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Electric field induced spectra of carbon disulfide and its dipole moment in an excited state

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Electric field induced spectra of carbon disulfide and its dipole moment in an excited state

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Content ELECTRIC FIELD INDUCED SPECTRA OF CARBON DISULFIDE AND ITS DIPOLE MOMENT IN AN EXCITED STATE by Hyun Chai Jung A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY • (Chemistry) June 1972 I I j l 72-26,023 JUNG, Hyun Chai, 1938- ELECTRIC FIELD INDUCED SPECTRA OF CARBON DISULFIDE AND ITS DIPOLE MOMENT IN AN EXCITED STATE. University of Southern California, Ph.D., 1972 Chemistry, physical University Microfilms, A XEROX C om pany, Ann Arbor, M ichigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. UNIVERSITY O F SO U TH ERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALI FORN1A 9 0 0 0 7 This dissertation, written by under the direction of h i,S— Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Gradu ate School, in partial fulfillment of require ments of the degree of D O C T O R OF P H IL O S O P H Y < r Dean Date J.vm. 1 9 . 7 . 2 . DISSERTATION COMMITTEE V Chairman PLEASE NOTE: Some pages may have indistinct print. Filmed as received. University Microfilms, A Xerox Education Company ACKNOWLEDGMENTS The author gratefully acknowledges David A. Haner who has given me the helpful conversations and good suggestions, and Roddy M. Conrad who gave me good suggestions. The author also acknowledges Jim Moore for the helpful conversations as a lab-mate, and Toni Remeikis for the good suggestions for electronics problems. Special thanks go to ct±±- American and Korean friends who have extended their good will to me while this work was being carried out. The sincere appreciation is expressed to Professor David A. Dows and his family who have treated me as a member of the family and provided the financial support and suggested the problem and under whose supervision it was concluded. TABLE OP CONTENTS Page ACKNOWLEDGMENTS ....................................... ii LIST OF TABLES.................................. iv LIST OP FIGURES.................................... . v ABSTRACT..............................................vil Chapter I. INTRODUCTION ............................... 1 II. THEORETICAL ..................... ..... 21 1. Upper State Wave Function............ 22 2. Transition Moments .................... 30 3. Electric Field Induced Spectra ........ 47 III. EXPERIMENTAL............................... 53 1. Instrumental.......................... 53 2. The Resolution and Focusing............'"59 S + 2 3. Rotational Analysis of £ Vibronic Band................................. 64 4. Electric Field Measurement ............ 70 5. EFS Signal Versus E2 ................ 71 6. K2/K1, Instrumental Constant Ratio Determination ..... ............ 76 7. Determination of CL|<||>I^ 77 8. EFS Peak Frequency Determination .... 78 9. Heights of the Peaks.................. 80 IV. OBSERVATIONS AND DISCUSSIONS.......... . . . 82 1. Upper Electronic State Dipole Moment . . 82 2. EFS of the Various Vibronic Bands ... 82 3. QEFS and Polarization Intensity Ratio . 91 4. EFS Sign Change and Possibility of A1 Determination.................. 95 V. CONCLUSIONS............................... 99 REFERENCES........................................... 101 iii LIST OP TABLES Table Page 1. Ground State Information for CS^ ............. 3 2. Upper State Configuration of CS^ ............. 4 3. Upper State Vibrational Frequencies of CS2 . . 5 4. Electronic Configurations and Their States . . 6 5. Direction Cosine Matrix Element ....... 23 6. Computed Results of Transition Moment .... 44 7. Actual Slit Width and Micrometer Readings . . 58 8. Hg Lines for Focusing....................... 63 9. Rotational Line Frequencies of sn ......... ss 10. E.H.T. Power Supply Meter Correction ......... 72 11. EFS Peak to Peak Signal Strength............. 74 12. Instrumental Conditions for K2/K^ ........... 77 13. EFS Peak Separations From vQ ............... 79 14. Id . ........................................... 80 15. Ia.c. and Ia.c./Id.c.......................... 81 16. Upper State Dipole Moment ................... 83 17. EFS Strength Ratio of 1 to // Polarization ............................... 94 iv LIST OP FIGURES Figure Page 1. Ground and Upper State Molecular Geometry of Carbon Disulfide ....................... 7 2. Asymmetry Parameter Versus Bent Angle <CS2 . . 9 3. Second Order Stark Shift ..................... 13 4. Time Varying Quantities in the Phase Detection . ...................... 15 5. Phase Detection Output and a Rotational Line..........................................19 6. Block Diagram of Instruments ................. 54 7. Schematics of Preamplifier ................... 55 8. Fore Monochromator Dispersion Pattern .... 57 9. Back Focusing Versus Machine Number ......... 6l 10. Machine Number Versus Order Wave Length ... 62 11. Rotational Structure of S£2 Band............. 66 0 12. Fortrat Diagram of S£2q Band................. 67 13. Combination Relations of R and P Branches..................................... 69 14. Calibration of E.H.T. Power Supply ........... 73 15. EFS Dependence of Field Square,................. 75 16. U^jij EFS and Absorption Spectra........... 85 17. U, EFS // and Absorption Spectra........... 86 v Figure Page 18. EFS of and Absorption Spectra ... 87 19. EFS of // and Absorption Spectra ... 88 20. EFS of -L and Absorption Spectra ... 89 21. EFS of // and Absorption Spectra ... 90 22. EFS of Sn20 -L and Absorption Spectra ... 92 23. EFS of n ] _ // an^ Absorption Spectra ... 93 24. IB F„ versus J .............................96 m om 2 25. I B0 versus J ................................97 m 2m vi ABSTRACT S+2 Rotational analysis of I vibronic band in the B0 o ^ electronic state of CS2 has been carried out and the ground and the upper state rotational constants were determined to be Bn = .IO63 ± .0003 cm-' * ' and BT = .1081 ± .0003 cm-1. Theoretical development of second order Stark effect for the dipole moment lying perpendicular to the symmetric top axis has been presented and the experimental electric field induced spectral intensities are shown to be proportional to the square of the applied electric field strength. Ia.c./Id.c. technique; the electric field induced spectral intensity versus the transmitted light intensity method was used to calculate the upper electronic state electric dipole moment and the average value of the dipole moment in the B2 state results to be 0.093 Debye. The electric field induced spectral strength ratio of the two polarizations, perpendicular and parallel to the applied electric field direction, are different in different vibronic bands. The crude experimental evidence shows that for the S system vibronic bands the perpendicular to parallel ratio of the electric field vii induced spectral intensities was almost 2 and for the R system vibronic bands approximately 0.7. A new way of determining the rotational constant A’ when B' is known may be developed through care-ful examination of the sign change of the electric field induced spectra. viii 4 CHAPTER I INTRODUCTION On March 8, 1883 absorption of light between 3000 A and 3400 A and a second absorption beginning at about 2580 A of carbon disulfide was reported by G. D. Liveing and J. Dewar (1) to the Royal Society of London. Before E. D. Wilson (2), who published the absorption spectra (650 bands) of CS2 in the near ultra violet region 2900-3800 A in the gas state, J. Pauer (3) confirmed Liveing and Dewar's work by noting 24 bands in the same region and I. M. Pauly (4) reverified it by observing 56 absorption bands. After E. D. Wilson's paper there have been many studies published on CS^ spectra, ultra violet (5, 6, 7, 8, 10, 29), infrared (11, 12, 13, , 15» 34), and Raman (16, 17, 18). Among the ultra violet spectra the widest ranges were photographed and examined by two groups of workers; one by W. C. Price and D. M. Simpson who took a low resolution spectrum (1200-3600 A) and tried to analyse the excited states and vibrational progressions of the excited states, the other by C. Ramasastry and K. R. Rao (8) who discovered a few more progressions (5) than Price and 1 Simpson. Much work has been done on a small portion of the ultra violet region of the spectra by absorption (9, 10, 19, 20), Zeeman (23, 24)* and magnetic rotation (6, 27) spectroscopy. Some of their significant conclusions are listed in tables 1 through 3- There are many disagreeing values among the authors as shown in the tables. For the electronic state of the absorption region 3300-3750 A, there are quite contradictory arguments; the rotational structure of the bands indicates that the excited state is singlet, whereas the magnetic effects contradict this conclusion. The spin selection rule holds less and less strictly with increasing spin orbit interaction, that is, with increasing atomic number; actually, singlet-triplet interactions have been observed even for such a relatively light molecule as CO in the Cameron band (28), a singlet-triplet transition of CS2 is conceivable. But the rotational