# Microwave spectra of certain benaldehydes and the dynamics of twofold internal rotors

код для вставкиСкачатьThis thesis, having been approved by the special Faculty Committee, is accepted by the Graduate School of the University of Wyoming, in partial fulfillment of the requirements for the degr ' " Dean of the Graduate School Date--Augus_t-_2^-197_Q Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MICROWAVE SPECTRA OF CERTAIN BEHZALDEHYDES AND THE DYNAMICS OF TWOFOLD INTERNAL ROTORS by CIBRARTR O F THE Ramesh K. Kakar UNIVERSITY OF WYOMING L ARAMIE A Thesis Submitted to the Department o f Physics and the Graduate School o f the U niversity o f Wyoming in P artial F u lfillm e n t o f Requirements fo r the Degree of Doctor o f Philosophy U niversity o f Wyoming Laramie, Wyoming August, 1970 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI N um ber: D P 14800 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and im proper alignm ent can adversely affect reproduction. In the unlikely event that the author did not send a complete m anuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform DP14800 Copyright 2007 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS I would lik e to express my deepest appreciation to Professor Edgar A. Rinehart fo r his patien t supervision and guidance. The frie n d ly atmosphere created by him in the Microwave Spectroscopy Laboratory made the task o f th is work an enjoyable one, I am p a rtic u la rly gratefu l to him fo r supporting me from his grant, throughout my graduate career. To Dr. C. R. Quade I owe additional thanks. We had soma in terestin g di scussions about th is work during the e a rly part of my graduate career. I ad d itio n , I would lik e to acknowledge the help provided by the Hewlett Packard Company, Palo A lto , C a lifo rn ia , by granting permission to use th e ir K-band Microwave Spectrometer fo r part o f th is work. F in a lly , my wife Sneh did more than her part in the completion of th is work. She displayed exceptional patience and tolerance, especially during the la s t few months o f th is work. To her I give my thanks and unending love. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . LIST OF FIGURES . . . . . ........................................................ . . LIST OF TABLES................................ .... . . . . . . . , . . . . . . . . . . . . . . . . . ii v . v ii CHAPTER I. II. INTRODUCTION . . . . . MICROWAVE SPECTRA OF BENZALDEHYDES Experimental . . . . . . . . . . . . Deuterated Benzaldehyde III. . . 1 . ................................6 . . Id e n tific a tio n o f Rotational Transitions . Benzaldehyde . . . . . . 6 . . . 7 ............................ 12 ..................................... 31 Para Fluorobenzaldehyde . . . Para Chiorobenzaldehyde . . . . ............................... 32 . . . . . . . 44 THE DYNAMICS OF THE TWOFOLD INTERNAL R O T O R ........................... 60 Potential E n e rg y ............................. 63 Kinetic Energy and Coordinate Transformations fo r IAM ...........................65 Hamiltonian Operator and the Basis o f Representation . 73 Results in the High B arrier Approximation . . . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. . 75 Page IV . V. STRUCTURE OF THE BENZALDEHYDE FRAMEWORK . . . .7 8 A N A L Y SIS OF SPECTRA WITH R ES PEC T TO THE THEORY . . . . 96 Height o f the Potential B arrier . . . . . . . . Calculation o f the Parameters fo r Analysis . . Further Developments o f Theory ........................ . . 96 . . 100 . .1 0 7 APPENDIX A. ASYMMETRIC ROTOR ENERGY LEVELS IN RIGID-ROTOR APPROXIMATION B. . . . ......................... . . . . . 109 COMPUTER PROGRAM FOR EVALUATION OF STRUCTURAL PARAMETERS................................................................................. 115 REFERENCES................................................ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 LIST OF FIGURES Figure Page 1 Low resolution fast-scan spectrum o f CgH^ CHO 2 High resolution spectrum o f a typical roational tra n s itio n o f CgH^ CHO . . ..1 0 ............................. 3 High resolution J = 19^-18 band o f Cl^C^H^ CKO . 