse centered at 400 nm was generated by frequency doubling
the output of a 1 kHz Ti:Sapphire amplier (Coherent Legend Elite HE+) in BBO. A white light
continuum probe was prepared by focusing the 800 nm Ti:Sapphire output onto a 3.0 mm thick
sapphire window. The probe spectrum spans the entire visible range and is shown in Figure 2.2A.
The pump was passed though a polarizer to set its polarization to the magic angle with respect
to the probe to eliminate rotational diusion eects. The pump and probe beams were attenuated
to 400 W and 120 W respectively with neutral density lters for sample and blank spectra.
The pump beam was modulated at 500 Hz using an optical chopper (Thorlabs). The probe was
spectrally resolved at a 1 kHz sampling rate using a 320 mm focal length spectrometer with 150
g/mm gratings (Horiba iHR320) and a 1340x100 CCD array (Princeton Instruments Pixis). The
focal spot size diameter for the pump (probe) was 18030m (150 30m). A cross correlation
of pump and probe was done using the nonresonant response of a 0.5 mm thick sapphire plate with
large pump power, 700 W. The cross correlation (SI Figure 1) shows that the probe pulse has
parabolic chip which is corrected by tting and time shifting data after collection. Each spectral
component has a nonresonant response time of about 200 fs which is considered the instrument
resolution. The samples were
owed through a fused quartz
ow cell with 0.1 mm of path length.
2.2.3 Computational
Computational Ground state geometries and molecular orbitals were calculated using B3LYP/6-
31+G* with the Q-Chem
39
software package. Singlet excitation energies and excited state geome-
2.3. RESULTS 11
tries were calculated using TD-B3LYP/6-31G*. All calculations were done in the gas phase.
2.3 Results
2.3.1 Steady State Absorption and Emission Spectra
First we will discuss the steady state absorption and emission of the molecule and relate it to the
enol and keto forms of the compound. As in other ESIPT molecules, there is a large shift between
the absorption and
uorescence bands in these molecules. Absorption occurs in the enol tautomer
of the molecule in the band of < 450 nm. Proton transfer occurs in the excited state and results
into the keto tautomer, which
uoresces in the 570 - 700 nm band. A weak emission centered at 420
nm is observed and attributed to enol
uorescence. Both absorption and emission wavelengths show
a blue shift with respect to increasing solvent polarity. Since the shifts in absorption and emission
are approximately the same energy, the Stokes shift is relatively independent of solvent (Table 2.1).
The large Stokes shifted emission is due to the signicant reorganization of the molecules in the
excited state associated with the proton transfer. It should be pointed out that some degree of
proton transfer is expected in the ground state as well
38
, as indicated by the long-wavelength tail
of the absorption spectrum (Figure 2.2 A). However, the ground state equilibrium is far shifted in
favor of the enol form for the compounds discussed in this paper.
2.3.2 Diol Transient Absorption
The purpose of our transient absorption (TA) measurement is to identify the time-scale of proton
transfer by pumping the enol tautomer and following the spectral signatures of the keto tautomer
in time. In such measurements, the signal arises from a net addition of at least three processes.
Ground state bleach (GB) results from the depletion of ground state population due to the pump
and contributes to the signal with a negative sign. Stimulated emission (SE) from an excited
species also results into a negative signal. Excited state absorption (EA) due to a pumped species
contributes with a positive sign. Fortunately, in the molecules in this study, the steady state
12 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
absorption and steady state
uorescence bands are widely separated, thus conveniently separating
GB and SE based on wavelength. Furthermore, the pump is only absorbed by the enol form, and
uorescence occurs from the keto form after proton transfer, making the interpretation of the data
relatively easy. The main signature of the proton transfer will be the emergence of a negative signal
due to SE in the
uorescence band. The purpose of the TA measurement is to resolve the emergence
of this band after pumping.
The time-resolved spectrum of the diol in methanol is shown in Figure 2.2. The pump is centered
near 400 nm in the absorption band, while the probe mainly spans the keto
uorescence band and
the region of separation between the absorption and
uorescence. As expected, the major feature of
the data is the emergence of a negative signal in the 590 nm - 700 nm band due to SE from the keto
form after proton transfer. Concurrent with the negative signal, a spectrally wide positive signal
with a peak near 480 nm also appears. The positive signal is assigned to EA from the keto form. Its
spectral overlap with the SE signal causes the peak of the negative signal to red-shift with respect to
the steady state
uorescence spectrum. A separate temporal slice of the negative signal over a 0.4
nm bandwidth is shown in gure 2.2D for clarity and is t to an exponential (residual plotted in SI
Figure 3). The time constant of this signal,jj = 71077 fs, is the time constant of proton transfer
in the excited state and is one of the main ndings of our work. Once again, the large separation
between the absorption and
uorescence bands, allows us to have almost non-overlapping pump
and probe and thus the GB signal does not contribute signicantly to our measurement. This is
convenient since it allows us to explain the transient spectrum at longer times only in terms of SE
and EA of the keto form. Although not directly relevant to proton transfer, a separate piece of
information is gleaned from the broad nature of the positive signal and its observed maximum near
480 nm. It gives a glimpse of the second excited state S
2
of the keto form. Based on this data
S
1
can absorb photons as low energy 600 nm to access S
2
, and shows maximum absorption for
480 nm photons. Such a relatively clear signal for the S
1
to S
2
transition is made possible by the
large separation between absorption and
uorescence bands which allows a clear spectral region for
measuring the EA signal alone, with little interference from the competing GB and SE processes.
2.3. RESULTS 13
2.3.3 Solvent Dependence
Transient absorption experiments in other solvents showed qualitatively similar dynamics. Fitting
a single exponential to the
uorescence band in chloroform (SI Figure 5) and cyclohexane (SI Figure
6) found time constants ofjj = 530 14 fs andjj = 1:23 0:32 ps respectively. This variation
is potentially due to the dierence in solvent polarity, where a more polar solvent is expected to
stabilize the charge transferred excited state more easily and result into a faster rate. However,
the observed rate in methanol does not conform to this trend and is potentially due to hydrogen
bonding. As is conventional, the data at the region of pump-probe overlap is not interpreted due
to several possible time-ordered interactions between the pump and the probe, as well as signal
contribution from the solvent and
ow cell (see SI Figure 2). The pump-probe overlap is measured
separately in a non-resonant medium and spans 200 fs (see SI Figure 1).
2.3.4 Ethoxy-ol Transient Absorption
To identify whether one or both protons get transferred in the excited state, we performed TA
experiments on the ethoxy-ol derivative, which is only capable of a single proton transfer, shown in
gure 6.1 B. As reported earlier
38
the steady state
uorescence spectrum of this compound (Figure
6.1 A) has a
uorescence peak which is slightly red-shifted with respect to diol, but otherwise
qualitatively similar. Since proton transfer in the excited state is associated with a signicant
geometry change, which manifests as a large Stokes shift, one may expect two proton transfers to
exhibit an even larger Stokes shift compared to a single proton transfer. A similar conclusion is
indeed supported by a recent TD-DFT calculation
40
. Based on this, a natural conclusion would
be to expect a much larger Stokes shift for the diol, if the diol did transfer both protons. However,
experimental
uorescence spectra show that the diol molecule has a slightly smaller Stokes shift
compared to the ethoxy-ol. Table 2.1 compares the predicted Stokes shifts from reference 40 for
single and double proton transfer in the diol to the the experimentally observed Stokes shifts in
the diol and the ethoxy-ol forms. Thus the similarity between the
uorescence spectra of the diol
and ethoxy-ol molecules is considered partial evidence that only one of the two protons in the diol
14 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
Experimental (cm
-1
)
Solvent
Compound methanol chloroform hexane
diol 9150 9051 9139
ethoxy-ol 9240 9513 9632
Calculated (cm
-1
)
Theory (TD-B3LYP)
Emitting species LR-PCM/TZVP
(a)
SS-PCM/TZVP
(a)
gas phase/6-31G*
(b)
KK* 7904 7017 4302
EK* 7339 5807 3657
K* - - 5887
(a) Dichloromethane PCM. See Table 4 in ref. 40. (b) This work.
Table 2.1: Experimental and calculated Stokes shifts for various ESIPT species.
molecule transfers in the excited state. With transient absorption spectroscopy we wanted to nd
out if there are dierences in dynamics between the two molecules.
The TA data for the ethoxy-ol is shown in Figure 6.1 and exhibits qualitative similarities to the
diol: a negative signal in the
uorescence band and a positive EA signal at shorter wavelengths.
Fitting of the transient at 650 nm, returned a time constant of 427 118 fs.
2.4 Discussion
2.4.1 Electronic Structure Calculations
The cause of proton transfer in the excited state is electronic charge redistribution. Thus to identify
the mechanism of the transfer, it is necessary to look at the spatial extent of the HOMO and LUMO
and the nature of charge redistribution induced by light. Our purpose here is a qualitative descrip-
tion of the phenomena in the excited state, with emphasis on gaining insight, rather than an exact
simulation of the process. We encourage further theoretical investigations on this front. TD-DFT
has proved to be a useful method for predicting spectroscopic properties of ESIPT compounds
41{44
.
The electronic structure of the diol has been studied previously
40
using TD-B3LYP/TZVP in a
dichloromethane ( = 8:93) PCM and is summarized brie
y below. Our purpose is to rst compare
the electronic structure of the diol and ethoxy-ol compounds. Second, we would like to identify the
2.4. DISCUSSION 15
Figure 2.2: TA of the diol in methanol. (a) Steady state absorption (blue) and emission (red)
spectra of the diol in methanol. Pump (dashed blue) and probe (dashed red) pulse spectra. (b)
1,3-Bis(imino)isoindole diol, shown in the enol-enol tautomer as it exists in the electronic ground
state. (c) Visible pump-white light probe TA over 4 ps. (d) A temporal slice of transient absorption
along the dashed line in (c) through = 650 nm. The stimulated emission shows single exponential
behavior. The solvent shows some TA features at short times (dashed blue line and Figure 2 in SI)
which are not interpreted or tted.
16 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
Figure 2.3: TA of the ethoxy-ol in methanol. (a) Steady state absorption (blue) and emission (red)
spectra of the ethoxy-ol in methanol. Pump (dashed blue) and probe (dashed red) pulse spectra.
(b) Ethoxy substituted isoindole, shown in the enol tautomer. (c) Visible pump-white light probe
TA over 4 ps. (d) A temporal slice of transient absorption along the dashed line in (c) through
= 650 nm.
2.4. DISCUSSION 17
Figure 2.4: Cartoon of the diol potential energy surface resulting from stepwise proton transfer
events. The blue arrow shows optical excitation of the EE tautomer, while the red arrows show
possible emission from EK* and KK* tautomers. Although this diagram is meant to be qualitative,
the spacing between levels and heights of the barriers are drawn based on calculations by Su
40
.
18 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
Figure 2.5: Frontier molecular orbitals of the diol and ethoxy-ol in the EE and E tautomers.
TD-DFT calculations suggest that the S
0
! S
1
excitation is primarily between the HOMOs and
LUMOs. Upon optical excitation electron density shifts from around the benzene and hydroxyl
groups towards the pyrrole and pyridine groups in both compounds.
2.4. DISCUSSION 19
electronic structure changes upon optical excitation that lead to proton transfer.
Su et al.
40
have calculated energy barriers to proton transfer in the ground and excited states
for the diol by a relaxed potential energy surface scan. In the stepwise mechanism (Figure 2.4),
only one N-H nuclear coordinate is scanned at a time (EE*! EK*! KK*). In the concerted
mechanism, both N-H coordinates are scanned symmetrically (EE*! KK*). In comparing the two
ESIPT mechanisms, they predicted the stepwise mechanism to have, in the excited state, a barrier
of 1322 cm
-1
for the rst proton transfer and a barrier of 2685 cm
-1
for the second proton transfer.
The concerted PES is predicted to have an excited state barrier of 4343 cm
-1
. Additionally, they
were able to optimize the geometry of the two transition states involved in the stepwise mechanism.
The concerted mechanism's transition state was not found, and in fact the calculation would only
converge to one of the two stepwise transition states. The smaller barrier to stepwise transfer as
well as the optimized transition states were used to predict that the stepwise mechanism is more
likely.
Using these computed potentials as guidance, we performed our own calculations to compare the
excited states of the diol to the ethoxy-ol, and to see if our predictions are compatible with experi-
mental spectra. It can be seen that electronic excitation in both compounds is very similar by their
almost identical absorption spectra (solid blue lines in Figures 2.2 A and 6.1 A). Gas phase TD-
B3LYP calculations found singlet excitations at 2.97 eV (399 nm) and 3.11 eV (417 nm) in rough
agreement with observed absorption maxima for the diol and ethoxy-ol respectively. TheseS
0
!S
1
excitations are predicted to be composed primarily of transitions between the frontier molecular
orbitals (Figure 2.5), for both compounds. The calculated HOMO! LUMO transitions shows
that electron density is expected to shift from the benzene and proton donating oxygen portion of
the indole to a more delocalised conguration with increased density on the pyrrole, pyridines, and
proton accepting nitrogens.
Excited state geometry optimization done by Su et al
40
on EE* shows that optical excitation leads
to a symmetric lengthening of both O-H bonds and the corresponding shortening of N-H bonds.
This suggests that excitation to the Franck-Condon region places the compounds on theS
1
potential
energy surface such that nuclear motion is induced along the proton transfer coordinates. They
20 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
have concluded that two step-wise proton transfers occur in the diol, based on the calculated barrier
heights in the potential energy surfaces along the proton transfer coordinates. However, it should
be born in mind that upon Franck-Condon excitation a large amount of excess vibrational energy is
available and distributed non-thermally among several modes. Experiment shows that vibrational
relaxation in the excited state while still in the enol form (i.e. prior to proton transfer) leads to
a weak
uorescence with a Stokes shift of 2500 cm
-1
, indicating that the optical excitation of the
enol form is distinctly not a 0!0 transition. Such non-equilibrium vibrational energy can render an
Arrhenius-like analysis of proton transfer less appropriate. For that reason, the utility of theoretical
models should be evaluated based on their ability to explain and possibly match the experimental
ultrafast measurements of proton transfer times, for example those presented in this work.
2.4.2 Stokes Shift Calculations
Chemical intuition would lead one to think that since a single ESIPT can result in a Stokes shift of
over 9000 cm
-1
, double ESIPT would produce an even larger Stokes shift. Following along this line
of reasoning, we refer to the experimentally measured Stokes shifts of the diol and the ethoxy-ol
(Table 2.1). As mentioned earlier, the diol, which in principle can transfer two protons, has a
slightly smaller Stokes shift compared to the ethoxy-ol which can transfer only one proton. This
observation gives rise to two interpretations: (1) two ESIPT processes occur in the diol and the
second has either a minimal eect on theS
0
S
1
gap or increases it slightly, thereby decreasing the
stokes shift in contradiction to chemical intuition, or (2) only a single ESIPT process occurs in the
diol and the observed
uorescence is from EK*. Theoretical investigations done in a PCM
40
and
our own gas phase calculations (Table 2.1) yield results in accordance with the chemically intuitive
idea that the second ESIPT should increase the Stokes shift by a substantial amount. Thus the
rst interpretation is not supported by theory, leaving the second interpretation as more plausible.
The experimentally observed slightly larger Stokes shift of the ethoxy-ol compared to the diol is
also supported by the gas phase calculations and seems to arise from the structural dierences that
are independent of proton transfer between the two cases. Thus this observation reminds us that
even when two equivalent protons are available for transfer, it is quite possible that only one will
2.4. DISCUSSION 21
transfer. This important point should be taken into consideration in the analysis of all excited state
multiproton processes.
2.4.3 Dynamics
Another plausible experimental measure in favor of double ESIPT would be biexponential dynamics
of the emergence of the SE band (i.e. emergence of the product). However, both the ethoxy-ol and
the diol exhibit dynamics that are t reasonably well with single exponentials withjj 427 fs
andjj 710 fs respectively. This similarity in the single exponential dynamics of the diol and
ethoxy-ol compounds lends more credibility to the single ESIPT mechanism in the diol. One may
argue that the diol dynamics is indeed bi-exponential, with the rst time constant too rapid (<
100 fs) for us to observe and assign within our time resolution. However, there is some reason to
rule out that possibility. A single proton transfer in ethoxy-ol occurs with a time-constant ofjj
427 fs and is conveniently measurable in our experiment. In a possible two-proton transfer scenario
in the diol, it is reasonable to argue that the rst proton transfer would also occur within similar
time-scales and would not remain obscured due to our time-resolution. Since the observed data for
the diol ts well to a single exponential, it is likely due to a single proton transfer only. Of course,
a possible concerted two-proton transfer process would also give rise to a single exponential. But it
can be ruled out based on other evidence, in particular the similarity of the Stokes shifts between
the diol and the ethoxy-ol, as argued in the previous paragraph.
Once again, while not directly relevant to proton transfer, comparison of the positive signal between
the diol and the ethoxy-ol forms reveals the dierences in theirS
2
S
1
gaps. The peak of the positive
absorption for the ethoxyl-ol occurs near 550 nm, in contrast to 480 nm for the diol form. Although
the ethoxy substitution does not seem to have strongly in
uenced the steady state absorption and
uorescence, it has managed to reduce the S
2
S
1
gap signicantly. The larger in
uence of the
ethoxy substitution on theS
2
surface compared to theS
1
surface is an interesting auxiliary nding
of this work. It may be argued that the S
2
state has a larger energy and spatial extent and thus
experiences the substituted ethoxy group more readily compared to the S
1
state. Full explanation
of this eect is outside the scope of this work.
22 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
2.4.4 Absence of Wavepackets
Previous work on smaller ESIPT molecules has shown that coherent nuclear motion, i.e. wavepack-
ets, imprint their signature on the visible TA data
24,30
. This phenomenon manifests as an oscillatory
component in the TA which lasts for a few ps. The oscillations often match in frequency to low en-
ergy (< 500 cm
-1
) skeletal modes of the molecule that move the geometry along the proton transfer
coordinate. This eect has been used to distinguish between concerted and stepwise double ESIPT
mechanisms based on the symmetry of the associated normal mode for other diol-like compounds.
In our data, no dominant oscillation in the TA traces are observed (see SI gure 4-6). The absence
of such oscillations in the results presented here is most likely due to the larger number of atoms
compared to previously studied ESIPT compounds. The larger size of the molecules gives rise to
a larger vibrational density of states at low energies, with no single frequency dominating the TA
signal, thus producing an eective damping of oscillations in the TA.
2.5 Conclusion
Understanding the correlated motion of protons and electrons on ultrafast timescales is a con-
temporary challenge in chemical dynamics. The molecules studied here are model systems for
understanding optically induced ultrafast proton transfer. Using broadband transient absorption
spectroscopy, we have identied the time-constants of proton transfer in two derivatives, one where
a single proton transfer is possible (ethoxy-ol) and one where, in principle, two proton transfers are
possible (diol). Based on similarity in dynamics, the magnitude of the Stokes shifts, and electronic
structure calculations, we conclude that a single ESIPT process in the diol is the most likely sce-
nario. We hope that these results can be benecial in designing chemical motifs for driving excited
state redox reactions where concerted motion of several electrons and protons are involved.