structure of the bands seems to contradict this assumption since no triplet structure was resolved even at the numerous perturbations which are usually effective in separating the components of a close triplet. Instead, the observed Zeeman effect was line broadening, with line width 5 = 2guQJH (23) where g is a constant, uQ is the nuclear magneton, J is rotational angular momentum quantum number, and H is the magnetic field strength. The linear dependence of J 3 TABLE 1 GROUND STATE INFORMATION FOR CS, B 000 o = 657.98 cm -1 0.10910 ± 0.00005 cm ^: rotational constant at ground vibronic state by Stoicheff (18) 1.55^5 ± 0.0003 A: bond distance of C = S at ground vibronic state by Stoicheff (18) observed band origin of sym. stretching vibration by Stoicheff (18) by Sirkar (17) (solid state) bending vib. by Stoicheff (18) by Sirkar (17) (solid state) asym. stretching vib. by Gailar and Plyler (52) V1 = 655.5 -1 cm : V2 = 396.8 -1 cm : V2 = 391.5 -1 cm : V3 = 1532.5 -1 cm : TABLE 2 UPPER STATE CONFIGURATION OF Cfi2 Wave Length 3300-3750 3300-3750 3300-3750 3300-3750 3300-3750 3300-3750 3300-3750 2900-3300 2200-1800 2200-1800 2200-1800 1600-1450 below 1450 Bent Angle Electronic r (C=S) References State In A 135.8° 180 (125) ? but > " ' " A 135 ± 10 'B, •u 'B, 1.64 Kleman (9) 1.522 Lleberman (20) 1.735 Lieberman (20) ? Ramasastry & Rao (8) 'Bp considerably Walsh (22) & increased Mulliken (21) ’tt ? 135 ? but < 1B 178-177 153 slightly bent 178-177 180 B2 of ^ "A, 'B, Kusch & Loomis (6) 1.64 Douglas & Milton (23) & Hougen (24) ? Ramasastry & Rao (9) & ? Price & Simpson (7) 1.66 Douglas 8c Zanon (10) 'Bp considerably Walsh (22) 8c increased Mulliken (21) ? ? Price & Simpson (7) ? ? Price S i Simpson (7) S c Tanaka, Jursa, 8c Le Blane (29) 5 UPPER TABLE 3 STATE VIBRATIONAL FREQUENCIES OF C c i u2 Wave Length in A Claimed in cm Frequency References (band head) 2750-3900 V = 270 Wilson (2) 2750-3900 V = 270 Watson (5) & Parker 2750-3900 V = 270 Jenkins (19) 2750-3900 V = 270 Kusch & (6) Loomis 2750-3900 V = 250 Price & (7) Simpson 3300-3750 V = 414 Ramasastry & Rao (8) 3300-3750 V = 289 Kleman (9) 3300-3750 V ' = 289 Ramasastry & Rao (8) to the line broadening leads A. B. Douglas (23) and Jon T. Hougen (24) to believe the excited electronic state to be the B£ multiplet component of a bent JA2 electronic state, whose other two multiplets and B^ are nearly degenerate with each other but are separated from the component. But according to Mulliken (35) the energy levels may be described as shown in Table 4. TABLE 4 ELECTRONIC CONFIGURATIONS AND THEIR STATES Electronic Configurations Linear D„ ■h Bent C + 1 —1 1 R u t , u 1 rS g g 1 > ro + i —f 1 . 2v (tt ) TT ( O a (O* allowed V < N forbidden for linear ground The forbidden 1B2 may be allowed because of the mixing with the allowed 1B2 , the very intense V system in the spectra. This argument is very feasible. The molecular configurations of the ground and electronically excited state CS2 are shown in Fig. 1. 7 o Fig, 1.'— Ground and upper state molecular geometry of carbon di-sulfide. r~ The double bond covalent radii of each atom (C : 0.665 A and S:0.94 A) (30) are taken for the comparison of sizes and the upper state bent angle was taken as 135° (23). The rotational energy levels of the almost prolate as follows: W (1) ... ( 2) (3) constant, J is a K ^ is a quantum the prolate are the constants for a given J and K og _ a _ r K = ---X'~-"C— ^ay’s asymmetry constant. Since K does not depend on the interatomic distances but only on the bent angle for the given isotopic species of C and S as shown in Pig. 2, Bp also depends on the angle only. K is near to -1 when the bent angle is larger than 125° and accordingly B is very small when P the angle is large. If the bent angle is 135° as given by Douglas and Milton (23), K = -0.9983 and B = 0.0004. J r asymmetric top molecules are expressed E = B * C J(J+1) + (A - B t °) W = K ? + C,B + C0B2 + 0oB3 + -1 1 P 2 p 3 P p _ C - B _ K + 1 p " 2A-B-C K - 1 where A, B, and C are the rotational total angular momentum quantum number, number for the projection of J along symmetric top axis, C^, C2J C^, . . . 1 50 ' 100 50 Fig. 2.— Asymmetry parameter vs. bent angle SC§. The coefficients are given in Appendix III of Microwave Spectroscopy by C. H. Townes and A. L. Schawlow (31) and for higher J there is a general expression by Wang (32). The terms of odd powers of in equation (2) are all cancelled when K_^ = 0, which is the case for E type bands of CS^. If the bent angle 135° was taken, since = 2 0.0004, the higher-than-B terms can be neglected. When P J = 12, K_1 = 0, C2 = -3003., C2Bp = -4.8*10“i|, (A - C) = 3-36 cm"1, (A - B- 2 ■C)*W = 1.6l*10“3 cm"1. B + C Therefore, (A - — 2— )*W terms are not important in other words, the asymmetry of the molecule may not be a serious problem unless the bent angle has far less than the angle 135°• Ray's asymmetry parameter K versus the bent angle for the CS2 is shown in Pig. 2. The designations for the vibronic bands are made according to the Kleman's (9) expressions; in the excited state the quantum number K_^ is defined as mentioned above and in the ground state the vibrational angular momentum quantum number J t is a good one. All the observed transitions are of parallel type, that is, Kll = ^'r • These parallel bands are designated as E, rr, A, < f > , T, H, I, K, L, or M bands according to = A" value, +1,2,3,4,5,6,7,8, and 9* The vibrational quantum numbers of the ground state bending vibration and upper state symmetric stretching vibration and the bending vibration are indicated as V1 V* V V’ V' VT 1* 2 1* 2 l5 2 zv" , n v £ , a v j ; , . . . o In the region 4300-3275 A of the ultra violet spectrum approximately 250 bands were ascribed to the R system, which follows regular progressions, and each of them are labelled as in the above description (9)* Some 25 other bands in the region 3700-3350 A form prominent progressions of the same type as the R progressions. But it appears difficult to classify them as R progres sions without violating the general selection and intensity rules. Bengt Kleman (9) assigned these bands as S type bands and designated them as S+V£ S+V£ S+V£ ZV£ , nVg , AV" , . . . where Z, II, A, . . . are +1,2,3> • • • and VI, is the ground state bending vibrational quantum number as in the R system and S + VI, is the upper electronic state bending vibrational quantum number starting from the unknown origin S. And there are about 30 unassigned bands in the region 3400-3275 A. Six of these seem to belong to the V system, which is the most intense part of the 12 spectrum 3300-2900 A. Most of the rest are Irregularly distributed £ bands. The unassigned bands except the six of the above mentioned are called U bands. Designation for a rotational line for a given vibronic band is ^ K^(AJ) K ^ where AK and AJ may be -2,-1,0,1,2 and the corresponding letter symbols are 0, P, Q, R, S for both AJ and AK respectively. When a symmetric top molecule with a dipole moment along the perpendicular to the top axis is placed in a reasonably strong electric field (about 50 KV/cm), the rotational motion of the molecule is affected such that the energy level of a rotational angular momentum quantum number J is split into ± J, ± (J-l), ± (J-2), . . . ±1, and 0, which are the corresponding azimuthal quantum numbers M for a given J. The second order Stark splitting occurs such that the higher M value lines shift the less distance toward the higher energy side from the original J level regardless sign of the M quantum number. The splitting patterns are given in Pig. 3 for the simple case of J = 3. Fig. 3a is a rotational line without electric field and Fig. 3b shows schematically the second order Stark shifts for each M component of the J = 3 case. Each component is assumed to have a functional form of S (v,E), the Lorentzian line shape. Since these intensity distribution m=0 max m=±l m = ±2 ■ m=±3 max C. Fig.— Second order Stark Shift,.' 11* spacings are far below the resolution-limit of the instrument, the overall envelope of Pig. 3c will be obtained. In order to study these phenomena a phase sensitive detection system for signals due to an alternating electric field with frequency w was applied. This technique was well explained in David A. Haner's (36) doctoral disserta tion (1968). When the field is increased, Pig. 3a changes into Fig. 3c regardless the sign of the field direction. Since the alternating field shows two positive and negative signs these spectral shape changes occur twice in a period of the sign wave of the applied electric field. The line is, therefore, modulated with frequency twice that of the field frequency. At the frequency vq and vm the modulation of intensity can be illustrated with the phase sensitive detector, which is a Fourier analyzer of the time dependent variations in intensity. The intensity change for a cycle of the applied field when the slit is set at v are shown in Pig. 4b and Fig. 4c. At v = v . the s s o * maximum absorption with maximum field and the minimum absorption with no field. The final output on the recorder from the phase sensitive detector is proportional to the Fourier series. Scanning on frequency over a complete rotational 15 a. E sincut d. E cos 2u>t Pig. 4.