4 Structure o f the monosubstituted benzene . 5 Structure of the aldehyde group . . . 29 . . . . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. . 53 . 86 92 LIST OF TABLES Table I Page Ground and f i r s t excited torsional state tran sitio n s o f C6H5 'CH0 II ........................................... 14 Second and th ird torsional state tran sitio n s o f C6H5 CHO ............................................................ 20 III Ground state Q-branch tran sitio n s o f CgHg CHO • * IV Rotational constants o f CgHg CHO in the ground and * f i r s t three excited torsional states ................................ V 22 Moments o f in e rtia and in e rtia defects of CgHg CHO in the ground and f i r s t three torsional states VI * * * • • * « • • • • • • • • 33 Second and th ird torsional state tran sitio n s o f CgHgCDO IX 30 Ground and f i r s t excited torsional state tran sitio n s o f CgH5 CDO • V III 25 R elative in te n s itie s o f selected ground and f i r s t torsional state tran sitio n s ................................................. V II 21 ............................. 40 Rotational constants of CgHg CDO in the ground and f i r s t three excited torsional states . . . . . . 41 X Moments o f in e rtia and in e rtia defects o f CgHg CDO . XI R elative in te n s itie s o f selected ground and f i r s t - » torsional state tran sitio n s .................................... . . . . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 43 Table Page X II Ground state tran sitio n s of FCgH4 CHO . X III Rotational constants andmoments of in e rtia of Ground state tran sitio n s o f Cl C6H4 CHO XV . . . . . . . . . . 45 ...............................49 FCgH4 CHO in the ground state XIV . ■35 CgH4 CHO and CV . . . . . . 37 . . 54 Rotational constants, moments o f in e rtia and quadrupole coupling constants o f Cl 35 CgH4 CHO and Cl 37 C6H4 C H O ............................. XVI 58 Comparison of calculated and observed ro tatio n al con stants A and B fo r the ground state of fluorobenzene and c h lo ro b e n z e n e ................................................ ...... 90 XVII Structural parameters o f the aldehyde group 93 X V III Comparison of the calculated and observed ground . . . state principal moments o f in e rtia for the fiv e mole cules XIX . . . . 94 Parameters fo r analysis o f the spectra of CgHg CHO and CgH5 CDO...................................................................................101 XX Comparison o f prin cipal moments o f in e rtia in the ground and f i r s t three excited torsional states o f CcH, CHO and CcHc CDO............................ ........ 6 5 6 5 XXI Comparison o f observed and calculated parameters o f analysis fo r CgHg CHO . XXII 103 . . . . . . . . . 104 Comparison o f observed and calculated parameters o f analysis fo r CgHg CDO . , . , . . . . . , Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. . 105 CHAPTER I INTRODUCTION With it s inherent accuracy and high resolution, microwave spectro scopy is very well suited fo r the study o f molecular structures and cer ta in intram olecular interactions o f polar molecules. This technique ap pears to be a useful tool fo r studying the effects of substitution in the benzene rin g . However, due to comparatively higher principal moments of in e r t ia , the microwave spectra obtained fo r such molecules are rich and d i f f i c u l t to analyze, and consequently few such molecules have been a t tempted. In the present work, structural information (fo r benzaldehyde frame work) was obtained, and the effec ts o f torsional motion o f the aldehyde group in benzaldehyde were studied. This study was undertaken as a step towards a b e tte r understanding o f the dynamics o f molecules with tv/of old b arriers to internal ro ta tio n . Molecules possessing internal rotors with rotational properties o f a symmetrical top are easier to tr e a t than those possessing twofold in te r nal ro to rs , and have been studied extensively. A review a r t ic le by Lin and Swalen^ discusses various th eo retical approaches with respect to the problem o f the former class o f molecules. In such molecules, the