2.6. SUPPORTING SPECTRA 23
2.6 Supporting Spectra
Below is the supporting data for calculating the time resolution and correcting the probe pulse
chirp. The single exponential ts are shown, along with their residuals. Lastly, we analyzed the
data for the presence of coherent vibrational motion, known as wavepackets, and determined that
they were absent from the data.
2.6.1 Chirp Correction and Blank Spectra
Time resolution in these experiments is determined by collecting a pump-probe signal of a nonres-
onant material such as sapphire or a solvent. This is known as cross correlation of the pump and
probe. The probe beam, due to to it's broadband spectrum, acquires a large chirp during super-
continuum generation and transmitting through dispersive optics. This eectively means that time
zero is slightly dierent for each probe wavelength. Since each probe wavelength is being detected
we can correct for this chirp with numerical post-processing. The MATLAB code used for this is
included in the appendix and is brie
y summarized here. The maximum of each wavelength slice
of the coherent spike resulting from cross correlation is found. Then a polynomial is t to these
maxima. Each wavelength slice is shifted such that it's time zero matches the rst slice's time zero.
In practice, the calculated shift for each wavelength slice may be smaller than the step size that
the data was collected at. Thus, before shifting, the data set is resampled at a higher frequency.
Once the time shifts have been applied to the data resampled again to the original experimental
sampling frequency.
24 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
Figure 2.6: Cross correlation of pump and probe in a 0.5 mm sapphire plate. (a) Nonresonant
response from sapphire ts well to a second order polynomial (dashed blue line). Fit parameters: a
= -0.0034
fs
2
nm
2
, b = 5.34
fs
nm
. (b) Chirp corrected version of the nonresonant signal. The instrument
resolution is approximately 200 fs for each spectral component. This t was applied to all sample
and blank spectra so that temporal evolution of many spectral components could be compared at
the same time.
Figure 2.7: Transient response of methanol in a quartz
ow cell.
2.6. SUPPORTING SPECTRA 25
2.6.2 Transient Absorption Fit Residuals and Fourier Transforms
Figure 2.8: (a) Time trace of the diol in methanol (Figure 2D reproduced here). (b) Residual of
exponential t in (a). (c) Time trace of the ethoxy-ol in methanol (Figure 3D reproduced here).
(d) Residual of exponential t in (c).
26 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
Figure 2.9: (a) Time trace of the diol in methanol with small step size (5 fs), probed in the
uorescence band at 625 nm. A gaussian window function (green line) is multiplied by the data
(blue line) to remove the oscillations present in the coherent spike, which are not from nuclear
motion. (b) Fourier amplitudes of the raw (blue line) and windowed (red line) data. No single
frequency is dominant.
2.6. SUPPORTING SPECTRA 27
Figure 2.10: (a) Time trace of the diol in chloroform with small step size (2 fs), probed in the
uorescence band at 600 nm. (b) Fourier transforming reveals a dominant mode at 332 cm
-1
which
is due to chloroform. A gaussian window function (green line) is multiplied by the complex Fourier
transform to lter out the oscillation due to chloroform. (c) Inverse Fourier transforming returns a
time trace without oscillations. (d) The residual of the exponential t in (c) is plotted.
28 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
Figure 2.11: (a) Time trace of the diol in cyclohexane with 10 fs step size, probed in the
uorescence
band at 600 nm. (b) Fourier amplitude shows no dominant modes. (c) Residual of the exponential
t in (a).
2.7. RELATIVE TIME CONSTANTS AND KINETIC ISOTOPE EFFECT 29
2.7 Relative Time Constants and Kinetic Isotope Eect
Despite there being two equivalent intramolecular proton transfer coordinates in the diol, the
ethoxy-ol had a rate constant that was approximately twice as fast. This dierence in rates was
previously not explainable. In collaboration with Welsch
45
this phenomemon was investigated using
a combination of theory and experiment.
Figure 2.12: Cartoon diagram of the molecular seesaw eect. The diol (left) contains two equivalent
hydrogen bonds which compete with each other. The ethoxy-ol (right) contains a single hydrogen
bond, allowing the geometry to relax to a decreased N-H bond distance.
2.7.1 Theory
Using TD-DFT the rst singlet excited state and transition state geometries for the diol and ethoxy-
ol were optimized. We found that the equivalent and symmetric hydrogen bonds of the diol have
a larger bond distance than that observed in the ethoxy-ol (Figure 2.13). The hydrogen bonds
of the diol \compete" with one another, as if they were balancing on a seesaw, where the single
bond in the ethoxy-ol is allowed to relax and shortens considerably. In order to prove that this
was not a steric pushing eect, the ethoxy chain was both rotated into a gauche conformation and
30 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
substituted for a methyl . However, it was found that these steric eects were small and the origin
of the decreased hydrogen bond length was primarily from the lack of a competing hydrogen bond
on the other side of the \fulcrum" of the molecule.
Figure 2.13: Depiction of the molecular seesaw eect. Optimized geometries for the ESIPT reactant
for the diol (top panel) and the ethoxy-ol (bottom panel) are shown from calculations at the B3LYP/
TZVP level of theory. ESIPT distances are shown in blue and given in angstroms, and the CCC
bond angles are shown in black. As illustrated at right, removing one of the hydrogen bonds,
as in the ethoxy-ol, eliminates the competition of the two hydrogen bonds and thus shortens the
remaining hydrogen bond.
2.7. RELATIVE TIME CONSTANTS AND KINETIC ISOTOPE EFFECT 31
Table 2.2: Calculated and Measured Proton Transfer Times, , of the Diol and the Ethoxy-ol and
Respective Relative Values
Method Molecule (fs) relative
B3LYP/TZVP diol 2358 1.55
B3LYP/TZVP ethoxy-ol 1520
B3LYP diol 3130 1.44
B3LYP ethoxy-ol 2177
M062X diol 3884 1.41
M062X ethoxy-ol 2755
CAM-B3LYP diol 1259 1.68
CAM-B3LYP ethoxy-ol 749
experiment diol 319 50 1.24 0.24
experiment ethoxy-ol 257 30
Table 2.3: Calculated and Measured KIE of the Diol and the Ethoxy-ol, as Well as the Respective
Relative Values
Method Molecule KIE relative
B3LYP/TZVP diol 7.67 1.42
B3LYP/TZVP ethoxy-ol 5.42
B3LYP diol 8.74 1.39
B3LYP ethoxy-ol 6.28
M062X diol 9.05 1.41
M062X ethoxy-ol 6.41
CAM-B3LYP diol 6.88 1.55
CAM-B3LYP ethoxy-ol 4.44
experiment diol 1.83 0.30 2.01 0.42
experiment ethoxy-ol 0.91 0.12
Using these geometries and semiclassical transition state theory, the proton transfer time constants
were calculated with a variety of functionals and compared to experimental results. All of the
functionals predicted that the time constant of the ethoxy-ol was lower than that for the diol as was
true for experimental values (Table 2.2. Although the absolute time constants agree qualitatively,
the relative time constants agree more quantitatively.
In order to test the validity of this theoretical approach for this system, the kinetic isotope eects for
each ESIPT was calculated and measured experimentally with transient absorption. The results are
shown in Table 2.3, and similar to the rates show qualitative agreement with experiment. Transient
absorption spectra and ts are shown in Figures 2.15, 2.16, 2.17, and 2.18.
32 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
2.7.2 Materials
1,3-bis(2-pyridylimino)-4,7-dihydroxyisoindole (diol) and 1,3-bis(2-pyridylimino)-4-ethoxy-7-
hydroxyisoindole (ethoxy-ol) were synthesized previously by Hanson.
38
To prepared the deuterated
samples (diol-d and ethoxy-ol-d) the hydroxylic protons were exchanged for deuterons by dissolving
and recrystallizing each compound in CH
3
OD (Sigma-Aldrich).
2.7.3 Transient Absorption
Spectroscopic grade acetonitrile solutions of each compound were made with0.3 OD in a 100m
path length fused silica
ow cell. The concentration for each solution was2 mM.
The transient absorption apparatus has been described previously
1
, with modications noted here.
Brie
y, the fundamental of a Ti:sapphire chirped pulse amplier was frequency doubled in type
II BBO to produce a pump pulse with center wavelength 393 nm. The pump was attenuated to
300 nJ with neutral density lters. Approximately 100 nJ of the fundamental was focused into
a 2 mm path length cuvet lled with DI water to generate a white light continuum probe pulse.
The probe was split into two arms, reference and sample, in a balanced detection scheme. The
sample arm is sent to a motion controlled retro re
ector and is focused to the same spot on the
sample as the pump. The reference arm has xed path length and passes through a point on the
sample that is never pumped. The spectra of both the sample and reference probes are detected
with a grating spectrometer and 100x1340 element CCD array. The balanced transient absorption
is then calculated via the expression A
balanced
= A
sample
A
reference
= log
Is;uIr;p
Is;pIr;u
, where I
is intensity and s, r, p and u stand for sample, reference, pumped, and unpumped. In this scheme
any shot to shot
uctuations in the intensity of the probe are captured in A
reference
and removed
from the real transient absorption that is induced by the pump.
The TA data was cropped at approximately 300 fs to exclude any dynamics associated with the co-
herent spike. Singular value decomposition
46
was used to determine the number of transient species.
The selection criterion for a signicant component was that it's singular value must be greater than
2% of the rst singular value. In all cases, the data was well described by two components. A
2.7. RELATIVE TIME CONSTANTS AND KINETIC ISOTOPE EFFECT 33
Table 2.4: Proton transfer time constants in femtoseconds measured in acetonitrile. For comparison
transfer times from ref
1
measured in other solvents are given.
Solvent diol diol-D ethoxy-ol ethoxyol-D
acetonitrile 319 583 257 235
methanol 710 N/A 427 N/A
chloroform 530 - - -
cyclohexane 1230 - - -
Figure 2.14: The coherent spike due to the interaction between the pump and probe in pure
acetonitrile and the sample holder.
large amplitude background component (rst singular value) which does not decay with time, and
a smaller second component which decays on femtosecond time scales. The latter is assigned to
the intramolecular proton transfer events on the basis that the growth of the stimulated emission
peaks in the transient spectra roughly match the steady state emission peaks ( 595nm).
1
. Each
transient was well described by a single exponential function, with the time constants reported in
Table 2.4.
2.7.4 Conclusion
The surprising result of the ethoxy-ol having a shorter proton transfer time than the diol was
explained in terms of a molecular seesaw eect. In the diol, the intramolecular hydrogen bonds
compete with each other, causing a strained geometry with longer hydrogen bonds, resulting in
a longer proton transfer time. Using semiclassical transition state theory a kinetic isotope eect
34 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
Figure 2.15: Transient absorption of the diol in acetonitrile. (left) Single exponential t of the
population dynamics retrieved by SVD. (right)
Figure 2.16: Transient absorption of the diol-D in acetonitrile. (left) Single exponential t of the
population dynamics retrieved by SVD. (right)
2.7. RELATIVE TIME CONSTANTS AND KINETIC ISOTOPE EFFECT 35
Figure 2.17: Transient absorption of the ethoxy-ol in acetonitrile. (left) Single exponential t of
the population dynamics retrieved by SVD. (right)
Figure 2.18: Transient absorption of the ethoxy-ol-D in acetonitrile. (left) Single exponential t of
the population dynamics retrieved by SVD. (right)
36 CHAPTER 2. EXCITED STATE PROTON TRANSFER IN A MODEL SYSTEM
was predicted and conrmed experimentally with femotosecond transient absorption. We speculate
that this seesaw eect may be a useful motif in the design of photocatalysts.
REFERENCES 37
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Chapter 3
Photobase Thermodynamics
3.1 Introduction
Understanding proton transfer reactions, in particular in the electronic excited state, has received
renewed attention in the context of solar-to-fuel light harvesting. The purpose of articial photo-
synthesis is to use energy from sunlight to drive redox reactions that convert abundant feedstock
to fuels. Such redox reactions often involve both electron and proton transfer, and often with cou-
pled kinetics. It is necessary to understand the mechanism of such reactions, and in particular to
understand how light excitation couples to electronic excitation and eventually to protonic motion.
A well documented case of proton transfer initiated by light occurs in photoacids, which are
molecules that become more acidic in their electronically excited state (pK
a
< pK
a
).
2{5
In some
cases, pK
a
can be as large as 12 units.
6
A hydroxyl group attached to a conjugated organic
ring such as naphthalene and pyrene is a common moiety in many photoacids. A large body
of knowledge exists for photoacids, the prototypical examples being 1-naphthol, 2-naphthol, and
8-hydroxypyrene-1,3,6-trisulfonic acid.
7{12
The fundamental processes leading to photoacidity have been discussed in the literature. Previous
works in this area by Fayer
13,14
, Solntsev
15,16
, Pines
4
, Nibbering
17
, and Hynes
18,19
have considered
whether optically induced charge transfer or electronic relaxation in response to proton transfer (i.e
39
40 CHAPTER 3. PHOTOBASE THERMODYNAMICS
stabilization of the conjugate base) is the main driver of the proton transfer. Later, we will pose
and address a similar question for photobases.
While the molecular physics of photoacids is of interest for investigating fundamentals about hy-
drogen bonding and proton transfer to solvents
14,20,21
, their transient pH jump
22
capabilities nd
application in a variety of challenging chemical kinetics problems, e.g. protein folding
23
and re-
solving the mechanism of an H
2
evolution catalyst.
24
They have been used as probes of solvent
environments on long
11
and transient timescales.
25
Additionally, they have been used in a steady-
state manner to control the local pH via light intensity, allowing for the optical regulation of an
enzymatic reaction.
26
Recently, a photoacid was used to change the steady state low frequency AC
proton conductivity of a material
27
and mediate an acid catalyzed polymerization reaction.
28
Photobases are compounds which become more basic in the excited state (pK
a
> pK
a
). Despite
their potential utility in studying or optimizing chemical reactions requiring pOH jump or assisting
the kinetics of reactions that require removal of protons, such as the O
2
evolution half reaction in
water splitting (2 H
2
O! O
2
+ 4 H
+
+ 4 e
{
), the available literature on their thermodynamic and
kinetic properties is sparse compared to that of photoacids. The common feature in many of the
reported photobases is a heterocyclic nitrogen, particularly in a naphthalene framework. Notable
examples of photobases are curcumin
29
, xanthone
30
, and 3-styrylpyridine
31
and the phenomenon
has been described in a review by Arnaut and Formosinho
2
. Reports of light induced basicity
include proton removal from water by 6-aminoquinoline
32
, pOH jump by photoexcitation of acri-
dine
33{35
and 6-methoxyquinoline
34,36,37
. Recently, 6-carboxy-2-naphthol was shown to contain
both photoacidic and photobasic functional groups.
38,39
We were led to this phenomenon by our earlier work on excited state intramolecular proton transfer
(ESIPT)
40
. We noted that optical excitation appears to redistribute charge within the molecule
in such a way that both the acidity of the proton donor and the basicity of the proton acceptor is
enhanced. From this we were led to investigate only the enhanced basicity component of the of the
ESIPT process. The acceptor moiety in our previous study was a nitrogen involved in a conjugated
system. Thus we sought to understand photobasicity in heterocyclic nitrogen containing compounds
with the hypothesis that photobasicity in such such systems will have similar trends and behavior
3.1. INTRODUCTION 41
as their photoacidic counterparts. As just mentioned, we found that such systems were referred to
in the earlier literature but were not studied or understood as extensively as the photoacids.
In this work, we investigate the origin and tunability of photobasicity in the 5-substituted quino-
line (5-RQ) family of heterocyclic nitrogen-containing compounds, comprising of 5-aminoquinoline
(AQ), 5-methoxyquinoline (MeOQ), quinoline (Q), 5-bromoquinoline (BrQ), 5-chloroquinoline
(ClQ), and 5-cyanoquinoline (CNQ), spanning a large range of electron-withdrawing capability
of the R group. This family was chosen so that it can be compared and contrasted to its photoacid
counterpart, 5-substituted 1-naphthol, which has been studied before for the eect of substitution
on ground and excited state pK
a
.
41
This work aims to answer the following questions: What are the electronic origins of photobasicity?
Is the pK
a
linearly tuned with respect to the Hammett parameter of the substituent? What is
dierent between the sensitivity of the ground and excited state pK
a
to the substituent? More gen-
erally, can the large knowledge of photoacid systems be extended to structurally similar photobases?
Is optically induced charge accumulation on the heterocyclic nitrogen the main contributor to pho-
tobasicity? And nally, at what value of the substituent's Hammett parameter is photobasicity
extinguished?
We hope that this work will help introduce photobases as modules in the toolkit of synthetic
chemists, and inspire incorporating them as functional elements in photocatalysts to drive reactions
in which removal of protons using light is necessary. Recently, calculations by Hammes-Schier's
group
42
revealed that it is possible to tune the energetic landscape of the catalytic cycle of a cobalt
diglyoxime hydrogen evolution catalyst with the choice of substituents on the ligands. They showed
that the reduction potentials of various steps of the catalytic cycle scale linearly with the Hammett
parameters of the substituents. We anticipate that tuning the local environment of an oxidation
catalyst with photobases and using the excited state pK
a
as a means of removing the protons in
an oxidation process will prove useful in lowering overpotentials.
42 CHAPTER 3. PHOTOBASE THERMODYNAMICS
3.2 Electronic Singlet States of Quinoline
We begin with an introduction to the electronic states of quinolines. It is known that two excited
electronic states of quinolines are accessible in the UV-visible range of the spectrum. The excited
states of quinoline are labeled following the common Platt notation for cata-condensed aromatic
systems as
1
L
a
and
1
L
b
.
43
The
1
L
a
state corresponds to atom centered excess charge charge density
compared to the ground state, while the
1
L
b
state corresponds to bond centered excess charge
density. Thus creating the
1
L
a
state via optical excitation pushes charge density on the heterocyclic
nitrogen, and as will be discussed later, is important in making it more basic. Transition to the
1
L
a
state corresponds to a broad lineshape, while excitation to the
1
L
b
state results into a sharper
absorption line, often with vibronic structures.