— Time varying quantities in phase detection. • r 0 16 line, the phase detected output resembles the first derivative of the absorption line shape; more precisely the electric field-induced spectra (EPS) for the Stark shift can be formulated as 4 w(v) = | /D IQ e“ «<v,E,t ,v ,J,K,M)CLcos 2wt dfc where l| (v) = Ia.c. is the second Fourier component of the transmitted light intensity with polarization at frequency v, I : transmitted light intensity without sample, T: one period of the field frequency, Qt t C = t— v NB , where h, c, N, and B are Plank’s he o p’ y > > p constant, speed of light, number of molecules in cubic centimeter, and Boltzman population factor for the rotational ground state (J,K), L: cell path length. The absorption coefficient a (apart from constants included in C) for a given rotational line for a rotovibronic transition of a symmetric top molecule with a dipole moment perpendicular to the top axis can be written as a(v,E) = J|<t’,v ',J’,K’,M',u£E| u ^ | t ,v , J ,K ,M,ub ,E> | 2S (v ,E) where t and v are the electronic and vibrational quantum numbers, ufe: the dipole moment lying perpendicu lar to the top axis, prime indicates the upper state and unprimed the ground state, u ^ : the dipole operator 17 where £ Indicates the polarization direction and b indicates the dipole direction perpendicular to the top axis . For th-e-moiecule CS2, the ground state is linear and has no dipole moment, naturally there is no field effect except the weak one due to the polarization (38). The above absorption coefficient a can be rewritten as a(v,E) = ub? |x,v,J,K,M>|2 S(v,E) After computing the rotational part of the transition moment and expanding the field dependent part of the exponential term into Taylor’s series and collect ing the necessary second Fourier coefficients of the expanded equation, the phase detected output is 2 where | < | |> | : vibronic part of the transition moment, B : field free rotational part of the transition moment, om 9 2 2 P2Ub]?b: second order Stark shift with field strength E, S^: the first derivative of the Lorentzian line induced transition moment. And Id.c. = IQ I < I I > I $ Bom ^o^, the transmittance of the light with no field on the sample. The final phase detected output has been pictured 18 in Pig. 5a along with a field free rotational line in Pig. 5b. The ratio of EPS over the field free transmit tance shows: I - 2 [B F 'S + Bp S ] u2 E2 Id. c. 2 m om 2 1 2m o b All the factors beside the upper state dipole moment are either computable or experimentally measurable. An experiment has been carried out using carbon disulfide as sample in the cell, and ^RO^, ^RO^2, and 0 84 S+2 R0J rotational lines of the 2o vobronic band (band origin 29241.84 cm"'*') have been selected for detailed study. The reasons for choosing these particular lines are: 1) the vibronic band EPS is the strongest one available in the absorption region 3300-3750 A; 2) the rotational analysis was available with our instrument; 3) the rotational spacings are large enough that EFS overlapping does not cause too much trouble for EPS strength measurement. This dissertation discusses: 1) the theoretical transition probability with the electric field induced effect and with parallel and perpendicular polarization of light to the applied electric field; 2) the theoretical second order Stark shift formula for the symmetric top molecule with a dipole moment perpendicular to the top axis; 3) the electric field induced spectral line shape 4 19 + • • • • • • m l i a. • ; • • • • • ' i i i l i £ I 1 I 1 ? * •••# •• - - - - - - - - - - - - - - - - - - V .1 .2 .3 .4 .5 .6 c •• • i - • • - • • •- - j____i i i i I .2 .3 A .5 .6 cm Fig. 5.— Phase detection output and a rotational line. F analysis and determination of the upper state dipole moment; 4) absorption and the electric field induced spectra of different species of the vibronic bands. CHAPTER II THEORETICAL The theoretical development of the electric field induced spectra to measure the upper electronic state dipole moments of diatomic molecules is due to David A. Dows and A. D. Buckingham (38); the extension of the theory to the symmetric top molecules was carried out by N. J. Bridge, D. A. Haner, and David A. Dows (39)- The second order Stark shifts for the dipole moment parallel to the top axis are given in Microwave Spectroscopy by C. H. Townes and A. L. Schawlow (31) and for the dipole moment perpendicular to the top axis the second order character was mentioned as an interesting subject in Roddy M. Conrad's doctoral dissertation (40). William Klemperer (50) et al., have obtained the dipole moment component which is perpendicular to the near symmetric top axis (u^) HCOF by static Stark splitting. John R. Lombardi (53) has discussed the Stark effect on spectral lines in asymmetric rotor spectra. In order to understand the second order Stark effect of the molecule CS2 in the upper bent electronic state it is necessary to know the electric field perturbed 21 22 wave function up to second order. 1. Upper State Wave Function The. derivation of the perturbed wave function up to second order followed the general scheme of perturbation theory (41). The first order perturbed wave function is simple and can be written as: . (1)/™ n _ y' <(JKM)"|Ab z| JKM> , tt,mN „ /n N i l > (JKM) - ub E (JKMy, he [ v (JKM) -v (JKM) " ] ^ JKM) where u^ is dipole moment perpendicular to the top axis, E is external electric field in Z direction, the prime on the summation sign means except (JKM)" = JKM, JKM are the rotational quantum numbers of the rotational wave function, with double primes indicating the perturbing wave functions, vhc (JKM) is the energy level of the state JKM, and with double primes indicating the energy level of the perturbing state (JKM)", The matrix elements <(JKM)"|Abz|JKM> are determined by looking up the following Table 5. The complete first order wave function is given in the next page. TABLE 5 DIRECTION COSINE MATRIX ELEMENT (31, 45) Matrix Element Factor Values of J1 J + l J J - 1 ^JJ' [4(J+l) (2J+1)(2J+3)] 1 [4J(J+l)] 1 [4j"\/ 4J2 - l]-1 ^a^JKJ'K 2 J+l)2 - K2 2K 2A / j2 - k2 ( ± lt|>c)JKJ,K±l + ~\/{J±K+1) (J ±K+2) - y ( j+k) ( j ±k+i) ±Vj+K)(J+K-l) JMJ'M 2\j (J+l)2 - M2 2M + 2 V j 2 - M2 (^X * 1(^Y^ JMJ'M±l +'(J ±M+1) (J ±M+ 2 ) "\J (J+M)(J±M+1) Aj (J+M)(J+M-l) < (JKM) " | A±£ | JKM> = < j > JJt (^i)JKJ'K' ( < ( > )JMJ'M» i = a, b, c internal coordinates £ = X, Y, Z external coordinates ro uo u, E b he 2k \ / ( ^ 7 V (J+K+l) (J+K+2) 2(J+l) (2J+1)(2J+3) [B(J+2) + (A-B)(2K+1)] ^J+1£+1>M M V (J-K)(J+K+l) 2J(JH) [(A-B)(2K+1) ^J,K+1,M J2 - M2 V (J-K) (J-T-l) 2^j (2J+1)(2J-1) [2BJ - (A-B)(2K+1)] J-1,K+1,M V'(JH)2 - M2 V (J-K+l)(J-K+2) 2 (J+l )~V (2J+1) (2J+3 ) [B(J+2)-(A-B)(2K+l)Y+1*K~1’M ■ i | r (J+K) (J-K+l) 2J(J+l) [(A-B)(2K-1)] J±K-1,M V J2 - M2 V (J+K)(J+K-l) 2JV(2J+1)(2J-1) [2BJ + (A-B)(2K-1)] "^J-1,K-1*M } ( 2) The second order perturbed wave function Is from the general formula 25 $ (2) “b^ I (JKM) h2Q2 (JKM)'f * U I < (JKM)'"[ Abz | (JKM)"*>< (JKM) " | Ah J JKM> bz1 (JKM)" [ v( JKM)-v (JKM),T0 [v (JKM)-v (JKM) " ] (JKM) i t n < (JKM )M1| Ab z | (JKM) > < JKM | Ah ^ | JKM> bz [y(JKM) - v(JKM)'"f ^ 1 (JKM)'M J 1 2 < (JKM),n |Abz|JKM>‘ [v (JKM) - v(JKM)1"] ^ JKM^ (3) Since every matrix element requires the condition J = i 1 or 0, K = t 1, and M = 0, a systematic system can be used to build the wave function. Starting from JKM there will be six wave functions which can be combined by the direction cosine Abz. They are (J+1,K+1,M), (J,K+1,M), (J-1,K+1,M), (J+l,K-1,M), (J,K-1,M), and (J-1,K-1,M). Each of these will combine with six other wave functions so the schematic will be, J, K, M J+1,K+1,M J+2,K+2,M J+l,K+2,M J ,K+2,M J+2,K ,M J+l,K ,M J ,K ,M 26 J ,K+1,M J-1,K+1,M J ,K-1,M J-1,K-1,M J+l K+2 M J K+2 M J-l K+2 M J+l K M J K M J-l K M J K+2 M J-l K+2 M J-2 K+2 M J K M J-l K M J-2 K M J+2 K M J+l K M J K M J+2 K-2 M J+l K-2 M J K-2 M J+l K M J K M J-l K M J+l K-2 M J K-2 M J-l K-2 M J K M J-l K M J-2 K M J K-2 M J-l K-2 M J-2 K-2 M (*») Prom the above schematic the perturbing wave functions and the numbers of coefficients can be found: 27 Perturbing Wave Functions Number of Coeffs. J+2,K+2,M 1 J+2,K ,M 2 J+2,K-2,M 1 J+l, K+2,M 2 J+l,K ,M 4 J+l,K ,M 2 J ,K+2,M 3 J ,K ,M 6 J ,K-2,M 3 J-l,K+2,M 2 J-l,K ,M 4 J-l,K-2,M 2 J-l, K+2,M 1 J-2,K ,M 2 J-2,K-2,M 1 Using these schematics and the table of direction cosines the second order part of the wave function is obtained. One can write the rotational part of the upper state wave function in an abreviated form as follows: UbE ^'JKM " ^JKM he {aJ+l,K+l,M ^J+1,K+1,M “ aJ,K+l,M ^J,K+1,M + aJ-l,K+l,M ^J-l ,K+1 ,M " aJ+L,K-l,M ^ J+l ,K-1,M + aJ,K-l,M ^J,K-1,M “ aJ-l,K-l,M ^J-1,K-1,M* 2_2 yb E + h2Q2 {ej+2,K+2,M ^J+2,K+2,M - ( 0J+2jKjM + 2 , ’ 3J+2,K,M) ^J+2,K,M + ^J+2,K-2,M ^J+2,K-2,M - (13j+1jK+2jM + 28 2 + PJ+13K+23M^ ^J+l,K+2 ,M 1 2 3 + ^ J+l3K3M + PJ+1,K,M + 0J+1,K,M + 4 ej+l9K,]Yp ^J+1,K,M 1 2 + ( ^ J+l,K-2 jM " 3J+1,K-2,M) ^J+1,K-2,M + 3J3K+23M + ej,K+2,M + 3&J,K+2jM^J sK+2,M " 2^ ^JKM + 2JKM + 32JKM + ^JKM + 52JKM + PJKM^ ^JKM 1 2 2 + ^ ^ J 3K-2 3M + ej,K-2,M “ ej,K-2,M^J,K-2,M 1 2 " ( ^ J-l,K+2 3M " 0J-13K+23M^J-13K+23M + ^1^J-liK,M " 0J-1,K,M + 33J-1,K9M + BJ-13K3M^J-13K3M ^ ^ J-l,K-2,M + ^ J-2,K+2,M ^ ^ gJ-2,K,M + ^J ^J-2,K-2,M 29 ^J-1,K-2,M^J-1,K-2,M + J-2,K+2,M -2,K,M + ^J-2,K-2,M + ^J-2,K-2,M (5) 2. Transition Moments The transition moment is <R'|TTV'| m*e^|TV|R> where TVR are the electronic, vibrational, and rotational wave functions, with prime indicating the upper state, m is the dipole operator, and e^ is a unit electric vector of the perturbation coefficients, the electric vector of the light wave must be expressed in the body coordinate system by using the direction cosines. The resulting expression is <T’V'|nn |TV><R'|A^|R> where the subscript indicates a coordinate a, b, and c. To determine which components of the vibronic transition moment result requires determination of which components of the dipole operator connect the ground and excited state of the molecule. This determination may be made by employing group theory. For carbon disulfide the electronic wave function of ground state has symmetry (93 22, 35) under the point group (43). Also the ground vibrational state of the 3500 A region E* O symmetry (9S 22, 35) under the point group (43). + Also the ground vibrational state of the 3500 A region E o symmetry (9, 44). The excited electronic state of the 3500 A region is known to be (35) if the molecule is linear, which is forbidden. The molecule is, however, 1 bent in the upper electronic state, I I state split into S 1 1 1 + Ap and Bg and the allowed Eu state which is higher 31 than state becomes ■'"B2 in the C^v point group (21, 22). The two ^B2 state are mixed so that 1 from I I becomes allowed. The v0 vibration g 2 bending has symmetry in the C2v point group. Accordingly the vibronic state of ^£2 is ^B2 which gives a transition moment oriented along Y axis in C2y group, that is, the a axis in the linear configuration. Taking £ be parallel to Z and Y the expression: <T'V,|m |TV><R'|A lR> and <T1V' |m_ | TV><R' | Aqv| R> 3, QuZ Si cl j l are the parallel and perpendicular components of the transition moment to the applied electric field. In order to calculate the rotational part of the transition moment the ground state wave function ijjJKM and the above derived upper state wave function i J j(JKM)' were used. The results obtained are as follows. Q branch // polarization i.,, i, i, „t2 _ K2M2 I ^ JKM^aZ^JKM I . ~ J2(J+1)2 2y2E2KM h2c2J(J+l) V (J+l)2 - K2 V(J+l)2 - M2 (J+l) ~\/ (2J+1) (2J+3) 1 ,1Q , 2f t , 3R , 4„ , 5r . 6f t \ KM 2 ^ JKM JKM JKM PJKM PJKM PJKM;J(J+l) + (lgJ-l,K3M + 23J-13KsM + 30J-1,K,M " 3J-1,K>M V j2 - k2 J2 - M2________ j (g) VTT2" J v 4J - l Q branch 1 polarization |<*> |A h >l2 = K2 (J+M)(J±M+1) ' JKM+11 aY1VJKM 1 9 ~ 4j (J+l) + U 2E2k V (J+M)(J±M+1) v -------------- A J(J+1) h e (J+l)2 - K2(+)V (J±M+1)(J±M+2 2 (J+l) "\ / ( 2J+1) (2J+3) 1 1 2 3 ^ 5 2 ( ^JKMll + ejKM±l + PJKM±1 + PJKM±1 + PJKM±1 6 » K\| (J±M) (J±M+1) JKM±1 2J(J+1) 1 2 3 * 4 + ^ ej-l,K,M±l + ej-lsK,M±l + ej-l,K,M±l " 3J-]/,M±l^ V J2-M2(±)V (J+M)(J+M-l) . /?n 2J V 4J2 - 1 R branch // polarization 2 [(J+l)2 - K2][(J+1)2 - M2] I f T+l K — 2 w \ J+ijKjli az, jjui (J+l) (2J+l)(2J+3) 2M2E2 V (J + 1 )2 - K2^/ (J+l)2-M2 h2c2(J+l) ~\J (2 J+l) (2 J+3) -X _ L 5 o J _ ^ 0 ' j J+l,KaM T J+l,KjM Y(J+1)2 - K2V 7 J+1)2 - M (J+l) Y(2J+l)(2J+3) 2 + rxf i + 2r + 3r 4r ^ KM ^ JKM JKM JKM “ JKM J(J+l) ! 2 V “ V ” JM 2 - ( eT_-, , m + eT_n „ M ) — — .---- ■ -— > (8) y ? - K 2 y j2-r J-ljK jM J-l,K1M/ , — 2 J AJ - 1 R branch j_ polarization 2 [(J+l)2-K2][(J±K+l)(J±M+2)] I^.T + 1 T C K y KtKmH “ J+1,K,M 1 aY JKM 4(J+1)2(2J+1)(2J+3) _ y2E2 V (J+1)2-K2t/(J±M+l)gdM+3 + ------------- h2c2(J+l)‘ \/(2J+l)(2J+3) 35 ^ R j_5n i R A J+l,K,M±1 J+l,K,M±1 J+l,K,M±1 ( + ) \/(J+l)2-K2 y J±M+1)(J±M+2) 2(J+l) y{2J+l)(2J+3) 1 2 3 ' 4 + ( ^JjKjM+l + 3J,K,M±1 + 3J,KsM±1 “ ^J SK,M±1^ K V (J+M)(J+M+l) 2J(J+l) “ ( 3J-1sK,M±1 + BJ-1,KjM±1'> (±) a/(J2-K2) l/ (J+M) (J+M+l) ------------ L . . . ------------} (9) 2J A/ 4J2-1 P branch // polarization i<*'J-1.n«i*aziwi2 - (j; kA (j2~m2)-------- J (4J-l) « 36 2y2E2 Yj2-k2 Y j 2 - j V ^j2~i 2 M X 2 2 W VU . MJ . -W -M ( ej+l,K,M + ej+l,K,M^ Y(J+D2-k2V (j+ D 2-p (J+l) y(2J+l)(2J+3) x /_ 1(3 J . , 3n I 4 g \ KM T \ P TLrM ~ p TVM P TVM ' P TVM ' ’ JKM T JKM JKM JKM J(J+1) 1 R + ^R + ^R + ^R 2 ^ J-l,K,M J-l,K,M J-ljK,M PJ-1,K,M c 6 V (J2-K2)(J2-M2) + ej-l,KaM + PJ-1,K,M^ /— p ^10) J Y 4J -1 P branch - 1 - polarization (J2-K2)(J+M)(J+M-l) I<^J-l,K,M±llAayl T> JKM 4J2 (4j2-1) _ 2^2 V J2-K2 y (J+M)(J+M-l) + - j -j -------------------------- X h c J Y 4J2-1 37 { ( ej+l,K,M±l + ej+l,K,M±l^ Y (J+l)2-K2 ( + )Y (J+M+l)(J+M+2) 2(J+l) y(2J+l)(2J+3) + PJKM±1 + 3JKM±1 + 3gJKM±l + ^JKM+l^ K -y^J+M)(J±M+1) 2J(J+l) 11 2 3 2 ( 6J-1,K,M±1 + PJ-1,K.M±1 + ej-lsK,M±l + BJ-1,K,M±1 + 50J-1,K.M±1 + ^J-ljK,M±l^ V (J+l)2-K2 (+)\/ (J±M+1)(J±M+2 ------------- ^ ---- (ID 2 (J+l) V(2J+D(2J+3) If the transition moment occurs through the b axis, i.e., perpendicular to top axis, the upper state K quantum number must differ by ± 1 from the ground state where K = A= 0. Only the second order perturbed part of the wave function affects the transition moment. This transition moment may be neglected for the observed bands of CS2 as predicted from the group theory. The calculated results are given in the following for completeness. Q branch // polarization h c aJ+1,K+l,M (J+K+l)(J+K+2) (J+l)2-M2 - a J,K+1,M 2(J+l)^(2J+1)(2J+3) ~\/ (J-K) (J+K+l) ' M 2J(J+l) + aJ-l,K+l,M ~\J(J-K) (J-K-l) Y j2"m2 aJ+l,K-l,M (J-K+l) (J-K+2) \j (J+l)2-M2 2(J+l) Y (2J+1)(2J+3) 39 Y(J+K)(J-K+l) M + aJ, K-l ,M 2J (J+l) + ^ 2 Y (J+K) (J+K-l) *\/~(J2-M2) -J--------- } (12) 2J *\/ 4J2-1 Q branch -L polarization 1 ^ ’jKMtllA |* >|2 = t!l!x h c ]/(J+K+l) (J+K+2) ( + ) (J±M+1) (J±M+2) aJ+l,K+1,M±1 ' 4(J+l) y(2J+l)(2J+3)' - a y (J-K)(J+K+lY y.(J+M)(J±M+l) J,K+1,M±1 4J(J+1) + aJ-ls K+l,M±1 /--g Y(J-K)(J-K-1) (±) y(J+M)(J+M-l) 4J 4J2-! ^J+l, K-l,M±1 Y(J-K+l)(J-K+2)(+) y (J±M+1)(J±M+2) 4(J+1)Y (2J+1)(2J+3) 40 ■y (J+K)(J-K+l) Y (J+M)(J±M+1) + jK"1 ,M±1 + a J-l,K-1SM±1 y (J+K) (J+K-l) (i) ~\J (J+M)(J+M—1) 4j yiu2-1 R branch // polarization 2 2 <l f j J+l' ,K3m I AbZ^JKMl = “2~2 X 3 3 n c yj+K+l)(J+K+2) "\/(J+l)2-M2 *aJ+l,K+l,M , ■ ~ 2(J+1) V (2J+1) (2J+3) y(J-K) (J+K+l) M + aJ,K+l,M 2J(J+1) y(J-K+l)(J-K+2) "\/(J+l)2-M2 + aJ+l,K-l,M . 2(J+l)y (2J+1)(2J+3) 2 } (13) 41 - a V(J+K)(J-K+l) M 2J(J+1) (14) R branch 1 polarization "^/ (J+K+l) (J+K+2 ) (?) - \ J (J±M+1) (J+M+2) {aJ+l,K+l,M±l ~ 4(j+i) y(2j+i)(2j+3) + a ■y (J-K)(J+K+l) y(J+M)(J±M+1) J,K+1,M±1 4J(J+1) + J+1,K-1,M 1 y(J-K+l)(J-K+2) (+) y (J M+l)(J M+2) 4(J+l) y (2J+L)(2J+3) V (J+K) (J+K+l) y rU+M)(J M+l) 2 1 ^ 7 ^ 3 1 - (15) 42 P branch J <^ J -1 ,K {aJ,K±l,] - a J jK-,1 P branch I< 1 ( , J-19K {a J,K+1,] // polarization ,mI 2 h2 2 X * h c (J-K)(J+K+l) M "\J (J-K) (J-K+l) V J2-M2 2J V 4J2-: (J+K)(J-K+l) M - a. ,M 2J(J+1) J-l ,K-1 'sj (J+K)(J+K-1) Y(J2-M2) ^ 2J -L polarization M ± l l A b Y ^ J K M > l v 2 2 X h c ■y (J-K) (J+K+l) ~ \ f (J+M)(J±M+1) 4J(J+1) (16) 43 a V(J+K)(J-K+l) "Y (J+M)(J±M+1) J»K_lsM 4J(J+l) •y(J+K)(J+K-l)(i) Y(J±M>(J+M-l) 2 aJ-l,K-l,Mil 0 } 4J V 4J -1, (17) 44 0 S+2 For the R branch of E0 band where the dipole moment measurement was carried out the intrinsic and induced transition moment along the top axis, abbreviated 2 2 as B and B0 u, E , are written and the computed om 2m b * ^ values of E B and E B„ for the quantum number m °m m 2m J = 30, 32, and 34 are given in Table 6. TABLE 6 COMPUTED RESULTS OP TRANSITION MOMENT Polari zation J = 30 32 34 2 B m om 10.3333 10.9999 11,6666 10.3333 10.9999 11.6666 E g m 2m -.7999*10"5 -.7079*10"5 -.6444*10~5 -,io6o*io”4 -.1031*10_i| -.1025*10“4 E B F* m om 2 .12l6*10_^ .Il40*10-5 .1084*10~5 _L_ .9172*10-5 ,8599*10"5 .8177*10"5 *The expression for are given in the follow ing section. 45 // polarization (K = 0) B = — ( j +a )1-j 2 — (l8) °m (2J+1)(2J+3) P P 2p2 [(J+l)2 - M22 Bp ] i E = - p X 2h c (2J+1)(2J+3) [(J+2)2 - M2] (J+3) { ----------------------------------- (J+2)(2J+3)(2J+5)[2B(J+2) + (A-B)22 (J+l)(J+2) (A - B)2 [(J+l)2 - M2] J (J+l)(2J+3)(2J+1)[2B(J+1) - (A-B)]2 (J2 - M2) (J + 1) --------------------------------------- } (19) (2J-1)(2J+1) B (2J+1)[2B(J+l) - (A-B)] _L polarization [(J+2)2 - (Mil)2](J+3) + (J+2)(2J+3)(2J+5)[2B(J+2) + (A-B)]2 [(J+2)2 - (M±l)2](J+3) (J+2)(2J+3)(2J+5)[2B(J+2) + (A-B]2 + 1 ' l 2 (M±l) (J+1)(J+2)(A-B)2 [(J+l)2 - (Mil)2] J (J+l) (2J+3) (2J+1) [2B(J+1) - (A-B)]2 46 (J+M+l)(J±M+2) B = (20) 0m 4 (2J+1) (2J+3) P P 1t2p2 (J±M+1) (J±M+2 ) B- U E = H-E X 2m 2h c (2J+1)(2J+3) (21) (J+M)(J +M-1) (2J+1)(2J-1)(2J+1) B (2B(J+l) - (A-B)] 47 3. Electric Field Induced Spectra The electric field dependence of the absorption coefficient as studied in our laboratory is well described in reference #39. Notation here is slightly different but easy enough to understand. The absorption coefficient, ct(v,E), for a roto-vibronic absorption line can be expressed. moment, Bm(E) the rotational part of the transition moment, and S(v,E) a normalized Lorentzian shape function. Since the electric field effect on the transi tion moment of the vibronic part is considered negligible, the only interaction between the external electric field and the rotating dipole has been treated as a perturbing hamiltonian such that the transition moment of the rotational part can be written as a function of electric field strength and also the rotational absorption line frequency can be expressed as a function of electric field strength; a(v,E) = |<||>|2 Z B(E)*S(v,E) r * ' * j j ] m (22) 2 where |<||>| is the vibronic part of the transition B (E) = B + B,E + B„ E2 + B0 E3 + B„ E^ . m ' om lm 2m 3m 4m (23) (24) The summation of Bm(E) over m results in the vanishing of all the odd powers of E; 2 B (E) = 2 (Bnm + B0 E2 + B, ) (25) j j i m m om 2m 4m The frequency shift due to F^E, the first order Stark effect, is neglected because there is no matrix element of ( ( J > b)JKJ rKT , that is, the perpendicular dipole moment matrix element is zero when AK = 0, which is the case for the ^B,-, 12+ transition (22) of CS0. 