University of Southern California Dissertations and Theses

Structural Studies Of Selected Boron-Carbon Compounds

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Structural Studies Of Selected Boron-Carbon Compounds

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Content CHEUNG, Ch.un-Ch.ung Stephen, 1937- STRUCTURAL STUDIES OF SELECTED BORON-CARBON COMPOUNDS. University of Southern California, Ph.D., 1970 Chemistry, physical U niversity Microfilms, Inc., A nn Arbor, M ichigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED STRUCTURAL STUDIES OP SELECTED BORON-CARBON COMPOUNDS by Chun-Chung Stephen Cheung A Dissertation Presented to the FACULTY OP THE GRADUATE SCHOOL UNIVERSITY OP SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OP PHILOSOPHY (CHEMISTRY) January 1970 UNIVERSITY O F SO U TH ER N CALIFORNIA TH E GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 9 0 0 0 7 This dissertation, written by ....Q hun_7_C hun£^ .............................. under the direction of h..\3... 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 T >?1 O Dean Date. DISSERTATION COMMITTEE Acknowledgments I wish to express my appreciation to Professor Robert A. Beaudet for his guidance and encouragement of this work and to Professor G. A. Segal for his help in the studies of carboranes with CNDO/2 molecular orbital theory. I also wish to thank G. B. Dunks and Professor M. P. Hawthorne for generously giving me the sample of CB^H^ » and Dr. R. E. Williams for many helpful dis cussions about carboranes. Acknowledgment is due the Computer Sciences Labora tory of the University of Southern California for use of its computers and for free computer time. ii Dedication To my wife, and my parents. iii TABLE OP CONTENTS CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. APPENDIX I. APPENDIX II. BIBLIOGRAPHY INTRODUCTION................................... 1 MICROWAVE SPECTRUM, STRUCTURE AND DIPOLE MOMENTS OP 2-CARBAHEXABORANE(9), CB5h9 ........................................ 4 A. Introduction......................... 4 B. Experimental......................... 8 C. Spectrum............................. 9 D. Stark Effects and Dipole Moment 20 E. Structure............................ 23 MICROWAVE SPECTRUM OP CD,BF„.................. 27 3 2 A. Introduction......................... 27 B. Experimental......................... 29 C. Spectrum and Results................. 29 THE STUDY OP THE MICROWAVE SPECTRUM OP DIMETHYL BORON FLUORIDE.................. 36 A. Introduction......................... 36 B. Theory............................... 38 C. Experimental......................... 43 D. Spectrum............................. 43 COMPUTER PROGRAM VSIX FOR SIXFOLD BARRIER INTERNAL ROTOR PROBLEMS............ 53 A. Introduction......................... 53 B. Theory............................... 55 STUDY OP SEVERAL POLYHEDRAL CARBORANES BY CNDO/2 MOLECULAR ORBITAL THEORY......... 67 A. Introduction......................... 67 B. CNDO/2 MO Theory.................... 79 C. Calculations......................... 81 D. Discussion........................... 91 COMPUTER PROGRAM QFIT......................... 99 COMPUTER PROGRAM VSIX......................... 102 ................................................. 107 iv LIST OP TABLES Table Page 1. The rotational constants of the eight major species of 10 2. R-branch transitions for the normal species ..... 12 3. R-branch transitions for the ^B(3) species ..... 13 4. R-branch transitions for the ^B(4) species ..... 14 5. R-branch transitions for the '^B(l) Species ..... 15 6. R-branch transitions of four doubly- substituted species ............................. 16 7. K=2<-3 band Q-branch transitions for normal species........................................... 18 8. Atomic coordinates from Kraitchman equations 23 9. Bond lengths ..................................... 24 10. Assigned transitions for CD^^^BPg m = 0 state.... 30 11. Constants determined for CDj^BF^ and CH51XBP2 ................ ?....f................. 33 12. Comparison of the calculated rotational constants with the experimental values......... 35 13. Q-branch transitions with clear second-order Stark effects............................... 47 14. Q-branch transitions with clear first-order Stark effects............................... 48 15. Structural parameters and dipole moments predicted by CNDO/2 calculations............... 71 16. Energy comparison................................... 83 17• The prediction of the valence electron densities....................... 84 18. Structural parameters of pentaborane........ 88 v LIST OP FIGURES Figure 1. Geometry of ...................... 2. Symmetry plane of ............... 3. Geometry of CD^BFg..................... 4. Geometry of acetone-type molecule.... 5. The infinite^- matrix for each pair of J and M. 6. Simplified matrix with interconnected elements....................................... 7. Matrixafter Wang's transformation) | m | = 3 + 6n elements............... for 8. Matrix J=f (after Wang's transformation) odd K, |m| = 6n elements............ for 9. Matrix (after Wang's transformation) even K, |m| = 6n elements........... for 10. Labeling convention for polyhedral carboranes.. 11. Structure of pentaborane.............. 12. Two possible rearrangement mechanisms for °2B4H6.......................................... 13. -2 Optimized intermediates for BgHg isomerization........................ 14. A comparison of rearrangement barriers C B L and B^H,-.................... 2 4 6 6 6 for 15. dsd rearrangement...................... Page 7 26 28 39 57 58 60 61 62 69 77 78 89 90 97 CHAPTER I INTRODUCTION After the determination of the structures of several boranes (boron hydrides), boron chemists began to speculate about the possibility of a large number of mixed boron-carbon hydrides. It appears that the first evidence of the existence of these boron-carbon hydrides was obtained in 1953 by Landesman and Shapiro'*' when they ignited mixtures of diborane and acetylene with a hot wire. Molecules with appparent molecular formulas of C B,H_, C B.H and C_B_H were detected among the products. d 3 d d 4 y d $ z 2 Later, Keilin subjected pentaborane and acetylene mixtures to a silent electric discharge and produced a number of carbon- 2 boron-hydrogen compounds. In 1956, Good and Williams repeated the Bj-H^-CgH^ synthesis. They isolated several products and identified the empirical formulas of C„B,H_, C_B_H„ and two 2 5 3 2 5 I isomers of C^B^Hg. These compounds were given the name carboranes. Since then, a very large number of carboranes have been discovered. A very thorough discussion of boron chemistry 1. H. Landesman and I. Shapiro, unpublished work. 2. B. Keilin, unpublished work. 3. C. D. Good and R. E. Williams, U. S. Patent No. 3030289 (1959). Chem. Abst. 21, 12534b (1962). 1 2 has been given by Lipscomb^. A more recent discussion of the 5 progress of carborane studies has been prepared by Williams. Boranes and carboranes form a very special class of compounds. Their structures, being very different from non- boron compounds, are almost unpredictable. The number of pairs of valence electrons in a molecule is normally much smaller than the number of bonds. Bridge hydrogens are often present. Carbon atoms are frequently bonded to five or six other atoms while boron atoms are normally bonded to five or six other atoms. In short, the valence electrons are so delocalized that these molecules may be considered as "superaromatic" systems. The structures of these highly irregular molecules can be expected to affect their chemistry. Mass spectroscopy, 11 B-nmr, infrared spectroscopy, X-ray diffraction, electron diffraction and microwave spectroscopy have been used to obtain structural information, and molecular orbital theories have been applied to study the electron delocalization. It is very conceivable that in the near future, general rules applicable to the chemical and the physical properties of all these compounds will be discovered. It is towards this goal that this author has devoted his dissertation research. 4. W. Lipscomb, "Boron Hydrides" (W. A. Benjamin, Inc., New York, 19&3)• 5. H. E. Williams, "Carboranes", manuscript to be published. The microwave spectra of a new carborane (CB-H.), a 5 9 molecule with a sixfold barrier to internal rotation (CD BF ), 3 2 and a double-top molecule dimethyl boron fluoride, were studied. A computer program was written to treat the rotational spectra of a molecule with a sixfold internal rotation barrier. A molecular orbital theory CNDO/2 developed by Pople and Segal was used to study several systems of carboranes. Two proposed mechanisms^ for the isomerization of cis C^B^Hg to trans C^B^Hg were also examined with the CNDO/2 theory. 6. J. A. Pople and G. A. Segal, J. Chem. Phys. 44, 3289 (1966). CHAPTER II MICROWAVE SPECTRUM, STRUCTURE AND DIPOLE MOMENT OP 2-CARBAHEXABORANE (9), CBcHn 0 y A. INTRODUCTION One of the most useful results one may obtain from the study of the rotational spectrum of a molecule is the structural data derived from the comparison of the accurately determined moments of inertia (or rotational constants) of different isotopic species. More than one set of moments of inertia can be defined because of the zero-point vibrations. The equili- brium moments of inertia, I , are related to a structure with averaged positions of the vibrating atoms. The effective moments of inertia, 1°, obtained directly from the rotational spectrum, are averaged over the vibrational state. 7 Kraitchman has developed exact solutions for the molecular coordinates in terms of the differences in equilibrium moments of inertia upon isotopic substitution. Since I 's are very difficult to obtain, the experimental values of I°'s are normally used in the actual calculations. This is equivalent 7. J. Kraitchman, Am. J. Phys. 21, 17 (1953)• 4 5 to making the assumption that the changes in I 1s upon isotopic substitution are the same as the changes in I°'s. Costain® has shown that this is a better approximation than fitting structural parameters to the moments. Two boron isotopes, and ^B, exist in nature in the ratio of 1:4* Usually several ^B-substituted molecular species in a natural sample (non-enriched with *®B) are fairly abundant. The rotational transitions of these species can be assigned from the microwave spectrum of the natural sample. And the coordinates of the substituted B atoms can be determined. The positions of the H or the C atoms (if present) can also be 13 2 determined if C- or H-enriched samples are available. New boron compounds, carboranes in particular, are being prepared or discovered at a very fast pace. The structural information about these compounds are of great importance to the boron chemists. Previous microwave investigations have confirmed or determined the structures of several boron compounds including: Q in 11 To pentaborane , 1-methyl-pentaborane , BHP^ , * 8. C. C. Costain, J. Chem. Phys. J22., 864 (1958) • 9. H. J. Hrostowski and R. J. Myers, J. Chem. Phys. 2 2, 262 (1954). 10. E. Cohen and R. A. Beaudet, J. Chem. Phys. 4 8, 1220 (1968). 11. T. Kasuya, W. J. Lafferty and D. R. Lide, J. Chem. Phys. 4 8, 1 (1968). 12. R. A. Beaudet and R. L. Poynter, J. Chem. Phys. 41» 2166 (1965). 6 2,3-C2B4H613, 2-methyl-l,5-C2B3H414, 2-C1-1,6-C^H^5, and cb5h?16. A new carborane, CB^E^ (2-carbahexaborane) has been recently 17 prepared. Dunks and Hawthorne reported that the analysis of the 4^B-nmr spectrum indicated two pairs of equivalent boron atoms, three bridge hydrogen atoms and a boron atom at an apical position. The spectrum was considered to be consistent with the pentagonal pyramid shown in Fig. 1. A molecule with such a geometry should have a non-vanishing dipole moment. Hence, the pure rotational spectrum should be observable. The microwave spectrum of the sample was investi gated to determine the coordinates of the boron atoms with the intention of confirming or disproving the proposed geometry. 13. H. A. Beaudet and R. L. Poynter, to be published. 14. L. Li and R. A. Beaudet, to be published. 15. G. McKown and R. A. Beaudet, to be published. 16. G. McKown and R. A. Beaudet, to be published. 17. G. B. Dunks and M. F. Hawthorne, J. Am. Chem. Soc. ,20, 7355 (1968). 7 O Hydrogen Atom Carbon Atom Boron Atom FIGURE 1. GEOMETRY OF CBcH„ . 0 7 8 B. EXPERIMENTAL The sample of CB H. was provided by Dunks and Hawthorne. J 7 The original sample, after taking the ^B-nmr spectrum, had been kept in a sealed nmr tube at room temperature for several months. It was purified by fractionation before use in the microwave study. No impurity problem was encountered in the study of the rotational spectrum. In an attempt to determine the positions of the bridge hydrogen atoms, part of the sample was returned to Dunks for partial deuteration by hydrogen-exchange. The mass spectrum of 2 the new sample indicated the presence of one H atom per molecule. The microwave spectrum between 8.2 and 37 • 5 gHz was observed with a conventional 100 kHz Stark modulated spectrometer. Frequencies were measured by interpolating between standard frequencies with a Collins Model 51 S-l receiver. The standard frequencies were obtained by multiplying the output of a 1 MHz crystal in a Hewlett Packard Model 5245 L frequency counter with a General Radio standard frequency multiplier. The uncertainties of the measured frequencies were generally less than +0.1 MHz. The spectrum was studied at dry-ice temperature and at pressures between 10-40/U . For better resolution, certain stronger lines were measured at pressures below 2 JH. . 