3.3 F orster cycle
The excited state acidity and basicity is commonly inferred from a thermodynamic cycle origi-
nally reported by F orster
44
, depicted in gure 3.1.c. The approximations and conditions for the
validity of the F orster cycle are discussed in several references
3,45
. In brief, it can be thought of
as a thermodynamic cycle involving the protonated and deprotonated forms in both ground and
excited states. The ground state pK
a
is determined by the dierence in energy between the ground
state protonated and deprotonated forms as pK
a
= G=(2:3RT ). This value is obtained from a
conventional titration experiment of the ground state. The next relevant quantity is the 0-0 energy
gaps between the ground state and the lowest excited electronic states for both the protonated
and deprotonated forms. The lowest excited state is chosen because of a general and reasonable
assumption in F orster cycle analysis, in which full electronic relaxation within the excited states
is completed before proton transfer (i.e. excitation to S
n
will rapidly decay such that the excited
state acid-base equilibrium is in S
1
). This separation of timescales is the basis for using thermo-
dynamic language and concepts such as equilibrium constants for a system in the excited state.
TheS
0
-S
1
gap between 0-0 vibrational states can be obtained from the absorption spectrum of the
protonated and deprotonated forms alone. However, in practice the vibronic features are poorly
3.4. HAMMETT ANALYSIS 43
distinguishable and it is best to obtain both the absorption and emission spectra for each species
and estimate the 0-0 gap as the average between the absorption and emission maxima. Further
details of the assignment of the 0-0 gaps for the set of compounds is given in the experimental
section. Once the 0-0 transition energies and G are known, the dierence in the excited state
protonated and deprotonated forms G
is uniquely dened and is related to the excited state pK
a
via pK
a
= G
=(2:3RT ). As a convenient reference number, an energy gap of 477 cm
-1
(59 meV)
corresponds to one unit of pK
a
at T = 298 K. See SI for full derivation.
As a representative spectrum of the 5-substituted quinoline family, the absorption and emission
spectra of BrQ in protonated and deprotonated forms are shown in gure 3.1.b. The spectra for
other compounds are shown in the SI. The characteristic sharp
1
L
b
states are prominent in the
absorption spectrum and do not show frequency shift due to protonation. The broad
1
L
a
peak, on
the other hand, seems to red shift with protonation. This is consistent with the picture described
earlier that optical excitation of the
1
L
a
transition creates excess charge density on the atom,
in particular the nitrogen heteroatom, thus rendering the corresponding peak more sensitive to
protonation. We need to identify the lowest energy 0-0 gap for the F orster cycle analysis. For
some compounds it is necessary to t the spectra with contributions from the
1
L
a
and
1
L
b
states
and isolate the peak position with the lower energy. As mentioned earlier, the gaps are found by
averaging the emission peak and the relevant absorption peak for each species. The results of the
F orster cycle analysis are presented in table 3.1.
3.4 Hammett Analysis
Our next goal is to plot the obtained energies and pK
a
values as a function of the known electron
withdrawing powers of the substituents. In physical organic chemistry there are systematic proce-
dures for quantifying the electron-withdrawing power of a functional group.
46
A commonly used
method is called the Hammett analysis. In brief, the acid dissociation constantK
0
of unsubstituted
benzoic acid is taken as a reference reaction (pK
a
= 4.2). To measure the in
uence of functional
groups R on this value, the acid dissociation constants K of a series of R substituted benzoic
44 CHAPTER 3. PHOTOBASE THERMODYNAMICS
S
0
1
L
A
ΔG*
ν
00
base
ΔG
ν
00
acid
1
L
B
1
L
A
1
L
B
BrQ + H
+
BrQH
+
S
0
BrQ BrQH
+
BrQ* BrQH
+
*
1
L
B
acid
1
L
B
base
1
L
A
base
1
L
A
acid
(b) (c) (a)
Figure 3.1: (a) The structure of 5-substituted quinoline. (b) Normalized absorption (solid) and
emission (dashed) spectra of 5-bromoquinoline in basic (blue) and acidic (red) aqueous solutions.
The approximate origin band energies of the two lowest lying singlet states are annotated. The
1
L
b
origin is observed as a sharp feature, while the
1
L
a
origin is estimated by averaging absorption and
emission maxima. For all other compounds in this study, the spectra can be found in the SI. (c)
Depiction of the F orster cycle as it applies to quinolines. The excited state equilibrium is between
the two lowest lying singlet states.
acids are measured. Through a large number of experimental measurements, a simple linear rela-
tion log
K
K0
= is veried, where is a constant and is a measure of the electron-withdrawing
capability of the functional group. Groups with larger pull the electronic charge away from the
acidic end of the molecule and thus result into easier dissociation of the proton. We note that
several variants of the Hammett parameter exist, some obtained with dierent reference reactions,
some accounting for the position of the substituent on the benzoic acid ring, and some dissecting
the inductive and resonance eects in electron withdrawing. We have chosen to use the known
Hammett parameter
p
of the studied substituents corresponding to the para- substituted benzoic
acid. In practice, correlation with all parameters can be made. We found that
p
had the best
correlation in the ground state, in accordance with prior work
47
, and
, had best correlation in
the excited state, though all parameters had similarly good correlations. Further information on
this is provided in the SI. The trends reported hold true for all parameters, but for the purpose of
displaying the information graphically we used
p
because it had the highest ground state correla-
3.4. HAMMETT ANALYSIS 45
tion. The values of
p
used in our work were obtained from Hansch
48
. We point out that the central
message of our work does not critically depend on a particular choice of Hammett parameters.
Figure 3.2 shows the dependance of the energies of various states on the Hammett parameters
p
of the substituents. To assist comparison of energy gaps for each compound, the S
0
(RQH
+
) state
is set as the reference of energy (the lowest red line in the gure). As expected, with increasing
Hammett parameter values, the gap G between the S
0
(RQH
+
) and S
0
(RQ) shrinks. Otherwise
stated, under equilibrium conditions, larger deprotonated population is expected with larger
p
, or
the acidity of the compound increases with larger
p
. The ground state pK
a
based on this gap is
shown in gure 3.3. If the dependency is tted to a straight line, a slope of = 1:6 is obtained.
This result for the ground state pK
a
is reasonably expected and is neither a surprise nor a main
point of this study.
Now we turn our attention to the excited state protonation gap, in particular for the most negative
value of the Hammett parameter
p
=0:7 corresponding to AQ. The most immediate observation
is that the excited state gap between the protonated and deprotonated forms is much larger than
the ground state. This implies that the protonation of the molecule in the excited state is much
more favorable than in the ground state. Translated in pK
a
form, this information is shown in
gure 3.3. Based on the F orster cycle estimate, upon optical excitation, AQ jumps from a pK
a
near 5 to a pK
a
near 16. This large increase in basicity upon optical excitation is the central point
of this work.
Next, we follow the trend in pK
a
with respect to the Hammett parameter
p
. A quick observation in
gure 3.2 shows that the excited state gap G
becomes smaller as
p
increases. The
1
L
A
(RQH
+
)
state remains the lower state throughout the range of our study0:7 <
p
< +0:7. However,
a gentle extrapolation shows that near
p
0:9 the
1
L
A
(RQH
+
) and
1
L
B
(RQH
+
) states must
become degenerate. We will comment further on this point later. Similarly, the
1
L
A
(RQ) and
1
L
B
(RQ) states become degenerate near
p
0:7. The protonation gap G
expressed as an
excited state pK
a
is shown in gure 3.3. Two central important messages of this work are contained
in this gure. The rst result is that the excited state pK
a
follows a linear relation with respect
to the Hammett parameter
p
. The second result is that the slope of this linear relation
= 8
46 CHAPTER 3. PHOTOBASE THERMODYNAMICS
Table 3.1: Approximate origin band transition energies, pK
a
, and pK
a
for the set of 5-R-quinolines.
R
1
L
base
a
1
L
base
b
1
L
acid
a
1
L
acid
b
pK
a
pK
a
pK
a
NH
2
27.0 31.8 21.9 31.8 10.6 5.3 15.9
MeO 28.3 31.9 23.4 31.7 10.2 4.9 15.1
H 31.9 31.9 28.7 31.9 6.7 4.8 11.5
Br 30.4 31.5 27.2 31.6 6.7 4.5 11.2
Cl 30.1 31.5 27.3 31.6 5.9 3.8 9.7
CN 31.8 31.3 30.2 31.3 2.2 3.2 5.4
Energies shown in cm
-1
10
3
is much larger than the slope of the ground state pK
a
. We will explain the possible origin of this
dierence along with a comparison to the photoacids shortly. This result is similar to the behavior
for 5-substituted 1-naphthol,
41
where the excited state has a linear but more sensitive dependence
on the Hammett parameter compared to the ground state.
Finally, we list some interesting observations in the series of molecules studied. Some of these
observations shed further light on the results presented so far and some may form a basis for
further studies.
3.5 Limit of Photobasicity
Inspired by the approach and possible crossing of states at high
p
values (gure 3.2), we investigated
the spectra of a substituted quinoline with
p
higher than -CN. An accessible choice for us was
R =NO
2
with
p
= 0:78. From gure 3.2 one infers that, given the linewidth of transitions, there
would not be much distinction between the
1
L
a
and
1
L
b
states and there would be minimal spectral
change upon protonation. Our measured absorption spectrum for the NO
2
Q is included in the SI.
Indeed, the sharp
1
L
b
features, which are present in CNQ, are no longer observed in NO
2
Q, and
there is minimal red shift upon protonation. For this reason, it is dicult to assign the ground and
excited state pK
a
values. However, since this behavior is consistent with gure 3.2, we plausibly
suspect that at this Hammett parameter value the protonated
1
L
a
and
1
L
b
states are close to
degeneracy. Furthermore, it is inferred that for NO
2
Q the drive for protonation in the excited state
G
is not very dierent from G. Thus this work not only reports a trend for photobasicity, but
3.5. LIMIT OF PHOTOBASICITY 47
Figure 3.2: The dependence of
1
L
a
and
1
L
b
states for protonated and deprotonated forms on the
Hammett parameter of the substituents. Straight lines are approximate ts (with the exclusion
of unsubstituted quinoline as described in the text). The lowest excited state is
1
L
A
(RQH
+
)
throughout the range of the study. The excited state G
for protonation is far more favorable
than the ground state G, giving rise to photobasicity. Hammett values for which the
1
L
a
and
1
L
b
states becomes possibly degenerate, are indicated by the vertical dashed line. The dierence
G = G
G, determining pK
a
seems to rapidly diminish upon crossing the point of
degeneracy of the
1
L
a
state for the deprotonated form.
48 CHAPTER 3. PHOTOBASE THERMODYNAMICS
Figure 3.3: Ground and excited state pK
a
of 5-substituted quinolines versus Hammett
p
parameter.
Lines of linear t are shown in solid. The two central ndings of our work are the linear dependence
of the excited state pK
a
on
p
and its larger slope
5.
also predicts that photobasicity can be turned o for a value of
p
0:8 due a substituent R=NO
2
.
3.6 Deviation of Quinoline's State Energies
Because Hammett parameters are not inferred from measurement of spectroscopic gaps, it is not
immediately obvious that one should expect the relationship in gure 3.2. Otherwise stated, the
Hammett analysis is not related to or based upon optical spectroscopy data, but rather demonstrates
a trend in ground state thermodynamic drives. The F orster cycle is built to relate spectroscopic
gaps to thermodynamics drives in the ground and excited states. Thus Hammett parameters are
indirectly and subtly related to spectroscopic gaps via the F orster cycle.
A notable break in the trends shown in gure 3.2 is quinoline itself. The behavior of its states with
respect to protonation is the same as the other compounds, that is
1
L
b
is invariant to protonation
and
1
L
a
red shifts upon protonation. However, the energies of these transitions are signicantly
3.7. ICT AND ANALOGY TO PHOTOACIDS 49
higher than the energies of the corresponding transitions in neighboring MeOQ and BrQ. For this
reason, they have been excluded from the ts shown in gure 3.2. Despite this apparent anomaly
the pK
a
value calculated with the F orster cycle for quinoline does lay in the same line as the other
compounds. These observations may seem odd at rst, but in fact the perceived oddity is claried
once we consider the origin of the Hammett parameters, which were meant to correlate ground
state equilibria to a reference reaction with a resulting linear relationship as pointed out in the
previous paragraph. We suspect that the spectroscopic gaps of unsubstituted quinoline (R=H) are
an exception to the correlations in gure 3.2 because of the small size of the hydrogen atom. Its
ability to modulate excited states by pushing and pulling electrons is captured, or rather dened,
with its Hammett parameter
p
= 0. What is not captured in
p
is how R extends the size of
the system. The other substituents are fairly large with respect to hydrogen and are larger
perturbations to the particle on a ring model of the molecule. Even if they do not participate in
the conjugation, they serve as partial extenders of electron density, thus lowering the transition
energies to the rst excited state. For R=H, the system is less delocalized and consequently
the
1
L
a
and
1
L
b
energies are larger compared to its neighboring compounds, as seen in gure 3.2.
As an argument in favor of this proposal, in the TD-DFT exitation energies and electron density
dierence maps, we do see that even though the
1
L
a
excitation is primarily HOMO to LUMO (
to ), electron density changes do occur on the substituent (gure S2).
3.7 ICT and Analogy to Photoacids
Previous work on intramolecular charge transfer in neutral photoacids (hydroxypyrene deriva-
tives
13,17
, naphthol derivatives
18,49
, and phenol derivatives
19,50
) has shown that ICT on the conju-
gate photobase is typically larger than ICT on the photoacid, although the reverse situation is true
in the cationic photoacid APTS.
14
Mulliken charge density analysis on the quinoline derivatives
studied has found approximately equal ICT on the photobase and conjugate photoacid upon opti-
cal excitation (gure S1), suggesting that they may be dierent than traditional photoacids. We
invite theoreticians to investigate the phenomenon more thoroughly with advanced charge analysis
50 CHAPTER 3. PHOTOBASE THERMODYNAMICS
methods.
3.8 Triplet States
We have not included any potential contribution from triplet states or the rates of intersystem
crossing or nonradiative decay. While it is possible that a T
1
acid-base equilibrium also exists,
it does not preclude the pK
a
values discussed above. Previous work has shown that in solvated
quinoline at low temperatures
uorescence originates only from hydrogen bonded species, while
phosphorescence arises from non-hydrogen bonded species
51
. Additionally they, and others
52
, have
pointed out that the broad, dual emission observed is from an excited state proton transfer.
3.9 Conclusion
In conclusion, we have measured the magnitude and tunability of photobasicity in 5-substituted
quinolines. The pK
a
and pK
a
in the studied set of compounds correlate to Hammett
p
parameter
over the chemical space investigated (0:7<
p
< 0:7). The 0-0 energies of the states themselves,
with the exception of unsubstituted quinoline, also obey a linear relation with respect to
p
. The
relative energies of the
1
L
a
states of the acid and base forms are responsible for the pK
a
values,
with the exception of the larger electron withdrawing region (
p
> 0.55). Synthetic eorts to in-
crease pK
a
or select a desired pK
a
value should focus on the relative interaction of the substituent
with the
1
L
a
states. We envision that this quantitative measurement of the substituent eect on
the ground and excited state equilibria will allow one to carefully select the desired pK
a
for an
application requiring removal of protons, for example in an oxidation catalyst.
3.10. EXPERIMENTAL SECTION 51
3.10 Experimental Section
3.10.1 Materials
A set of six compounds in aqueous solution had their absorption and emission spectra measured:
5-aminoquinoline (AQ), 5-methoxyquinoline (MeOQ), quinoline (Q), 5-bromoquinoline (BrQ), 5-
chloroquinoline (ClQ), and 5-cyanoquinoline (CNQ). The absorption of 5-nitroquinoline (NO
2
Q)
was also analyzed. AQ, MeOQ, BrQ, and CNQ were purchased from Combi-Blocks. Q, ClQ, ad
NO
2
Q were purchased from Sigma-Aldrich. All compounds were used without further purication.
3.10.2 Steady State Spectroscopy
Absorption spectra were obtained using a Cary 50 UV-vis spectrophotometer. Emission spectra
were collected on a Jobin-Yvon Fluoromax 3
uorimeter. Addition of HCl or NaOH to aqeuous
solutions of each compound were made to titrate the pH which was measured with a Hanna Instru-
ments HI 2210 pH meter. The procedure reported by Schrager
53
was used to calculate the pK
a
from spectroscopic data. Brie
y, singular value decomposition was used to nd the variation of
quinoline/quinolinium population with pH. This variation was tted to the Henderson-Hasselbach
equation to determine the pK
a
.
3.10.3 F orster cycle Calculations
In using the F orster cycle to calculate pK
a
, the 0-0 transition energies of the acid and base forms
need to be identied.
45
The sharp
1
L
b
vibronic progressions were observed from UV-vis absorption
spectra for all compounds except the deprotonated form of AQ. The longest wavelength peak in the
progression was taken as the
1
L
b
0-0 transition.
52
. Fluorescence spectra were collected to identify
each species' emission maxima. As reported before, the absorption and emission maxima for a
given species were averaged as a means to estimate the
1
L
a
0-0 transition for both protonated
and deprotonated forms.
3
In the cases where the
1
L
a
and
1
L
b
absorption bands were overlapping,
numerical values for the peak positions were obtained by tting the spectra with Gaussians. Details
on estimation of pK
a
based on this data is presented in the discussion section.
52 CHAPTER 3. PHOTOBASE THERMODYNAMICS
The emission of the neutral MeOQ and Q species were weak compared to their cations. In these
cases the emission in methanol was used to identify the peak of the neutral species. This energy
was corrected by subtracting the solvatochromatic shift observed for the cation peak in water and
methanol solutions. All absorption and emission spectra and ts for each compound are available
in the SI.
3.10.4 Computational
Electron density dierence maps and Mulliken charges were computed using the Q-Chem
54
software
package and plotted with VMD
55
. Ground state geometries were optimized with B3LYP/6-31+G*.
Excited state electron densities and Mulliken charges were calculated using TD-DFT/B3LYP/6-
31+G* and plotted at the 0.0005 isosurfaces.
3.11 Supplemental Information
The absorption and emission spectra associated with all of the quinoline compounds are included
at the end of chapter 4.
3.11.1 The F orster cycle and its approximations
In addition to the F orster cycle it is also possible to obtain pK
a
values via a
uorescence titration.
However, in cases where one species has a low quantum yield, the titration does not result in an
accurate pK
a
. The issues associated with this are detailed by Lasser and Feitelson
56
. There are
also possible quenching eects that may interfere with getting reliable pK
a
values when titrating
in extremely basic conditions (pH > 15). For these reasons, we chose to use the F orster cycle to
calculate pK
a
.
Although the F orster cycle is a thermodynamic cycle and is analytically correct, several practical
assumptions need to be made to use it. These are discussed in detail by Weller
45
and Ireland
3
.
3.11. SUPPLEMENTAL INFORMATION 53
Formally, the F orster cycle is dened as
H
H =hc(~
base
00
~
acid
00
) (3.1)
and the approximation that
H
H = G
G (3.2)
is made so that equilibrium constants can be related to the spectroscopic observables. Using the
relation
G =k
B
T ln(K
a
) =
k
B
T
log(e)
pK
a
(3.3)
we arrive at the form of F orster cycle equation used to calculate change in pK
a
upon excitation.
pK
a
pK
a
=
log(e)hc
k
b
T
(~
base
00
~
acid
00
) (3.4)
Assuming T = 298 K and collecting constants, Eq. 3.4 can be expressed as
pK
a
=
~
00
477 cm
-1
(3.5)
The necessary approximation in Eq. 3.2 is that S
S = 0, which is a good assumption if the
entropy of protonation of the excited state is similar to that of the ground state.