2 g 2 2 2 The second order Stark shift FgU E is expressed w , A 2 - u2E2 ((J+l)2-M2)(J+K+l)(J+K+2)_____________ F nU E p p \ p ^ he 4(J+1) (2J+1)(2J+3)(2B(J+1)+(A-B)(2K+1)) + M2(J-K)(J+K+l) 4J2(J+1)2(A-B)(2K+1) (J2-M2)(J-K)(J-K-l)__________ 4J2(2J+l)(2J-l)(2BJ-(A-B)(2K+1)) ((J+l)2-M2)(J-K+2)(J-K+l)______________ 4(J+1)2(2J+1)(2J+3)(2B(J+l)-(A-B)(2K-1)) M2(J+K)(J-K+l) 4J2(J+1)2(A-B)(2K-1) (J2-M2) (J+K) (J-K+l)____________ } (2g) 4J2(2J+1)(2J-l)(2BJ+(A-B)(2K-1)) 49 For K = 0, the E type band of CS2; p u2e2 = u2E2 ( ((J+l)2-M2)(J+2)________________ 2 h2c2 2(J+l)(2J+1)(2J+3)(2B(J+1)+(A-B)) + (j2~m2)(j-i)________________ j (27) 2J(2J+1)(2J-1)(2BJ-(A-B)) The absorption coefficient a(v,E) can be rewritten; o(v,E) = |<||>|2 K B + B, E2 + . . .) - ---- -T oo--o M om 2l" * (v-v°-P2u2E2)2+b2 Expanding a(v,E) in a Taylor’s series in powers of the field around E = 0; ct(v,E) a(vJE)E=Q + (dE)Ei0 + 2! ^29^ aH j E= 0 The expansion is valid when the Stark shifts are small, that is, for the CS2 molecules there is only second -1 order Stark shift which is in the order of 0.0005 cm or less in the range of electric field strength 40-60 KV/cm, while the b half width at half height of the rotational absorption line is 0.13 cm-2' or larger. From equation 29 all the coefficients of odd powers of E vanish after summing over M and the remaining terms can be rewritten; ct(v,E) = |<||>|2 (aQ + a2E2 + a^E4 + . . .) (30) 50 where an = £ B S (31) 0 m om o “2 * £ (Bom P2 S1 + B2m So <32) “4 - £ < V o + B2mP2Sl + BomP2S2> <33) 1_ and o * f o,2 , .2 (v-Vq) + b O _ b -2 ( y - V p ) / O ii ' J 1 v (( ^ x 2 s 2 " ((v-v ) + b ) ~, 0,2 .2 b 3(v-v0) - b S2 n ,, 0.2" .2,2 ((v-v0) + b ) B and B„ are the transition moments derived in the om 2m previous section (equations 6 to 11 and especially for branches of Z type vibronic bands equations 18 through 21). The specific expression for B^m can not be written unless the perturbed wave function up to 4th order is available. The fourth order term in electric field strength has been disregarded as it will be shown in the experiment that the EPS strength appears to be linear with the electric field squared in the range of electric field applied. The absorption coefficient, a(v,E) for a given 51 roto-vibronic line gives the following relation between Io the initial and I(v,E) by Lambert— Beer's law; I(v,E) = Io exp(- CL a(v,E)) (35) Expanding the field dependent part of equation 35 into a series approximation and substituting equation 30 into equation 35; I(v,E) = Ioe"CLl < I I > I o tQ {1-CL J < | | > | 2 (a2E2 + a^E^) + C. 2~ l2|i I . 1 >il a2 E4} (36) Since the even harmonics of applied field frequency are the subjects of interest, the powers of E are expressed as following; E = E Sin wt o e2 = e2 .(l.-oos 2wt.) (37) O 2 ^4. _ „4 (3-4 cos 2wt + cos 4wt) ~ o ------------- 8 Substituting equation 37 into equation 36 and arranging into harmonics; I(v,E) = Id.c. + Igw cos 2wt + I^w cos 4wt (38) 52 2 Id.c.(v,E) = Io exp(-CL|<||>|2 a )(1 - CL^ <1I > ^ — a 2 E 2 + . . . ) ( 3 9 ) IPw(v,E) = I exp (-CL | < | j > | 2 an)(— a?E2 + CL | < | 1 > j 2 e4 _ C2L2 I < 1 I > I ^ a2^ + . . . ) (HO) 2 UjjEi Jj C . I 4 w ( v > E ) = J o exp(-CL|<| | > | 2 a 0 ) C C L l g l l > ai.E^ + In practice the higher-than-second term of Id.c. and I2 can be neglected. The observable Id.c. and Ia.c. (e I- ) and their ratio can be written as follows: 2w Id.c. = K1Iq exp (-CL|<||>|2 a ) (H2) Ia.c. = K2Iq exp (-CL|<||>|2 aQ)» ( O L M M i + B 2 m S 0 ) ) u 2 E 2 ( 4 3 ) = rr- CLI -4 ^> ^ E(B F.S. + B„ S )u2E2 ( 4 4 ) Id.c. 2 m om 2 1 2m o where the and K2 are the instrumental constants. CHAPTER III EXPERIMENTAL 1. Instrumental The detailed description of the Instrument used In our laboratory for the purpose of studying EPS Is given in David A. Haner's doctoral dissertation (36) and N. J. Bridge, D. A. Haner, and David A. Dows' work on formaldehyde (39). The block diagram of the instrument is shown in Pig. 6. Two components, the preamplifier and the recorder were replaced with new ones. The new recorder is Sargent (46) model DSRG which has two adjustable pens on the same chart paper. Each pen is run by a separate channel so that two different variables can be recorded simultaneously. The new pre amplifier is to amplify the D.C. and A.C. signals from the photomultiplier. The schematic of the preamplifier is given in Pig. 7* It has three outlets; one for the D.C. signal, one for the A.C., and one for D.C. and A.C. signals together. Light produced by a mercury-Xenon compact arc lamp (528-B) (47) is predispersed into various orders through the fore-monochromator (N.J.B.) (48), 53 CELL EBERT F.M. EBERT M T . SPECTROMETER PRE. A M P. SIG. G EN EFS. REC. Pig. 6.— Block diagram of instruments. IOOK \W\r 6 0 0 K VvVv VvA/v GAIN 5M <VWv 'V W V vwv X 99o8^- + 15V OUTPUT D.C. 8t A.C. 5.1 K 15 V 2 7 0 OUTPUT ♦ 0.15/xF ■*» 0.15/xF ■*- 4 7 0 0 />F ♦ iCGO pr 5 0 0 pF 250 pF I0/3F 0.5 /x F ^ ! /xF RECORDER ABS E F S PAR +15 V - 5V OUTPUT <•)— l A.C. ONLY ui VJ1 56 "Ebert P.M." in the block diagram. The calibration patterns are given in Pig. 8. The lines show the maximum light intensities of the given order (in Roman numerals). The order sorted light enters the narrow slit and is dispersed in the one meter Ebert scanning spectrometer (model 78—-420 by Jarrel Ash Company (49)). This spectrometer is built with a replica grating from a master ruled by interferometric control. The grating has 7620 lines/inch, total ruled dimension of 7 inches by 3 inches, and blaze angle 59°• The dispersed and focused light goes out through the exit slit, which is identical in width to the entrance slit of the monochro mator. Both slits are framed in a ring so that their width can be controlled by a micrometer. The actual width of the slit was slightly off from the micrometer readings. The measured width and the micrometer readings are given in the following table 7- ■ The finely resolved light after the exit slit from the spectrometer goes into the electric field cell. The sample in the cell interacts with the light. This inter action varies with the A.C. electric field strength applied through the E.H.T. power supply (N.J.B.) and controlled by the Heathkit model AG-10 Sine-Square generator. The light is then transmitted through the Glan-Taylor type polarizer, procured from Karl Lambrecht, XX'" XX' XX ''~ x x " _ JLm mmMm mmMm mmMm XV'" ^ 4 0 0 \ 0 0 0 = 9 5 5 4 6 n u m b e r FIS' g.-F.K. 41SP ersi°n Pattern' 58 TABLE 7 ACTUAL SLIT WIDTH Micrometer Readings in y Actual Width in y Micrometer Readings in y Actual Width in y 0 3 60 50 5 5 70 59 10 10 80 67 15 15 90 75 20 19 100 on CO 25 22 120 100 30 26 140 115 35 30 160 132 40 35 180 150 45 38 200 165 50 43 Chicago, Illinois, to an EMI 6255-B photomultiplier. The multiplied signal is led to the preamplifier where the amplified A.C. and D.C. signals are separated. The D.C. signal is the time average transmitted light intensity for the given frequency and the A.C. signal is the variation of the transmitted light intensity due to the electric field effect on the molecules. The amplified D.C. signal was recorded on the strip chart and the amplified A.C. signal was led to a 59 Princeton Applied Research Corporation (PAR) Lock-in Amplifier3 Model J.B.5. The PAR was locked with the overtone of the electric field frequency in order to catch the A.C. signal which measures the change in transmitted light intensity caused by the applied A.C. electric field. The output from the PAR is led to the second channel of the recorder. 2. The Resolution and Focusing The theoretical resolution of the instrument for the eleventh order 5^60 A is 680,000. The criterion for the resolution of the spectrometer has been taken from David Garvin's (51) National Bureau of Standards Report. Approximate measurement on the isolated Hg 5460.776 & line shows the resolution to be 400,000. The minimum slit width for the practical diffraction limit (51) is 3.1y, which is almost equal to the slit width when the micrometer for the slit control is set to zero. The measured minimum slit opening was 3y as in table 7. The optimum region of the order wave length (nX) for the spectrometer is from 54,000 to 60,000, which is equivalent to machine number from 44,000 to 53s500. For the slit opening lOy to 50y with which the most of the EPS were taken the useful resolution was .1 cm ^ to -1 -1 .5 cm in the spectral range of 25j000 cm to For the measurement of the upper electronic state dipole moment of the CSg molecule, the EFS was taken at seventeenth order (in the band which has band origin 29,341.70 cm " * ■ ) and slit 20u; the J = 24 and 26 of the branch are clearly resolved at .26 cm-1. When a slit of 30y was used, the observable resolution of J = 10 and 12 lines of the branch is .36 cm-' * ' . Fine focusing of the Jarrell Ash spectrometer was done by adjusting the mirror position. The two bottom screws are fixed. The top screw is connected to a micrometer. The micrometer readings of the best focusing range for the various Hg isotope fine structures have been plotted versus the machine number in Fig. 9* With these Hg emission lines the calibration between the machine number and the order wave length was found and is shown in Fig. 10. The Hg lines used for the focusing and the correlation between machine number and order wave length are listed in table 8. The Arabic numbers on Fig. 8 and Fig. 9 indicate the corresponding Hg lines in table 8. 