9 Dc biasing of the 100 kHz square wave was used to measure the Stark effects. The details are described in Sect. V in the discussion of the dipole moment and Stark effect. G. SPECTRUM The spectrum of 2-carbahexaborane(9) was extremely rich. Transitions have been assigned for the eight most abundant isotopic species (Table l). Relative intensities of the trans itions are in good agreement with the natural populations of the various species. The boron nuclear quadrupole moments were found to cause some line broadening in the low J transitions, but the effects were not large enough to be a problem for the study of the four major isotopic species. The Stark lobes were clearly resolved for a few of the c-type transitions, including all the J = 2*-l lines and some of the J = 3 2 lines of the three most abundant species. The lone lobes of the l(0,0)*- 0(0,0) transitions were observed for all the species listed in Table 1. Since the ^B-nmr spectrum indicated 2 pairs of equivalent B atoms, the molecule must have a plane of symmetry. Hence, the normal species and the ^B(l) species could have only two non-zero dipole moment components along the principal axes. Strong c-type and weak a-type transitions were actually observed and identified. The atoms C(2) and B(l) must be on the ac- 10 TABLE 1. THE ROTATIONAL CONSTANTS OP THE EIGHT MAJOR SPECIES OP CBcH„ 5 9 Isotopic Natural Rotational Constants Determined Species Abundance Prom the Spectra ($-age) (MHz) A B c Normal 35 5334.130 5296.895 3280.552 10B(3) 16 5449.072 5303.606 3324.585 10B(4) 16 5439.794 5317.759 3327.660 10B(1) 8 5378.323 5340.682 3280.482 A + B A - B c 10B(l) and 10B(3) 4 10849.10 147.50 3324.45 10B(l) and 10B(4) 4 10847.80 124.20 3327.70 10B(3) and 10B(4) 4 10880.90 ' 3371.59 ] 10B(5) and 10B(5) 4 10880.90 • 3373.3 3 J a. Uncertainties are + 0.050 MHz for A, B, C and +0.20 MHz for A + By A — By C. b. It is uncertain which constant belongs to which species. 11 plane. When B(3) or B(4) is isotopically substituted, B(l) and C(2) are no longer on the plane and non-vanishing values are 1 expected for all three dipole components. The JUL^ of the B(4) species was found to be large enough for the b-type transitions to be observed. The transitions 2(l,l)«-l(0,l) , 2(2,l)«- l(l,l) and J = 44-3 (with K»4*"3) were used to determine the rotational constants for the four major species. The assigned H-branch lines are listed together with the calculated values in Tables 2-5. Some of the larger discrepancies are due to the diffi culty in determining the frequencies of accidentally overlapped lines. In the cases of the four "4?^ species", the low J transitions were very weak and broad. Only three low J H-branch transitions were assigned for each of these species ( See Table 6). The assignments were based on the Stark effects. The J = 1<-0 lines showed single, clear but broad lobes, while the J = 4«-3 and the J = 5<-4 lines showed extremely fast symmetric Stark effects. Unfortunately, the frequencies of these transitions were only sensitive to C and A+B. ■ As a result, only two constants could be determined accurately from these R-branch transitions. Also, A-B was estimated for two of these species from high K Q-branch transitions (K = 7<r-Q and 8 <-9 bands) without considering the centrifugal distortion effects. Seven Q-branch bands were found to be in the frequency range of our instrument (K = 2<-3 up to K = 8«~9)« The K = TABLE 2. R-BHANCII TRANSITIONS FOR THE 12 NORMAL SPECIES Transitions Obs. (MHz) Frequencies Cal. (MHz) Obs.-Gal. (MHz) c-Tyne 1(1;C)-C (0 ,0) 1CC51.15 10631.03 0.12 2(2,1)-1 1,1) 21299.29a 21299.29 0.00 2(l»l)-1 0,1) 21224.82a 21224.82 0.00 2(2,0)-1 1,0) 21262.57 21262.56 0.01 3(2,2)-2 3(l,2)-2 1,2) 0,2) 31892.05 31893.07 31891.03 0.00 3(3,l)-2 2,1) 31949.06 31949.25 -O.I9 3(3,0)-2 2,0) 31895.07 31895.12 -0.05 3(2,l)-2 1,1) 31837.45 a-T.vne 31837.54 -0.09 3(2,l)-2 2,0) 29745.95 29746.22 -0.27 3(0,3)-2 3(i,3)-2 0,2) 1,2) 21718.25 21718.46 21717.95 0.05 3(l,2)-2 1,1) 25841.25 25841.49 -0.24 3(2,2)—2 2,1) 25732.30 24732.34 -0.04 3(3 *0)-2 1,1) 33986.40 33986.44 -0.04 4(2,2)-3 2,1) 36523.20 36523.34 -0.14 4(0,4)-3 4(l* 4)—3 0,3) 1,3) 28279.30a 28279.30 28279.30 0.00 4(3,2)-3 3,1) 36307.25 36307.59 -0.34 4(l,3)-3 4(2,3)-3 1,2) 2,2) 32349.15 32350.50 32347.97 -0.08 5(o,5)-4 5 (1,5) -4 0,4) 1.4) 34840.28 34840.40 34840.40 -0.12 a. Transitions used to determine the rotational constants. 13 TABLE 3. R-BRANCH TRANSITIONS FOR THE 10B(3) SPECIES Frequencies Transitions Obs. (MHz) Cal. (MHz) Obs.-Cal. (MHz) c-Type 1 ( 1»o)-0(o,o) 10752.80 10752.68 0.12 2(2,1)-1(1,1) 21650.82a 21650.82 0.00 2(1,1)-1(0,1) 21359.89a 21359.89 0.00 2(2,0)-l(l,0) 21513.15 21513.15 0.00 3(2,2)-2(l,2) 32258.15 32258.03 0.12 3(1*2)-2(0*2) 32227.33 32227.27 0.06 3(3,1)-2(2,1) 32481.00 32480.94 0.06 3(3,0)-2(2,0) 32289.05 32288.80 0.25 3(2,1)-2(1,1) 32044.83 a-T.voe 32044.80 0.03 3(2,l)-2(2fO) 29766.97 29767.12 -0.15 4(2,2)-3(2,l) 37178.45 37178.42 0.03 4(0,4)-3(0,3) 4(1,4)-3(1,3) 28647.25a 28647.38 28647.13 0.00 4(3*2)—3(3*1) 36420.30 36420.36 -0.06 5(0,5)-4(0,4) 5(l,5)-4(l,4) 35296.40 37296.37 35296.37 0.03 a. Transitions used to determine the rotational constants. 14 TABLE 4. R-BRANCH TRANSITIONS FOR THE uB(4) SPECIES Frequencies Transitions Obs. (MHz) Cal. (MHz) Obs.-Cal. (MHz) c-Type l(l,0)-0(0 ,0) 10757.50 10757.55 -0.05 2(2,1)-1(1,1) 21637.14s 21637.14 0.00 2(l*l)-l(0,l) 21393.07S 21393.07 0.00 2(2,0)-l(l,0) 21520.53 21520.55 -0.02 3(2 * 2)-2(l,2) 32272.20 32272.66 -O.46 3(l* 2)-2(0,2) 32250.90 32250.96 -0.06 3(3,l)-2(2fl) 32458.97 32459.04 -0.07 3(3,0)-2(2,0) 32294.30 32294.36 -0.06 3(2,l)-2(lfl) 32092.87 32093.09 -0.22 3(2,l)-2(2,0) a.-Tjrpe and b 29853.40 -Type 29853.48 -0.08 4(3,2)-3(3,l) 36511.35 36511.66 -0.31 4(2,2)-3(3,l) 36430.60 36430.75 -0.15 4(3,2)-3(2,l) 37243.63 37243.72 -0.09 4(0,4)-3(0,3) 28671.64 4(1,4)-3(1,3) 4(0,4)-3(l,3) 28671.57a 28671.50 28671.49 0.00 4(l,4)-3(0,3) 28671.64 5(0,5)-4(0,4) 35326.85 5(1,5)-4(1,4) 5(0,5)—4(1,4) 35327.16 35326.84 35326.84 0.31 5(l,5)-4(0,4) 35326.85 a. Transitions used to determine the rotational constants. 15 TABLE 5. R-BRANCH TRANSITIONS FOR THE 10B(l) SPECIES Frequencies Transitions Obs. (MHz) Cal. (ivIHz) Obs.-Cal. (MHz) c-Type l(l,0)-0(0,0) 10719.18 10719.01 0.17 2(2,1)-1(1,1) 21475.65s 21475.65 0.00 2(1,1)-1(0,1) 21400.37s 21400.37 0.00 2(2,0)-l(l,0) 21438.35 21438.52 -0.17 3(2,2)-2(l,2) 32157.02 32156.25 0.25 3(l,2)-2(0,2) 32154.97 3(3,l)-2(2,l) 32213.83 32213.79 0.04 3(3,0)-2(2,0) 32159.10 32159.06 0.04 3(2,l)-2(l,l) 32100.65 32100.88 -0.23 a-Type 3(0,3)-2(0,2) 21762.10 21761.50 -0.35 3(1,3)-2(1,2) 21761.60 4(2,2)-3(2,l) 36744.35 36744.30 0.05 4(o ,4)-3(o ,3) 0 28322.80 28322.80 0.00 4(1,4)-3(1,3) 28322.80 4(3,2)-3(3,l) 36526.10 36526.12 -0.02 4(1,3)-3(1,2) 32482.12 32481.00 0.14 4(2,3)-3(2,2) 32479.59 VJ1 0 1 0 * * 34883.76 34883.65 -0.11 5(1*5)—4(1 * 4) 34883.76 a. Transitions used to determine the rotational constants. 16 TABLE 6. R-BRANCH TRANSITIONS OP POUR DOUBLY SUBSTITUTED SPECIES8, 10, 'B(l) 10B(1) XUB(3) XUB(3) Transitions and ^B(3) and ^B(4) and ^B(4) and ^B(5) (MHz) (MHz) (MHz) (MHz) 10, 10, l(l,0)-0(0,0) J K 4<- 3 4<- 3 j = 5 ^ 4 K « 5*-4 10843.25 10847.94 10880.90 10880.90 28691.00 28716.90 29040.75 29052.85 35539.90 35371.95 35784.13 35799.64 a. In the case of the last two species, it is uncertain which set of frequencies belongs to which species. 17 8«-9 and the K = 7<"8 hands could be tentatively assigned for six species (with possible misassignment of + 1 for J). It is possible to trace up to J « 45 in some bands. There are enough transitions in the frequency range of the instrument for a very detailed centrifugal distortion analysis. But the centrifugal distortion effects do not appear to be large, and no useful information would come from such a tedious analysis. In Table 7 some transitions belonging to the K = 2*- 3 band of the normal isotopic species are listed. The transition frequencies of this band are extremely sensitive to A-B. Centrifugal distortion effects were partially corrected by including a single correc- 2 2 tion term D..P P in the Hamiltonian. D.. was chosen to be jk z jk 0.0020 MHz. In an attempt to determine the coordinates of the bridge hydrogen atoms, a portion of the original sample was returned to Bunks for partial deuteration by hydrogen-exchange. The infra red spectrum of the product was inconclusive about the presence of H atoms. The mass spectrum did show a cut-off peak at m/e = 77. This indicated that at least part of the sample has been singly deuterated. The microwave spectrum of this sample was studied. Only a few new lines were found in addition to the ones which had been observed before. No resolvable Stark effects or band patterns were recognized among these new lines. They appeared to belong to traces of impurities incurred in the hydrogen-exchange process. The absence of the lines of TABLE 7. K=2<-3 BAND Q-BRANCH TRANSITIONS FOR 18 NORMAL SPECIES Transitions Obs. (MHz) Frequencies Gal. (MHz)a Obs.-Cal. (MHz) 20(18,2)-20(18,3) 8203.13 8203.00 0.13 19(17,2)-19(17,5) 8488.43 8488.19 0.24 18(16,2)-18(l6,3) 8751.92 8751.57 0.35 17(15*2)—17(15*3) 8992.12 8991.74 0.38 16(14,2)-16(14,3) 9208.14 9207.68 O .46 15(13,2)-15(13,3) 9399.22 9398.78 0.44 14(12,2)-14(12,3) 9565.30 9564.91 0.39 13(11,2)-13(11,3) 9706.92 9706.48 0.44 12(10,2)-12(10,3) 9824.78 9824.46 0.32 ll(9,2)-ll(9,3) 9920.70 9920.39 0.31 10(8,2)-10(8,3) 9996.46 9996.25 0.21 9(7*2)-9(7»3) 10054.48 10054.39 -0.09 8(6,2)-8(6,3) 10097.35 10097.36 -0.01 7(5*2)-7(5,3) 10127.70 10127.83 -0.13 6(4,2)-6(4,3) 10148.12 10148.32 -0.20 6(5*2)—6(3*3) 10184.38 10184.31 0.07 7(6,2)-7(4,3) 10192.86 10192.67 0.19 8(7 »2)-8(5,3) 10205.62 10205.44 0.18 9(8,2)-9(6,3) 10224.19 10224.00 0.19 10(9,2)-10(7,3) 10250.10 10249.96 0.14 ll(lO,2)-ll(8,3) 10285.27 10285.17 0.10 12(11,2)-12(9,3) 10331.85 10331.73 0.12 13(12,2)-13(12,3) 10392.16 10392.04 0.12 TABLE 7. (Continued) 19 Frequencies Transitions Obs. (MHz) Cal. (MHz)a Obs.-Cal .(MHz) 10(13,2)-14(11,3) 10468.85 10468.80 0.05 15(14,2)-15(12,3) 10564.88 10564.98 -0.10 16(15,2)-16(13,3) 10683.83 10683.91 -0.08 17(16,2)-17(14,3) 10828.95 10829.16 -0.21 18(17,2)-18(15,3) 11004.33 11004.59 -0.26 19(18,2)-19(16,3) 11214.06 11214.28 -0.22 20(19,2)-20(17,3) 11462.24 11462.41 -0.17 a. Corrected with a centrifugal distortion term D J(J+1) <K2> for the energy levels, where Djk = 0,0020 MHz • 20 deuterated species could be the result of insufficient deuter- 2 ation. But it was more likely due to the loss of the H atoms from the undesirable hydrogen-exchange with a small trace of H^O present in the microwave cell. 13 The identification of the spectrum of the C species has also been attempted without success. The very low population of the species (0.35$) and the abundance of observable lines made the attempt very difficult. Unfortunately, the preparation of 13 a ^C-enriched sample is impractical because of the low yield of the synthesis. D. STARK EFFECTS AND DIPOLE MOMENT In a conventional Stark modulated spectrometer the dipole moment is measured by observing the splitting of the M degen eracy when the modulated electric field is applied. Normally it involves measuring the voltage at the top of the square wave when the bottom is at ground potential. A simple modification of the square wave generator allows the bottom of the square wave to be biased above the ground potential with a regulated dc power supply. This dc Bias voltage is more easily measured and repro duced than the top of the square wave. Furthermore, the top of the square wave can be modified to have an exponential decay to eliminate interfering Stark lobes. From second order pertubation theory, the Stark effects on 21 18 an energy level of an asymmetric rotor is given by V * . i x=a,b,c 2J+1 r1 J(2J-1) W°T - W°_1 T , *2 (j+-q2-»2 *», ..t+1 t1 i + J(J+1) wJT - W°T, + (J+1)(2J+3) w JT - wJ+ i r J - <ajt + bj?“2) e2 where is the unperturbed energy of the J T level, /A-^ and /A are the components of the dipole moment along the prin- c cipal axes, the S’s are the direction cosine matrix elements, and the prime on the second summation indicates that it extends over all states except the (J,T ) state. The Stark frequency shift is given by ■ [(Aj'r - ajt> + - bjt} m2] e2 2 2 or (A + B^M )E where t refers to the particular transition and B-^’s can be measured from the experimental Stark effects, and the dipole moment components can be calculated from these. 18. S. Golden and E. B. Wilson, Jr., J. Chem. Phys. 16,, 669 (1948). 22 The electric field calibration of the Stark cell was made 19 with the J = lf-0 transition of carbonyl sulfide . All dipole moment measurements were performed on the same day. The molecular dipole moment was determined from the M = 0 lobes of the 2(l,l)4-l(o,l) and 2(2,l)l(l,l) transitions of the normal species. The symmetry of the molecule allowed only two non-vanishing dipole moment components. A-type and c-type transitions were observed, therefore /i^=0. JU.^ and JUL were determined to be 0.65 D and 1.38 D. The total dipole moment of the molecule was determined to be 1.53 D. It made an angle of 25° with the c-axis. The molecule is almost a symmetric oblate top. ^B(3) or ■^B(4) substitution could be expected to cause a large rotation of the principal axis system along the c-axis. While /A ' c should not be affected by such a rotation, and /AA^ should be changed. From the M = 0 Stark lobes of the transitions 2(l,l)f- l(0,l) and 2(2,l) <r l(l,l), and JlA^ were determined to be. 0.61 D and 0.22 D for the ^B(3) species (a rotation of 20°) and 0.49 D and 0.43 D for the ^B(4) species (a rotation of 42°) 19. S. A. Marshall and J. Weber, Phys. Rev. 105. 1502 (1957)• 23 E. STRUCTURE The coordinates of the B atoms in the molecule were deter mined from the rotational constants of the normal species and the three singly-substituted species. The center-of-mass coor dinates of the B atoms are listed in Table 8. The bond lengths derived from the coordinates are listed in Table 9* The uncer tainties listed in Table 9 were calculated from the uncertainties of the rotational constants. The true uncertainties in the bond lengths are probably of the order of + 0.01 X due to the use of the effective moments of inertia in place of the equilibrium moments of inertia in the Kraitchman equations. TABLE 8. ATOMIC COORDINATES FROM KRAITCHMAN EQUATIONS Atom Coordinates8, (£) a. b. c. B(l) 0.0000 0.0000 +0.8792 B(3) +0 . 