3.11.2 Choosing a set of Hammett parameters
Hammett parameters were developed to quantitatively capture a functional group's ability to donate
or withdraw electrons. They were derived empirically from measuring the eect a functional group
had on the equilibrium of a reference reaction, e.g. the
p
constants were determined from the
acid-base equilibrium of para substituted benzoic acid.
46
When using them to describe the eect on system signicantly dierent than the reference reac-
tions, it is not clear which set is the most appropriate to use. It is also possible that an excited
state equilibrium may resemble a dierent reference reaction more closely than the ground state
54 CHAPTER 3. PHOTOBASE THERMODYNAMICS
Table 3.2: Hammett parameters and thermodynamic measurements
R pK
a
pK
a
m
p
+
NH
2
5.3 15.8 -0.16 -0.66 -1.30 -0.15
MeO 4.9 15.1 0.12 -0.27 -0.78 -0.26
H 4.8 11.5 0.00 0.00 0.00 0.00
Br 4.5 13.6 0.39 0.23 0.15 0.25
Cl 3.8 12.7 0.37 0.23 0.11 0.19
CN 3.2 5.4 0.56 0.66 0.66 1.00
Table 3.3: Reaction constants and correlations
R
2
R
2
*
m
2.6 9.5 0.82 0.47
p
1.6 6.9 0.85 0.72
+
0.9 4.3 0.74 0.68
1.6 7.7 0.81 0.86
equilibrium.
In practice, correlations are typically made with several sets of parameters for comparison. We found
that for ground and excited state quinoline correlations to other parameters did not qualitatively
change our conclusions and chose to present
p
in the main body of the paper. The other correlations
and the reaction constants are listed below with the Hammett parameters from reference 48 and
our pK
a
measurements.
3.11.3 Charge Density Analysis
There has been much discussion about intramolecular charge transfer (ICT) and its role in pho-
toacidity. Calculations of the Mulliken charges on the oxygen in 2-naphthol have illustrated that
although both ROH and RO
{
undergo partial ICT upon excitation, it is the stabilization of conju-
gate base after proton transfer which is the greater contributor.
49
Experiments, in particular Stark
shift measurements
13
, on hydroxy pyrene trisulfonic acid (HPTS), are congruent with the latter
notion, but also show that the eect can be reversed (acid form has greater ICT) for the cationic
photoacid APTS.
14
We nd that in substituted quinolines the calculated Mulliken charge on the heteroatom is roughly
3.11. SUPPLEMENTAL INFORMATION 55
Figure 3.4: Calculated Mulliken charge on the heterocyclic nitrogen in 5-substituted quinolines
when in the ground state (o), excited state (x), protonated (red), and deprotonated (blue) as a
function of experimentally measured pK
a
.
correlated with pK
a
and pK
a
(gure 3.4). ICT occurs upon excitation on both the free base and
conjugate acid causing a negative excess charge to build on the nitrogen. Unlike 2-naphthol
8
,
the amount of optical ICT for both forms is nearly equivalent. The results suggest that optically
induced ICT in RQ prepares the initial charge density dierence on the heteroatom to initiate
proton transfer. After proton transfer, the charge density on the heteroatom is reduced to values
far lower than the ground state RQ because of sharing electrons in the newly created bond with
the proton.
To better visualize the ICT process and the substituent eect on it, electron density dierence
maps were calculated for Q, AQ, 1-naphthol, and 5-cyano-1-naphthol (gure 3.5). The changes in
density show a general migration of electrons from the distal ring towards hydrogen bond accepting
nitrogen in quinoline. Similarly, the direction of electron migration is reversed in the case of 1-
naphthol. Addition of electron withdrawing groups to the distal ring in 1-naphthol resulted in the
56 CHAPTER 3. PHOTOBASE THERMODYNAMICS
creation of photoacids with negative pK
a
values
7,57,58
. We predict that further substitution of the
distal ring in quinoline will result in even larger pK
a
values than the ones presented in this paper.
However, the use of an amine in the 8 position may interfere with the acid-base equilibrium via
intramolecular hydrogen bonding.
Electron density dierence (EDD) maps showed an increase in density on the heterocyclic nitro-
gen upon optical excitation (gure 3.5). Similarly, a decrease in density on the phenolic oxygen
upon excitation in 1-naphthol derivatives is computed. Experimentally, the addition of an elec-
tron donating (withdrawing) group in the 5 position will enhance photobasicity (photoacidity) in
quinolines (1-naphthols). The computational model shows that optical excitation does push (pull)
electrons from the functional group towards the proton acceptor (donor) site of the molecule. The
larger sensitivity of the excited state pK
a
to the Hammett parameter is likely due to the larger
polarizability of the excited state charge density. A diuse and polarizable excited state is likely
to respond more sensitively to the electron withdrawing strength of a substituent than the more
conned ground state charge density.
3.11.4 Photoacid-like behavior of MeOQ
In acidic solution, dual emission from MeOQH
+
is observed, if the higher lying
1
L
b
state is excited.
Excitation spectra monitored at the MeOQ* and MeOQH+* peaks were distinct.
Explanation for this is proton release to form MeOQ*, in which case it may be temping to make
the conclusion that neutral MeOQ is a photobase and cationic MeOQH+ is a photoacid. One
may calculate a pK
a
for the photoacid as well using the F orster cycle in the way we have above.
However, the assumptions inherent in the F orster cycle no longer hold in the case of this potential
photoacid. There is no quasi-equilibrium established between the
1
L
b
state of the cation and the
1
L
a
state of the neutral species. The quasi-equilibrium that is established is between the netural
1
L
a
state and the cationic
1
L
a
state. A more succinct way of explaining this is that reversible
proton transfer is part of the internal conversion process in MeOQH+*. We cannot make the same
separation of timescales argument (excite state lifetime >> than IC) for two IC processes since it
is reasonable to assume that they occur with similar timescales.
3.11. SUPPLEMENTAL INFORMATION 57
Figure 3.5: Comparison of the in
uence of the substituent groups on photoacidity and photobasicity.
Electron density dierence maps show theS
1
electron density minus theS
0
electron density. Green
(red) indicates an increase (decrease) in density upon excitation. Electron donating (withdrawing)
groups are shown to enhance photobasicity (photoacidity).
Figure 3.6: Excitation spectra of 5-methoxyquinoline in acidic aqueous solution shows two distinct
species corresponding to the protonated and deprotonated forms. A solvent Raman peak is labeled
with \R".
58 CHAPTER 3. PHOTOBASE THERMODYNAMICS
Figure 3.7: Excitation dependent emission in excess acid suggests photoacid-like behavior. Exciting
the higher lying
1
L
b
state releases the proton to form the neutral MeOQ* species. A solvent Raman
peak is labeled with \R".
We expect similar behavior with AQ since it has the same state ordering as shown for MeOQ,
however evidence of dual emission is inconclusive due to its low quantum yield.
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62 REFERENCES
Chapter 4
Photobase Kinetics
4.1 Introduction
Control over proton transfer is of primary importance in a wide range of chemical scenarios. Optical
control of proton transfer may be achieved in molecules that change their acidity in the excited
state. Photoacids are molecules that become signicantly more acidic upon absorption of light, and
therefore serve as agents that can control local proton concentrations with light.
1{5
They have been
widely used in a range of applications, including studying catalytic mechanisms
6
, protein folding
7
,
and optical regulation of enzymatic activity.
8
Despite the large body of literature on photoacids, there remains a signicant lack of work on their
counterparts, photobases, which are molecules that undergo an increase in pKa upon light absorp-
tion. A few notable examples of photobases are quinoline
9,10
, acridine orange,
11
3-styrylpyridine
12
,
and xanthone
13
. Recently, we reported a systematic study of the thermodynamic drive for pro-
ton removal in the excited state (pKa*) of a series of 5-substituted quinolines using F orster cycle
analysis based on singlet states.
14
However, the existence of the thermodynamic drive for proton
transfer in a singlet state does not account for relaxation via intersystem crossing or imply that
deprotonation by a photobase is kinetically feasible at all. Therefore, in this study, we investigate
the eects the substituents have on the kinetics of proton transfer. In particular, we show that
63
64 CHAPTER 4. CHAPTER TITLE
several competing relaxation pathways exist in the excited states of quinolines, some of which are
capable of proton transfer as expected while others are not.
Previously, it has been observed that quinoline undergoes an excited state proton transfer reac-
tion, acting as a Bronsted-Lowry base, accepting a proton from water, thus transiently generating
a hydroxide ion. There are some studies on the dynamics of substituted quinolines in aqeuous
media
15{17
, but none that investigate the eects of substituents electron donating/withdrawing
capabilities (Hammett parameter
18,19
) in a systematic way. This sensitivity of photobasicity to
substituents is the subject of this paper.
It is reasonable to hypothesize that a relationship between the thermodynamic drive (i.e. pKa* as
inferred from the F orster cycle
20,21
based on singlet states) and the rate of proton transfer exists.
Therefore strongly electron-donating substituents, which result in a larger pKa*, will also result
in a faster rate of proton capture in the excited state. However, it is known that triplet states
have a signicant role in the photophysics of quinolines.
22{26
We nd that the relative energies
of triplet states and the intersystem crossing rates are sensitive to the substituents. This renders
the excited state proton transfer process more complicated than can be captured by the linear
free energy relationships inferred from the energetics of the singlet states. This is in contrast to
the structurally similar photoacid family of 1-naphthols, for which triplet states do not play a
role and a correlation between thermodynamic drive and proton transfer rate has been reported
27
.
Interestingly, we provide evidence that, in some cases, triplet states can undergo proton transfer.
Since triplet states have longer lifetimes, this nding will be important for chemical applications of
photobases which require a sustained pOH jump.
Similar to photoacids that have been used to study catalysis mechanisms, protein folding dynamics,
and enzyme activity regulation, we envision photobases to be another tool in studies that would
require optical control over proton removal. We hope that elucidating these fundamental excited
state processes in quinolines will allow photobases to become functional moieties in catalytic systems
that require photo-mediated removal of protons.
4.2. EXPERIMENTAL SECTION 65
4.2 Experimental Section
4.2.1 Materials
5-aminoquinoline, 5-methoxyquinoline, 5-bromoquinoline, and 5-cyanoquinoline were purchased
from Combi-Blocks. Quinoline and 5-chloroquinoline were purchased from Sigma-Aldrich. All
compounds were used without further purication.
4.2.2 Steady State Spectroscopy
Absorption spectra were obtained using a Cary 50 UV-vis spectrophotometer. Emission spectra
were collected on a Jobin-Yvon Fluoromax 3
uorimeter.
4.2.3 Transient Absorption
Pump pulses were generated by pumping an OPA (OPerA Solo, Coherent) with the output of a 1
kHz Ti:sapphire amplier (Legend Elite HE+, Coherent). UV pump pulses were generated by two
successive doubling stages of the OPA output. A white light continuum probe was prepared by
focusing the 800 nm Ti:sapphire output onto a 3 mm thick rotating CaF
2
window. Before white
light generation, a polarizer was set to rotate the probe beam to the magic angle with respect to the
pump to eliminate rotational diusion eects. The pump beam was modulated at 500 Hz using an
optical chopper. The probe was detected using a 320 mm focal length spectrometer with 150 g/mm
gratings (Horiba iHR320) and a 1340x100 CCD array (Princeton Instruments Pixis). A balanced
detection scheme was employed to eliminate noise due to
uctuations in the probe spectrum. The
probe arm of the apparatus was split with a 50/50 beamsplitter into two arms: sample and reference.
The beam in the sample arm was directed to the sample and focused and overlapped with the pump
beam. The reference arm was passed through the sample but in a location that is not pumped.
Both probe beams were detected by displacing their focal planes on the CCD such that the sample
and reference beams are contained by the top half and bottom half of the CCD respectively. The
signal resulting from the sample beam contains the transient absorption and
uctuations due to the
instability of the probe. The signal resulting from the reference beam only contains the
uctuations.
66 CHAPTER 4. CHAPTER TITLE
The reported transient absorption signals were calculated by subtracting the reference signal from
the sample signal. The focal spot size diameters for the pump and probe were 29 m and 95
m respectively. Cross correlations of the pump and probe were collected using the nonresonant
response of the
ow cell lled with DI water (Figures S40, S41, S42). The width of this nonresonant
response is shorter than the 1 ps time step-sizes used in these experiments which we report as our
eective time resolution. Aqueous solutions of0.3 mM for each compound were prepared. The
pH of each solution was adjusted with NaOH and HCl. The samples were
owed through a fused
quartz
ow cell with a 0.1 mm path length. Each sample was pumped near its
1
(,
) absorption
maximum with pulse energies of 300 - 500 nJ. NH
2
Q was pumped at 333 nm, MeOQ was pumped
at 310 nm, and Q, ClQ, BrQ and CNQ were pumped at 287 nm. Samples were pumped at several
dierent powers to check that the signals reported were linear in pump power (Figures S43, S44,
S45, S46).
4.3 Results and Discussion
The set of molecules investigated showed a surprisingly wide variety of spectral features and re-
laxation mechanisms despite their chemical similarity. We discovered cases of singlet state proton
transfer (NH
2
Q, MeOQ) and triplet state proton transfer (Q, CNQ). Additionally, we have evi-
dence that proton transfer does not occur in two of the compounds (ClQ, BrQ). As a result of the
complexity of this set of data, each compound must be treated individually. We rst outline our
guidelines for identifying the relevant chemical species involved in the analysis of kinetics. Then
we describe the dynamics of each compound in order of increasing complexity. A summary of the
ndings on these excited state dynamics is shown in Table 4.1 where the compounds are ordered
by increasing Hammett parameter of the substituents.
4.3.1 Identication of Transient Chemical Species
Formally, all transient absorption (TA) spectra contain a sum of three components: excited state
absorption (ESA) (positive A), stimulated emission (SE) (negative A), and ground state bleach
4.3. RESULTS AND DISCUSSION 67
(GSB) (negative A). These features often overlap spectrally, and in some cases can be separated
by comparison to steady state data and curve tting. We use the following spectroscopic signatures
and assumptions for interpretation of our ultrafast data.
Protonated form/acid: We can identify the TA spectrum of the acid species by forcing proto-
nation in the ground state with a pH two units lower than the pK
a
and exciting the acid species.
We will refer to this as the acid-form spectrum. In all cases but one (CNQ), this spectrum does
not have signicant time evolution, meaning it relaxes to its minimum on the order of our time
resolution (1 ps). In most cases the transient SE band matches the steady state
uorescence
spectrum. We display the
uorescence spectrum inverted and scaled for easier comparison to the
SE peaks.
Deprotonated form/base: We can identify the TA spectrum of the base form by forcing de-
protonation with a pH two units greater than the pK
a
and exciting the base species. We assign
the transient spectrum immediately after excitation to the base form. This assumes that proton
transfer is always slower than our time resolution of 1 ps. Studies of similar compounds typically
report proton transfer times in the 10 - 1000 ps range.
1
Direct comparison to steady state emission,
as is done for the acids, is not possible for the deprotonated forms since their quantum yield for
uorescence in water is quite low.
Singlet state: Although a singlet state is always initially excited, ISC may be ultrafast (<1 ps)
in heteroaromatic systems
28
. Therefore, the rst spectrum in a time series must have its spin state
identied. The presence of a SE band, ideally one that matches steady state
uorescence data, is
indicative of a singlet state. In cases where the overall signal is positive due to overlap with ESA
bands, the line shape is t with a combination of negative and positive Gaussians to extract the
SE band.
Triplet state: Excited states of compounds that have low quantum yield in steady state mea-
surements, no transient SE signal, but do have transient ESA, are assigned to triplet states. The
presence of these features can be determined if tting the line shape can be done with only positive
Gaussian functions.
Chemical exchange: An isosbestic point in a series of time ordered spectra is evidence of pop-
68 CHAPTER 4. CHAPTER TITLE
ulation transfer between two chemically distinct species. When an isosbestic point is present, the
time-ordered spectra contain a band (either ESA or SE) which decreases in magnitude while an-
other band simultaneously increases. The time constant associated with this process is extracted
using Singular Value Decomposition (SVD)
29,30
of the full 2D data set and curve tting with ex-
ponentials. If there is evidence for chemical exchange between singlet and triplet states the time
constant is assigned to intersystem crossing (ISC). If exchange is between base and acid forms it is
assigned to proton transfer (PT).
Finally, our data suggests rapid internal conversion (<1 ps) both within the singlet and triplet
manifolds, consistent with Kashas rule. For this reason we do not concern ourselves with chemical
exchange within a given spin manifold. Using the above guidelines, we now describe the dynamics of
each compound in order of increasing complexity, with a summary of the ndings provided later in
Table 4.1. The full two-dimensional data sets for all compounds are included in the supplementary
information. We present spectral slices of this data throughout the paper.
4.3.2 5-methoxyquinoline
In 5-methoxyquinoline (MeOQ) we observe evidence for singlet state photobasicity. Fluorescence
measurements in protic and aprotic solvents show two distinct emission wavelengths (Figure S12).
These distinct spectral features will serve as markers for the protonation state of the emitting
molecule. In chloroform MeOQ emits at 388 nm and in aqueous solution at a pH below its pKa it
emits at 512 nm. Solvatochromism alone cannot account for this dierence. Therefore, we assign
the two emission wavelengths to the deprotonated and protonated forms respectively. In aqueous
solution with pH greater than the pKa, the molecule still emits near 512 nm. This implies that even
though the molecule is deprotonated in the ground state, it captures a proton from water in the
excited state and emits in the acidic form. To further prove this point, we measured the emission
spectra in methanol, which is harder to deprotonate than water. Interestingly, we observed two
distinct peaks, one near 415 nm, and another near 506 nm (shown inverted in Figure 6.2 B). This
indicates that only a fraction of the excited MeOQ population captures protons from methanol and
the rest remains in the deprotonated form. While this observation provides evidence for excited
4.3. RESULTS AND DISCUSSION 69
Figure 4.1: 5-methoxyquinoline transient absorption in water. (A) TA spectra at pH 3.0 (solid),
steady state
uorescence in acidic water displayed inverted and scaled (dashed); (B) TA spectra at
pH 7.0 (solid), steady state
uorescence in methanol displayed inverted and scaled (dashed).
state proton transfer, our ultrafast TA data described below measures the kinetics and provides
further supporting evidence.
The acid-form transient absorption spectrum (Figure 6.2 A) contains an SE band that matches
the
uorescence spectrum and shows neither signicant relaxation nor chemical exchange. This
indicates that when the protonated molecule is excited, it remains in the protonated form in the
excited state without any signicant dynamics.