moments o f in e rtia do not depend e x p lic itly upon the angle o f ro tation o f the internal ro to r. The dynamics o f internal rotation is quite well under stood fo r these molecules. However, since these molecules are a ll o f a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. £ benzaldehyde spectrum using an assumed structure fo r the molecule. In order to minimise errors* the structure fo r the benzaldehyde framework was determined in the present work. The study of the microwave ro ta tio n al spectrum o f CgHg CHO, CgHg CDO, p - chlorobenzaldehyde and p - flu o ro benzaldehyde helped in the determination of the structure. These mole-, cules are sim ilar in the sense th a t each has an aldehyde group attached to one side of the benzene rin g . obenzaldehyde and g The chlorine and flu o rin e , in p - chlor - fluorobenzaldehyde respectively, in the position para to the aldehyde group, i t is assumed, do not change the enviornment of the aldehyde group from th at which exists in benzaldehyde. Substitu tions w ill c e rta in ly produce disto rtio n s in the regular hexagonal struc ture of benzene. However, i t is noticed th at such distortions produce neg lig ib le e ffe c t on the moments of in e r tia . These are therefore ignor ed and a regular hexagonal structure fo r the benzene skeleton, in ben zaldehyde, is assumed. Attempts to analyze the microwave rotational spectrum o f benzalde8 hyde have been made e a r lie r . In th is previous attempt, approximately 90 1 ines of the a-typ e, R-brarich tran sitio n s were reported. A character is t ic o f the assigned lin es was the occurence of two lin e s , o rig in a lly interpreted to be doublets, fo r each tra n s itio n . In these measurements i t was not possible to ascertain re la tiv e in te n s itie s within a pair of lin es because of poor signal-to-noise ra tio and a rich spectrum with much interference from Stark lobes of other lin e s . At one time i t was f e l t th at the orig in of a pair was an internal rotation doublet v/ith d i f f e r ent rotational co efficie n ts fo r each torsional substate. However, th is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 single type, v/here the internal rotor and hindering potential have a threefold symmetry a x is , th e ir study has not helped in pinpointing the orig in o f the potential barriers hindering internal ro ta tio n . I t is hop ed th at an understanding of the dynamical behaviour o f molecules with twofold potential barriers to internal ro tation w ill provide a wider ba sis of attack toward understanding the o rig in of these potential b a rr i2 ers . 34 Burkhard and Irwin s * approach fo r solving the wave equation fo r % an asymmetric molecule with an asymmetric top rotor takes on a compli cated form and the results do not lend themselves e a s ily to the analysis of the spectrum and the determination o f the b a rrie r o f a sp ecific molecule. Quade and Lin's treatment of the internal ro tation in completely asymmetric molecules on the other hand, contains a minimum of complica ting features and can re a d ily be applied. Their theory is general in the sense th at i t is applicable to a ll molecules in which the internal rotor is not a symmetric top. The assumptions used in deriving the Ham ilto n ia n operator fo r the internal ro tation in th is treatment are ( 1) the molecule is rig id except fo r the degree of freedom fo r internal ro tatio n ( 2) the top ( i . e . internal ro to r) and the framework ( i . e . remainder of the molecule) each posses planes o f symmetry. Quade tightened the sec ond of the above assumptions and imposed the condition of a twofold axis o f symmetry on one of the rig id portions o f the molecule. This theory fo r molecules with twofold potential barriers has been applied to the analysis of the present data. E a r lie r , Quade's theory was applied to the analysis of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 was not consistent with the expected high b a rrie r to internal ro tatio n and large reduced torsional in e r tia . Therefore, the o rig in o f the p air o f lin es remained uncertain fo r a number o f years. B arriers