5 6 3 5 +1 .3 0 5 6 -0.1940 B(4) - 1 .1 5 0 5 +0 . 9 1 4 9 -0.1270 B(5) - 1 . 1 5 0 5 - 0 . 9 1 4 9 -0.1270 B(6) +0 . 5 6 3 5 - 1 .3 0 5 6 -0.1940 a. Signs of the Coordinates are assigned to be consistent with the B-nmr structure. 24 TABLE 9. Bonds B(3)-B(4) B(4)-B(5) B (l)-B (3) B (l)-B (4) BOND LENGTHS Lengths (A)a 1.759+0.005 1.830+0.008 1.782+0.002 1.781+0.003 a. Uncertainties are based on the uncertainties in the deter minations of the rotational constants for the four major species. It is interesting to note that the ^B(l) substitution has no effect on the rotational constant C. The apex B atom must be very close to the c-axis. The large separation between B(3) and B(6) is a good indication that the lone C atom is close to the base plane if it is bonded to B(3) and B(6). The position of the C atom and the location of its H atom (the H atom bonded to the C atom) were optimized with respect to energy using the CNDO/2 MO theory described in Chapter VI. In this optimization the experimental values were used for the B atoms while reasonable 25 20 orientations were assumed for the H atoms bonded to the B atoms. The optimized positions of the C atom and its H atom were such that: R ^ ^ ^ l ^ l ^ A , RCB^ ) =1* and/.HCB(l)=129.7° The predicted RgB^) may appear to be too short, but it should 21 be compared to the short BB bond in hexaborane (**3(3)13(4) 0 O 1.60 A). A picture showing the predicted position of the C atom in the symmetry plane is given in Fig. 2. The C atom appears to be almost coplanar with the base B atoms. The rotational constants of the optimized structure are : A = 5277 MHz, B = 5267 MHz, C = 3222 MHz, in good agreement with the experimental values. We may conclude that the proposed geometry based on the ^B-nmr spectrum appears to be the correct geometry. 20. The assumptions were: all Rgg^^=1.20 A, all ^Bg(^)=^*34 A, the apex H was on c-axis, B(3)H(t) and B(4)H(t) were on the plane of the base B atoms, ZB(3)B(4)H(t) = Z.B(5)B(4)H(t) = Z.B(4)B(3)H(t)=128.6°, and all three B-H(b)-B bonds bent down below the base by 57°• These arbitrary assumptions were partially based on the BH bonds determined for penta- borane^, in which the base BH(t)'s were found to bend up by 3° above the base while the bridge H's were found to bend down by 57° • 21. F. L. Hirshfeld, K. Eriks, R. E. Dickerson, E. L. Lippert, Jr., and W. N. Lipscomb, J. Chem. Phys. 28, 56 (1958). t o 5 •H X a S 1 a : b (1) a-axis mid-^oint of B (4 )-B (5) FIGURE 2. SYMMET ------- - " > predicted position of G(2) CNDO/2 theory mid-point of B(3;)-B(6) RY PBftSIE OF CB5H9 ( V J cr\ CHAPTER III MICROWAVE SPECTRUM OF CD^BFg A. INTRODUCTION The properties of small molecules are usually of fundamental interest because of their importance in the understanding of more complex molecules. The structures of most carbon-boron compounds are very complex. Accurately determined structural parameters of the relatively simple molecules of these compounds are very useful for comparison purposes. One of the relatively simple carbon-boron compounds is methyl boron difluoride which may be considered as a symmetric top attached to a rigid framework with a small sixfold barrier hindering the internal rotation. The hydrogen species, CH^BF^, has been studied by electron 22 23 diffraction and by microwave spectroscopy. The parameters of the framework structure, -CBF^, were determined to within o 0.03 A by electron diffraction. The microwave study did not yield enough information to determine the structure of the molecule but the experimental rotational constants were found 22. S. H. Bauer and J. M. Hastings, J. Am. Chem. Soc. 64, 2686 (1942). 23. E. Naylor, Jr., and E. B. Wilson, Jr., J. Chem. Phys. 26, 1057 (1957). 27 28 to be consistent with the electron diffraction result. The dipole moment of the molecule and the sixfold barrier hindering the internal rotation of the methyl top were also determined by the microwave study of CH,BF„. The deuterated species, CD^BFg (Fig. 3),was prepared and its rotational spectrum was studied. The results are reported •z> FIGURE 3. GEOMETRY OF 0D,BFo . 5 2 in this chapter of this dissertation. The rotational constants of this isotopic species provide an additional check for the structure. The experimental values of the rotational constants of the two species were found to be quite consistent with a normal methyl top attached to a framework with parameters deter mined from the electron diffraction study. The dipole moment was found to agree with that of CH,BF_ within experimental uncertainties. The quantum defects of the two species, as a measure of the zero-point vibrations, were calculated from the experimental values of the rotational constants. 29 B. EXPERIMENTAL (CD ) B was prepared by the reaction of etherated BP, and j j 3 CD^Mgl in ether under flowing dry Ng. With the original inten tion to prepare (CD^JgBF, BF^ and (CD^)^B were mixed in the ratio of 1:2 and kept at 270°C for three days. The details of the synthesis are described in the preparation of (CD2)„BF in Chapter IV. The ^'''B-nmr spectrum showed the product to consist of (CD^)^B, (CD^J^BP and CD^BF^ in the approximate ratio of 3*4:3. Further heating did not change the ratio appreciably. The spectrum of the mixture was observed between 8,200 MHz and 37»500 MHz at dry ice temperature with a conventional 100 KHz Stark modulated spectrometer. C. SPECTRUM AND RESULTS All the strong transitions up to J = 10 for the m = 0 state of CD^^BFg were assigned and listed in Table 10. The intensities were generally weak. The low J transitions were broadened by the unresolved quadrupole hyperfine structure and probably also by the superimposed ^ B isotope transitions. The three J = 2*-l transitions and the 4(1 »4) 4(l>5) transitions were identified by their Stark effects. The general features of the Stark effects and the intensities of the other assigned transitions were in agreement with the predictions. The dipole 30 TABLE 10. ASSIGNED TRANSITIONS FOR CD3n BF2 m = 0 STATE Transitions Observed Frequencies Calculated Frequencies 1(0,1) -0(0,0) 11032.8 11033.2 2(0,2) - 1(0,1) 21025.6 21025.6 2(1,1) - 1(1,0) 24785.2 24785.2 2(1,2) - 1(1,1) 19347.5 19347.3 3(2,1) - 2(2,0) 36538.2 36538.6 3(0,3) - 2(0,2) 29659.3 29659.8 3(1,2)- 2(1,1) 36343.1 36343.1 3(1,3) - 2(1,2) 28458.4 28458.2 3(2,2) - 2(2,1) 33099.2 33098.9 3(1,2) - 3(1,3) 16041.4 16041.7 4(1,4)- 3(1,3) 37185.7 37185.7 4(1,5)- 4(1,4) 25470.0 25471.9 5(2,3)- 5(2,4) 19686.9 19685.7 6(3,3)- 6(3,4) 12672.5 12670.0 6(2,4)- 6(2,5) 30106.5 30107.1 7(3,4)- 7(3,5) 22436.5 22435.4 8(3,5)- 8(3,6) 33873.8 33876.0 8(4,4)- 8(4,5) 13906.4 13904.8 9(4,5)- 9(4,6) 24450.5 24451.9 10(5,5)-10(5,6) 14647.4 14649.4 a. With centrifugal distortion corrections. 31 moment^ was determined from the |M | = 1 lobe of the 2(0,2) <- l(0,l) transition. The Stark effects for the m = 0 state of this molecule are the same as those for an asymmetric rigid rotor. The theory of the rigid rotor Stark effects and the dipole moment determination is described in Chapter II. The electric field calibration of the Stark cell was made with the J = 14-0 transition of carbonyl sulfide. The high J lines were found to deviate from the pseudorigid rotor pattern by as much as 20 MHz. A centrifugal distortion 2 2 correction term -D..P P was included in the Hamiltonian to 2 improve the fitting. Without considering the effects of the different zero-point vibrations, the ^®B isotopic species was expected to have rota tional constants B and C higher than the normal species by about 0.8 MHz and 0.3 MHz respectively while A^F^ only) would remain the same. The very weak and very broad ^ B low J lines were not sufficiently removed from ^ B lines to be identified. High J transitions of CD^^BFg were not observed in the expected locations. However, since the boron atom is near the center of mass, the rotational constants of CD^BF^, even if precisely determined, could not help in determining the structure. The small difference between the rotational constants of CD_^BF_ 3 and CD^^^BF^ would be more sensitive to the zero-point vibration than to the structure. 32 A computer program was written to compute the transitions for molecules with sixfold barriers. The program, VSIX, is described in Chapter V together with a discussion of the theory for the rotation of a molecule with a sixfold internal rotation barrier. Some centrifugal distortion corrections were allowed 23 for the |mj> 0 states just as in the case of CH^BP^. The low J transitions for |mf = 1 and 2 were affected only slightly by the small sixfold barrier (Vg was determined to be 13*77 cal/mole for CH,BF.). For the m = 0 state, rigid rotor type calculation 3 2 with A^Fg only) = 10584*10 MHz yielded almost identical results as low barrier type computations with Vg = 13.77 cal/mole and A = 10585*35 MHz. Very weak and very broad lines with obscure Stark effects appeared near the expected frequencies for most of the jmf = 1 and 2, J = 2<-l transitions. The |m| = 3 levels were expected to be extensively split by the small barrier. Several extremely weak lineB with obscure Stark effects appeared near the expected frequencies for the |m J = 3 state (assuming that Vg is the same as in CH^BF,,). The frequencies of these transitions should be extremely sensitive to small changes in V,. Since V^ of CD_BF_ may be slightly different from that of o 0 5 2 CH^BF2, no positive assignments could be made without Stark effect identifications. Thus Vg for CD^BF^ was not determined. It can be shown that 1^ - 1^ - I^BFg) = 0 for non vibrating masses in this molecule. As a measure of zero-point vibrations, the quantum defect could be defined as 33 A = l0 - IB - V bf2) in analogy to the inertial defect of o 2 planar molecules. They were found to be 0.328 and 0.257 amu-A for CD_BF_ and CH,BF . These positive values indicate the 3 2 3 2 domination of the in-plane vibrations over the out-of-plane motions. If we exclude the change in the zero-point vibration effect upon substitution of CH, with CD,, it is obvious that 3 3 A I^(BF2) s 0 and Alg = ®nly one additional piece of structural information could be derived from this substitution, and this is not enough to determine the positions of the hydrogen atoms, i.e., the distance of each H atom from the principal a-axis and the distance of each H atom from the plane made by the b-axis and the c-axis. Furthermore, this information cannot be related to some simple and physically meaningful relationship with the bond lengths or the bond angles. However, the experimental rotational constants (see Table ll) can be used as an additional check on the structure. TABLE 11. CONSTANTS DETERMINED FOR CD 11BF and CH 11BF a Constants C D XiBF„ CH,iXBF0 3____2______________ 3 2 A (BF2 o n l y ) 10585.35 MHz 10586.73 MHz B 6876.04 MHz 8329.01 MHz C 4157.13 MHz 4650.52 MHz 1.63+0.04 D 1.67+0.02 D Centrifugal Distortion Bjk= < - ),®24 MHz V. 13*77 cal/mole a. Naylor and Wilson's work 34 The parameters determined from the electron diffraction study are R^g = 1.60A, Rgp = 1.30A and Z. CBF = 120°. Since ^A^^2^ determined from the more accurate microwave studies gives a perpendicular distance of 1.121A from the carbon-boron axis to each F atom, a slight correction should be made in either Rgp or Z.CBF. Naylor and Wilson found those frame para meters to be reasonably consistent with the rotational constants 2 of CH,BF0. With more rotational constants available now we 3 * may examine the consistency a little more closely. If we choose a regular methyl top = 1.100A and Z-HCB = 109*45°) in 0 O addition to the framework parameters R.,g = 1.60A, Rgp = 1.30A and Z. CBP = 120.43° (equivalent to Rpp = 2.242A) the calculated rotational constants are only in error by about 20 MHz. If we 0 allow R^jj to be increased by as little as 0.005A the discrepan cies could be kept to within 12 MHz. A comparison is given' in Table 12. 35 TABLE 12. COMPARISON OF THE CALCULATED ROTATIONAL CONSTANTS® WITH THE EXPERIMENTAL VALUES Experimental Calculated (Rcb = 1.600A) Calculated (Rcb = 1.605A) ch3bf2 a (bf2) 10586.73 10585.48 10585.48 B 8329.01 8352.06 8317.50 C 4650.52 4668.54 4657.72 cd3bf2 a (bf2) 10585.35 10585.48 10585*48 B 6876.04 6898.69 6871.04 C 4157.13 4176.69 4166.54 a. Assuming a symmetric methyl top (Rn„ = 1.ioa, Z hcb = 109-45°) , RBp = 1.30A and Z CBF = 120.43 . CHAPTER IV THE STUDY OF THE MICROWAVE SPECTRUM OF DIMETHYL BORON FLUORIDE A. INTRODUCTION When an internal rotor forms a single bond with an asym metric framework, the free rotation of the rotor is hindered by a potential barrier. The determination of this potential contributes to the understanding of intramolecular forces. While nmr and other techniques have been employed to study some very high barrier cases, microwave spectroscopy is the best tool to determine the barrier when it is less than four or five kilocalories per mole. When a molecule has one threefold symmetric top such as -CH^, we have a single top problem. The rotational transition spectral lines are split into doublets by the barrier. The magnitudes of the splittings are related to, among other para meters, an effective barrier s. The quantity s in turn depends on the potential barrier as well as the moment of inertia of the top along its symmetry axis. For molecules with two equivalent but non-coaxial tops, such as acetone, quartets and triplets are expected for the ground state instead of doublets. The theory is more complex but it can be related to the calculations of single top problems, 3 6 37 Additional interesting information other than the threefold barrier may be obtained from the study of a double top molecule. The microwave spectrum of acetone has been studied by Swalen and Costain2^, and by Nelson and Pierce2^. The threefold barrier was found to be slightly less than 800 cal/mole. This relative low barrier made the assignment and the fitting of the spectrum very difficult. The quartets were hard to recognize due to the large and uneven splittings. Fortunately, the presence of the resolved Stark effects in the low J transitions made the assignment possible. Beside obtaining structural information and determining both the barrier and the dipole moment those authors found the methyl tops tilting towards the carbonyl bond by about 1.5°» But the gearing effect between the two tops was not determined. Dimethyl boron fluoride, Me^BF, is isoelectronic with acetone but the IT -bonding electrons are absent in the former. The study of the microwave spectrum of Me^BF may provide a good comparison between the two molecules. The comparison of the threefold barriers would allow us to estimate the contribution of the 7f -bonding electrons to the height of the potential 24. J* D. Swallen and C. C. Costain, J. Cham. Phys. j51, 1562 (1959). 