When the base form is pumped (Figure 6.2 B) two SE bands, similar to the dual
uorescence
in methanol, exchange with one another. The wavelength mismatch between the SE and the
uorescence bands is due to solvatochromism and the overlapping ESA feature. Decomposition of
the overlapping ESA and SE features is shown in Figure S15. From the spectral signatures above,
the isosbestic points at 410 nm and 480 nm are assigned to chemical exchange between acid and
base forms. The time constant associated with this interconversion is 23 ps and is assigned to
proton capture from water in the singlet state.
70 CHAPTER 4. CHAPTER TITLE
4.3.3 Quinoline
In quinoline we observe evidence for triplet state photobasicity. The acid-form spectrum shows
the same behavior as that of MeOQ: there is minimal relaxation on the timescale probed, SE that
coincides with the
uorescence maximum (Figure 4.2 A), and no evidence for chemical exchange.
There is a nearly 25 nm wavelength mismatch between the SE and
uorescence which may be due
to the presence of an underlying ESA band near 400 nm similar to that observed in the spectrum of
MeOQ. This ESA band, most likely
1
L
a
!
1
(n,
), may also be responsible for the sharp features
in the TA that look like a vibronic progression. When the base form is excited, in stark contrast to
MeOQ, the transient spectra only contain ESA features (Figure 4.2 B). The absence of SE bands,
even at short delay times, suggests rapid triplet formation (ISC) after excitation as discussed earlier
under the identication of transient chemical species section. This observation corroborates the low
uoresence quantum yield observed in high pH water. From these observations we assign these
ESA bands to triplet-triplet absorption. Principle component analysis shows conversion between
two major species within the triplet manifold corresponding to the isosbestic point near 500 nm
that we plausibly assign to protonated and deprotonated triplet states. The conversion between
these two species, i.e. protonated and deprotonated triplets, occurs with a time constant of 28 ps.
4.3.4 5-chloro and 5-bromoquinoline
In 5-chloro and 5-bromoquinoline we have evidence that proton transfer does not occur. The acid-
form spectra of the halogenated compounds (Figure 4.3 A and C) were similar to quinoline and
MeOQ, showing minimal relaxation, an SE band that roughly matches the
uorescence, and no
chemical exchange. The TA spectra of the excited base form (Figure 4.3 B and D) show only ESA
features, suggesting rapid ISC similar to quinoline. However, they do not show a clear isosbestic
point. Population transfer, i.e. chemical exchange, between species could not be identied via
principle component analysis. This suggests that no proton transfer occurs after triplet formation.
Ultrafast proton transfer that is less than 1 ps is unlikely, given the longer time-constants observed
for other photobases both in the current study and elsewhere.
1
4.3. RESULTS AND DISCUSSION 71
Figure 4.2: Quinoline transient absorption in water. (A) TA spectra at pH 2.4 (solid), steady state
uorescence in acidic water displayed inverted and scaled (dashed); (B) TA spectra at pH 7.0. As
explained in the text, these TA spectra are evidence for rapid triplet formation, which is consistent
with the lack of steady state
uorescence. Triplet-triplet absorption energies used to construct the
state diagram in Figure 4.6 are marked withy and *.
72 CHAPTER 4. CHAPTER TITLE
Figure 4.3: Halogenated quinoline transient absorption in water. (A) 5-chloroquinoline TA at pH
1.8 (solid), steady state
uorescence in acidic water displayed inverted and scaled (dashed); (B) 5-
chloroquinoline TA at pH 5.3. (C) 5-bromoquinoline TA at pH 1.9 (solid), steady state
uorescence
in acidic water displayed inverted and scaled (dashed); (D) 5-bromoquinoline TA at pH 5.3. The
sharp feature at 570 nm is an artifact from pump scatter.
4.3. RESULTS AND DISCUSSION 73
Figure 4.4: 5-cyanoquinoline transient absorption in water at pH 1.2 (A); pH 7.0 (B);
4.3.5 5-cyanoquinoline
In 5-cyanoquinoline we observe evidence for triplet state photobasicity. In acidic media 5-
cyanoquinoline has a large
uorescence quantum yield. However, the acid-form spectrum contains
many broad positive ESA features (Figure 4.4 A). The
uorescence roughly matches a feature that
is concave up, although it is dicult to separate it from the ESA features even with curve tting.
There are some dynamics present in the ESA features. However, we are hesitant to assign them
based on the complex shape and poor ts obtained.
The excited base form transient spectra (Figure 4.4 B) look similar to that of quinoline: one ESA
band at early times that exchanges for another ESA band at later times. Just as in quinoline, proton
transfer occurs after initial rapid triplet formation. This is consistent with the poor
uorescence
quantum yield for CNQ in the base form. The exchange process within the triplet manifold has a
time constant of 40 ps and, as is the case for quinoline, is assigned to triplet state proton capture.
74 CHAPTER 4. CHAPTER TITLE
4.3.6 5-aminoquinoline
For 5-aminoquinoline we have evidence for singlet state proton transfer and further relaxation to
the triplet state. Unlike the other compounds investigated, NH
2
Q has low
uorescence quantum
yield in both acidic and basic conditions. The acidic transient spectra (Figure 4.5 A) show dynamics
and evidence for chemical exchange: an isosbestic point at 570 nm. At early times the TA contains
a sharp ESA feature at 545 nm and a broad SE band on the red edge of the spectrum, indicating
that it is a singlet. These features disappear and become two ESA bands, indicating the formation
of a triplet. The time constant associated with this exchange is 36 ps and is assigned to ISC of the
protonated form.
Under basic conditions we initially see an SE band on the red edge of the spectrum, indicating a
singlet state (Figure 4.5 B). Within 40 ps, the sharp ESA band at 545 nm that was also present in
the singlet acidic spectrum appears, indicating proton capture by the singlet state. From this point
onward, the time evolution of the spectra seems to be similar to that of the photoexcited acidic
form. This is evidenced by chemical exchange at later times (Figure 4.5 C), although the isosbestic
point is not very well-dened. Furthermore, the nal spectrum at t=200 ps is similar to the acid-
form spectrum, a protonated triplet. The slight mismatch in shapes of the nal spectra (Figure
4.5 D) is due to a small negative band at 515 nm in the acid-form spectrum, which is emission
from contaminating MeOQ as justied in the SI (Figure S9). The above description suggests a
two-step process, in which the singlet state rst captures a proton and then intersystem crosses to a
triplet state. Decomposition of this data required two components. The rst component has a time
constant of 41 ps and is assigned to singlet state proton transfer. The second component had a time
constant of 27 ps and is assigned to ISC. However, the t obtained for this second component is
poor resulting in a large uncertainty for this time constant (Figure S8). For this reason, we report
the 36 ps time constant obtained from the acidic solution measurements as the ISC time constant
in this two-step mechanism.
4.3. RESULTS AND DISCUSSION 75
Figure 4.5: 5-aminoquinoline transient absorption at pH 3.4 (A); pH 8.2 at early times (B); and
pH 8.2 at late times (C); Transient spectra of acidic and basic solutions at long time delays. (D)
76 CHAPTER 4. CHAPTER TITLE
Table 4.1: Ultrafast dynamics of 5-substituted quinolines in their base and cationic forms ordered
by Hammett
p
parameter.
R
p
Species (ps) Assignment
NH
2
-0.66 acid 36 ISC
NH
2
-0.66 base 41 singlet PT
OCH
3
-0.27 base 23 singlet PT
H 0.00 base 28 triplet PT
Cl 0.23 base N/A N/A
Br 0.23 base N/A N/A
CN 0.66 base 40 triplet PT
4.3.7 Electronic States in Quinoline and Quinolinium Ion
From the data in the previous section we realize that the excited state dynamics of the quino-
line family is diverse and complicated. There is no obvious trend in kinetics with respect to the
substituents Hammett parameters, in contrast to proton transfer in the 1-naphtol photoacid family
reported previously.
27
Furthermore, triplet states are often involved. These observations necessitate
that we examine the data in the context of the electronic structure of quinoline and quinolinium
ion. Quinoline's rst two singlet states are both of (,
) character and are commonly referred
to by the notation introduced by Platt
31
as
1
L
a
and
1
L
b
. The
1
L
a
state exhibits atom centered
electron density and has a broad absorption, while the
1
L
b
state exhibits bond centered electron
density and has sharp vibronic features. We discussed the eects of substitution and protonation
on the energies of these states in our previous work, which is brie
y summarized below. While
the energy of
1
L
b
is relatively independent of protonation and substituent,
1
L
a
is very sensitive to
both. Protonation lowers the energy of
1
L
a
by 3200 cm
-1
in quinoline. Substitution with electron
donating groups in the 5 position also lowers the energy of
1
L
a
. Additionally, the energy of
1
L
a
has been shown to be in
uenced by hydrogen bonding and other solvent interactions.
32
The third electronic absorption is of
1
(n,
) character and is deeper in the UV near 230 nm.
This state is also red shifted by substitution of electron donating groups (Figure S39). Although
this
1
(n,
) state is relatively far into the UV, its corresponding triplet,
3
(n,
), is approximately
degenerate with the
1
L
a
and
1
L
b
states. For that reason, it is important to consider its involvement
in intersystem crossing. This is particularly important, since the El-Sayed rule predicts that states
4.3. RESULTS AND DISCUSSION 77
Figure 4.6: Approximate singlet (blue) and triplet (red) state ordering in quinoline and quinolinium
ion in water. Degenerate levels are drawn with slight displacement for clarity. Proposed mechanisms
for
uorescence of quinolinium (left) and triplet photobasicity of quinoline (right).
with dierent orbital angular momenta can have fast rates of ISC.
23,33,34
Given the sensitivity of
1
L
a
and
3
(n,
) to the solvent environment and substituent, we expect that
the ordering of states may switch and thus qualitatively change the observed dynamics. In Figure
4.6, we show the estimated ordering of states for quinoline. The ordering of states in the gure is
based on the known properties in quinoline in the literature, our work, and several assumptions
and approximations, which are summarized in Table 2. The energies for
1
L
a
and
1
L
b
are the
0-0 transitions from our previous work
14
. The
1
(n,
) energy were taken as the UV absorption
maximum (Figure S18). The assumptions associated with assigning the triplet states are discussed
in detail below.
We used the lowest vibronic peak from the room temperature cyclodextrin matrix phosphorescence
as
3
L
b
35
. It has been shown that the cyclodextrin environment is nonpolar, and the
1
L
b
state does
not undergo a signicant solvatochromatic shift.
36
Therefore, it is reasonable to use the cyclodextrin
78 CHAPTER 4. CHAPTER TITLE
Table 4.2: Approximate energy levels of quinoline and quinolinium ion in water
Index Species State E(cm
-1
) Method of Assignment
1 base
1
(n,
) 43500 Absorption (Figure S18)
2 base
1
L
a
31900 Absorption/emission, Table 1 in ref 14
3 base
1
L
b
31900 Absorption, Table 1 in ref 14
4 base
3
(n,
) 32100 [5] + 17100 cm
-1
(TT absorption, * in Figure 4.2 B)
5 base
3
L
b
15000 Room temperature phosphorescence, Figure 3 in ref 35.
6 base
3
L
a
15000 Assumed degenerate with [5]
7 acid
1
(n,
) 42500 Absorption (Figure S18)
8 acid
3
(n,
) 32400 [12] + 20600 cm
-1
(TT absorption,y in Figure 4.2 B)
9 acid
1
L
b
31900 Absorption, Table 1 from ref 14
10 acid
1
L
a
28700 Absorption/emission, Table 1 in ref 14
11 acid
3
L
b
15000 Assumed degenerate with [5]
12 acid
3
L
a
11800 Assumed [11] - [12] is equal to [9] - [10], i.e. protonation
shifts
3
L
a
by the same as
1
L
a
.
encapsulated quinoline
1
L
b
state energy in our diagram. We used ESA peaks in our ultrafast data
(Figure 4.2, denoted by * andy) and assigned them to triplet-triplet absorptions. Soon after
photoexcitation of the deprotonated form of quinoline (t = 1 ps), the peak of the ESA band is
at 585 nm. We assign this process to excited state absorption within the triplet manifold. The
gap within the triplet states of the base form involved in ESA in Figure 4.6 is determined by this
data. The ESA band in the TA spectra moves to a higher energy of 490 nm after proton transfer.
Similarly, we assign the gap between the
3
L
a
and
3
(n,
) in quinolinium based on this data. The
lowering of the
3
L
a
state with respect to the
3
L
b
state upon protonation by approximately 3200 cm
-1
as shown in Figure 4.6 is justied based on comparison to the singlet states. There is experimental
evidence in the absorption spectra conrming lowering of
1
L
a
with respect to
1
L
b
upon protonation.
However, this assumption may not be quantitative, since it is observed by others that pK
a
for
triplets tends to be smaller than it is for singlets in other molecules.
11
Therefore, the shift of
3
L
a
with respect to
3
L
b
, may be considered a theoretical maximum.
4.3.8 Observed Kinetics
Figure 4.6 shows our estimates for the ordering of the energy levels in quinoline and illustrates the
experimental ultrafast observations. In acidic solution, quinoline becomes protonated in the ground
4.3. RESULTS AND DISCUSSION 79
state and has a high quantum yield of
uorescence. This suggests that internal conversion is faster
than intersystem crossing (ISC). Therefore quinoline relaxes to
1
L
a
, below the nearest triplet state,
and ISC is prevented (Figure 4.6, left). In basic solution, deprotonated quinoline is excited into
a dense manifold of states allowing ISC to occur, thus quenching the
uorescence. After internal
conversion in the triplet manifold, proton transfer can take place (Figure 4.6, right).
We cannot estimate the ordering of the states for the other compounds without phosphorescence
data. However, we propose that each derivative has a qualitatively similar electronic structure to
quinoline, albeit perturbed by the substituents. Absorption spectra of the quinoline family show
that small increases in the electron donating capability of the substituents red shift the
1
L
a
14
and
1
(n,
) states (Figure S39). It is plausible to assume that the energy of the
3
(n,
) is also lowered
by electron donating substituents. The intersystem crossing rate is therefore extremely sensitive to
substitution in the 5 position. This sensitivity may be the reason this family of photobases contains
such diverse photophysics for compounds that are chemically very similar.
Previously, we had compared the pK
a
values of 5-R-quinoline photobases to the structurally
similar 5-R-1-naphthol photoacid family.
14,27
This analysis showed that the singlet pK
a
values in
quinoline photobases followed a Hammett relation, analogous to the 1-naphthol family. In the 1-
napthol system the rates of proton transfer as a function of substituent Hammett parameter were
shown to follow Marcus theory applied to proton transfer. In the quinoline family, however, there
is no trend of rates with respect to substituents Hammett parameter (Table 4.1). Qualitatively,
we see that two categories arise: in molecules with electron withdrawing substituents ISC is faster
than 1 ps and in molecules with electron donating substituents ISC is either slow or not observed.
Here, special attention must be given to 5-aminoquinoline, which undergoes proton transfer in a
singlet state, but ultimately relaxes to a protonated triplet state. It has been reported that 7-
hydroxyquinoline forms water wires between the alcohol substituent and heterocyclic nitrogen.
37,38
Similarly, we suspect that solvent-solute hydrogen bonding in AQ may complicate its dynamics.
Since these eects are not captured by the Hammett parameter, it may be the reason that AQ does
not properly t into the above two categories. Ultrafast experiments on 5-(piperidin-1-yl)quinoline
may be useful in separating the electron donating and hydrogen boding eects in this system, as
80 CHAPTER 4. CHAPTER TITLE
have been done for 3-(piperidin-1-yl)quinoline.
39
.
4.4 Conclusion
Proton capture dynamics in the 5-R-quinoline family of photobases, where R =fNH
2
, CH
3
O,
H, Cl, Br, CNg, were investigated. The pK
a
values calculated based on singlet states for these
compounds are changed in a linear fashion according to the Hammett equation. However, such a
relationship is not observed in the dynamics of proton capture due to the involvement of triplet
states. MeOQ undergoes singlet state proton capture with a time constant of 36 ps and pK
a
=
+10. Quinoline and CNQ undergo triplet PT with time constants of 28 ps and 40 ps respectively. In
the halogenated compounds there is evidence that proton transfer does not occur. Finally, NH
2
Q
appears to undergo singlet state proton transfer and subsequent intersystem crossing with time
constants of 41 ps and 36 ps respectively. While we cannot accurately estimate the pK
a
of triplet
states without phosphorescence measurements, we expect them to be smaller than the reported
singlet pK
a
values, as is common for other photobases and photoacids.
2,11
In analogy to their
photoacid counterparts, these large pKa jumps, especially in long lived triplet states, may nd
applications in photomediated catalytic processes that require removal of protons. These diverse
dynamics, which change qualitatively with a small perturbation on the molecular framework, could
benet signicantly from further theoretical investigation with particular attention to details such
as state-ordering, intersystem crossing, solvation, and hydrogen bonding.
4.5. SUPPORTING SPECTRA 81
4.5 Supporting Spectra
4.5.1 Absorption, Emission, and Transient Absorption Spectra by Com-
pound
5-aminoquinoline
Figure 4.7: Absorption spectra (left) and titration curve (right) for 5-aminoquinoline in aqueous
solution.
82 CHAPTER 4. CHAPTER TITLE
Figure 4.8: UV absorption spectrum of 5-aminoquinoline under acidic (red) and basic (blue) con-
ditions.
Figure 4.9: Emission spectra of 5-aminoquinoline in aqueous solution.
4.5. SUPPORTING SPECTRA 83
Figure 4.10: Transient absorption of 5-aminoquinoline at pH 3.4.
84 CHAPTER 4. CHAPTER TITLE
Figure 4.11: Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) =ae
(x=tau)
+c; Coecients (with 95% condence bounds): a = -0.3632 (-0.3831,
-0.3432); c = 0.09813 (0.07681, 0.1195); tau = 36.15 (29.91, 42.39); Goodness of t: SSE: 0.05554;
R-square: 0.9396; Adjusted R-square: 0.9383; RMSE: 0.02418.
4.5. SUPPORTING SPECTRA 85
Figure 4.12: Transient absorption of 5-aminoquinoline at pH 8.2.
86 CHAPTER 4. CHAPTER TITLE
Figure 4.13: Population dynamics of rst component obtained from singular value decomposition of
TA data. Fitting equation: f(x) =ae
(x=tau)
+c; Coecients (with 95% condence bounds): a =
-0.2837 (-0.2911, -0.2763); c = -0.01002 (-0.01352, -0.006514); tau = 40.92 (38.53, 43.31); Goodness
of t: SSE: 0.007521; R-square: 0.9856; Adjusted R-square: 0.9853; RMSE: 0.008805.