to internal rotation of the aldehyde group in benzaldehyde have been determined using other methods also, v iz . using nuclear mag netic resonance (NMR) techniques0 and from the infared spectrum*0 . Bar r ie r heights, Vg, obtained in both cases were higher than those obtained in the present microwave work. These being 7.9 kcal/mole by the NMR method and 6.4 kcal/mole from the d ire c t measurement o f the torsional frequency fo r liq u id benzaldehyde in the infared region of the e le c tro magnetic spectrum. In the case of the NMR technique, b a rrie r heights in the range of 5 to 20 kcal/mole may be determined by measuring the widths of resonance lin es as functions of temperature. However the time scale is such th a t, i f the b a rrie r height is less th at about 5 kcal/m ole, the internal rotation appears to be free ^ . This e ffe c t is possibly respon sib le in introducing a large source of error in the measured values near the 5 kcal/mole mark. Fately e t . a l d e t e r m i n e d the torsional frequency in the infrared region fo r benzaldehyde both in the liq u id and in the gaseous s tate . Their results emphasized th at i f one is to deduce a to r sional b a rrie r which is due only to forces within the molecule, i t is absolutely necessary to make observations on gaseous samples. S trik in g ly d iffe re n t results were obtained in 1iquids and in vapors due to the in fluence o f neighboring molecules. 133 c m "\ Thus they obtained the results = 6,69 kcal/mole in the liq u id phase and v 4.92 kcal/mole fo r the gas phase of CHO. * = 111 cm""*, These investigators also Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. = 5 report = 104.5 c n f \ Vg. =. 5,13 kcal/mole fo r CgH^ CDO in the gas phase. A more recent work 12 by th is group includes the d ire c t measurement of torsional frequencies fo r p - chiorobenzaldehyde and p - fluorobenzalde- hyde in the in fra - red region. Hanyu, B r itt and Boggs trum of nitrosobenzene. 13 have analyzed the microwave ro tatio n al spec They reported a-type R-branch tran sitio n s fo r the molecule in several torsional states. From the torsional dependence o f the in e rtia defect and r e la tiv e in te n s ity measurements, they were able to estimate the b a rrie r to internal ro ta tio n , Vg = 1350 cm~^. In many respects the spectra o f benzaldehyde and nitrosobenzene are s im ila r. This arise s, o f course, because both molecules are benzene d e riv a tiv e s , with comparable barriers to internal rotation and large reduced torsion al moments o f in e r tia . Another sim ilar molecule on which extensive studies have been made 5 14 15 is phenol * and several o f it s isotopic species . Although phenol has been found to have a high b a rrie r to internal ro ta tio n , the reduced in e rtia fo r the torsional mode is small (in contrast to benzaldehyde). The tunneling frequency appears d ire c tly in the fin e structure o f the microwave rotational spectrum and th is has le d >to an accurate determina tio n of the b a rrie r to internal ro tation o f Vg = 1175 cm” *. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER II MICROWAVE SPECTRA OF BENZALDEHYES •Experimental Commercially available samples o f benzaldehyde, p - chlorobenzaldehyde and p - f 1uorobenzaldehyde were used. The deuterated benzaldehyde (CgHg CDO) sample was prepared by Merck, Sharp and Dohme of Canada and was supplied with 98% D. A ll the samples, except p . - chiorobenzaldehyde, were vacuum transferred once, p - chiorobenzaldehyde occurs in the solid state a t room temperature but has s u ffic ie n t vapor pressure and was used in the solid state . A ll measurements were made a t room temperature with the sample pres sure in the 3-30 mtcrr range. A ll the data, except th at fo r p - chioro benzal dehyde, was taken on the Wyoming Hewlett-Packard Model RE05-8400 B Microwave Spectrometer. Data fo r p - chiorobenzaldehyde in the range 18.0 - 26.5 GHz only was taken on a sim ilar spectrometer situated in Palo Alto a t the Hewlett Packard Company. The microwave source fo r th is spectrometer consists of a backwardwave o s c illa to r which is always frequency s tab ilized by