45,000 5 0 ,0 0 0 B A CK FOCUSING (in p) Pig. 9.— Back focusing versus machine number. M A C H IN E NUM BER (in thousands) 62 45 c. 55 60 ORDER W A V E LENGTH (in thousands) i Pig. 10.— Machine number vs. order wave length. r 63 TABLE 8 Hg LINES FOR FOCUSING § Order nX A Machine # 1. XV 3654.83 54822.45 44942 2. XV 3663.28 54949.20 45127 3. XVIII 3125.66 56261.88 47091 4. XVIII 4358.34 56658.42 47703 5. XVII 3341.48 56805.16 47932 6. XIV 4077.81 57089.34 48382 7- XVI 3650.15 58402.40 50533 8. XVI 3654.83 58477.28 50657 9. XVI 3663.28 58612.48 50888 10. XIX 3131.55 59499.45 52443 11. XI 5460.73 60068.03 53480 S+2 1 • Rotational Analysis of £n Vibronic Band S+2 The calibration of the vibronic spectrum was done by using the Iron emission lines produced by an Iron Hollow Cathode (Westinghouse,- Ne gas filled). The Iron' lines 3872.504 A and 3873-783 A in the 15th order appeared between J = 48 and 50 and between J = 22 and 26. Since the absorption spectra were taken in the 17th order every time, the fore-monochromator had to be changed to 15th order while the emission lines were appearing and changed back to 17th order afterwards. Since the wave lengths of the Iron lines were given in air they were corrected for vacuum in 15th order by using the Edlein formula (42) and converted into wave number units. Then the frequencies in 15th order are changed into the corresponding frequencies in 17th order. Knowing the difference 9-52 cm-’ * ' between the two frequencies and the chart distance 53-91 cm between the two emission lines, the whole spectrum of vibronic band was analysed and the frequency of each rotational absorption line was assigned as shown in table 9. The absorption spectrum with rotational structures is shown in Pig. 11 and the Portrat diagram is in Pig. 12. Through the Portrat diagram the band origin and the band head (P) were found to be 29241.84 cm-' * ' and 29235.45 cm-1. This particular band has been analysed by Douglas and Milton J 0 2 4 6 8 10 12 14 16 18 20 22 24 65 TABLE 9 ROTATIONAL LINE FREQUENCIES OF BAND P(J) R(J) J P(J) R (J) 29241.84 26 29237.42 29248.91 29241.29 42.32 2 8 37.15 49 .49 40.94 42.72 30 36.92 50.14 40.75 43.23 32 36.68 50.77 40.38 43.72 34 36.49 51.43 C\J o o 44 .25 36 36.26 52.07 39-61 44 .76 38 38.06 52.81 39.27 45.28 4o 35.95 53.45 38.96 45.85 42 35.30 54.30 38.59 46.38 44 35.64 55.08 38.29 47.00 46 35.45 55.98 38.01 47.57 48 35.45 37-68 48.29 50 35.45 CD O' ro. to o- 01" ABSORPTION Fig. 11.— Rotational structure of £o 66 band. Pig. 12.— Fortrat Diagram of ZQ band 68 (23), who found the band origin to be 292*11.70 cm 1 and by Kleman (9) has assigned the band head to be 29235-1 -1 cm In order to find the rotational constants B' and B" the conventional method was used. Since the combined relations (R(J-1)-P(J+1) )/(J+|) = 4b" + *ID(3J2+3J+1)/(J+|) (R(J)-P(J))/(J+|) = *JBr - *JD(3J2+3J+l)/(J+|) hold for the linear to linear poly atomic molecules as well as diatomic molecules and the upper bent electronic state of CS2 is close to linear, (R(J-1)-P(J+1))/(J+|) versus (J-l) (R(J) - P(J))/(J+1) versus J were plotted. As shown in Pig. 13 at the low J quantum number the points are scattered far away from the line *JB' and 4B'f. This phenomenon may be partly because at low J quantum number the spacings are so small that the rota tional lines overlapped one another and because of the instrumental resolution limit it may not be able to pick the right frequency of each rotational line. The centrifugal distortion constant D does not seem to show too much effect within the range of J <_ 50. 4B' = .4332 B ' = . 1083 I_JL ■ 4B"=.4259 B' =. 1065 ntjrh i — i— i— i— i—f — t — i — i— — J — i — i — I —1 — I —l — I — I —I — l — i— ■ — I — I — l — l — I — l —I — l —i — i — I — 1 i I I I I ■ » « « 1 ■ » ■ ■ 1 i t i i 5 10 15 20 25 30 35 - 40 Fig. 13.— Combination relations of R and P branches. 70 Through the combination relation plot the rota tional constants Br and B" were obtained and their values were .1083 cm ^ and . 1065 cm ^ respectively. The least square fitting of the listed data in table 9 gives B' = .1081 ± .0003 and B" = .1063 ± .0003 cm-1 respectively and D is approximately 0.l65if10-^ cm"1 from the equation (28) v = vQ + (B'+B") m + (B’-B") m2 - 4 D m3 where m = -J for P branch and m = J+l for R branch and D" was approximated as D’ and the symbol D used for both centrifugal distortion constants of upper and ground states. 4. Electric Field Measurement The high voltage sine wave with variable amplitude and resonance frequency was applied to the electric field cell through E.H.T. power supply to which the different frequency and amplitude sine waves were input by a Heathkit Sine-Square Generator, model AG-10. The resonance frequencies were around 190, 219* 253, 279, and 332 cycles/sec. Among them 190 and 219 cycles/sec. provided high enough voltage to produce EFS of CSg molecules. Calibration of the electric field strength meter readings of E.H.T. power supply was necessary for the two resonance frequencies in order to know the voltage difference between the two plates in the cell. The high voltage was measured on an oscilloscope (Hewlett-Packard Company Model hp 122A) through a voltage divider and a high voltage probe (Tektronix Inc. 010-0178-00). The measured voltages were divided by the meter readings in order to get the multiplication factors. Plotting the multiplication factors versus meter readings, straight lines were obtained; these lines were used to obtain the voltage applied to the electric field cell. The experimental data and the plottings are given in table 10 and Pig. I1 ! . 5. EPS Signal Versus Sd-2 The EPS of J = 30, 32, and 34 of io vibronic band were taken over a range of electric field strengths from 19-7 KV/cm to 26.4 KV/cm. In order to observe the variation of EPS signal with respect to different electric field magnitudes, the positive to negative EFS peak differences of J = 30, 32, and 34 were recorded. The above three EPS peak to peak signal strengths are almost the same experimentally as well as theoretically, differences being masked by experimental noise; the average peak to peak signal is given in table 11. 72 TABLE 10 E.H.T. POWER SUPPLY METER CORRECTION Meter Readings Resonance Frequency Calibrated Multiplica- Voltage tion Factor 13-7 KV 12.9 10.9 9.9 8.8 219 C./S. 219 218 218 218 21.0 KV 2 0.0 17.5 16.0 16.0 1.53 C./S. 1.55 1.61 1.62 1.65 16.0 1*1.9 13.7 13.1 12.1 11.0 189 190 190 190 190 190 2*1.5 23.0 22.0 21.0 19.5 18.5 1.53 1.5k 1.60 1.60 1.61 1.68 "Note that the applied voltage is expressed as peak voltage and the meter reading is rms voltage." M ULTIPLICATION FACTOR 2.0 1.5 219 cycles/sec x 190 cy cles/sec O L 1.0 I I I I I ! I I J I I L 0 5 10 METER READINGS 15 20 Fig. 14.--Calibration of E.H.T. power supply, i ■ > 74 TABLE 11 EFS PEAK TO PEAK SIGNAL STRENGTH E Meter 12 13 14 15 16 17 17.5- 18.2 E KV/cm 19.7 20.9 22.0 23.2 24.3 25.4 25.7 26.4 Av. p. to p. Diff. of EPS 69.0 63.2 64.0 79.4 81.6 88.8 96.8 88.6 The average signal strengths of the above table, with the maximum and minimum signal strength at each electric field strength,indicated by the up and down arrows, are plotted versus electric field squared in Pig. 15- A solid line is drawn from the origin through the average points. The average signal strength shows a linear relation with the electric field squared except the points are scattered a little bit. This linearity of signal strength versus electric field squared proves that the higher-than-E terms in the equations 39, 40, and 41 can be disregarded and equations 42, 43, and 44 are applicable to a good approximation. E F S STRENGTH (arbitrary units) Fig. 15.— EFS dependence of field square. 6. Kg/K^, Instrumental Constant Ratio Determination The Instrumental constant ratio K2/K-L has been determined by using a mechanical chopper in front of the fore-monochromator to chop the initial beam and measuring the intensities of light through D.C. and A.C. channels where the A.C. channel was locked on the chopper frequency and the other Lock-in Amplifier conditions are given in table 12. The measured intensity ratio Ia.c./Id.c. can be expressed in the following equation: T/2 Ia K2 1/T Io Sin (211 t/T)dt o Id.c. K1 Io/2 K2 2 k x n The chopped light was approximated as a square wave because the shape shown on a scope was square except some photon noises. The measured intensity ratio was 28.5/69*5 and after correction for the PAR gain and the recorder i r span voltage, the 2/K-^ is 80.6, under conditions of the EPS experiment. 