25. Nelson and L. Pierce, J. of Mol. Spect. _18, 544 (19^5)• 38 barriers. Further, the comparison of the tiltings in the two molecules may point out whether the tilting in acetone is essentially due to the attraction of the TT-bonding electrons or due to the repulsion between the two bulky methyl groups. The determination of the dipole moment of Me^BF, the partial struc tural information and the possible detection of the gearing effect are also among the objects of the study of its microwave spectrum. B. THEORY The total torsion-rotational Hamiltonian for an acetone- type molecule (Fig. 4)<with two identical internal rotors and two planes of symmetry may be expressed as H = H 1 + H,, + H._ + H» + H . r tl t2 t rt where H' = A'P2 + B'P2 + C P2 r z z z x y y Htl = Ppl + < V 2) (l-°°s3o^)' Ht2 = Fp2 + (V3/2) (1-cos3o( 2) = F' (P1P2+P2Pl) + V12COS3 ^00830^ + V^2sin3e<18in3c<’ 2 + sixfold barrier terms and higher order terms and Hrt - - 292pb(p,-p2) with the following definitions: A' = (fi^/2)(l/r I ); B1 « Z Z Z X (H2/2)(l/rxIx)} Cy - fe2/2Iy ; F - (ti2/4I*) (0/rx) + (l/rz)) ; F* = (li2/4I0<) ((l/rx)-(l/rz)j ; V^is the threefold barrier} and V' are the gearing potential barriers; Q = A B' ; Q = 1 & X XX z 39 FIGURE 4. GEOMETRY OF ACETONE-TYPE MOLECULE. XgA^ ; P^, P and P^ are the total angular momentum operators while and p^ are the angular momentum operators of the tops; I , I and I are the moments of inertia of the molecule about x’ y z its principal axes x, y and z; the x-axis has been chosen at the intersection of the two planes of symmetry, the y-axis is through the center of mass and perpendicular to the plane of the heavy atoms, and the z-axis is through the center of mass in the plane of the heavy atoms and perpendicular to the x-axis; X and X are the direction cosines between the top symmetry x z axis and the x and the z principal axes; 1^ is the moment of 2 inertia of a top along its symmetry axis; r = 1 - (2X^1^/^); 2 r = 1 - (2X I ,/l ); of, and are the internal rotation angles z ' z «r z' ’ 1 2 0 of the tops. IP may be considered as the rotational Hamiltonian of a molecule with two free rotating tops. H+1 and H are the 40 torsional Hamiltonians for two non-interacting tops with a threefold harrier V^. represents the interactions of the tops as well as the sixfold and higher order harrier terms. H stands for the torsion-rotation interaction, rt A convenient representation of this total torsion-rotational Hamiltonian is ir (T ’ w^ere V^JKm '8 are symmetric rotor hasis set while U and U are the single top tor- vr i v2 2 sional eigenfunctions for H^^ and H ^ (v*s are the main torsional quantum numbers and CT* s are the symmetries of the sublevels). H£ and H ^ will introduce off-diagonal elements in v*s. Pour different sublevels exist for the ground torsional state where v^ = v^ = 0. There are an A sublevel ( < 7 " ^ = 0, (7*2 = 0) , an E^ (or Eg) sublevel (doubly degenerate, (7^ = - = 1 or (7^ = - (Tg = -l), an E^ sublevel (doubly degenerate, cr^ = ^2 = 1 or <7^ = <T ^ = -l), and a Q sublevel (quadruply degenerate, & ^ = 0, cTg = + 1 or = + 1, = 0). An effective Hamiltonian may be written for this ground state. Ha_ = H + fI (W<>n)AnPn + W^"n^XnPn) Ot: r n=l' OTT x x OTT z z' where the symmetry of T is either A, E^(or Eg), E^ or Q, while H = A P2 + B P2 + C P2 with A = t2/2I and B = li2/2l . The r z z x x y y z ' z x ' x (+n) perturbation coefficients W'- ''s come from the van Vleck trans formation folding the elements offdiagonal in v into the (+n) particular block, are Senera^^y different for different T . The effects of the kinetic interaction between the two tops are generally negligible. The effects of the potential 41 interaction between the two tops (the and terms) are usually very small for the ground state. and VJ can only be evaluated accurately from the excited states. Neglecting the interactions of the tops, the ground state perturbation coeffi- (+n) cients ' may be related to the corresponding coefficients of a single top problems = ^cr i ^Otr * The sin£le top coefficients have been tabulated by Herschbach for the range of s = 12-100 (s = 4V^/9P). Also, a computer*^ program is available for the computation of W” for any given value of s. The non-vanishing elements of Pn and Pn in the symmetric rotor X 2 5 representation have also been tabulated in reference 26. Usually, terms are the smallest terms necessary to be considered. The solution of the secular equations can be carried out by matrix-diagonalization. The odd n coefficients are identically zero for the A level, so the A species may be considered as a pseudorigid rotor (+2) (rotational constants being modified by ' terms) with some centrifugal distortions (from W ^ terms). The Q species and the E species may be considered to be near pseudorigid rotors (with different rotational constants for the Q and E sublevels), 26. D. E. Herschbach, unpublished tables. 27. Y. S. Huang, Dissertation, Appendix I, Univ. of So. Calif., 1969. 42 being modified by the effects of ^q- ^ and terms. For a very high barrier case (V^> 3000 cal/mole), all the ground state species degenerate. The spectrum is that of a ( + 2) rigid rotor. For a moderately high barrier case, only ^q* ^ . terms need to be considered. Most of the transitions are ex pected to appear as equally-spaced triplets (A, Q and E's). With a lower barrier, the Q transitions will be shifted from the center, while the E.. (or E„) and the E, transitions will be split i d 3 C +1 ^ 25 by the terms. A simple relation will hold for this situation ^A = ^0 + (4/3W(2) ^ ( o r E,) ’ 1/B = )?o - (2/3)/i^2) 3 » V»0 + (l/3)^(2) + (1/4)^1) + (l/4)^1^ ' where is the expected transition frequency for an unperturbed (2) rigid rotor, Alt ' is the splitting arising from the second order(n=2) coupling effects, while A and A are the first 8. 0 order (n=l) contributions to the splittings. When the barrier is lowered further to about 700 cal/mole in the case of -CH_ 3 tops, Ai/2^ , and will begin to increase very rapidly. & D Besides, the higher order terms will begin to have appreciable effects. The quartets will be very difficult to recognize. Acetone probably has the lowest barrier that has ever been determined by microwave study for a double top molecule. The 43 assignment of the rotational spectra of molecules with consider ably lower barriers may be very difficult. The Stark effects of the A sublevel (ground state) transi tions may be expected to be the same as that of an asymmetric rotor. The odd n terms will introduce first order Stark effects into the transitions of the Q and the E sublevels, particularly when the barrier is relatively low. C. EXPERIMENTAL The sample of the normal isotopic species, (CH^^BF, was provided by Professor A. Burg. The mass spectrum confirmed the identity. The microwave spectrum between 8.2 and 33*0 MHz was studied at dry ice temperature using a conventional 100 kHz Stark modulated spectrometer. The deuterated species, (CB^JgBF, was prepared in two steps from a sample of CD,I purchased from a commercial source. 3 (CD^)^B, the product of the first step, was prepared from the reaction between etherated BF^ and Grignard reagent CD^Mgl. A three-necked flask equipped with a large funnel, a special condenser (for use with dry ice and isopropanol mixture) and a dry-Ng gas inlet was used. The condenser served as a gas outlet through two traps to a three-way stop-cork which could lead either to a pump or to a mercury bubbling one-way breather. 3.85gm. of Mg turnings and a magnetic stirrer were introduced 44 into the flask. The system was vacuum sealed with silicon grease. Moisture in the system was removed by pumping for two hours with occasional warming of the glassware and periodical flushings with dry N^. The gas inlet was temperately replaced by a small funnel for the preparation of the Grignard reagent. The condenser was cooled and the magnetic stirrer was turned on. 8 ml. of CD^I and 55 ml. of dry ether were quickly introduced into the two funnels. The Grignard reagent was prepared slowly with occasional cooling of the flask in an ice-water bath. After l/2 hr. of preparation and 1 hr. of waiting for the com pletion of the formation of the reagent, the smaller funnel was replaced by the gas inlet. Under the flowing dry N^, 4*0 ml. of etherated BF^ and 20 ml. of dry ether quickly introduced into the large funnel. (CD^)^B was formed by dropwise addition of the BF^ solution into the mixture in the flask. The dry flowed slowly through the flask, the condenser and the traps, and exited through the mercury bubbling one-way outlet. The (CD^)^B gas carried by the nitrogen was collected in the traps which were cooled by liquid N^. After purification by fractional distillations in vacuum, the product had a volume of about 1 ml. in liquid form at dry ice temperature. The ^B-nmr spectrum of it showed only one peak at about the same position as the peak of (CH^)^B. Half of the (CD^)^B was introduced together with gas BP, into a stainless steel bomb in the volume ratio of 2.1 si. The mixture was heated at 45 270°C for three days. The ^ ' * ‘ B-nmr spectrum indicated the product to consist of (CB^)^B, (CD^gBF and CD^BF^ in the approximate ratio of 3*483» Further heating had no effect on this ratio. Several futile attempts were made to separate the products through gas-phase chromotography. The peaks of the (CD_)„BF 5 2 and CD^BP^ were not sharp enough to avoid considerable over lapping. This mixture, after the removal of most of the (CD ) B, was used for the microwave studies of (CD„)„BF and 5 5 3 2 CD^BFg (Chapter II). D. SPECTRUM It is reasonable to assume that the bonds in (CH,)_BF are 5 2 similar to those in CH^BF^. Under this assumption, the rota tional constants of (CH^^BF may be estimated to be close to 8565 MHz, 7467 MHz and 4205 MHz respectively, with the molecular dipole moment along the x-axis. This is a fairly asymmetric molecule with Ray's asymmetry parameter X 5^0.50 where K = (2B -A —C )/(A —C ). The effective rotational constants A' x z y z y z (+2) and B^ are expected to be modified by the W'- ' terms as the barrier is lowered from infinity. In the limit of a vanishing barrier (the free rotor case) the effective A1 and B' for the z x A sublevel of the ground torsional state are expected to increase by about 700 MHz and 170 MHz. For a molecule with the above predicted rotational 46 constants, the b-dipole R-branch transitions with J = l<-0, 2<-l and 3 <r-2 should be within the frequency range of the microwave spectrum. Many b-dipole low K Q-branch transitions should also be within the range. . But the Q-branch bands (same K's with various J's) are not expected to be easily recognizable due to the degree of asymmetry. Some recognizable quartets or triplets should appear for the ground torsional state transitions of this double top molecule unless the barrier is so high that the molecule is practically a rigid rotor or so low that the splittings become too large and too uneven. The Stark effects of the ground torsional state A-sublevel transitions should be the same as those of an asymmetric rotor while the (and perturbation terms are expected to introduce first order Stark effects into the Q- and the E-sublevel transitions. The spectrum of (CH^^BF was found to be quite rich, with first order lines dominating the region above 28 kMHz and second order lines dominating the region below 22 kMHz. The entire range between 8.2 - 33*0 kMHz was scanned. The Stark effects of over 500 of the stronger transitions have been examined. The frequencies of these transitions were measured with wavemeters which have an average accuracy of about + 5 MHz. A few of the more interesting transitions were measured accurately with the frequency-measuring marker system described in Chapter II. 47 No lines were found to exhibit the Stark lobes character istic of low J H-branch transitions. Since the identification of these transitions has usually been the first step in the assignment of rotational spectra, difficulties were anticipated after the failure to recognize these transitions. Clear Stark lobes characteristic of Q-branch transitions were observed in six lines, two with first-order Stark effects and four with second-order Stark effects. The Stark effects of these lines are tabulated in Tables 15-14* The two first order lines are definitely J = 5 and J = 6 transitions. The second order lines are most likely transitions with J = 5, 6, 7 and 8, with possible errors of + 1. TABLE 13. Q-BRANCH TRANSITIONS WITH CLEAR SECOND-ORDER STARK EFFECTS Frequencies No. of Assignment Stark Coefficientsa (MHz) Lobes of J (lRRz/fvolt/cm) J Observed A B. * G __ t 15681.9 5 5+1 10 .8 X 10'7| 0.40 X 16999*5 4 6+1 11.0 X 10~7| 0.29 x io~6 20919*1 5 7±x 10.5 X 10-7| 1.08 x 0 1 21408.8 6 8+1 11.0 X 10"7| 0.58 x 10-7 2 2 a. Stark effects_= (A + B,M )E with relative intensities of the lobes °c M . x T b. A^_ cannot be determined very accurately from the data. The values in the table are the maximum limits of the magnitudes. 