phase-locking techniques and can be swept over any part or a ll o f a frequency band (26.5 - 40.0 GHz in the case o f the Wyoming spectrometer). The frequency can be read d ire c tly on a counter as the source is always locked to the same harmonic of a reference o s c illa to r . The spectrometer employs 33.333 kHz square wave Stark modulation^5. The Stark - modulated signals are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 demodulated by a broad-band crystal detector. The demodulated 33.333 kHz signal is am plified, phase detected and can be displayed on a meter, recorder or oscilloscope. In the present case, chart display was used fo r observing tra n s itio n frequencies. With th is arrangement i t was pos sib le to measure frequencies with an accuracy o f b etter than ± 0.05 MHz with this spectrometer, i f care was taken to ensure th at no d isto rtio n resulted from sweep speeds. The spectrometer also has a c a lib ra tio n arm fo r more accurate re la tiv e in ten sity measurements. This arm provides a calibrated signal th at is compared to the signal from the tra n s itio n in the molecule. This is accomplished by passing microwave power through a microwave modulator, which modulates the power a t a 33.333 kHz ra te . This small amount of modulated microwave power, which can be adjusted in phase and amplitude, is added back into the Stark c e ll. The signal from the Signal C alibrator is then compared to the signal from the sam p le. Ident i fic a tio n of Rotational Transitions The microwave rotational spectrum fo r each of the molecules stud ied in th is work, consists of a large number o f closely spaced high J lin es whose weakness prevents th e ir id e n tific a tio n by means o f the Stark e ffe c t. Therefore fo r the purpose of assigning and id en tifyin g the lin es and to obtain an idea of how the spectra of these benzaldehydes would appear an approximate t r ia l structure was assumed fo r each one o f them. C-F anc C-Cl bond distances used in th is structure fo r p - flu o r - obenzaldehyde and p - chiorobenzaldehyde were calculated from the B ro tation al spectra o f fluorobenzene 17 and chlorobenzene 18 respectively. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R These were calculated to be C~F = 1 .300 and C-Cl - 1.713 R. Structur al parameters from other molecules such as benzene derivatives and acetaldehyde were the basis of choice of t r i a l structure fo r the benzalde hyde framework. Thus the ring group was assumed symmetrical with the bond distances C-C = 1.397 R and C-H = 1.084 R. The C-C bond connecting the aldehyde group was assumed to be 1.480 R with C-0 = 1,211 R, C-H = 1.193 R, / CCH » 124° 6 ' , and / CCO = 123° 2 3 '. This assumed, structure was accurate enough to assist in the assignment of the spectra. I t was now possible to predict general features of the rotational spectrum fo r any one of these molecules. The in e rtia tensor 19 with re spect to the center of mass o f the molecule was diagonalised to y ie ld approximate values fo r I . I , , I„ , the principal moments of in e r tia . a D C And since the principal moments of in e rtia are inversely proportional to the 20 rotational constants ' , an approximate set of rotational constants (ex pressed in MHz) As B, and C respectively was thus obtained. Using the expression fo r the energy levels of an asymmetric rotor (see Appendix A) i.e . ECA.B.C) = ^(A+C)J( J + l) + !s(A~C')E(K) (1) and the appropriate selection rules fo r rotational tran sitio n s an approx imate spectrum fo r the molecule was calculated. This calculation fo r a ll these benzaldehydes predicted th at they are near prolate symmetric top molecules and from th e ir configuration i t was observed that each has a large component of dipole moment along Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 the "a" axis. These approximate calculations fu rther predicted th at a- typ'e R-branch transitions should consist of small regions with a high concentration of lin es separated by large regions with a few lin es in them. These small regions of high concentration of lin es arise due to the s lig h t asymmetry. However, most o f these 2J+1 