77 TABLE 12 INSTRUMENTAL CONDITIONS FOR K2/K.. DETERMINATION PAR Gain Recorder Span in mV la. c. Id.c. Instrumental Conditions for EFS .05 20 20 Instrumental Conditions for la.c./Id.c. .001 50 20 7. Determination of CL|<|(>I^ The product of three quantities: C a quantity introduced in Chapter I; L the length of the cell; and p |<||>| the square of the transition moment of vibronic part was obtained from the rotational absorption lines. The transmitted light intensity is expressed as I = Io exp (- CL |< 1 1 > I 2 Z B * S ). At a rotational line ^ 1 11 1 m om o center where SQ = 1/H b, b = .136 cm"'1 ' (the observed line half width at half height), E B is a computed m om value, and the transmittance I/Io is measurable. Now CL j <||>|2 is expressed as CL|< j|>|2 = log (Io/I)/(E SQ* 0.43429). The average value for the three rotational lines resulted to be 0.272. 8. EPS Peak Frequency Determination The EFS strength of carbon disulfide for a given rotational line is to be determined with two components, SQ shap.e (Lorentzian line shape) and its first derivative S-^ shape such as : Y = A S +BS, o 1 where A and B are the proportionality constants, which are A = Z B„ and B = Z F„ in the theory, m 2m m om 2 Rewriting the above equations: y = — A + 1 -2xB pip p p nb x +1 nb (x +1) where x = (v-v )/b is the frequency variable and b is the half width of the rotational absorption line at half height. The first derivative of the above equation is: r - — 2 A 3 U 3 - 3 ( | j ) X 2 + X + I j ] nb (x +i) A0 RD Solving the part in brackets [ ] the x values such that Y1 = 0 were found for J = 30, 32, and 3^* Taking the line half width at half height b = 0.136 cm 1 for J = 30, 32, and 3^5 the frequency separations from the rotational line center for EFS peaks were calculated and are shown in the following table. 79 TABLE 13 EFS PEAK SEPARATION FROM J = 30 32 34 V o X + peak 29250.133 • 555 29250.773 .556 29251.422 .555 X - peak -.598 -.596 -.599 v-v 0 + peak 0 -j .07 6 .076 v-v o - peak -.081 -.081 CM CO O 1 The actual EFS, however, is the product of Y and exp (- CL I<I I>I 2 I B * S ). The theoretical frequency i ii i m om o separations from rotational line center are slightly increased. The computed separations are .083 and .096 cm-1 for the positive and negative EFS peaks of the three rotational lines. The experimental EFS peaks for J = 32 show at .05 cm-' 1 ' and -.23 cm"^ from the rotational line center. These deviations are due to the too slow time constant applied on PAR as shown by reversing the direction of scan. The 0.2 cm-' 1 ' resolving power of the instrument 80 is also expected to broaden the line. 9. Heights of the Peaks The positive and negative peaks for a given rotational line are slightly different. The reason is that one of the peaks has an addition of and SQ shape contributions and the other has the difference between and S shape contributions, o Half of the peak to peak distance of the signal for the given rotational line was taken as Ia.c. signal for both peaks and Id.c. was taken for transmittance at the point where the positive peak appears. The observed values of Ia.c. and Id.c. and their ratio Ia.c./Id.c. are given in the following tables. TABLE 14 Id. c. 15.0 15.7 15.7 Id. c . 81 TABLE 15 la.c./Id.c. E Meter E Corr. I = 30 32 34 la. c. la. c . la. c. la. c. la. c. Ia.c. Id .c . Id. c. Id.c. 12 19-7 3.85 .245 3.75 .239 2.35 .149 13 20.9 2.65 .169 3-55 .226 3.25 .207 14 22.0 2.75 .175 3-50 .223 3.25 .207 15 23.2 3.85 .245 3.65 .232 3.95 .252 16 24. 3 3-70 .236 4 .85 .308 3.65 .232 17 25.4 3.80 .243 5.15 .328 3-90; .249 17-5 25.7 4.25 .261 5.35 .341 4.55 .290 18.2 26.4 4.90 .312 4.25 .271 4.15, .264 CHAPTER IV OBSERVATIONS AND DISCUSSIONS 1. Upper Electronic State Dipole Moment Prom equation 44 of Chapter II and the experimen- K 9 tally determined values of 2/KE, CL[< f[>| , and b and the computed values of E B Fn and £ B~ the m om 2 m 2m dipole moment of upper electronic state " ' ‘ Bg was determined. Since there are positive and negative peaks for each rotational line, the sum of Sn and S and the 1 o difference of S^ and Sq shapes were used to get u+ and u_. The final average dipole moment is concluded tn be u = .093 Debye. The calculated results are given 8.V G * in the following table. This allows a check calculation that the Stark shifts of carbon disulfide for M = 0 of J = 32 and E = 50 KV/cm will be about .36 * 10 ^ cm ^ _ U Z and for M = 32 about .54 * 10 toward the higher energy side from the original energy level. 2. EFS of the Various Vibronic Bands EFS of the various types of vibronic bands were searched for the absorption region from 3200 A to 3800 A. 82 83 TABLE 16 UPPER STATE DIPOLE MOMENT J = 30 32 34 E u+ u- u av. u+ u- u av. u+ u- u av. 12 .108 .119 .113 .106 .119 .113 o\ CO 0 .097 .094 13 .085 .094 .09 0 .097 .106 .102 .098 .108 .104 14 .082 .090 .085 .093 .100 . 096 .095 .103 .099 15 .093 .102 .097 .091 .097 .095 .104 .114 .109 16 . 0 8 6 L T V C T V O .091 .098 .107 .102 .090 .098 .095 17 .084 .093 .089 o VO -J .106 .102 .090 .097 .094 17-5 .086 .095 .091 .098 .107 .103 .095 .105 .100 18.2 .091 .097 .094 . 085 .098 .092 .089 .096 .093 The total u average Is .093 Debye, with a precision of about .01 Debye from table 16. 84 The very intense V system which spans 3200-3300 A has not shown any significant EPS except a few irregular signals. Most of the U bands have been tried, but no recognizable EFS were observed except in U.^, which seems to have a resemblance to a £ type band. EPS taken for both polarizations along with absorption spectra are shown in Pigs. 16 and 17- A number of £ type bands have shown definite S+3 S+2 1,7 0,9 1.5 0,10 EPS. They are £o, £o, £o, £o, £o, and Eo . S+4 S+l S+2 S+l Besides the above £ type bands £o, Eo, £2, £2, S 1,8 0,10 2,5 2,4 0,8 0,7 1.4 1,7 £ 2, Eo, £o, £o, £o, £o, £o, £o, £2, 0,9 0,6 £o, and £o were tried but EFS were not obvious. With better tuned instrumental conditions one may observe a few more EPS among those of unobvious bands and for longer wave length bands. £ type band EPS are all alike and the typical ones are shown in Pigs. 18 and 19 for S type and Pig. 20 and Pig. 21 for R type. S+2 S+l 0,9 Among H type bands HI, HI, and ni have S 0,10 1,7 1,6 shown obvious EFS but HI, ni , HI, and III EPS were not so definite and yet they show some indication of EPS. It would be worth trying those bands with better tuned instrumental conditions. No evident EPS were 0,8 1,5 observed for ni and Hi bands. There were no 85 ABSORPTION Pig. 16.— EPS j_ and absorption spectra. (Frequency increases downward) 86 ABSORPTION Pig. 17.— EPS // and absorption spectra. (Frequency increases downward) 87 M + ABSORPTION 12 to S+2 Pig. 18.— EPS of Eo J_ and absorption spectra. (Frequency increases downward) ABSORPTION Fig. 19.— - ' + 12 « S+2 • -EFS of So // and absorption spectra (Frequency increases downward) ABSORPTION 89 20 ro - 0,9 Fig. 20.— EFS of Eo _L and absorption spectra. (Frequency .increases to left) 90 0,9 Pig. 21.— EPS .of So // and absorption spectra. (Frequency increases to left) 91 noticeable resemblances between structures of different H S+2 type bands. Ill EPS along with the absorption spectrum is shown in Figs. 22 and 23* S+2 S+l S 0,6 For A type bands, A2, A2, A2, and A2 S+2 were tried. Only A2 showed evidence of EFS. For other bands it would be worth trying over again with better instrumental conditions before concluding whether they have EFS or not. 1,5 < ( > 3 was attempted, but no recognizable EFS was observed. Since this band is located above 3600 A, to be more exact 3672.17 A, the absorption itself was not too strong and naturally the rotational lines are not so clearly- resolved as in the shorter wave length bands. In order to improve the EFS signal, a few things are suggested: 1) There must be a more stable and higher voltage supplied for the electric field, and 2) a stronger and shorter wave length light source will give a great deal of help. 3. QEFS and Polarization Intensity Ratio 0 S+2 The forbidden Q branch of the So band of CSg has shown a particularly strong EFS signal in parallel polarization of the light and negligible in perpendicular 92 ABSORPTION S+2 Pig. 22.— EPS of IIo J_ and absorption spectra. (Frequency increases downward) 93 ABSORPTION S+2 Pig. 23.— EPS of III // and absorption spectra. (Frequency increases downward) polarization while the absorption spectra show no change for the two polarizations. 0 3+2 Besides the Q EFS of So band, the EFS intensity ratio of perpendicular to parallel polarization has shown rather unusual variation for various vibronic bands. Because of the unsteady electric field strength the quantitative picture was not revealed but the polariza tion intensity ratio, perpendicular to parallel, has shown rather interesting qualitative features. The observed results are shown in the following table. TABLE 17 EFS STRENGTH RATIO OF J_ T0 // POLARIZATION Vibronic S+2 S+3 0,9 S + 2 0,9 S+l Bands Eo Uiu So Eo ni III A5 1/1 1 Ratio 2.0 2.0 1>II .7 2.0 .7 !>l 1 In general, the S system shows j_/\\ to be almost 2 and the R system shows 0.7* U-^ may be classified as S system if this ratio is the character istic of each system. 