48 TABLE 14. Q-BRANCH TRANSITIONS WITH CLEAR FIRST-ORDER STARK EFFECTS Frequencies No. of Assignment Stark Coefficients*5 (MHz) Lobes of J (MHz/(volt/cm) Observed8, C^ 23144.8 4 5 0.0103 29661.8 5 6 0.0125 a. No. of lobes observed on each side. b. Stark effects = C^ME. No quartets or triplets were recognized in the entire spectrum. The neighborhood of each of the six lines with clear Stark effects was very carefully examined, but no quartets were recognized. It is interesting to note that the frequency ratio of the two clear first-order lines is almost exactly 7*9 which may mean K = 4«-3, and K = 5<"4 transitions. These two lines do not fit a rigid rotor pattern exactly, and they probably belong to some E- or Q-sublevels, not necessarily belonging to the ground torsional state. Without the assignment of the ground state A-sublevel transitions of a double top molecule, the assignment of transi tions belonging to other sublevels will be extremely difficult. Thus, in this case the only clues one may work on are the four clear second-order transitions which appear to belong to some A-sublevels, most likely to the ground state A-sublevel because of their intensities. The first excited A-sublevel is expected to have much higher torsional energy (v^ = v^ = 3) which would result in much weaker transition intensities. The ground state A-sublevel transitions are expected to have a pseudorigid rotor pattern (possibly modified by some centrifugal distortion correction terms both from the terms and from the other molecular vibrations). The frequency of . 00 (H). . . . IX) a Q-branch transition is (E^, - E^.>i;/2(A-C) where E^. and E « are constants (depending on X ) for the upper and lower rotation al energy levels involved in the transitions. Two tools were used to aid the fitting of the Q-branch lines. A graph was plotted for b-dipole transitions with log^0(E^( - E^,/) for various transitions up to K = 5*"4» against X from 1.0 to 0.35* Logio(observed frequencies) were then plotted on a long strip of graph paper. Attempts were made to match some of the observe lines with the graph. The second tool used was a computer program QFIT, written to fit Q-branch rigid rotor type transi tions to two constants (A-C) and X • This program was modified 28 from a similar program LINFIT which fits E-branch transitions as well as Q-branch transitions to rotational constants A, B and C. The program QFIT and the preparation of the data are 28. E. A. Beaudet, unpublished work. 50 described in Appendix I. It was hoped that after the positive identification of the Q-branch transitions for the A-sublevel it might be easier to fit the A-sublevel R-branch lines and to match the other members of the quartets. This attempt to fit at least two of the four clear second-order lines with some other Q-branch lines was given up after numerous trials and after much effort. The failure to fit Q-branch transitions to a pseudorigid rotor pattern may be due to the presence of centrifugal dis tortion effects (partly from ) . There appear to be three possible explanations for the absence of the recognizable low J R-branch lines. These lines may have been extensively broadened by the effects of the boron nuclear quadrupole moment couplings. In this case, the line intensities will be weakened and the Stark lobes may be too unclear to recognize. The boron atom is expected to be fairly close to the center of mass. The low J transitions of the ^ B species may not be removed far enough from those of the species. This overlapping may obscure the Stark effects. Accidental overlapping with some stronger lines may also be responsible for obscuring the Stark effects of some of these low J lines. The absence of recognizable quartets or triplets may be the result of either very high barrier or fairly low barrier. The presence of the many first order lines seems to support 51 the latter point of view. The splittings of the quartets depend on the effective barrier parameter s(4V^/9F)« This parameter is expected to be larger for (CD^)2BF2 than for (CH^^BFg. Smaller splittings should result from larger s. It is reasonable to expect that some closely spaced quartets (or even triplets) may be recog nized in the microwave spectrum of the deuterated species. This is true in the case of acetone. Closely spaced triplets were observed in the (CD^^CG spectrum while the corresponding quartets in the (CH^^CO spectrum were found to be widely split. (CD^)2BF was prepared. The sample was contaminated by (CD ) B and CD,BF_.^ The intensities of the lines in the 5 5 j 2 spectrum were generally very weak. No quartets (nor triplets) were recognized in the spectrum. And no clear Stark lobes of (CD^)2BF transitions were observed. One tentative conclusion may be drawn from the results. The hindrance barrier of dimethyl boron fluoride is probably significantly lower than that of acetone. The high barrier approximation approach is not a good approach for a double top molecule with a barrier much lower than the barrier of acetone. The low barrier approximation approach for a double-top molecule 29. The transitions belonging to CD BFg were assigned with this sample as reported in Chapter II. 52 has not been fully developed, but the barrier V, is very unlikely to be low enough for the low barrier approximation to be useful (less than 100 cal/mole). Even if is low enough, the success of the low barrier approximation will depend on the assignment of the ground state A-sublevel transitions which should follow a near pseudorigid rotor pattern. Unless the R-Branch transi tions of the lowest A-sublevel are recognized or the Q-branch transitions are fit, the problem cannot be solved irrespective of the barrier. CHAPTER V. COMPUTER PROGRAM VSIX FOR SIXFOLD BARRIER INTERNAL ROTOR PROBLEMS A. INTRODUCTION The s t u d y of hindered internal rotation has long been a subject of interest. One type of internal rotation problem deals with a molecule consisting of a C^v top coaxial with a C ^ frame. Such a molecule usually has a small sixfold rotational barrier, and, in certain cases, a detectable twelvefold barrier. The torsion rotation Hamiltonian has been treated in several 23 50 51 52 55 papers. ’ ’ ’ ’ The microwave spectra of several molecules exhibiting sixfold barriers have been studied. These include CH,BF0 , 25 CD BF ,5^ CH„N0o , 50 CD,N0 50 CF..N0 55 toluene, 56 52 52 5 2 - 5 ^ 5 t 30. E. Tannenbaum, R. Myers and W. Gwinn, J. Chem. Phys. 26, 1057 (1957). 31. E. B. Wilson, Jr., C. C. Lin and D. R. Lide, J. Chem. Phys. 21, 136 (1955). 32. C. C. Lin and J. D. Swalen, Rev. Mod. Phys. 12, 841 (1959)• 33- D. R. Herschbach, J. Chem. Phys. 11., 91 (1959)» 34* Chapter III of this dissertation. 35. W. M. Tolies, J. Chem. Phys. 41, 3019 (1965). 36. H. D. Rudolph, H. Dreizler, A. Jaeschke and P. Wendling, Z. Naturforsch 22a. 940 (1967)» 55 37 38 39 24 p-chlorotoluene, p-fluorotoluene, N-methylpyrole, 4-methylpuridine^ and B-methyl-1,5-C0B,H < : 5 4 In the 1950's, the unavailability of fast computers for diagonalization of large matrices made it necessary to use approximations for estimation of the rotational energies of this type of molecule. In recent work, the energy calculations appear to be more satisfactory. However, in most of the reported work the transition frequencies do not appear to have been calculated by using exact selection rules. Apparently, the observed R-branch transition frequencies were matched to the energy differences between energy levels of the same value of M, the same value of m, and the same parity of K. To predict the transitions, an explicit calculation of the dipole matrix elements is necessary. A computer program VSIX was written to perform this type of calculation. It computes the energies of the torsion rotation eigenstates and predicts the frequencies and the relative inten sities of the allowed transitions. A review of the theory is given in the following section. A description of VSIX, including a flow chart and the input data preparation, is given in detail in Appendix II. 37. G„ E. Herberich, Z. Naturforsch, 22a. 761 (1967). 38. H. D. Rudolph and H. Seiler, Z. Naturforsch, 20a. 1682 (1965). 39« W. Arnold, H. Dreizler and H. D. Rudolph, Z. Naturforsch 23a. 301 (1968). 40. H. D. Rudolph, H. Dreizler and H. Seiler, Z. Naturforsch ' 22a. 1738 (1967). B. THEORY 55 HAMILTONIAN The rotational Hamiltonian for a molecule consisting of a C„ top coaxial with the z-axis^"* of the whole molecule can be Jv written as H = CP 2 + BP 2 + AP 2 - 2ApP + Fp2 + V x y z z where C - ifc2/lx,B = ih2/ly,A = £fc2/(lz-3*) ,P - Iz-I«) f and I are the moments of z and V = £ gVgn£l-cos(6neO} • *x» I n= 1 inertia of the whole molecule about its principal inertial axes while 1^ is the moment of the top about its symmetry axis. P , Py and Pz are the components of the total angular momentum P along the principal axes and p is the total contribution of the top atoms to the z-component of P. Vr and V,„ are usually very small and it is convenient to O \ d express :the true wavefunctions C^'s in terms of the free— rotor basis set functions |J K M m) - Vjkm exP(im°0 where ^ i s the usual symmetric rotor wavefunction, and m (an integer) is the vibrational quantum number associated with the internal rotation. If we define J4 = (H - DP2)/(A - D) the basis set has the following non-vanishing elements (J K M m|>/ |j K M m) = K2 - mdK + fm2 (j K M m| j&f | J K+2 M b ) - ib{(j2-(K+l) 2) ((J+1)2-(K+1)2)|^ (J K M m|^|j K M m+6n) = V£n 41• The top is usually coaxial with the z-axis rather than the x-axis or the y-axis. where D EIGENVALUES The energy levels E's are related to the eigenvalues \'s of The last two terms are usually ignored because they have no effect on the transition frequencies or the relative intensities. The solution of the eigenvalues X.'s becomes a problem as the elements offdiagonal in m create an infinitely coupled infinite matrix for a certain J and a certain M is illustrated in Figure 5 in which the m's are arranged in ascending order while the K elements are arranged periodically from -J to J. The diagonal blocks are identical to that of the solution of an asymmetric rigid rotor in a symmetric basis set except for the 2 addition of -mdK + fm in the diagonal. The problem is simplified twelvefold if we notice that the even K's are never connected to the odd K's and that m mixes only with m+6n. Such a matrix can be factored into twelve matrices. An example is shown in Figure 6. Those factored matrices con taining m = Jn elements can be further simplified because they are antidiagonal-symmetric as well as diagonal-symmetric. Such a matrix can be transformed by Wang's transformation into a matrix with two non-vanishing blocks: H by E = DJ(J+1) + (A-D)X + iV6 + iV12 s ecular equation. & is diagonal in J and M. The form of the s \ V S V S \ \ \ 57 N N \ \ s \ V S \ V \ \ \ \ \ \ s \ V \ s \ \ \ % v \ \ s S s s \ S \ V \ \ V % \ V \ s % \ \ V \ % s s \ \ s N \ S s N \ 'v- \ \ \ \ \ / / / / s s \ s \ m=-7 -6 -S \ -U -3 -A -1 o 1 \ 2 3 4 5 6 K 7 " 1 K=-J i - ■ non-vanishing element -jprptr w x h ■ \ 1 V. \ \ \ v \ s s \ V s s v \ \ \ FIGURE 5. THE INFINITE Jbp MATRIX FOR EACH PAIR OF J AND M. DIAGONAL m BLOCK 58 m-12 m-6 m m+6 m+12 % V ; s \ \ v \ \ V \ \ s V* \ \ S ' \ \ s V \ \ % Vj"y£/yl > V \ , 1 X \ \ \ \ s < \ \ llpll . wwflT \ v ; \ \ \ \ \ s <J*. Vii b \ \ \ \ \ ! \ \ V . S N \ \ \ \ V s \ \ \ S'-' ' V S \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ s \ \ \ s \ ' W ' sV N \ O ^ \ s ^ \ % S \ \ \ \ < \ \> % N ' FIGURE 6. SIMPLIFIED MATRIX WITH INTERCONNECTED ELEMENTS. where T is f c « / % * . i * ,*ir V *. * - i s - i s •J. j! •n •/» xt < r c or 1 j. j. V» - f t * A w + J <JT <1, ft 'd / / K for even or odd dimensioned matrices. The blocks are called (+)- A p blocks and (-)-blocks with the new basis function Jx{| J K M m) + | J -KM -m)} . The energy matrices for |m| = Jn are shown in Figures 7-9 and those for |m| 4 = 3n are shown in Figure 6. They are still infinite matrices. Since is usually much smaller than the difference in energy between the m and the m+6 states, only negligible errors would be introduced by truncating the matrices, retaining only those m states directly connected to the parti cular state m under consideration. In the case of the unlikely high sixfold barriers or in the case of the smaller difference in energy between the m and the m+6 states of a CF^ top, the truncation errors can be kept negligible by retaining the first indirectly connected m's in the matrices. After the diagonalization, the eigenvalues X belonging to the m state can be selected by examination of the coefficients of 42. When K = 0, m = 0 the basis function remains J J 0 11 0) , |m| = 3 1m i = 9 | m | = 15 60 ±\/z s \ \ FIGURE 7. MATRIX J4" (AFTER WANG'S TRANSFORMATION) FOR |m| = 3 + 6n ELEMENTS # 61 m = 0 | m | =6 |m| = 12 |m| = 18 ■ — 7K.--- ✓ \ / \ 7 ^ 7 m \ / s / / I n W \ / \ \N. / / \ N / \ \ \ \ \ \ \ IV,; IX 'Vs ' ' s ' IJZ*CT1 \ Vv f \L \ \ \ \ \ \ \ N S. \ \ \ \ \ \ N S V ' V s S ''S' S S s '-'o \ \ \ 11 \ \ \ \ \ \ \ V* \ \ S ^ s s ' S S s s \ \ ' S ' \ \ \ \ \ \ V v N v' \ \ \ \ \ FIGURE 8. MATRIX JH" (AFTER WANG'S TRANSFORMATION) FOR OLD K, (m| = 6n ELEMENTS . 62 m=0 |m|=6 |m|=12 |m| =18 I X For (+)-block a = 0, b = a/2(J K=0 M m=0|j^|J K=2 M m=0) , c = J2V'6 , d = r/2V\, 12s e = Y12’ f “ V6* For (-)-block a = b = c = d = 0, e = -VJj2, f = -V£. FIGURE 9. MATRIX (AFTER WANG'S TRANSFORMATION) FOR EVEN K, |m| = 6n ELEMENTS. 