lin es c a lle d , the high K_.j lin es in the case of a near prolate symmetric top, l i e close to the band centers giving rise to these small regions with high concentra tion of lin e s . The lines s ig n ific a n tly removed from these clumps are the low K_-j lin e s . In these near symmetric roto rs, the band centers are approximately (B +C) MHz apart MHz in thecaseof asymmetric 21 as compared to thedifference top. Therefore i f the of 2 B sum (B + C) c a l culated from the t r ia l structure is very much d iffe re n t from the true sum, the t r ia l structure w ill calculate the location of band centers which are fa r removed form the actual locations. To avoid th is , fa s t- scan low-resolution spectra were taken fo r each molecule. This c le a rly emphasized the near-symmetric top character of these molecules and clumps were observed in each case th at were a constant number of MHz apart (See Figure 1 ). The difference between these band centers being approximately equal to the sum of the rotational constants B "and C. The i n i t i a l in d i vidual values of B and C were now obtained by using the fa c t that a ll these molecules are planar in th e ir equilibrium configurations and there fore 1 + 1 - A B “ 1 C Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 3 3 4 6 0 MHz 3 6 2 4 0 M Hz 3 9 0 0 0 MHz 3 0 7 0 0 MHZ V ll m r . II Figure 1. Fast-scan low-resolution spectrum of CgHg CHO. emphasizes the near symmetric-top nature o f the molecule. I t c le a rly The fr e quency difference between band centers helped in the calculation o f ground-state rotation al constants fo r the molecule. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The i n i t i a l value fo r A was assumed to he the same as th at calculated from the t r ia l structure. Intervals fo r the high lin es which were quite insensitive to the t r ia l structure, fa c ilita te d assignment of these lin e s . As an example, i f the rotational constants A,B and C are s lig h tly o ff from th e ir true values say by 15 MHz, 2 MHz and 2 MHz respectively the calculated tran sitio n frequencies fo r 10g ^ 9g Q and 10^ 3 tions w ill be in error by an appreciable amount. £ trans^‘ However, the frequency interval between the two calculated values w ill be very close to the ac tual interval i . e . about 35 MHz fo r CgHg CHO (compare in Table I ) . There fore the problem was reduced to f i t t i n g the lines observed near a band center with the in tervals fo r tran sitio n s calculated on the basis o f the t r ia l set of rotation al constants. When three lin es were assigned i t was possible to calculate an improved set of rotational constants by using Eq. (1) and the selection rule fo r a-type R-branch tran sitio ns (see Appendix A). These improved rotational constants helped to assign more intense low K_-j lin e s , which are considerably shifted from the high K_^ series and are more sensitive to the values of rotational constants. These therefore helped to determine more accurate rotation al constants. The rotational spectrum of a molecule was "considered id e n tifie d in the ground state when the following conditions were s a tis fie d : 1. The principal moments of in e rtia calculated from the ro - rational constants yielded a near zero value fo r the in e rtia defect A 3 I C - I d - I, . 0 This arises because each of these molecules is plan- ar in its equilibrium configuration. r The in e rtia defect w ill be s lig h tly d iffe re n t from zero because of the zero point vib ratio ns. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 2. The rotation al constants calculated the frequencies fo r other observed tran sitio n s . These conditions were s a tis fie d and the ground state tran sitio ns were id e n tifie d in the case of a ll these benzaldehydes. The data and characteristics of the rotational spectrum fo r each molecule are given below. Benzaldehyde (CgHg CHO) In an e a rlie r attempt to analyze the microwave rotation al spectrum of benzaldehyde, a ch aracteristic o f the assigned lin es was the occuren ce o f two lin e s , o rig in a lly interpreted to be doublets. This was, how ever, not consistent with the expected