4.5. SUPPORTING SPECTRA 87
Figure 4.14: Population dynamics of second component obtained from singular value decomposition
of TA data. Fitting equation: f(x) = a1e
(x=tau1)
+a2e
(x=41)
+c; Coecients (with 95%
condence bounds): a1 = -1.719 (-2.739, -0.6982); a2 = 1.393 (0.3303, 2.455); c = -0.01268 (-
0.03476, 0.009393); tau1 = 26.82 (19.51, 34.12); Goodness of t: SSE: 0.1807; R-square: 0.7877;
Adjusted R-square: 0.7811; RMSE: 0.04338.
88 CHAPTER 4. CHAPTER TITLE
Contamination from MeOQ
Figure 4.15: Transient absorption of 5-aminoquinoline in acidic and basic solutions at long time
delays (left); Transient absorption of 5-aminoquinoline at a negative delay (probe hits rst) and
the
uorescence spectrum of 5-methoxyquinoline inverted for comparison (right).
The slight mismatch in the acid-product and base-product spectra (SI Figure 4.15) arises from
contamination of MeOQ in the tubing used to do each experiment. To prove that this is contam-
ination and not an actual transient absorption the collected TA spectrum at a negative delay is
displayed. At negative delays, the sample is probed rst, and then pumped. This results in no TA,
however, the trailing pump will cause spontaneous emission of any
uorescent compound present
and is collected by our camera. This results in a small, negative band that exactly matches the
emission spectrum of MeOQ.
4.5. SUPPORTING SPECTRA 89
5-methoxyquinoline
Figure 4.16: Absorption spectra (left) and titration curve (right) for 5-methoxyquinoline in aqueous
solution.
Figure 4.17: UV absorption spectrum of 5-methoxyquinoline under acidic (red) and basic (blue)
conditions.
90 CHAPTER 4. CHAPTER TITLE
Figure 4.18: Emission spectra of 5-methoxyquinoline in various solvents.
ex
= 340 nm
Figure 4.19: Transient absorption of 5-methoxyquinoline at pH 3.0.
4.5. SUPPORTING SPECTRA 91
Figure 4.20: Transient absorption of 5-methoxyquinoline at pH 7.0.
Figure 4.21: Transient absorption spectra of 5-methoxyquinoline decomposed into Gaussian func-
tions.
92 CHAPTER 4. CHAPTER TITLE
Figure 4.22: Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) = ae
(x=tau)
+c; a = 0.3839 (0.3777, 0.3901); c = -0.0758 (-0.07938, -0.07222);
tau = 23.29 (22.37, 24.21); Goodness of t: SSE: 0.005699; R-square: 0.9942; Adjusted R-square:
0.994; RMSE: 0.007705.
4.5. SUPPORTING SPECTRA 93
quinoline
Figure 4.23: Absorption spectra (left) and titration curve (right) for quinoline in aqueous solution.
Figure 4.24: UV absorption spectrum of quinoline under acidic (red) and basic (blue) conditions.
94 CHAPTER 4. CHAPTER TITLE
Figure 4.25: Emission spectra of quinoline in two solvents.
Figure 4.26: Transient absorption of quinoline at pH 2.4.
4.5. SUPPORTING SPECTRA 95
Figure 4.27: Transient absorption of quinoline at pH 7.0.
96 CHAPTER 4. CHAPTER TITLE
Figure 4.28: Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) =ae
(x=tau)
+c; a = -0.3884 (-0.3942, -0.3826); c = 0.1312 (0.1263, 0.136); tau =
28.43 (27.19, 29.67); Goodness of t: SSE: 0.004946; R-square: 0.9949; Adjusted R-square: 0.9948;
RMSE: 0.007373.
4.5. SUPPORTING SPECTRA 97
5-chloroquinoline
Figure 4.29: Absorption spectra (left) and titration curve (right) for 5-chloroquinoline in aqueous
solution.
Figure 4.30: UV absorption spectrum of 5-chloroquinoline under acidic (red) and basic (blue)
conditions.
98 CHAPTER 4. CHAPTER TITLE
Figure 4.31: Emission spectra of 5-chloroquinoline in various solvents.
Figure 4.32: Transient absorption of 5-chloroquinoline at pH 1.9
4.5. SUPPORTING SPECTRA 99
Figure 4.33: Transient absorption of 5-chloroquinoline at pH 5.3
100 CHAPTER 4. CHAPTER TITLE
5-bromoquinoline
Figure 4.34: Absorption spectra (left) and titration curve (right) for 5-bromoquinoline in aqueous
solution.
Figure 4.35: UV absorption spectrum of 5-bromoquinoline under acidic (red) and basic (blue)
conditions.
4.5. SUPPORTING SPECTRA 101
Figure 4.36: Emission spectra of 5-bromoquinoline in acidic and basic aqueous solution.
Figure 4.37: Transient absorption of 5-bromoquinoline at pH 1.9
102 CHAPTER 4. CHAPTER TITLE
Figure 4.38: Transient absorption of 5-bromoquinoline at pH 5.3
4.5. SUPPORTING SPECTRA 103
5-cyanoquinoline
Figure 4.39: Absorption spectra (left) and titration curve (right) for 5-cyanoyquinoline in aqueous
solution.
Figure 4.40: UV absorption spectrum of 5-cyanoquinoline under acidic (red) and basic (blue)
conditions.
104 CHAPTER 4. CHAPTER TITLE
Figure 4.41: Emission spectrum of 5-cyanoquinoline in acidic solution.
Figure 4.42: Transient absorption of 5-cyanoquinoline at pH 1.2
4.5. SUPPORTING SPECTRA 105
Figure 4.43: Transient absorption of 5-cyanoquinoline at pH 5.3
106 CHAPTER 4. CHAPTER TITLE
Figure 4.44: Population dynamics obtained from singular value decomposition of TA data. Fitting
equation: f(x) =ae
(x=tau)
+c; a = -0.3942 (-0.4039, -0.3845); c = 0.07762 (0.07321, 0.08203);
tau = 39.82 (37.67, 41.97); Goodness of t: SSE: 0.01258; R-square: 0.9874; Adjusted R-square:
0.9872; RMSE: 0.01139.
4.5. SUPPORTING SPECTRA 107
4.5.2 UV Absorption Trends
Figure 4.45: Maximum absorption energy of the
1
(n,
) transition of free base and protonated
quinolines as a function of Hammett parameter,
p
. Strong electron donating substituends (negative
p
) red shifts the state energy. Protonation also red shifts this energy.
4.5.3 Auxiliary Ultrafast Data
Spot Size Measurement
The pump and probe spot sizes were measured to be 29 m and 95 m respectively using the
razor blade method. The beam is clipped at the focal point with a razor blade mounted on a
translation stage and the transmitted intensity is measured using a photodiode as a function of the
stage position. A sigmoidal shaped curve as a function of distance results. Dierentiating this curve
produces a gaussian shape that is representative of the focal spot intensity prole. The FWHM of
this gaussian is calculated and reported as spot size.
108 CHAPTER 4. CHAPTER TITLE
Cross Correlations
Cross correlation of the pump and probe pulses is measured in a quartz
ow cell lled with DI
water. The width of the coherent spike due to the solvent and
ow cell is typically reported as the
time resolution (500 fs), however, in this study we measured in step sizes of 1 ps and report this
as our eective time resolution.
Figure 4.46: Cross correlation of 287 nm pump pulse and CaF
2
white light continuum in water.
4.5. SUPPORTING SPECTRA 109
Figure 4.47: Cross correlation of 310 nm pump pulse and CaF
2
white light continuum in water.
110 CHAPTER 4. CHAPTER TITLE
Figure 4.48: Cross correlation of 333 nm pump pulse and CaF
2
white light continuum in water.
4.5. SUPPORTING SPECTRA 111
Power Dependence
The transient absorption was measured as a function of pump power to check for a linear relationship
to verify that the signals being measured are actually a third order, pump-probe signal and not
another higher order nonlinear process.
Figure 4.49: Transient absorption power dependence of 5-aminoquinoline.
Figure 4.50: Transient absorption power dependence of 5-methoxyquinoline.
112 CHAPTER 4. CHAPTER TITLE
Figure 4.51: Transient absorption power dependence of 5-bromoquinoline.
Figure 4.52: Transient absorption power dependence of 5-cyanoquinoline.
REFERENCES 113
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Small, E. W. Biophysical journal 2000, 78, 405{415.
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A: Chemistry 1988, 42, 293{300.
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4594{4603.
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120, 12920{12927.
Chapter 5
Pump-Probe Transient Absorption
5.1 Introduction
Transient absorption (TA) is a well known experimental technique for measuring chemical dynam-
ics. It goes by several dierent names which are often used interchangeably but do have specic
meanings. Pump-probe is probably the most common term. It is also the most specic, and it refers
to the geometry of the laser beams used to perform transient absorption. Pump-probe geometry is
the classic two pulse experiment and is depicted in Figure 5.1. Another geometry that results in
transient absorption is referred to as transient grating geometry. This is a three pulse experiment
where the pump is split into two equivalent arms which strike the sample at the same time but
from dierent angles. The most general term used to describe nonlinear optics experiments of this
nature is four wave mixing (FWM). FWM simply means that there are three incident electric elds
which generate a fourth eld that is detected. TA is probably the most common FWM experiment,
another one being coherent anti-Stokes Raman scattering (CARS).
Under the nonlinear optics and density matrix mathematical formalism, TA is a third order spec-
troscopy.
1{3
The electric eld of a pump pulse has two interactions on a system's density matrix,
one with the ket and another with the bra, simultaneously. This prepares the system in a population
state. After a time delay chosen by the experimenter, the electric eld of a probe pulse makes the
115
116 CHAPTER 5. PUMP-PROBE TRANSIENT ABSORPTION
third interacts with the system forming a coherence state with either a higher energy level (excited
state absorption) or the ground state (stimulated emission). Ground state bleach is admittedly
confusing in this formalism and is best understood in a more colloquial way. If a molecule has been
excited it's ground state population is depleted and it can't absorb where it normally does.
The experiments presented in this thesis are all femtosecond electronic transient absorption (more
specically, UV-pump broadband white light-probe), but the ideas discussed below also apply to
IR TA as well as slower time scales.
5.2 Principles of Operation
In the pump-probe geometry a pump pulse coherently prepares an ensemble of molecules in an
excited state which evolves as a function of time. A probe pulse comes later to investigate the state
of the system. Figures 5.1 and 5.2 show the pump-probe geometry and signal calculation.
The TA signal is calculated as follows:
A =A
ES
A
GS
A() = log(
I0
I
on()
) log(
I0
I
off
) = log(
I
off
I
on()
)
Three types of transitions contribute to a TA signal, excited state absorption (ESA), stimulated
emission (SE), and ground state bleach (GSB). ESA is absorption of the probe pulse at a wavelength
that is not normally absorbed in the ground state. This results into less intensity being transmitted
at this wavelength when the pump is on, and is shown as a positive feature in a TA dierence
spectrum. SE occurs when the probe pulse stimulates the an excited molecule to emit a photon.
This is the same principle behind the operation of a laser gain medium. SE doesn't technically
change the transmittance of the sample, but the detector will see the emitted light as a higher
intensity. The calculated TA signal from SE is positive. GSB, strictly speaking, is not a transition,
but rather a lack of a transition. When a molecule is excited, it can no longer absorb where it
did in the ground state, the transition is said be bleached. GSB will match the linear absorption
spectrum of a sample and, because it results in higher transmission of the probe, is also a negative
TA feature.
5.2. PRINCIPLES OF OPERATION 117
Figure 5.1: A transient absorption experiment done in pump-probe geometry. Top: A sample (S)
will have some absorption cross section. A white light probe is transmitted through the sample and
it's intensity detected with a spectrometer. Bottom: A pump pulse prepares the molecules in a
sample in an excited state. This pumped sample (S*()) is now a function of time. Another probe
pulse is transmitted through the sample at some specied delay, . The transmitted intensity is
detected with a spectrometer.
118 CHAPTER 5. PUMP-PROBE TRANSIENT ABSORPTION
Figure 5.2: Transient absorption signal calculation. Top: The intensities of the pump on and pump
o cases shown in gure 5.1. See text for description of GSB, SE, and ESA. Bottom: The log of
the ratios of the intensities shown in the top gure are plotted. Typically, because TA signals are
small, this optical density is multiplied by 1000 and plotted in mOD.
To get a reasonable signal to noise ratio, the above pump-on pump-o spectra are taken many
times, (usually around 500 - 2000 times) and averaged for each time point. Experimentally, this is
performed by modulating the pump beam with an optical chopper. Our laser's repetition rate is 1
kHz, which means collecting for 1 s will result in 500 pulse pairs/ 500 averages.
5.3. TA WITH BALANCED DETECTION OF BROADBAND PROBE 119
Figure 5.3: A traditional pump-probe transient absorption experiment. Pump and probe pulse
trains with an optical chopper dividing the repetition rate of the pump. The intensity of the probe
when unpumped (I
u
) is compared to the intensity of the probe when pumped (I
p
). The dierence
absorption is typically small and multiplied by 10
3
to be shown in units of optical density 10
3
(mOD).
5.3 TA with Balanced Detection of Broadband Probe
In an ideal world the probe beam would maintain constant intensity from one pulse to the next.
In practice, there is slight deviation in the spectral shape of the probe between pulses. Such power
uctuations of the probe may be incorrectly interpreted as transient absorption. The way to check
to see if the probe has enough stability is to block the pump and take a few averages. Ideally, you
should nd a TA spectrum that is a
at line (or noisy line) centered on zero. However, I have found
in practice that no matter how much I ddle with the probe, or how many averages I take, there
are \features" that appear in the TA spectrum when the pump is o, as shown in gure 5.4.
120 CHAPTER 5. PUMP-PROBE TRANSIENT ABSORPTION
Figure 5.4: Top: White light continuum spectrum generated in water. Bottom left: Transient
spectrum of 1000 pulse pair averages of the WLC spectrum with the pump o. Bottom right:
Another example. Although one may expect the spectral
uctuations to be random certain features
appear even after a large number of averages. A broad peak on the blue side and high frequency
oscillations on the red side are often seen.
The solution to this problem is to create a reference signal by beam splitting the probe arm.
The sample probe arm contains the usual transient absorption signal due to the pump, plus any
anomalous TA due to power
uctuations. The reference probe is equivalent to the sample, but it
is aligned through the sample such that it does not get pumped. Therefore, the reference signal only
contains the power
uctuations. The balanced TA signal is calculated by subtracting the reference
signal o of the sample.
A
balanced
= A
sample
A
reference
= log
Is;uIr;p
Is;pIr;u
where I is intensity and s, r, p and u stand for sample, reference, pumped, and unpumped. This
subtractions requires a four pulse sequence, depicted in gure 5.5.
5.3. TA WITH BALANCED DETECTION OF BROADBAND PROBE 121
Figure 5.5: In a balanced detection scheme the probe is split into sample and reference arms. The
reference is slightly misaligned so it never feels the in
uence of the pump. Alternatively it may be
delayed in time to achieve this. The reference pulse pair only contains instability of the probe (i.e.
the transient spectra shown in gure 5.4), while the sample contains the instability and the pump
induced TA. The averaging scheme shown subtracts the instability terms leaving only the real TA.
Bonus points: why is the re
ected portion of the beam splitter the sample arm?
Actually detecting these signals is slightly more challenging, since they are both sent into the same
spectrometer. Additionally, there are hardware limitations imposed by our CCD array. The camera
can only acquire spectra at 1 kHz. Now, with a balanced setup, we have two 1 kHz beams coming
in parallel. The solution, was to double chop the pump beam down to 250 Hz, and chop the probe
beam down to 500 Hz. Now there are two 500 Hz beams coming in parallel, which can be collected
by our camera. When double chopping it is possible to congure the phase of the choppers such
that the pump and probe pulses will never be coincident in time. This must be checked using a
photodiode and oscilloscope. The spectrometer must be aligned such that one spectrum is in the
top 50 rows of the camera, and the other is in the bottom 50 rows. The camera must be congured
to bin the rst 50 rows and read out one spectrum, then bin the second 50 rows and read out one
more spectrum.
122 CHAPTER 5. PUMP-PROBE TRANSIENT ABSORPTION
Figure 5.7: Intensity pattern on the CCD array when collecting both sample and reference in image
mode. Check to see that each beam remain within the top of bottom half and does not bleed into
the other. Notice how each intensity pattern is slanted towards the center at the right hand side
of the array (red side of spectrum). This is unavoidable in this alignment scheme. These are water
white light pulses, spectrum shown in gure 5.4.
Figure 5.6: Alignment of sample and reference beams through sample and into a monochromator
for detection. All focusing optics are shown as lenses for the purpose of clarity. Most are in fact
curved mirrors. The y dimension is normal to the surface of the table, z is along the direction of
beam propagation, x is orthogonal to y and z.
5.3. TA WITH BALANCED DETECTION OF BROADBAND PROBE 123
Figure 5.8: Setup of optical hardware. Using this three chopper scheme it's possible to set the
pump/probe phase incorrectly. Check it with a photodiode and oscilloscope to be sure. Adjust the
phase of the choppers if necessary.
Figure 5.9: Setup of electrical hardware. SDG delays do not have to be 1 and 2 specically.
124 CHAPTER 5. PUMP-PROBE TRANSIENT ABSORPTION
5.3.1 White Light Supercontinuum Generation
A supercontinuum is a fancy way of saying very broad spectrum. A few mW of the 800 nm
center wavelength pulse from the regen is focused onto a material such as sapphire. Through a
series of nonlinear processes, the 800 nm photons are upconverted (and downconverted) resulting
a spectrum that spans most of the visible range and into the near IR (to about 2 m). There
are several materials that we have successfully used to generate a white light supercontinuum to
be used as a probe pulse in TA experiments. They are sapphire (Al
2
O
3
), DI water, and calcium
uoride (CaF
2
), and each method has advantages and disadvantages.
Sapphire is the easiest to set up, simply place a sapphire plate in a xed mount and focus the laser
onto it. The disadvantage is that the super continuum only goes to about 420 nm. A less signicant
disadvantage is that the generated beam has really bad spatial chirp. This is not usually a problem,
but I have some reason to believe that it interferes with the balanced detection scheme outlined
above.
DI water requires a
ow cell to set up. It has a slightly broader usable range than sapphire, down
to about 400 nm, and the generated beam is very spatially homogeneous. I have used it successfully
in a balanced detection setup. The
ow cell tends to be kind of thick which will create a larger
chirp on the probe pulse that will hurt the time resolution slightly.
The primary reason for using calcium
uoride is that it can generate light down to 350 nm. It is
also spatially homogeneous and I have used it in a balanced detection setup. It is, of course, the
most dicult to set up. If you try to set it up like sapphire, you will see that as you wiggle it
around it generates light, but as soon as you let it sit still it stops. This is due to some thermal
eect that stops the nonlinear process. The solution is to employ a device that rotates the plate.