63 the eigenvectors. The torsion rotation energy levels E may then be calculated from the equation E = DJ(J + 1) + (A - D) SELECTION RULES The exact selection rules can be obtained from the explicit calculation of the dipole matrices. The discussion given below is for the |mj f 3n case in which the basis functions are I J K M m)'s, but the same result can be derived for the |m| = 3n case in which the basis functions arejjjjJ K M m) + | J -K M . The eigenfunctions can be expressed as a linear combination of the free rotor wavefunctions <P in, 1 l,{ where (A is independent of M. Since there is very little mixing between different m's only very insignificant errors in intensity calculation will be introduced by the approximation ^ J l l m f ^ ^ J m T , K lJ K M m) • The dipole matrix for a transition is = M m r l / ^ H ^ J ' M ' m V ^ ~ m'r,K^Jlm'r',K1^ K M m ^ cos® IJ ' ) where/U is the magnitude of the dipole moment and 6 is the angle between the dipole moment and the space-fixed axis (the electric field of the electromagnetic wave). Since the function exp(im<>0 64 is independent of 9 , the selection rule is Am = 0, and (J K M m | cos 6 |J'K'M'm') = (J K M |cos & | J'K'M') $ mm,. King, Hainer and Cross^have shown that (J K M j cos© j J'K'M') vanishes unless K = K', M = M', and J = J' or J'+l. Furthermore, they have shown that KM (J K M | cos 5-1 J KM) = J(J+1) a 2 {((j+l)2-M2)((j+l)2-K2Jj (J K M (cos ©I J+l K M ) - ■ ----------------- (J+1) ((2J+1)(2J+3)J The Q-branch transitions for the |m|>0 states are usually too weak to be observed because the mixings between different K's are small when m 4 = 0. The dipole matrices for the R-branch transitions are HA cL {((J+1)2-M2)((J+1)2-K2)]^ r i j j mr,K j+1 m'T' ,k-------- -r K (J+1) ((2J+1)(2J+3)J* The net absorption intensity^ (integrated) is j 8 l T 5NAf I I 2 2 M=-J JckT ij* 0 where N is the total number of molecules per unit volume, c is the velocity of light, k is Boltzmann's constant, T is the 43* G. W. King, R. M. Hainer and P. C. Cross, J. Chem. Phys. 11. 27 (1943). 44* C. H. Townes and A. L. Schawlow, "Microwave Spectroscopy" (McGraw-Hill, New York, 1955). 65 absolute temperature, )? is the transition frequency andAf is the fractional difference of the molecules in the two states involved in the transition. A f is proportional to (hl?Q/kT)exp(-E/kT) where E is the torsion rotation energy of the lower level and h is Planck's constant. The nuclear spin statistical weights are expected to affect the absorption intensities in two ways. The statistical weight ratio for the I ml = 3n states and the (ml = { = Jn states is lsl or Is(l6/ll) depending on whether the spin of the top atoms is j s - (in the case of -CH^ or -CF^ tops) or 1 (in the case of -CD^ tops). The spins of the frame atoms are expected to affect the intensities according to the parity of K. The treatment is the 45 same as that for a rigid rotor. The effect is different for each molecule so it has to be treated individually. Therefore, this effect is not included in the program VSIX. One may define a relative intensity ratio Ire- j _ by comparing the transition intensities with the intensities of a particular transition. If the m=0, K=0, J = 1<"0 transition is chosen to be the standard, it can be shown that for the R-branch transi tions 45* E. B. Wilson, Jr., Chem. Phys. j£, 276 (1935) • 66 Ire^ = top-atom nuclear spin statistical weight „ 3 X -----| exp(-E/kT) vsT/Tot* { ( ( ^ D2 - m2K ( j , D2 - k 2 )}^ X £ - j| k J ” T 'K J+1 m T’ 'K (J+l)((2J+l)(2J+3))* J. STARK EFFECTS For the | m ] = 3n states, the expression for the Stark effects is similar to that for a rigid rotor as described in Chapter II : A e = (A, + B,M2)E2 . For the |m| + 3n states, the Stark effects t t ' are of first order : AE ■ J M . tK os8I^ M a ^J'M m » r> = C ME . t When m = 0 the Stark effects are practically the same as those for an asymmetric rotor. When |m| + 0 the first order Stark coefficients C^ or the second order Stark coefficients A^ and B^ can be obtained by making use of the relation (J K M m |//Ecosd |j'K'M'm') {((j+i)2-k2 )((j+i)2-m 2)}^ - -^E --------^ S . for J'=J+1 (j+l)f(2J+l)(2J+3)]^ 101 mm or j(j+l) ^KK' ^MM' Smm« for J'=J Since the eigenfunctions ( fi are already provided by the eigenvalue computation(in terms of | J K M m) ) ,the Stark coefficients can be provided by adding a "multiplication and summation" subroutine to the computer program. This subroutine has not been added to VSIX. CHAPTER VI STUDY OP SEVERAL POLYHEDRAL CARBORANES BY CNDO/2 MOLECULAR ORBITAL THEORY A. INTRODUCTION Carboranes and boranes form a class of complex molecules which usually have highly delocalized valence electrons. Very unusual bonds are often found in these molecules. Bridge hydrogens are often present. Carbon is frequently coordinated to five or six other atoms, while the coordinate number of boron is normally five or six. In order to explain the chemistry of these compounds one must first understand the complex structures. Simple valence theories are unable to explain the structures of compounds having highly delocalized electrons. Molecular orbital theory is a useful tool in the study of this class of compounds. One particular family of polyhedral carboranes is the C^Bjj series. Several possible isomers with the carbon atoms at different positions are possible for each member of this series. This is an interesting group of compounds to study because several of the isomers have been found. The structures and the relative stabilities of the known isomers have been determined. The available experimental data will provide a comparison with theoretical predictions. 67 68 Hoffmann and Lipscomb^ used a Hiickel type LCAO - MO theory to attempt to explain the bonding in the trigonal bipyramids, the octahedrons, the pentagonal bipyramids and the icosahedrons. They also tried to predict the chemical properties and the relative stabilities of the various possible isomers. The structures and the conventional labelings for these C_B„ 2 N-2 N systems (N = 5, 6, 7 and 12) are illustrated in Pig. 10. The calculation was of the 3N type^ in which only three chosen hybridised orbitals are included for each B or C atom. The s orbitals of H atoms and one arbitrarily chosen hybridised orbital for each skeleton atom were left out of the calculation. Standard bond lengths of 1.752. were used for all skeleton bonds. This 3N calculation was oversimplified in two respects: the exclusion of the bonds joining boron and carbon to hydrogen, and the use of arbitrarily chosen bond lengths. The hydrogen bonds were assumed to be normal non-polar single bonds. If the H atoms were far from neutral, an incorrect number of valence electrons would be attributed to the skeleton system. Besides, errors in the nature of the skeleton bonds might have been introduced when the hybridised orbital for boron or carbon was arbitrarily chosen for the H bonds. The charge 46. H. Hoffmann and W. N. Lipscomb, J. Chem. Phys. 36, 3489 (1962). OS. Trigonal bipyramid (b) Octahedron Pentagonal bipyramid (d) Icosahedron FIGUBE 10. LABELING CONVENTION FOB POLYHEDBAL CABBOBANES 70 distributions and the nature of the bonds predicted by this 3^ calculation must be considered to be quite unreliable. The use of arbitrary standard bond lengths is justified only when there is justified reason to believe that the presumed structure is fairly close to the actual structure or to the optimized structure corresponding to a local energy minimum (if the molecule has not been discovered). Experimental data (in Table 15) have shown many of the actual bond lengths to be very different from the assumed values of 1.75&* We may expect incorrect bond orders or bond strengths to be predicted by such a calculation. The energy is highly dependent on the bond orders and the structural parameters. Relatively large uncertainties must therefore be allowed in the relative stabilities concluded from the energy comparison for the various isomers. A more logical way to treat the problem is to vary the structural parameters for each molecule so as to optimize the total molecular energy. Such a structure will be referred to as the optimized structure in the rest of this discussion. All the valence electrons should be included in the calculation. Com parisons then should be made among the optimized structures, rather than the arbitarily chosen structures (they will be referred to as the standard structures in the rest of this discussion). Experimental data, when available, should be 71 TABLE 15. STRUCTURAL PARAMETERS AND DIPOLE MOMENTS PREDICTED BY CNDO/2 CALCULATIONS Species Calculated Values Experimental Values TRIGONAL BIPYRAMIDS Vs' 2 B(l)-B(2) I.629! B(2)-B(3) 1.789! /* = 0.0 1>5-C2B3h 5 C(l)-B(2) 1.567! £ L In the 2-Me thy1-derivative , B(2)-B(3) I.764! B(2)-B(3) = I.84A and /* 22 0.0 B(3)-B(4) = 1.87!. 2’3"C2B3H5 C(2)-C(3) 1.600! C(2)-B(4) 1.706! B(l)-C(2) 1.568! B(l)-B(4) I.6O4! 2.74B lf2-C2B3H5 C(l)-C(2) 1.488! C(1)—B(3) 1.566! C(2)-B(5) 1.568! C(2)—B(3) 1.697! TABLE 15. (Continued) 72 Species Calculated Values Experimental Values lf2-C2B3H5 B(3)-B(5) 1.612a /*(in plane) 2.78D /({out of plane) 2.37D //{total) 3.80D OCTAHEDRONS B6H6'* B(l)-B(2) 1.702a B9 0.0 1,6.C2b4h6 C(l)-B(2) 1.640a In the 2-Cl-derivative , B(2)-B(3) 1.680a B(2)-B(3) = 1.70a and /* 0.0 B(3)-B(4) = 1.68a 2,3-C2B4H6 C(2)-C(3) 1.538a 1.540ac C(2)-B(5) 1.646% 1.6ooa C(2)-B(l) 1.637a 1.627a b (i)-b (4) 1.686a 1.72ia B(4)-B(5) 1.702a 1.752a // 4.35D 1.50D 73 TABLE 15. (Continued) Species Calculated Values Experimental Values PENTAGONAL BIPYHAMIDS B7H7 2 B(l)-B(2) 1.77li B(2)-B(3) 1.6422. / * == 0.0 i ,7-c2b5h7 C(l)-B(2) i.7io2 B(2)-B(3) 1.6092 / * s 0.0 1,2-C2B5H7 G(l)—C(2) 1.6282 C (l) —B (3) 1.6832 C(l)-B(4) 1.7192 C(2)-B(3) 1.5682 B(3)-B(4) 1.62l2 B(4)-B(5) 1.6322 B(7)-C(2) 1.7192 B(7)-B(3) 1.7332 B(7)-B(4) 1.7672 y4( (in plane) 3.756D TABLE 15. (Continued) 74 Species Calculated Experimental Values Values 1,2-C2B5H? /^(out of plane) 3.212D ./((total) 4.942D 2,3-C2B5H7 B(l)-C(2) 1.709^ B(l)-B(4) 1.7522. B(l)-B(5) i .76o2 C(2)-C(3) 1.4862 C(2)-B(6) 1.5832 B(4)-B(5) 1.6472 A 6.212D 2,4-C2B5H7 B(l)-C(2) 1.7142 1.7082d B(l)-B(3) 1.7422 1.8182 B(l)-B(5) 1.7502 1.8152 C(2)-B(3) 1.5802 1.5462 C(2)-B(6) 1.5842 1.5632 B (5) —B(6) 1.6502 1.65l2 /< 2.358D 1.32D 75 TABLE 15 (Continued) Species Calculated Values Experimental Values ICOSAHEDRONS B12H12 B(l)-B(2) 1.764i 1.755 and 1.780 for M = 0 .0 K2B12H12e 1’12-°2B10H12 C(l)-B(2) 1.702i B(2)-B(3) 1.738& B(2)-B(7) i.76ai M = 0.0 1’2-C2B10H12 " 8.50D Assuming all skeleton = 5.29D bonds to be 1.75^. a. Ref. 14 b. Ref. 15 c. Ref. 13 d. Ref. 12 e. Ref. 4 76 compared, with the predicted values. Particularly, the accurately determined structural parameters should be compared with the predicted values. The ability to predict correct structural parameters is a necessary condition for a satisfactory MO theory, A molecular orbital theory, CNDO/2, introduced by Pople and g Segal was used by this author to restudy these carboranes. A brief description of the theory is given in next section. To provide an additional check on the ability of the CNDO/2 theory in structural prediction for polyhedral boron compounds, pentaborane (Fig. ll) was also studied. Some carboranes will rearrange to different isomers at elevated temperatures. The rearrangement of 2,3-C0B^Hg from the cis form to the trans form was examined. The CNDO/2 theory was used to study the inversion barriers for two proposed A 2 mechanisms^" (Fig. 12). BgHg” was used as a model in the barrier calculation. 77 Boron # Terminal Hydrogen ( H(t) ) O Bridge Hydrogen ( H(b) ) FIGURE 11. STRUCTURE OF PENTABORANE . 78 (a) intermediate ( 3 similtaneous dsd rearrangements) intermediate FIGURE 12. TWO POSSIBLE REARRANGEMENT MECHANISMS FOR 0oB,H/r . 79 B. CNDO/2 MO THEORY Pople and Segal^’^8’^ have introduced an approximate self- consistent molecular orbital theory in which the overlap distri bution ^u(l) ^v(l) °f any two atomic orbitals and is neglected in all electron repulsion integrals (complete neglect of differential overlap). In the second version of this theory^ (CNDO/2), the penetration effect of a valence electron into the core of another atom has been set to zero. In the CNDO/2 approximation, the coefficients c^u of the LCAO-SCP molecular orbitals O'. = £ c. d> ~ i u iu T u are normalized eigenvectors of the Hartree-Fock matrix F with elements F = --Hi + A ) + ((P.A - Z.) - H ? - 1)) y *A uu u u' *>' AA A' uu * AA + - V and F = fi’-S - %P uv "AB uv 2 uu AB where < f > is an atomic orbital of Atom A and (£>„ of Atom B. That part of the diagonal matrix element of < p which is identical to the core Hamiltonian of the Atom A on which is centered has 47* J* A. Pople, D. P. Santry, and G. A. Segal, J. Chem. Phys. 42, S129 (1965). 48. J. A. Pople and G. A. Segal, J. Chem. Phys. 42* SI36 (1965). 