95 This interesting phenomena also appeared in the EPS of propynal studied by Roddy M. Conrad and David A. Dows (40) in our laboratory. In their work, the EPS intensity ratio of perpendicular to parallel polarization p T O £T was far larger than 1 for PK and R4 bands and far P less than 1 for Q K. This may lead to a generalization of Q (AJ = 0) EPS being parallel polarized. 4. EPS Sign Change and Possibility of A1 Determination Plotting the computed results of SB P„ and m °m ^ £ B0 versus J as shown in Pigs. 24 and 25 > the rather m curious high values of E B„ and sign change for m SB Fn at J = 18 gave rise to questions whether the m om 2 EFS sign change at J = 18 or particularly high induced effect at the point play the major role in the EPS. Indeed, in the experiment, there is a rather unusual shape at J = 18 and J = 20, the shape of EPS at J less than 16 are shown inverted from the shape of EPS of J S+2 larger than 20 in SO band. The choice of J = 30 - 34 for dipole measurement was in part to avoid this anomalous region. Prom the Stark shift formula, equation 27 of Chapter II, if K _> 1, F^ = «>, when 2B’J = (AT-BT) (2K+1) and 2B'(J+1) = (A'-B1)(2K-1). If K = 0, F2 = < » when 2B'J = A'-B'. These tell us that for the 5xl05 4xl05 3xlOS 2xl0S I x 105 £BomF« m * -IxlO5 -2 x l0 5 -3xlO S -4 x l0 5 -5xlOS I I I I I I I I I I L 16 18 20 22 24 26 28 30 32 34 J ON -2x10 -4x10 SB 2m -6xl05 -8x10 -10x10 Pig. 25.— 2 B0 versus J. m 2m 98 band K _ > 1 there will be two places where the EFS changes sign. But for the band K = 0, the E type band, only at J = (A,-B')/2B’ the EFS signal changes sign. For the S+2 Eo band, the sign changes at J = 18 as mentioned above. This phenomena leads to a new way of determining the rotational constant A' when B’ is known. In practice the crossing point was observed to be J = 18 (in this work) and when B' = .1081 cm 1, A' =4.0 cm-' * ' and if (23) B' = .1129 cm A' = 4.176 cm compared to 4 3 cm-1 DouSlas anci Milton (23). When the induced part B2m acts the major role in the EFS, E B0 = “ when 2B’ (J+l) = A'-B’, or m ^ J = (A'-B1)/(2B'-l), This causes the shape change such that the positive peaks which occur at higher frequency than the rotational line center are bigger than negative peaks. The positive peaks are supposed to be bigger than the negative peaks for the whole band. And particularly around J = 18 - 20, the positive peaks are supposed to be much bigger than negative peaks. Indeed, the experiment shows that the positive peaks are mostly bigger than negative peaks and around J = 18 - 20 the positive peaks are eminently bigger than negative peaks for the both P and R branches. Again, this phenomena indicates that the proposed approximation of EFS line shape is acceptable without going to any further expanded terms. CHAPTER V CONCLUSIONS EFS of carbon disulfide have been used to study the second order Stark shift due to the dipole moment lying perpendicular to the symmetric top axis. The measurement of the dipole moment on the b axis of the bent excited state B2 of the molecule has been accomplished through the ratio of EFS line strength versus the transmittance of light. This method can be extended to any ABA type triatomic molecule unless the bent angle is smaller than 125° in which case asymmetry will be important, and to any symmetric or near symmetric top molecules with dipole moment perpendicular to the top axis. The polarization intensity ratio of EFS has been observed to be a characteristic of roto-vibronic bands and its theoretical study is suggested to be very significant in order to understand the polarized light interaction with the polar molecular motions in the electric field. Also, EFS sign change has been noticed along the progression of J of band as predicted in the theory. If this sign change occurs at different places 99 100 according to the vibronic bands, it may be helpful not only to determine A', the rotational constant along the top axis, when B’ Is known, but also to classify the vibronic species of the various bands. At present R, S, U system multiplicity and complete vibrational analysis of the upper electronic 1 S state Bp from the (H )J erg configuration or perhaps ^ o - 3 Q the Bp component of Ap state, presumably from I I ^ Hu configuration, remains in question. The V-system remains as intense spectra with a untouchable curiosity except a few very weak EPS by Roddy M. Conrad (40) and weak magnetic rotational spectra by Barton Palatnick (27) indicating an almost linear or slightly bent state. A more detailed study of Zeeman effect and more careful examination of overall EPS of various vibronic bands may be helpful to understand the upper electronic state nature. REFERENCES 1. G. D. Liveing and J. Dewar, Proc. Roy. Soc. London, 353 71 (1883). 2. E. D. Wilson, Astrophys. J., 50, 155 (1919) - 3. J. Pauer, Ann. Physik, 61, 363 (1897). 4. I. M. Pauly, Astrophys. J., 69, 34 (1929). 5. W. W. Watson and A. E. Parker, Phys. Rev., 37> 1013 (1931). 6. P. Kusch and F. W. Loomis, Phys. Rev., 55, 850 (1939). 7. W. C. Price and D. M. Simpson, Proc. Roy. Soc. London, A 165, 272 (1938). 8. C. Ramasastry and K. R. Rao, Part I, Indian J. Phys., 21, 313 (1947); Part II, Proc. Natl. Inst. Sci. India, A 18, 177 (1952a); Part III, Proc. Natl. Inst. Sci. India, A 18, 621 (1952b). 9. Bengt Kleman, Can. J. Phys., 4l, 2034 (1963). 10. A. E. Douglas and I Zanon, Can. J. Phys., 42, 627 (1963). 11. H. C. Allen, E. K. Plyler, and L. R, Blaine, J. Am. Chem. Soc., 78, 4843 (1956). 12. A. H. Guenther, T. A. Wiggins, and D. H. Rank, J. Chem. Phys., 28, 682 (1958). 13. R. C. Lord and J. K. McCubbin, Jr., J. Opt. Soc. Am., 47, 689 (1957). 14. C. R. Bailey and A. B. D. Cassie, Proc. Roy. Soc. London, A 132, 236 (1931). 15. D. M. Dennison and N. Wright, Phys. Rev., 38, 2077L (1931). 101 16. 17. 18. 19. 20. 21. 2 2 . 23. 24. 25. .26. 27. 28 . 29. 30. 31. 32. 33. 102 P. Krishnamurti, Ind. J. Phys., 5, 105 (1930). S. C. Sirkar, Ind. J. Phys., 10, 189 (1936). B. P. Stolcheff, Can. J. Phys., 36, 218 (1958). P. A. Jenkins, Astrophys. J., 69, 34 (1929). L. N. Lieberman, Phys. Rev., 60, 496 (1941). R. S. Mulliken, Can. J. Chem., 36, 10 (1958). D. A. Walsh, J. Chem. Soc. London, 2266 (1953). A. E. Douglas and Earl R. V. Milton, J. Chem. Phys., 41, 357 (1964). Jon T. Hougen, J. Chem. Phys., 4l, 363 (1964). R. A. McFarlane, Appl. Optics, 3> 1196 (1964). P. K. Cheo and H. G. Cooper, J. Appl. Phys., 36, 1862 (1965). Barton Palatnick, Ph.D. Dissertation, Columbia University (1968). Molecular Spectra and Molecular Structure, Vol. I, Spectra of Diatomic Molecules, G. Herzberg, D. Van Nostrand Company, Inc., Princeton, New Jersey (1964). Y. Tanaka, A. S. Jursa, and P. J. Le Blaine, J. Chem. Phys., 28, 350 (1958). J. Kleinberg, W. J. Argersinger, Jr., and E. Griswold, Inorganic Chemistry, D. C. Heath and Company, Boston, p. 86. C. H. Townes and Schawlow, Microwave Spectroscopy, McGraw Hill Book Co. (1955). S. C. Wang, Phys. Rev., 34, 243 (1929). G. R. Wilkinson, Department of Physics, King's College, London, unpublished results. 103 34. Della Agar, Earle K. Plyler, and E. D. Tidwell, J. Res. Natl. Bur. Std., 66a 3, 259 (1962). 35- R. S. Mulliken, Phys. Rev., 60, 506 (1941). 36. David A. Haner (David A. Dows), Doctoral Dissertation, University of Southern California (1968). 37* David A. Haner and David A. Dows, J. Chem. Phys., 49, 601 (1968) . 38. David A. Dows and A. D. Buckingham, J. Molec. Spec., 12, 189 (1964). 39- N. J. Bridge, D. A. Haner, and David A. Dows, J. Chem. Phys., 48, 4196 (1968). 40. Roddy M. Conrad (David A. Dows), Doctoral Disserta tion, University of Southern California (1968). 41. Leonard I. Schiff, Quantum Mechanics, McGraw-Hill Book Company (1968), p. 247- 42. Edlein, Bengt, J. Opt. Soc. Am., 43, 339 (1953)- 43. G. Herzberg, Electronic Spectra of Poly Atomic Molecules, D. Van Nostrand Co., Inc. (1966), p. 601. 44. G. Herzberg, Infra Red and Raman Spectra of Poly Atomic Molecules, D. Van Nostrand Co., Inc. (1964), p. 276. 45. M. W. P. Stranberg, Microwave Spectroscopy, Methuen, London (1964). 46. E. H. Sargent and Co., 4647 W. Poster Ave., Chicago, Illinois. 47. Enghard Hanovia, Inc., Hanvia Lamp Division, 100 Chestnut St., Newark, New Jersey 07106. 48. N. J. Bridge, Department of Chemistry, University of Kent, Canterbury, England. 49. Jarrell-Ash Company, 26 Pawell St., Newtonville 60, Massachusetts. 104 50. John R. Lombardi, David Campbell, and William Klemperer, J. Chem. Phys., 46 , 3482 (1967) - 51. David Garvin and Edward L. Weiss, Natl. Bureau of Standards Report 8643* 52. N. M. Gailar and E. K. Plyler, J. Res. Natl. Bur. Stds., 48, 392 (1952). 53* John R. Lombardi, J. Chem. Phys., 48, 348 (1968).

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Creator Jung, Hyun Chai (author)

Core Title Electric field induced spectra of carbon disulfide and its dipole moment in an excited state

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Chemistry

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry, physical,OAI-PMH Harvest

Language English

Advisor Dows, David A. (committee chair), Porto, Sergio P.S. (committee member), Segal, Gerald A. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-500390

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