However, because CaF
2
has a crystal axis, it cannot be rotated like a wheel. Doing so will cause the
polarization of the generated probe beam to change as the rotation angle changes. For this reason,
it must be rotated in a \window washing" motion, such that the crystal axis of the plate remains
xed with respect to the optical axis. I've constructed a small device to so such a motion, but as
you can imagine having moving parts introduces more
uctuations in the probe intensity.
REFERENCES 125
References
[1] Mukamel, S. Principles of nonlinear optical spectroscopy; Oxford series in optical and imaging
sciences; Oxford University Press, 1995.
[2] Shen, Y. The Principles of Nonlinear Optics; Pure & Applied Optics Series: 1-349; Wiley, 1984.
[3] Hamm, P. Principles of Nonlinear Optical Spectroscopy: A Practical Approach Or: Mukamel
for Dummies. 2005; http://www.mitr.p.lodz.pl/evu/lectures/Hamm.pdf.
126 REFERENCES
Chapter 6
Singular Value Decomposition of
Spectroscopic Data
6.1 Introduction
If you've spent any time talking to Jahan you will surely hear him praise the usefulness of the Fourier
transform. I would argue that a close runner up in terms of utility for data analysis is singular value
decomposition (SVD). It is an algorithm that can be used to decompose a two-dimensional data
matrix which contains signals from multiple species, e.g. chemicals with overlapping absorption
spectra, into individual spectra. I have used it in my analyses of the pKas of quinoline compounds
(chapter 3) from pH titration data and for the extraction of time constants from from ultrafast
transient absorption data.
First I will introduce the algorithm with a minimal example, a small matrix of arbitrary column
vectors. Next, an example of using SVD for image compression is given, which I believe helps
to illustrate how it works to nd redundancies in data sets. Next, I will construct a fake, but
realistic looking data set and demonstrate how to extract chemically meaningful information from
it. Finally, I will outline a scenario where SVD is an inappropriate method of analysis that may
127
128 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
lead to confusing results.
A basic understanding of linear algebra is required to implement SVD. An excellent refresher on the
fundamentals of linear algebra is covered by Hendler
4
and is highly recommended reading. Below,
I will demonstrate the utility of SVD by guiding the reader through a minimal example and then
through a simple, simulated spectroscopic data set. These examples are based on the references by
Henry
5
and Schrager
6
.
These examples are done with the MATLAB software package. Any text that is in the monospaced
font may be copied and pasted into the MATLAB environment for experimentation.
Please see this chapter's bibliography for a list of recommended reading on all things SVD.
6.2 Minimal example
Consider the column vectors
v1 = [1 ; 1 ; 1 ; 1 ; 1];
v2 = [0 ; 0 ; 0 ; 0 ; 1];
v3 = [1 ; 2 ; 2 ; 2 ; 2];
and a matrix constructed from these vectors
A = [v1 v1*2 v1*3 v1*4 v2 v2+v1 v3]
A =
1 2 3 4 0 1 1
1 2 3 4 0 1 2
1 2 3 4 0 1 2
1 2 3 4 0 1 2
1 2 3 4 1 2 2
6.2. MINIMAL EXAMPLE 129
These vectors are linearly independent from each other, which you may verify on your own. The
matrix, A, has dimensions
size(A)
ans =
5 7
and rank
rank(A)
ans =
3
The rank of a matrix is the number of linearly independent vectors needed to represent it. It should
be relatively clear that in this case it should be 3 beause of the way A was constructed.
Matrices that have a rank lower than their smallest dimension are said to be rank decient.
Matrices with a rank equal to their smallest dimension are said to be full rank. Another way to
think about rank decient matrices is that they contain redundant information. Vectors resulting
from multiplication by a constant, or from addition of two vectors don't contain new information.
E.g. instead of sending someone all of the numbers in A, you can send them the three linearly
independent vectors in A, and the rules for consructing A. The essence of SVD is to nd these
rules, when only A is known.
130 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
6.3 Addition of noise
Now let's dene matrix with small random numbers. This is a simulation of noise, which is present
in any experimental data set.
% Seed rng with a constant so the numbers come out the same each time the
% code is run.
rng(1);
N = (rand(size(A))-0.5).*0.2
N =
-0.0166 -0.0815 -0.0162 0.0341 0.0601 0.0789 -0.0803
0.0441 -0.0627 0.0370 -0.0165 0.0937 -0.0830 -0.0158
-0.1000 -0.0309 -0.0591 0.0117 -0.0373 -0.0922 0.0916
-0.0395 -0.0206 0.0756 -0.0719 0.0385 -0.0660 0.0066
-0.0706 0.0078 -0.0945 -0.0604 0.0753 0.0756 0.0384
What happens when a small amount of noise is added to a rank decient matrix?
rank(A+N)
ans =
5
We see that addition of noise makes the matrix full rank. This fact is important when
analysing a real experimental data set, which will always contain noise.
6.4. RANK APPROXIMATION 131
6.4 Rank approximation
Is there a way to approximate the rank of a matrix, which we know to be rank decient, but contains
noise? Singular value decomposition is one method to achieve this.
SVD is easily applied in MATLAB using the command
[U,S,V] = svd(A+N);
SVD breaks the input matrix into three matries such that A =USV
y
V contains information about the row space of A, and U contains information about the column
space of A. Since our matrix A was dened somewhat arbitrarily, the columns of U and V do not
have much meaning. The meaning of these vectors will be more apparent in the following section
when we examine a simulated spectral data set.
6.5 Singular values
S is a diagonal matrix which contains the weighted importance of the vectors in U and V, known
as singular values.
S
S =
12.8947 0 0 0 0 0 0
0 2.9327 0 0 0 0 0
0 0 0.9315 0 0 0 0
0 0 0 0.1562 0 0 0
0 0 0 0 0.0855 0 0
132 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
Figure 6.1: Dimensional analysis of data decomposition by SVD. Top: When the SVD algorithm
is applied to a data matrix, D, three matrices are returned such that D = USV
y
. U and V
contains information about the column space and row space of D, respectively. S is a diagonal
matrix which contains the singular values. Bottom: An example data set can be constructed by
multiplying a set of spectra and decay proles, where each row/column represents features of a
chemical species. Some numerical work and often times assumptions are needed to turn SVD (top
decomposition) into a chemically insightful form (bottom decomposition).
6.5. SINGULAR VALUES 133
The sigular values can be interpreted as how important each vector is in creating the dataset.
stem(diag(S))
ylabel('Singular Value')
xlabel('Index #')
We see three large values, and two smaller ones. The three large values indicate that there are three
linearly independent vectors which account for most of this dataset.
SVD can be thought of as a generalization of diagonalization for non-square matrices. The singular
values, are similar to eigenvalues. We can make a rectangular matrix square by multiplying it by
it's transpose, AA
y
, or vice versa, A
y
A. The square root of the eigenvalues of this new matrix are
equivalent to the singular values obtained via SVD.
We will do this for the original matrix, A, and compare it's singular values to the noisy matrix,
A+N
sqrt(eig((A*A')))
134 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
ans =
0.0000 + 0.0000i
0.0000 + 0.0000i
0.8224 + 0.0000i
2.8109 + 0.0000i
12.9778 + 0.0000i
Now we see that, without noise, there are three non-zero, singular values, indicating the data set
contains three linearly independent vectors.
How do we know whether a small singular value is due to noise or another linearly independent
vector? A good rule of thumb is if it is 2% of the rst singular value it is not signicant. This
approach is sensitive depending on the signal to noise ratio in a real experiment. More sophisticated
methods for rejection of singular values are outlines in this paper (CITE)
Using the 2% rule we see that we can eliminate the last two singular values.
% Convert singlar values to percentages of the first value
sv_percent = diag(S)./S(1,1).*100
sv_percent =
100.0000
22.7434
7.2240
1.2116
0.6629
6.5. SINGULAR VALUES 135
We can now create a rank 3 approximation of our noisy data set by cutting out the last two columns
of U and V, and the last two rows and columns of S. This cropping should preserve the original
dimensions of the dataset. Alternatively, you can set all of the values in the last two columns to
zero.
Crop the matrices at index n, for an n'th rank approximation.
n = 3;
U_c = U(:,1:n);
V_c = V(:,1:n);
S_c = S(1:n,1:n);
% Reconstruct the dataset with only the important singular values/vectors
% Don't forget to transpose V
A_c = U_c*S_c*V_c'
A_c =
0.9907 1.9164 2.9893 4.0292 0.0668 0.0770 0.9195
0.9709 1.9686 3.0269 3.9951 0.0339 -0.0647 1.9827
0.9602 1.9565 3.0050 3.9554 0.0204 -0.1089 2.0888
0.9663 1.9626 3.0160 3.9779 0.0338 -0.0657 2.0112
0.9299 2.0077 2.9061 3.9391 1.0758 3.0755 2.0383
We nd that the reconstructed matrix, A c, has singicantly less noise than the original noisy
matrix, A+N. They can be compared visually to see that some of the noise has been ltered out.
h = figure();
h = figure('Position', [100, 100, 1200, 275]);
136 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
subplot(131);
imagesc(A)
title('Original matrix')
xlabel('A')
subplot(132)
imagesc(A+N)
title('Noisy matrix')
xlabel('A+N')
subplot(133);
imagesc(A_c)
title('Filtered noisy matrix')
xlabel('A\_c')
6.6 Image Compression
SVD can be used as a form of image compression. The idea is to nd redundancies in an image, keep
the most signicant ones and toss out the less important onces. Similar to the minimal example
above, we can toss out the "noise" in an image, which may contribute signicantly to it's le size,
but have a very small impact on the percieved quality of the image.
% Load and convert original image to grayscale
z = imread('myimg.png');
z = rgb2gray(z); % convert rgb image to grayscale
6.6. IMAGE COMPRESSION 137
z = im2double(z); % convert image to double
figure();
imshow(z);
xlabel('Original grayscale image of z');
% Decompose into z = U*S*V'
[U,S,V] = svd(z);
% Examine sigular values
s = diag(S);
figure();
stem(s);
xlabel('n');
ylabel('S(n,n)');
title('Singular Values of z');
138 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
Unlike the minimal example where we knew there to be three signiant singular values due to the
way the matrix was constructed, there is no obvious repeating pattern in most photographs, with
the exception of Shayne's head being cropped onto a copy of my body due to his absence during
the time of this group picture.
We see that there are many signicant singular values, and no obvious cut o point. As we did
above, we will choose to make a rank approximation.
% Make k'th rank approximation of the input matrix
k = 100;
Uc = U(:,1:k); % Compressed version of U
6.6. IMAGE COMPRESSION 139
Sc = S(1:k,1:k);
Vc = V(:,1:k);
zc = Uc*Sc*Vc'; % don't forget the prime when reconstructing z
figure();
imshow(zc);
xlabel(['k = ' num2str(k) ' rank approximation of z']);
We see a slightly fuzzier version of the input image results. If scaled down, such as for a thumbnail,
the reduction in quality may not be signicant.
But wait! It appears that we have just made a matrix that is the same size as in the input, i.e.
same le size, but now it looks worse! How does this actually achieve compression? While it is true
that the reconstructed matrix zc has the same size as the input (441x618 = 272,538 numbers), the
truncated decomposition matrices are much smaller.
140 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
After truncating at k = 100, Uc contains 411x100 = 41,100 numbers, Vc contains 618x100 = 61,800,
and while S has the dimensions of the input image, it is diagonal, so we really only need to know
the 100 singular values that we kept. The sum o all these matrix sizes is 103,000 numbers, which
is approximately half of the data of the orignal input. A user could store Uc, Vc, and diag(Sc) to
save on disk space, or transmit these matrices to save on bandwidth. When the image is viewed,
the matrix zc is computed from these stored/transmitted values.
6.7 Simulated Spectroscopic Data
Now I will create a larger, more realistic looking, but still easy to interpret, data set, which resembles
a time-resolved spectroscopy experiment.
Consider two chemical species, X and Y. Each has a representative absorption spectrum and con-
centration prole as a function of time.
% Define wavelength axis and absorption spectra of X and Y
lambda = 400:650;
xa = 1.3*normpdf(lambda,500,3)+1.2*normpdf(lambda,510,3)...
+1.1*normpdf(lambda,520,3)+normpdf(lambda,530,3)+50*normpdf(lambda,510,20);
xa = xa./max(xa);
ya = normpdf(lambda,550,20)+2*normpdf(lambda,600,50);
ya = ya./max(ya);
figure(); plot(lambda,xa,lambda,ya);
xlabel('Wavelength (nm)');
ylabel('Absorption (OD)');
legend(['X' ; 'Y'])
6.7. SIMULATED SPECTROSCOPIC DATA 141
% Define concentration profiles for X and Y
t = 0:1000;
% Single exponential decays with 150 and 500 fs time constants.
xc = exp(-t/150);
yc = exp(-t/500)+0.5;
figure(); plot(t,xc,t,yc);
xlabel('Time (fs)');
ylabel('Concentration (mM)');
legend(['X' ; 'Y'])
142 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
This data is meant to simulate a kinetics experiment. That is, time t=0 is dened by some impulsive
event, such as a laser pulse being absorbed. After this event the concentrations of the species X
and Y changes. We can use their absortion spectra to measure their concentration as a function of
time. A simulated transient absorption data set can be constructed as follows.
% The "absorption spectra" matrix
A = [xa' ya'];
% and the "concentration" matrix
C = [xc' yc'];
% the data matrix then can be constructed
D = C*A';
rank(D)
ans =
2
6.7. SIMULATED SPECTROSCOPIC DATA 143
% Make some noise!!!
D = D + (rand(size(D))-0.5).*0.2;
rank(D)
ans =
251
We see that the rank of the simulated data is 2 and, as before, the addition of noise makes the
matrix full rank.
figure(); imagesc(lambda,t,D); colorbar;
xlabel('Wavelength (nm)');
ylabel('Time (fs)');
Now the task is, given the noisy data matrix, extract the original spectra and/or concentration
proles. In many cases, especially with transient absorption, you may not know a priori how many
144 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
species are present in the mixture. SVD should rst be used to approximate the rank of the data
matrix.
[U,S,V] = svd(D);
stem(diag(S))
ylabel('Singular Value')
xlabel('Index #')
xlim([0 20]);
I have truncated the stem plot for the purpose of clarity, but it extends out to the full dimension
of the matrix. We see that only two of the singular values are signicant by visual inspection. The
other's are non-zero, but small, and due to noise. Their values are the so-called noise
oor.
Now let's inspect the rst three columns of V, which contains spectral (row) information
vc1 = V(:,1);
vc2 = V(:,2);
vc3 = V(:,3);
figure();
6.8. ORTHOGONAL BASIS SPECTRA VERSUS SPECIES ASSOCIATED SPECTRA 145
plot(lambda,vc1,lambda,vc2,lambda,vc3);
legend(['V col 1' ; 'V col 2' ; 'V col 3']); xlabel('Wavelength (nm)');
The rst thing to notice is that the third column of V looks like noise. This means that it is not a
signicant contribution to the original dataset. Accordingly, the third sigular value is very small.
Next, we see that columns 1 and 2 have some resemblance to spectra, e.g. they have gaussian
shapes. However, they are distinctly not the original absorption spectra that we dened above. In
fact, the "spectra" in the columns of V have negative values in them, which is non-physical for an
absorption spectrum. Note: this is only non-physical in this example, typically transient absorption
dierence spectra often have negative features in them due to stimulated emission and ground state
bleach.
6.8 Orthogonal Basis Spectra Versus Species Associated
Spectra
The "spectra" that the SVD algorithm returns are not associated with any species. They are,
146 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
however, orthonormal vectors, i.e. their inner product with themselves is 1, and the inne rproduct
between dierent vectors is 0.
vc1'*vc1
ans =
1.0000
vc2'*vc2
ans =
1.0000
vc1'*vc2
ans =
6.4510e-17
I will refer to these vectors as basis spectra. In contrast, the chemically meaningful spectra, which
we have dened in this example, are often referred to as species associated spectra (SAS).
The task for the experimenter analysing the data is to transform the basis spectra into species
associated spectra. The species associated spectra can be reconstructed by a linear combination
of basis spectra.
6.9. ROTATION OF BASIS SPECTRA 147
In the case where there are two species present this transformation can be done by multiplying
the basis spectra by a rotation matrix and comparing the result to the original species spectra.
If the original species spectra are already known, this is simple. However, as is the case with
transient absorption spectroscopy, you may not know what species are present. You may have to
make assumptions or place contraints on the rotated spectra, e.g. rotate until a certain region is
non-negative, or rotate until it can be t with a single gaussian. These assumptions will be system
dependent and need to be considered carefully.
6.9 Rotation of Basis Spectra
% Group the basis spectra
B = [vc1 vc2];
% Define an angle and 2D rotation matrix
theta = 5.2;
R = [cos(theta) -sin(theta); sin(theta) cos(theta)];
% Rotate basis spectra
B_r = B*R;
% Normalize rotated specta for comparison to species spectra
br1 = B_r(:,1); br1 = br1./max(abs(br1));
br2 = B_r(:,2); br2 = br2./max(abs(br2));
% Plot and compare to species spectra
148 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
figure();
plot(lambda,xa,'b',lambda,ya,'r',lambda,br1,'b--',lambda,br2,'r--');
xlabel('Wavelength');
ylabel('Nomalized Absorption');
legend(['Species X ' ; 'Species Y ' ; 'B\_r col 1'; 'B\_r col 2']);
title(['theta = ' num2str(theta)]);
This angle of 5.2 was found by creating a loop around the above block of code and changing the
angle slowly while inspecting the graphs.
% We can convert this rotation to a complex number via
Z = 1*exp(i*theta)
Z =
0.4685 - 0.8835i
6.10. ROTATION IN 3D 149
There is no scaling after rotation so the magnitude is 1. Now we can see that this rotation is
equivalent to linear combination of basis spectra as follows
% Species associated spectrum for X, as a linear combination of basis spectra
SASX = real(Z).*vc1 + imag(Z).*vc2;
figure(); plot(lambda,SASX);
xlabel('Wavelength (nm)'); title('SASX');
6.10 Rotation In 3D
In principle, a similar process can be done when there are three contributing species, and thus
the SAS will be a linear combination three basis vectors. You will have to use three, 3D rotation
matrices however and iterate through all of their angles. I believe that quaternions, the extension
of complex numbers to a 3rd dimension, are a more convenient way to make these 3D rotation, but
I have not thought about how to actually do it in great enough detail to provide a tutorial on it.
150 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
6.11 Extraction of Dynamics from SVD
The same discussion above applied to the column vectors contained in the U matrix. In this
example, this matrix represents the time dependence of the concentration of the species. However,
as is the case for spectra, U contains orthonormal basis concentration proles, rather than the
species associated proles that have chemical signicants.