80 been replaced by + V - <ZA - *> fAk where 1^ is the atomic ionization potential, A^ is the atomic electron affinity, Z^ is the charge of the core of A and T is the average interaction between two valence electrons of Atom A. P is the charge density and the bond-order matrix occ P = 2 £ C. C. , UV 1 1U iv’ and the diagonal terms of this matrix represent atomic orbital charge densities. PAA is the total charge on Atom A P.. = I A P . AA u uu AB» average interaction energy between an electron in any valence atomic orbital of A and another in an orbital of B, is evaluated theoretically from valence s orbitals. i3 a bonding parameter given by ■ « ft + ft > o where ^ 3^ is chosen empirically but depends only on the nature of Atom A. , the overlap integral between atomic orbitals <p and <pv, is calculated with Slater atomic orbitals (with an effective charge of 1.2 for hydrogen). Initial estimates of the LGAO coefficients are obtained from a Hiickel-type theory using matrix elements F (o) = -i(l + A ) uu' ' u u' and P (o) = /ST-qS , uv' ' / AB uv’ and the final solution is approached by an iterative scheme until —8 self-consistency, measured by stability to 10” a.u» in the 81 energy, is achieved. The computer program for the CNDO/2 calculations was made available to this author by Professor Segal. The input data consists of the number of atoms, the total charge, the multi plicity, and, for each atom, the atomic number with the cartesian coordinates. An option has been added to the program so that bond lengths and bond angles may be used in place of cartesian coordinates. The calculations were performed on the IBM 360/65 computer at the U.S.C. Computer Laboratory. C. CALCULATIONS There are three possible isomers of C0B,H._, two of C_B,H.., £ y 0 2 4 6 four of C^B^H^ and three of C2Bio^12’ ®ne necessary (but not sufficient) condition for any stable molecule to exist is the existence of a local energy minimum with respect to geometric changes. The structures corresponding to the energy minima were determined for all these isomers except for I^-C^B^qH ^ and 1,7-c2B^qH^2* To° much computer time would be necessary to optimize the structures for these two species. Optimized -2 structures were also determined for the corresponding ions, The bond lengths were determined to within O.OOlSL except for 1,2-CgB^Hy, 2,3-C2B^H^ and 2,4-C2Bj.H^ where the precisions were only 0.004^. Bond lengths were assumed to be 1.20& and I.I08. 82 for all the B-H and the C-H bonds. Some empirical assumptions about the H bond angles were utilized during these optimizations: (l) the in-plane H bonds bisected the exterior angles of the skeleton atoms; (2) the opposite apex H bonds were colinear;(3) in the case of 1,2-C0B,H,. and 1,2-C„B_Hr7. the base skeletal atoms 2 2 5 2 5 ( were coplanar with the H atoms attached to them. The errors introduced by these assumptions were not expected to be signi ficant. Calculations were also performed for all these isomers using standard bond lengths of 1.75^ for all the skeleton bonds. These results provide a comparison with the optimized structures as well as with the results of Hoffmann and Lipscomb. The energies are compared in Table 16. The charge distri butions are listed in Table 17. The parameters of the optimized structures are tabulated and compared with the available experi mental data in Table 15. In the calculation for the structure of pentaborane, all the independent structural parameters including the H orientations were optimized. The optimization was carried to an accuracy of O.OOlS. for each bond length and 0.05° for each bond angle. The 9 49 50 predicted structural parameters and the experimental data 49* K. Hedberg, M. E. Jones and V. Schomaker, Proc. Natl. Acad. Sci. U. S. 28, 679 (1952). 50. W. J. Dulmage and W. N. Lipscomb, Acta. Cryst. 260 (1952) . 83 TABLE 16. ENERGY COMPARISON Molecules Hoffmann- Lipscomb Calculations CNDO/2 Calculations With Standard Bond Lengths CNDO/2 Calculations With Optimized Structures V s " 2 -184.44 ev.a -5,8766 a.u. -5.9611 a.u. 1,5-02BjH5 -197.04 -5,5446 -5-7748 2,3"C2B3H5 -194.32 -5.5030 -5.7021 1,2-CjBjHj -195.42 -5.5259 -5.7578 V s " 2 -221.50 -7-5544 -7.5760 1 >6-C2B4H6 -231.96 -7.1525 -7.2603 2>5-°2B4E6 -231.62 -7.1518 -7.2820 B7H7~2 -252.84 -8.9747 -9.0699 1’7"C2B5H7 -260.90 -8.4517 -8.5861 1,2-C2B5H7 -262.98 -8.4998 -8.6713 2,3-C2B5H? -263.30 -8.5431 -8.7552 2,4-C2B5H? -263.78 -8.5683 -8.7439 B12H12"2 -426.98 -l6.7606 -16.7647 1,2-C2BioHi2 -435-68 -16.1893 1’7-°2B10H12 -436.00 -16.2122 1,12-C2BioHi2 -436.00 -16.2205 -16.2436 & • 1 £L>U« “ 27*21 ev. 64 TABLE 17. THE PREDICTION OP THE VALENCE ELECTRON DENSITIES8, Species Hoffmann- Lipscomb Calculations CNDO/2 Calculations With Standard Bond Lengths CNDO/2 Calculations With optimized Structures TRIGONAL BIPYRAMIDS V s " 2 B(1),B(5) 3.623 3.32l(l,192)b 3.292(1.226) b(2),b(3),b(4) 3.251 3.095(1.230) 3.089(1.232) 1,5-C2B3H5 C(1),C(5) 4.396 4.012(0.928) 3.984(0.965) B(2),B(3),B(4) 2.736 2.963(1.077) 2.962(1.071) 2,3-c2b3h5 0(2),c(3) 3.829 3.917(0.936) ■ 3.860(0.944) B(1),B(5) 3.196 3.052(1.035) 3.097(1.051) B(4) 2.950 3.107(1.013) 3.094(1.004) 1,2-02B3H5 c(i) 4.273 4.032(0.925) 3.805(0.956) C(2) 3.729 3.884(0.955) 3.988(0.965) B(3),B(4) 2.870 3.022(1.049) 3.020(1.045) b(5) 3.256 3.024(1.038) 3.099(1.057) OCTAHEDRONS ■ A ' 2 all B 3.333 3.109(1.224) 3.101(1.232) i ,6-o2b4h6 e(i),o(6) 4.050 3.892(0.955) 3.892(0.975) all B 2.975 3.019(1.058) 3.022(1.060) TABLE 17. (Continued) 4--------------------------------- 85 Species Hoffmann- Lipscomb Calculations CNDO/2 Calculations With Standard Bond Lengths CNDO/2 Calculations With Optimized Structures 2,3-C2B4H6 C(2),C(3) 3.889 3.900(0.948) 3.859(0.966) B(1),B(6) 2.997 3.007(1.066) 3.018(1.067) B(4),B(5) 3.H4 3.012(1.067) 3.019(1.072) PENTAGONAL BIPYRAMIDS B7H7 2 B(1),B(7) 2.956 2.839(1.301) 2.902(1.253) B(2)toB(6) 3.418 3.170(1.174) 3.137(1.201) 1*7_C2B5H7 C(1),C(7) 3-597 3.695(1.013) 3.711(0.994) B(2)toB(6) 3.161 3.100(1.025) 3.082(1.036) 1>2"C2B5H7 C(l) 3.454 3.688(1.009) 3.697(0.988) C(2) 4.046 3.975(0.914) 3.905(0.943) B(3),B(6) 3.087 3,032(1.036) 3.041(1.057) B(4),B(5) 3.269 3.098(1.027) 3.087(1.047) B(7) 2.788 2.878(1.152) 2.902(1.101) 2,3-C2B5H? C(2),C(3) 3.952 3.928(0.923) 3.864(0.956) B(4)>B(6) 3.165 3.023(1.049) 3.044(1*069) b (i),b(7) 2.689 2.858(1.146) 2.893(1.097) B(5) 2.610 3.105(1.040) 3.090(1.063) TABLE 17. (Continued) 86 Species Hoffmann- Lipscomb Calculations CNDO/2 Calculations With Standard Bond Lengths CNDO/2 Calculations With optimized Structures 2,4-C2B5H7 C(2),C(4) 4.171 3-979(0.928) 3.909(0.956) B(5),B(6) 3.179 3.033(1.048) 3.045(1.067) B(1),B(7) 2.666 2.867(1.131) 2.895(1.094) B(3) 2.969 2.978(1.048) 3.007(1.065) ICOSAHEDRONS B12H12' 2 all B 3.167 2.988(1.179) 2.990(1.177) 1,2-C2B10H12 C(1),C(2) 3.706 3.815(0.935) B ( 3) * B (6) 2.919 2.953(1.072) b (4),B(5), B(7),B(11) 3.027 2.966(1.076) B(8),B(10) 3.162 2.990(1.083) B(9),B(12) 3.158 2.978(1.089) C(1),C(7) 3.852 3.825(0.945) B(2),B(3) 2.899 2.956(1.067) B(5),B(12) 3.026 2.957(1.083) B(4),B(6) B(0),B(11) 3.030 2.970(1.077) B(9)»B(lO) 3.162 2.991(1.082) a. 4«0 for neutral C, 3*0 for B and 1.0 for H. b. Electron densities of H they attach to. atoms are quoted behind the atoms 87 are comt-ired in Table 18., _ p In the study of the C^B^Hg rearrangement mechanisms, BgHg was used as a model to calculate the rearrangement barriers. It -2 is much easier to carry out the optimization for the BgHg intermediates because of their exact and C^, symmetries. The difference between the energy of the optimized structure for an intermediate and the energy of the optimized structure in the octahedral form represents the minimum value of the barrier for that particular mechanism. The optimized structures and the _ 2 barriers for BgHg intermediates are shown in Fig. 13. Using _2 BgHg as a model the difference in energy, strictly speaking, _2 only represents the predicted barrier for the BgHg rearrange ment and not for the C^B^Hg rearrangement. It is necessary to have some indication that the calculated barriers for the two species are of the same order of magnitude. A calculation was performed for C2B^Hg assuming all the skeleton bond lengths were 1.652. for both the intermediate and the octahedrons. A similar calculation was performed for BgHg-^ using 1.70& as standard bond lengths. The barriers were compared in Fig. 14. Since the two values differ by less than 10$, the use of BgHg*"^ as a model may be considered to be justified. 88 TABLE 18. STRUCTURAL PARAMETERS OP PENTABORANE Experimental Parameters CNDO/2 Calculation Micro wave8 . Electron , Diffraction v c X-ray Bond B(l)B(2) 1.68li 1.687+0.005 1.700+0.017 1.66+0.02 Bond B(2)B(3) 1.7284 1.800+0.003 1.805+0.014 1.77+0.02 Bond B(l)H(t) 1.1944 1.22(assumed) 1.234+0.066 1.205+0.06 Bond B(2)H(t) 1.2024 Bond B(2)H(6) 1.3644 1.35+0.02 1.359+0.077 1.35+0.04 Angle B(l)B(2)H(t) 130.38° 136.17+0.50 120+20° 115+5° Angle between B(2)H(t) and the base 6°(up) 3°(up) 19°(up) 24°(up) Exterior Angle between planes B(l)B(2)B(3) and B(2)H(b)B(3) 182.28° 196+2° 187+10° 190+5° Angle between B(2)H(b)B(3) and the base 56°(down) 57°(down) 58°(down) 6l°(down) a. Ref. 9 b. Ref. 49 c. Ref. 50 89 (a) D,, intermediate a = 1.50 A b - 1.73 £ = 141° BH bond - 1.20 8. (assumed) Barrier = O .48 a.u. c = 1.74 2 d = .1.59 2 P - 153° BH! bond = 1.20 2. (assumed) Barrier < = 0.54 a«u. (b) intermediate. FIGURE 13. OPTIMIZED INTERMEDIATES FOR BgHg2 ISOMERIZATION . 90 octahedron octahedron trans C IS C2B4H6 Assumptions t octahedron B6H 6 Assumptions : octahedron -2 all skeleton bonds = 1.65& all skeleton bonds = 1.70& BH - 1.20l BH = 1.20& CH = 1 .102. (defined in Fig.13)=135° ° < = 135° FIGURE 14. A COMPARISON OF REARRANGEMENT BARRIERS FOR AND B.HT2 2 4 ° 6 6 . 91 D. DISCUSSION ENERGY COMPARISON The energies calculated with the CNDO/2 theory using the standard bond lengths and those using the optimized structures are tabulated in Table l6, together with the results of Hoffmann and Lipscomb. For convenience, they are to be referred to as the CND0/2(S), the CNDO/2 (0), and the 3N calculations. The CNDO energies are not to be directly compared with the values of 3N calculation. The energy reference in the 3N calculation is different from that in the CNDO/2 calculations. Therefore, the energies predicted for the isomers of each system are to be com pared within each type of calculation. These orders represent the predictions of the relative stabilities. For the C0B,H.. system, all three calculations correctly * j 0 predicted the most stable isomer to be 1,5-C2B^H^, the only known isomer. For the CgB^Hg system, both isomers are known but the trans form is the most stable one. The CND0/2(0) calculation slightly favored the cis isomer while the other two slightly preferred In the case of CgB^H^, both the CNDO/2(S) and the 3N calcu lations slightly favored 2,4-C2B^.H^, the only known isomer, while the CND0/2(0) calculation favored 2,3-C0BcH„ by about 0.01 a.u. 92 in energy. 1,2- and 1>7“^2^10^12 have not been optimized because too TT -2 much computer time would be necessary. For B^gH and 1,12- C^B^H^g, the optimized structures and the CND0/2(O) energies were found to be very close to the standard structures and the CND0/2(S) energies. One may expect the two CNDO results to be parallel. The CND0/2(S) calculation predicted the correct order of stabilities for the three isomers all of which were known, while the 3N results could not choose the more stable form between 1,7- and 1,12-CgB^QH^g. Some observations may be discussed here. First, although it may be just a coincidence, the two standard calculations using the same bond lengths gave almost parallel predictions. This probably means that the exclusion of the hydrogen bonds did not have significant effects upon energy comparisons between the possible isomers. Secondly, the optimized structures were found to be quite different from the standard structures in bond lengths and bond angles, except in the case of the icosahedrons. As a necessary result, the CND0/2(s) energies are much higher than the CND0/2(0) values (the local energy minima). Calcula tions using arbitrarily chosen bond lengths as unrealistic as these must be treated with a large uncertainty in applying them to energy comparisons. The small preferences in the CNDO/2(S) and the JN calculations for the most stable isomers are probably within these uncertainties. These correct predictions 93 using arbitrary bond lengths must be considered lucky coinci dences since choice of another bond length could change these predictions. Thirdly, in all the calculations carbon always preferred the lowest possible coordinate number. Twice, there was a choice between either two B-C bonds or one B-B bond plus one C-C bond, without affecting the coordinate numbers of carbons. The CND0/2(0) calculation slightly preferred the latter. It chose the less stable form for C.B.H, and the unknown isomer 2 4 6 for C^B^H^. Also, this calculation consistently underestimated the bond lengths of weak B-B bonds. The cause of the wrong preferences may be the slight overestimation of the B-B bond strengths. In the energy comparison using CND0/2(0) calculation, one should allow about 0.02 a.u. for uncertainty in energy. Among the unknown isomers, 2,3-C.B_H„ is probably the only com- 2 5 I pound likely to be discovered. 1,2-Cr i BI .Hr7, 1,7-C„BcH,7 and 2,3- 2 3 ( 2 ol C^B^Hj. were predicted to be much higher in energy than the most stable isomers. They also involved higher coordinate numbers for carbon atoms. l^-C^B^H,. was predicted by CND0/2(0) to be higher in energy by 0.017 a.u. than the known isomer ( barely within the energy uncertainty limit),. But the increase in the coordinate number for cne carbon probably renders 1,2-C_B,H_ unlikely to be discovered. 94 STRUCTURAL PARAMETERS The parameters of the optimized structures are tabulated in Table 15. Experimental data are compared with them when available. It appears that the agreements are very good except for the long B-B bonds. The theory consistently underestimated the lengths of weak B-B bonds. Otherwise, the average errors are within 0.03&, only slightly higher than the uncertainties in most x-ray or electron diffraction studies. The complete structure of pentaborane has been experiment ally determined. Because of its symmetry, it is practical to include all H parameters in the structural optimization attempt. The results (Table 18) are in remarkable agreements with the experimental values, except for the base B-B bonds. This is consistent with the carborane results that for very weak B-B bonds the theory underestimated the lengths. The results also illustrate the ability of the CNDO/2 theory to predict the orientations of the bridge hydrogens. Further, it is very gratifying to find the optimized B-H bonds axe very close to 1.2o2. , the value assumed in the carborane calculations. CHARGE DISTRIBUTIONS AND BOND STRENGTHS Charge distributions present useful information for the prediction of sites for electrophilic and for nucleophilic reactions, while bond orders may be helpful in the prediction of positions of bond cleavages. The valence electron distributions 95 as predicted by the ?N calculation, the CNDO/2(S) and the CND0/2(0) calculations are tabulated in Table 17. The electron densities of the H atoms are given in parentheses after those atoms to which they are attached. It appears that the differences in bond lengths did not greatly affect the net charges on the atoms. This is apparent upon the comparison of the two CNDO/2 results. The 3N results, however, are very different from the CNDO/2 results. The 3N calculations predicted very polar atoms, at least partly due to the exclusion of the H bond3. The signs of net charges on several atoms were predicted by the 3N calculation to be opposite to those by the CNDO/2 calculations. Without experimental evidence, it would be unjustified to discredit a set of results. But, because of the exclusion of H bonds, the 3N-type predictions may be considered to be much less reliable than the CNDO/2 pre dictions . The bond orders using arbitrary structural parameters are meaningless since they are expected to be very sensitive to the bond lengths (and bond angles). As for the optimized structures or the real structures, the geometries and the bond lengths are themselves fairly good indications of bond strengths. The dipole moments appear to be consistently overestimated. Small bendings of the H bonds did not affect these values significantly. The CNDO/2 theory is probably not capable of predicting very accurate dipole moments for the polyhedral 96 carboranes and boranes, although it has been shown by Pople and Gorden^ to be successful in predicting this property for a broad spectrum of molecules. REARRANGEMENT 2 4 ° The rearrangement of cis C^B^Hg to trans C^B^Hg was reported (50 by Onak, Drake and Dunks' to take place at a temperature just above 250°C. No detailed kinetic data was available but the rearrangement was believed to be a unimolecular reaction and it took several hours for the rearrangement to be completed. An energy barrier may be estimated from this information using the unimolecular rate equation k^ = A exp(-E/kT) where A » 10^/sec and E is the barrier. If the rearrangement is -4 / completed in several hours k^ is probably about 10 /sec. since T is about 250°C or 523°K, kT » 1.05 kcal/mole. The barrier E should be about 42 kcal/mole or 0.08 a.u. in energy. A dsd (diamond-square-diamond) scheme^ has been proposed as the basic mechanism for most of the carborane rearrangements. This scheme (Pig. 15) > involving breaking of a bond and forming another bond, has been used to explain several simple rearrange ments^’^. For the C^B^Hg rearrangement two complex mechanisms 51. J. A. Pople and M. Gorden, J. Am. Chem. Soc. 82., 4253 (1967)* 52. T. Onak, R. P. Drake and G. B. Dunks, Inorg. Chem. 2, 1686 (1964). 97 FIGURE 15. dsd REARRANGEMENT . 98 have been proposed^: (1) three similtaneous rearrangements involving an approximate intermediate; (2) the breaking of three bonds followed by the forming of a new bond to create an approximate intermediate . They are shown in Fig, 13. In the CNDO/2 calculation, the barrier was found to be O .48 a.u. for the first mechanism and 0.54 a.u. for the second* r These values are about six or seven times higher than the barrier estimated from the experimental information. Although these values were calculated indirectly using a model, a calculation described in Section C did indicate that the barriers from the CNDO/2 theory should be approximately the same for two molecules. It is quite unlikely that the CNLO/2 theory would over estimate the barriers by sixfold or by 0 .4 a.u. The two proposed mechanisms should be considered equally unlikely. The rearrangement probably goes through another path. APPENDIX I COMPUTER PROGRAM QFIT A. DESCRIPTION The Q-branch transition frequencies depend on two rotational parameters: A-C and U, where X= (2B-A-C)/(A-C). This program, QFIT,is written to determine these two constants from the frequencies of a given pair of tentatively assigned Q-branch transitions. A reasonable initial guess of A-C and K should be provided in the input data. The two constants are determined from the transition frequencies through an iterative scheme. Using these determined constants, the program proceeds to predict the frequencies of Q-branch transitions up to a specified upper limit of J for the specified types of transitions (depend ing on which non-vanishing dipole moment components are present). This program can handle one or more problems in each run. In each problem, one or more pairs of transition frequencies can be entered for fitting. Each entrance (pair) is treated as an individual calculation. The input data for each problem includei (1) the identification of the problem; (2) the upper limit of J; (5) the information as to which dipole moment components are non-vanishing; (4) the desired accuracy in the fitting of the given pair _________________________________. 9 . 9 ____________________________________ 100 of transition frequencies to A-C andX; (5) the initial guess of A and C; (6) the number of pairs of frequencies entered for fitting; (7) the transitions and the frequencies. B. PREPARATION OP DATA CARDS Card Al. Identification of the job Card A2. Number of problem in this job Format 12A6 Format I5 Repeat the following cards for each problem Card Bl. Identification of the problem Upper limit of J Card B2. Card B3. Card B4. Card B5. Non-vanishing dipole moment components (0 for non-vanishing, and 1 for vanishing) 1. a-type 2. b-type 3. c-type Desired accuracy in the fitting (MHz) Initial guesss 1 . X . 2. A (MHz) 3. C (MHz) Format 12A6 Format I5 Format 315 Format F7.2 Format 3EI8.9 101 Card B6. Card B7. Number of pairs of transitions Format 15 entered One card for each transition Format 615, F11.2 1. J (lower level) 2. (lower level) 5. Kq (lower level) 4. J (upper level) 5. (upper level) 6. Kq (upper level) 7. Frequency (in MHz) APPENDIX II COMPUTER PROGRAM 7SIX A. DESCRIPTION The function of this program is to compute the torsion- rotation energies, the frequencies of the allowed transitions, and the relative transition intensities, for a molecule with sixfold internal rotation harrier. The theory has been reviewed in Chapter V. The program is composed of a main program and three subroutines: EIGENJ, TRANSI and HDIAG. The main program reads in all the data including the number of problems and the parameters for each problem. These include the identification, the predicted rotational constants, the experimental transition frequency range, the spin of the top atoms, the option to print out the eigenvectors, the option to include the twelvefold barrier, the predicted sixfold barrier, the predicted twelvefold barrier (if the option is being taken), the number of torsional states under consideration, and the minimum J and the maximum J for each state. After all the data have been read in, the main program goes through a complex routine (illustrated in the float-chart). The torsional states are handled one at a time. The odd K and the even K portions are treated separately. In the case of ImI = 3n, the (+)- and the (-)-blocks are treated separately also. At each situation the main program calls EIGENJ to 102 10'3 provide the relevant energy levels and the corresponding eigenvectors for each J from the minimum J up to the maximum J. After all the relevant energy levels are on hand, the main program then calls TRANSI to compute the relative intensities ^rel Chapter V) for all the allowed transitions. When the subroutines EIGENJ is called, it sets up the appropriate truncated matrix and calls HDIAG to diagonalize it. The eigenvectors are examined and those having the largest component belonging to the particular |m| are chosen. The corresponding eigenvalues are selected and the rotational energies are computed. These energies and their corresponding eigenvectors are then returned to the main program. When the subroutine TRANSI is called, it selects those allowed transitions (Am = 0 and AJ = l) with frequencies in the specified range. The intensities are calculated and compared with that of the transition J = l<-0, m = 0 and K = 0. The effects of the top atom nuclear spin statistics are included in the calculation. The transitions with relative intensities greater than 0.1 are given in the output. Subroutine HDIAG diagonalizes a real and diagonal-symmetric matrix by Jacobin's method. A flow chart for the routine in the main program is given in Section B. The input data format is described in Section C. B. FLOW CHART 104 data for first problem START EXIT data for next problem 'T.ast^v. iroblem Y first m tk_ odd K No next m Yes No even K ( ■ .even K Yes (+)-block No Yes No & No (-)-block -)-block minimum J Yes J+1 No call EIGENJ Yes call TRANSI maximum J SUBROUTINE EIGENJ SUBROUTINE SUBROUTINE TRANST HDIAG 105 C. PREPARATION OF DATA CARDS Card Al. Identification of the job Card A2. Number of problem in this job Format 12A6 Format 15 Repeat the following cards for each problem Card Bl. Identification of the problem Card B2. Rotational constants (MHz) 1. A (Frame only) 2. B 3. C 4. Top (about the axis) Card B3. Frequency range (MHz) 1. Lower limit 2. Upper limit Card B4. Option instructions 1. Multiplicity of the top atoms (l for H or F, 2 for D) 2. Output of eigenvectors (0 for printing, 1 for omission) 3. Twelvefold barrier (0 for consideration, 1 for no) Format 12A6 Format 4^18.\ Format Fll.3, Format 315 F12.3 Card B5. Card B6. Card B7. Barriers (cal/mole) Format 2F7.2 1. Sixfold barrier 2. Twelvefold barrier (set to 0.0 if is not being considered) Total number of tortional Format 15 states |m|r under consideration Repeat for each |mj 1. |m| Format 515 2. Minimum J 3. Maximum J BIBLIOGRAPHY Arnold, W.f Dreizler, H., and Rudolph, H. B., Z. Naturforsch 23a. 301 (1968). Bauer, S. H., and Hastings, J. M., J. Am. Chem. Soc. 64, 2686 (1942). Beaudet, R. A., unpublished work. Beaudet, R. A., and Poynter, R. L., J. Chem. Phys. 2166 (1965). Beaudet, R. A., and Poynter, R. L., to be published. Cohen, E., and Beaudet, R. A., J. Chem. Phys. 4§.> 1220 (1968) . Costain, C. C., j. Chem. Phys. £2> 864 (4958)* Dulmage, W. J., and Lipscomb, W. N., Acta. Cryst. 2> 260 (1952). Bunks, G. B., and Hawthorne, M. P., J. Am. Chem. Soc. 90. 7355 (1968). Golden, S., and Wilson, Jr., E. B., J. Chem. Phys. 16, 669 (1948). Good, C. B., and Williams, R. E., U. S. Patent No. 3030289 (1959), Chem. Abst. 21> 12554b (1962). Hedberg, K., Jones, M. E., and Schomaker, V., Proc. Natl. Acad. Sci. U. S. 2§, 679 (1952). Herberich, G. E., Z. Naturforsch 22a, 761 (1967). Herschbach, B. R., unpublished tables. Herschbach, B. R., J. Chem. Phys. 2i> 91 (1959)* Hirshfeld, F. L., Eriks, K., Bickerson, R. E., Lipper, E. L., and Lipscomb, W. N., J. Chem. Phys. £8, 56 (1958). Hoffmann, R., and Lipscomb, W. N., J. Chem. Phys. 26* 3489 (1962). Hrostowski, H. J., and Myers, R. J., J. Chem. Phys. 22, 262 (1954). 107 108 Huang, Y. S., Dissertation, Appendix I, Univ. of So. Calif., 1969. Kasuya, T., Lafferty W. J . , and Lide, D. R., J . Chem. Phys. 4 8, 1 (1968). Keilin, B., unpublished work. King, G. W., Hainer, R. M., and Cross, P. C., J. Chem. Phys. 11, 27 (1943). Kraitchman, J., Am. J. Phys. 21, 17 (1953)• Landesman, H., and Shapiro, I., unpublished work. Li, L., and Beaudet, R. A., to be published.' Lin, C. C., and Swalen, J. D., Rev. Mod. Phys. 12, 841 (1959)• Lipscomb, W., "Boron Hydrides" (W. A. Benjamin, Inc., New York, 1963). McKown, G., and Beaudet, R. A., to be published. Marshall, S. A., and Weber, J., Phys. Rev. 105. 1502 (1957). Naylor, Jr., R. E., and Wilson, Jr., E. B., J. Chem. Phys. 26, 1057 (1957). Nelson, R., and Pierce, L., J. of Mol. Spect. _18, 344 (1965)• Onak, T., Drake, R. P., and Dunks, G. B., Inorg. Chem. 1, 1686 (1964). Pople, J. A., and Gorden, M., J. Am. Chem. Soc. 8£, 4253 (1967). Pople, J. A., Santry, D. P., and Segal, G. A., J. Chem. Phys. 41, S129 (1965). Pople, J. A., and Segal, G. A., J. Chem. Phys. 41, SI36 (1965). Pople, J. A., and Segal, G. A., J. Chem. Phys. 4 4, 3289 (1966). Rudolph, H. D., Dreizler, H., Jaeschke, A., and Wendling, P., Z-. Naturforsch 22a. 940 (1967). Rudolph, H. D., Dreizler, H., and Seiler, H., Z. Naturforsch 22a. 1738 (1967). Rudolph, H. D., and Seiler, H., Z. Naturforsch 20a. 1682 (1965). Swallen, J. D., and Gostain, C. C., J. Chem. Phys. 2I> 1562 (1959). Tannenbaum, E., Myers, R., and Gwinn, W., J. Chem. Phys. _26, 1057 (1957). Tolies, W. M., J. Chem. Phys.,42, 3019 (1965). Townes, C. H., and Schawlow, A. L., "Microwave Spectroscopy" (McGraw-Hill, New York, 1955). Williams, R. E., "Carboranes", manuscript to be published. Wilson, Jr., E. B., Chem. Phys. 2» 276 (1935). Wilson, Jr., E. B., Lin, C. C., and Lide, D. R., J. Chem. Phys. 22, 136 (1955).

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Creator Cheung, Chun-Chung Stephen (author)

Core Title Structural Studies Of Selected Boron-Carbon Compounds

Degree Doctor of Philosophy

Degree Program Chemistry

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

Tag chemistry (physical chemistry),OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Beaudet, Robert A. (committee chair), Ogawa, Masaru (committee member), Segal, Gerald A. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-401248

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Document Type Dissertation

Rights Cheung, Chun-Chung Stephen

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