First, let's examine the rst two columns of U.
uc1 = U(:,1);
uc2 = U(:,2);
figure(); plot(t,uc1,t,uc2);
xlabel('Time (fs)');
legend(['U col 1' ; 'U col 2']);
Similar to the basis spectra, they look like exponential decays, but are non-physical if they are
meant to represent population due to the negative values.
6.11. EXTRACTION OF DYNAMICS FROM SVD 151
Since we know that the species associated decays (SAD) can be expressed as a linear combi-
nation of the basis decays, then each basis decay is also a linear combination of SADs. In transient
absorption spectroscopy the usual result is rst order exponential kinetics. This means that we can
simply t one of the basis spectra with a sum of exponential functions to extract time constants.
Fitting can be done with the MATLAB curve tting application.
General model:
f(x) = a1*exp(-x/tau1)+a2*exp(-x/tau2)+c
Coefficients (with 95% confidence bounds):
a1 = 0.00996 (0.007225, 0.01269)
a2 = 0.03076 (0.0285, 0.03301)
c = 0.01537 (0.01482, 0.01593)
tau1 = 152 (129.4, 174.5)
tau2 = 495.6 (448.2, 543)
Goodness of fit:
SSE: 5.475e-05
R-square: 0.9994
Adjusted R-square: 0.9994
RMSE: 0.0002344
152 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
Figure 6.2: The rst column of U contains information about the dynamics of the data set. It is an
orthonormal basis vector of U, which by itself is not chemically meaningful. However, it can also
be expressed as a linear combination of the decay proles we dened earlier. This is demonstrated
by tting the orthonormal vector with a sum of exponential functions.
We see that the 150 and 500 fs time constants are recovered.
6.12 Generalization to Other Systems
The example given above was tailored for time domain spectroscopy. However, please keep in
mind that SVD as an algorithm is completely general. In my research I have used it to work up pH
titration for the extraction of pKas. It is analogous to the above example, except absorption spectra
are taken of a solution a many pH values, rather than time delays. Instead of exponential decays
in the U matrix, a sigmoidal shaped curve appears, which can be t to the Henderson-Hasselbalch
equation to calculate pKa. If there were multiple protonation states (either on a single molecule like
in universal indicator or if there was a mixture of molecules) then, as in the example above, a sum
of Henderson-Hasselbalch equations should be used to t the data. Another potential application
in identifying the reduction potentials of species in an electrochemical reaction. Spectra may be
acquired as a function of voltage in this case. More generally, it can be used to nd redundancies
in any data set, even when x and y slices of the data are a bit abstract like in a photograph.
6.13. POTENTIAL PIT FALLS 153
6.13 Potential Pit Falls
While SVD is very broadly applicable to 2D data sets, there are some instances of condensed phase
molecular physics which may produce wonky results.
SVD is well suited when there are long-lived (relative to whatever timescale you are working with),
well dened chemical species which exchange quickly with each other, e.g. acid base reactions in
the ground and excited states. However, continuous processes such as solvent shell relaxation after
excitation or wavepacket motion along a potential energy surface that may modulate a
uorescence
wavelength will produce strange looking, but mathematically correct, results from SVD.
Here I've constructed a 2D data set by specifying a gaussian spectrum centered at 400 nm. As a
function of time, the center frequency shifts to 500 nm in 1000 fs. This could theoretically be a
simple model of how the stimulated emission wavelength changes as there is nuclear relaxation in
the excited state.
Figure 6.3: A Gaussian function centered at 400 nm that shifts linearly to 500 nm in 1000 fs. Noise
is added at 10% of the maximum value. This is a simple simulation of how excited state relaxation
may manifest in transient spectroscopy.
154 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
Figure 6.4: The singular values obtained from SVD of the above data, expressed a percent of the
rst singular value.
Figure 6.5: The rst three columns of the U matrix obtained from SVD
6.13. POTENTIAL PIT FALLS 155
Figure 6.6: The rst three columns of the V matrix obtained from SVD
Applying the SVD algorithm to this data set returns nine singular values that are above the 2%
limit. Additionally, examination of the spectra and decays shows their odd behavior. These features
can be explained in the following way.
When there is a continuous relaxation, many basis vectors are required to model the behavior. SVD
is poorly poised to address such a physical system. A more general tting technique, such as global
tting will be more appropriate
156 CHAPTER 6. SINGULAR VALUE DECOMPOSITION
REFERENCES 157
References
[1] Thompson, C. If You Liked This, Youre Sure to Love That. 2008; http://www.nytimes.com/
2008/11/23/magazine/23Netflix-t.html?_r=0.
[2] Austin, D. We Recommend a Singular Value Decomposition. http://www.ams.org/samplings/
feature-column/fcarc-svd.
[3] Wall, M. E.; Rechtsteiner, A.; Rocha, L. M. ArXiv Physics e-prints 2002,
[4] Hendler, R. W.; Shrager, R. I. Journal of Biochemical and Biophysical Methods 1994, 28, 1{33.
[5] Henry, E.; Hofrichter, J. Methods in Enzymology 1992, 210, 129{192.
[6] Schrager, R. I.; Hendler, R. W. Analytical Chemistry 1982, 54, 1147{1152.
158 REFERENCES
Appendix A
MATLAB Code
These scripts are all located in the group's PROGRAMS/MATLAB Dropbox folder.
A.1 dechirp.m
This code is used remove chirp from a data set such as in gure 2.6.
function [z_dechirped] = dechirp(z_chirp,z_data)
%% Fit chirp from chirp matrix
% z should be TA data matrix with x as wavelength and y as time
% i.e. each row is a spectrum, and each column is a kinetic trace
[~,t0] = max(z_chirp); % time zero as a function of wavelength index
% It will look bumpy, fit a parabola to it.
[row,col] = size(z_chirp);
159
160 APPENDIX A. MATLAB CODE
x_index = 1:col;
c = polyfit(x_index,t0,2);
t0_fit = c(1).*x_index.^2 + c(2).*x_index + c(3);
%{
% Plot fit on top of chirp data
figure();
imagesc(z_chirp);
hold on;
plot(x_index,t0,x_index,t0_fit);
%}
%% Remove chirp from data matrix
% Interpolate z_data to 10X more points, increase (or decrease) the step
% size if needed
step = 10;
[row,col] = size(z_data);
y_index = 1:row;
y_index_interp = 1:1/step:row;
Z = zeros(length(y_index_interp),col); % initialize resampled array
for j = 1:col
Z(:,j) = interp1(y_index,z_data(:,j),y_index_interp);
end
A.1. DECHIRP.M 161
% shift each kinetic trace based on fit
x_index = 1:col;
t0_fit = c(1).*x_index.^2 + c(2).*x_index + c(3); % calc fit for the data matrix
t0_fit = round(t0_fit.*step); % "interpolating" the fit, rounding is required b/c
% circshift must take integers
shift = t0_fit - t0_fit(1);
for j = 1:col
Z(:,j) = circshift(Z(:,j),-shift(j));
end
% Resample data back to original size
z_dechirped = zeros(size(z_data));
for j = 1:col
z_dechirped(:,j) = interp1(y_index_interp,Z(:,j),y_index);
end
figure();
imagesc(z_dechirped);
end
162 APPENDIX A. MATLAB CODE
A.2 defaultGraphingOptions.m
I've received several compliments on how presentable my graphs look throughout the years, and
this script is behind most of that. The secret is that most of my work is actually motivated by
laziness. This script just changes some of rendering defaults in MATLAB like the line thickness
and font size to make graphs look more presentation worthy. You make it run in the MATLAB
start up le and literally never have to touch it again.
% Run this script to set your defaults to the values below and make your graphs
% prettier and more readable
% Closing MATLAB resets them
% Feel free to modify to your liking
% Add to C:\Program Files\MATLAB\R2015b\toolbox\local\startup.m
% to run at startup
% See
%http://www.mathworks.com/help/matlab/creating_plots/default-property-values.html
% for details
% These commands are costructed in the following way
% 'Default' 'Object Type' 'Object Property' and 'Property Value'
% Not sure what object a certain propery belongs to?
% When plotting things you can save the object's info to a variable, try
% obj = colorbar; or obj = plot(x,y); or [c,obj] = contourf(z); for example.
% If you print the value of obj it will tell you the object type (Colorbar,
% Line, and Contour in these exmples). It will also list a bunch of it's
% properties (The Contour object has LineColor, LineStyle, LineWidth, etc
% properties.
A.2. DEFAULTGRAPHINGOPTIONS.M 163
% You can assign properties using a command such as
% [cData,obj] = contourf(z); obj.LineStyle = '--'; obj.Fill = 'off';
fontSize = 16;
lineWidth = 2;
fontName = 'Helvetica';
% Text options
set(groot,'DefaultTextInterpreter','tex')
% Line options
set(groot,'DefaultLineLineWidth',lineWidth)
% Axes options
set(groot,'DefaultAxesFontSize',fontSize)
set(groot,'DefaultAxesFontName',fontName)
set(groot,'DefaultAxesXMinorTick','on')
set(groot,'DefaultAxesYMinorTick','on')
set(groot,'DefaultAxesLineWidth',lineWidth)
set(groot,'DefaultAxesTickLength',[0.020 0.020]);
% Figure options
set(groot,'DefaultFigureColormap',feval('jet'))
%Default cmap in 2015b is something
164 APPENDIX A. MATLAB CODE
% atrocious called 'parula'
% The MATLAB guy told me parula is a type of bird, which exhibits these colors.
% Contour options
%set(groot,'DefaultContourLineColor','flat'); % used to be "shading flat"
% in older versions
% !!! Problem !!! This breaks the plot() function and I can't figure out
% why.
% Colorbar options
set(groot,'DefaultColorbarLineWidth',lineWidth);
close
clear fontSize lineWidth fontName;
A.3 TAt.m
Extremely useful for decomposing TA data into Gaussians. Calls the gaussianFitTA.m script above.
Creates nice looking plots that are labeled as ESA and SE/GSB.
%% Transient Absorption Fit
% Fit positive and negative going gaussians to spectra and plot the results
% Inputs: xi (nm)
% yi (mOD)
% Define xi,yi by grabbing from a plot using
A.3. TAFIT.M 165
% [xi,yi] = getxyData();
%% Choose starting values
% pick amplitudes (+/- 1 should work fine), and center wavelenghts (nm)
% enter zeros for peaks not used in the fit
% sigma is already chosen at reasonable values
title_str = 'NH_2Q, acid, \tau = 100 ps';
% Peak 1: a1*normpdf(xwn,mu1,sigma1)
a1 = -1;
lambda1 = 428;
% Peak 2: a2*normpdf(xwn,mu2,sigma2)
a2 = 0;
lambda2 = 0;
% Peak 3: a3*normpdf(xwn,mu3,sigma3)
a3 = 0;
lambda3 = 0;
%% Do necessary cropping here
% Defaults
i1 = 1;
i2 = length(xi);
i2 = 400;
x = xi(i1:i2);
166 APPENDIX A. MATLAB CODE
y = yi(i1:i2);
%% Convert to wavenumbers so that the gaussians are actually gaussians
xwn = 10000./(x./1000);
checkInputs = true;
if(checkInputs)
figure();
subplot(211)
plot(yi);
title('Input Data'); xlabel('index'); ylabel('\DeltaA (mOD)');
subplot(212)
plot(x,y);
title('Cropped Input'); xlabel('Wavelength (nm)'); ylabel('\DeltaA (mOD)');
end
%% Clean up inputs and set bounds
aGuesses = [a1 a2 a3];
lambdaGuesses = [lambda1 lambda2 lambda3];
muGuesses = 10000./(lambdaGuesses./1000); % convert to wavenumbers
A.3. TAFIT.M 167
% Remove zeros to fit with the correct number of gaussians
include = aGuesses ~= 0;
aGuesses = aGuesses(include);
include = muGuesses ~= inf; % lambda = 0 gets converted to inf wn
muGuesses = muGuesses(include);
% Set reasonable boundary parameters based on guesses
% amplitudes
aLows = zeros(size(aGuesses));
aHighs = aLows;
for j=1:length(aGuesses)
if(aGuesses(j) > 0) % positive going peak (ESA)
aLows(j) = 0;
aHighs(j) = inf;
else % negative going peak (STE, GSB, pump scatter)
aLows(j) = -inf;
aHighs(j) = 0;
end
end
% center energy
168 APPENDIX A. MATLAB CODE
muLows = zeros(size(muGuesses));
muHighs = muLows;
muError = 2000; % C'mon, you can't be more wrong than 2000 wn in your guess,
% you're supposed to be a spectroscopist!
muLows = muGuesses - muError;
muHighs = muGuesses + muError;
% standard deviation energy
sigmaGuesses = zeros(size(muGuesses));
sigmaGuesses = sigmaGuesses + 1000; % Always start with 1000 wn
sigmaLows = zeros(size(sigmaGuesses));
% zero std is a bit non-physical but okay as a limit
sigmaHighs = sigmaLows + 5000; % Extremely broad
[yf,res,params] = ...
gaussianFitTA(xwn,y,aGuesses,aLows,aHighs,muGuesses,muLows,muHighs...
,sigmaGuesses,sigmaLows,sigmaHighs);
%% Plot data nicely for publication
% Extract parameters and plot each guassian separately
n = (length(params)-1)/3; % number of peaks that were fit
gaussians = zeros(n,length(x));
peak_label = '';
for j = 1:n
A.3. TAFIT.M 169
index = (j-1)*3;
a = params(index+1);
mu = params(index+2);
sigma = params(index+3);
gaussians(j,:) = a*normpdf(xwn,mu,sigma);
lambda = round(1E7./mu); % center wavelength
if(a<0)
peak_label = [peak_label; 'STE, ' num2str(lambda) ' nm'];
else % Could also be GSB! Or pump scatter
peak_label = [peak_label; 'ESA, ' num2str(lambda) ' nm'];
end
end
z = params(end); % constant offset is last parameter
gaussians = gaussians + z;
figure();
stem(x,res);
xlabel('Wavelength (nm)'); ylabel('Residual (mOD)');
title(title_str);
xlim([min(x) max(x)]);
figure();
plot(x,y,x,yf);
hold on;
plot(x,gaussians);
xlabel('Wavelength (nm)'); ylabel('\DeltaA (mOD)');
title(title_str);
170 APPENDIX A. MATLAB CODE
legend(['Data ';'Fit ';peak_label])
xlim([min(x) max(x)]);
A.4 svdplots.m
Simple scripts that plots the outputs of SVD in a more readable format.
%% Description
% Plot the first n components of U and V
% Plot diag(S) normalized to first singular value
% x and y are axes that contain meaningful units, if unavailable use
% [r,c] = size(z); x = 1:c; y = 1:r;
function [U,S,V] = svdplots(x,y,z,n)
[U,S,V] = svd(z);
%% Normalized singular values
% s(1) is normalized to 100%
s = diag(S);
s = s./s(1).*100;
figure();
stem(s)
title('diag(S)');
A.4. SVDPLOTS.M 171
ylabel('% of 1^{st} s.v.');
xlabel('singular value #');
xlim([1 n+10]);
ylim([0 s(2)*1.1]);
%% U matrix, row information
figure();
plot(y,U(:,1:n));
l = 1:n;
legend(num2str(l'));
xlabel('y units'); % Not general
title('U(:,1:n)');
%% V matrix, column information
figure();
plot(x,V(:,1:n));
l = 1:n;
legend(num2str(l'));
xlabel('x units'); % Not general
title('V(:,1:n)');
end
172 APPENDIX A. MATLAB CODE
A.5 svdrank.m
Outputs a low rank approximation of a matrix and the residual. Useful for judging what the
appropriate rank of your dataset is.
% Performs SVD on matrix A and outputs the rank r'th approximation as A_r
% The residual data R = A - A_r is also an output.
function [A_r,R] = svdrank(A,r)
[U,S,V] = svd(A);
A_r = U(:,1:r)*S(1:r,1:r)*V(:,1:r)';
R = A - A_r;
figure();
imagesc(A_r);
title(['Rank ' num2str(r) ' Approximation']);
figure();
imagesc(R);
title(['Rank ' num2str(r) ' Residual']);
end
Appendix B
Trigger Circuit Diagram
After installing the Pixis CCD array there was an issue with getting it to start collecting data
with reproducible phase with respect to pump on/pump o. The issue is that it is controlled by
LabVIEW, which does not do well with precisely timed hardware functions. The solutions was to
create a \camera ready" signal, then to begin collection. This circuit eectively gates the SDG
pulse train, which is used to clock the camera's acquisition of each spectrum at 1 kHz.
When LabVIEW readies the camera (an event with poor time precision) the ArduinoSendEdges.vi
program sends a pulse to the corresponding input. After this happens, the circuit waits for an edge
on \Trig In", typically provided by the chopper controller. Once it sees this edge the gate is now
opened, and SDG pulse can pass through the nal AND gate to the camera. After acquisition is
nished another ArduinoSendEdges.vi pulse closes the gate.
173
174 APPENDIX B. TRIGGER CIRCUIT DIAGRAM
Figure B.1: Logic and connection diagram of circuit that triggers the Pixis camera. \Arduino"
is a digital output pin on an Arduino microcontroller that is controlled with the LabVIEW Ar-
duinoSendEdges.vi program. \Trig In" is usually the output of an optical chopper control box.
\SDG In" is one of the delays from the signal delay generator. \Trig Out" is sent to the Ext Sync
on the Pixis camera. The AND and OR gates perform their corresponding logic operations on their
inputs as one may expect. The JK chips set to \
ip-
op" mode are less well known, but simply
change their output state (either from 0 to 1 or vice versa) when a rising edge is detected on the
input. A red indicator LED is placed such that when the gate is open the LED is illuminated.
Abstract (if available)
Abstract
The concept of an acid-base reaction is one of the most fundamental and important constructs in the field of chemistry. Under the Brønsted-Lowry definition an acid is a proton donor, and a base is a proton acceptor. When proton donors and acceptors are located on the same molecule the acid-base reaction is referred to as tautomerization. The ubiquity of proton transfer reactions in nature is not understated. Protons play major roles in photosynthesis, medicine, our sense of sour taste, and nitrogen fixation. ❧ As our society moves towards a more sustainable energy economy, we seek methods for the generation of chemical fuels, such as hydrogen gas, methanol, and methane, that do not rely on fossilized carbon. Production of these fuels from readily available feedstocks like water and carbon dioxide will be energy storing, endothermic reactions. An abundant, carbon neutral, option for providing this thermodynamic drive is solar radiation. In addition to being thermodynamically unfavorable, solar fuel generation involves redox reactions that require the reorganization of multiple electrons and protons. Plants and certain bacteria have developed the molecular machinery necessary to manipulate these charge carriers in a process referred to as proton coupled electron transfer (PCET). Significant scientific effort has been made to create artificial photosynthetic systems which, rather than producing sugars as is done in plants, produce fuels such as hydrogen and hydrocarbons.
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Ultrafast dynamics of excited state intra- and intermolecular proton transfer in nitrogen containing photobases
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Publication Date
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Defense Date
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