high b a rrier to internal rotation and large reduced torsional in e r tia . The o rig in of the p a ir of lin es remained uncertain fo r a number of years. In the present work, the data taken with a more sensitive spectro meter, makes i t clear th at each member of a pair of lin es has a d if f e r ent in te n s ity , with one lin e o rig in atin g in the ground and the other in the f i r s t excited torsional state 20 . Nearly two times the o rig inal num ber of 1ines have been assigned, including some* fo r the second and th ird excited torsional states. Rotational co efficien ts have been derived from the data fo r each torsional state fo r which lin es have been observ ed. I t has also been possible to obtain an estimate of the b a rrie r hin dering internal ro tation from re la tiv e in te n s ity measurements. The rotation al spectrum of benzaldehyde was observed in the fr e quency range 26.5 - 40.0 GHz. The spectrum was found to be rich and the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. nearly 225 assignedlin es a t best represent the region covered. 25% of the lin es observed in Although someQ-branch lin es were observed fo r the ground s ta te , most o f the lin es id e n tifie d were a-type R-branch tra n s i tio n s , J -*• J + 1, K .j were found. = 0. The lin es were r e la tiv e ly weak. resolve Stark components; mined. For several values of J complete series in I t was not possible to hence, the dipole moment has not been deter The transistions observed in the lower part o f the frequency re gion covered (low J tra n s itio n s ) were less intense than those observed in the upper part (high J tra n s itio n s ). r ie s , For a p a rtic u la r J -> J + 1 se the in ten sity increased with a decrease in the value of K_j. fo r high J and low Only some rotation al lin es were assigned fo r th is mole cule in the second and th ird excited torsional states. However, fo r the ground and f i r s t excited torsional states complete series were observed. This data is reported in Tables I and I I . A search was made fo r selected b-type Q-branch and R-branch tran sitions and several Q-branch lin es were id e n tifie d fo r the ground state of the molecule. These are lis te d These assigned in Table I I I . Q-branch lin es assisted in deriving the rotational constants fo r the ground state of benzaldehyde.- A ll the other ro ta tio n al co efficie n ts fo r higher torsional states were derived using the as signed lin es lis te d in Tables I and I I . These co efficie n ts are given in Table IV fo r each torsional s ta te . Thecalculated values fo r tran sitio n s frequencies were obtained by using a computer program w ritten by Beudet 22 . This program is w ritten in Fortran and o rig in a lly compiled fo r an IBM 7090 computer. I t was s lig h tly modified to run on PHILCQ 2100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE I Transition Frequencies (in MHZ) of CgH^CHO fo r the Ground and F irs t Excited Torsional States CgHgCHO v=Q Transition , ^ 99 ,0 109 ,2^ 99 , 1 v-1 Observed Calc-Obs Observed Calc-Ob! 27783.55 + .18 27808.02 + .22 27798.02 -.1 2 27822.33 + .07 27818.66 + .11 27843.25 .00 109 1 1° 8 , 2"<' 98,1 98 s2 , " 97,2 107 ,4- 97,3 107 3 o 1 + .09 6 ,3* 27851.35 * 27875.93 , ~ 96 ,4 105 ,5* 95 , 4 105 ,6* 95 ,5 27908.40 10, 4,6 28048.83 -.0 2 28073.27 .00 27983.86 1 o CO 10A 6 , 4A 28008.21 + .03 28620.83 -.3 7 106 5 9. _ 4,5 + .03 + .04 27906.50** -.0 9 27932.86 -.0 8 27930.65** 29318.30 -.1 6 29337.74 + .01 102,9^ 92,8 27079.55 -.01 27104.83 -.0 9 101»9- 91 ,8 28112.57 -.0 2 28131.90* • ° , ^ 94,6 103 ,7X ' 93,6 103 ,8^ 93 ,7 102 ,8* 92 ,7 1 4 7 27906.50** 27930.65** Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FABLE I (Continued) C6H5CHO_ v = 0 Trans1tion Observed v = 1 Calc-Obs Observed Calc-Obs 10.1 ^10io ,o ^ 30560.40 + .41 30587.23** 30574.28 -.0 5 30601 .35 30593.17 -.0 6 30620.44** 10.2 ^1010,1 J 9.2 * 10 9,1 9.3 ^10 9,2 J -.1 7 8.3 '*'10 8,2 ^ 8.4 - 10 8,3 J 7.4 "‘1° 7,3 ^ 7.5 - 10 7,4 J + .01 6.5 "*10 6,4 5,7 ^ 10 5,6 4,7 ^ 10 4,6 4,8 ^10 4,7 3,8 ^ 10 3,7 3,9 ^ 10 3,8 2,9 ^ 10 2,8 2 ,1 0 ^ ° 2,9 l , l < f 10 1,9 l , l l " 10 1,10 0 , 11^10. 0,10 -.0 6 -.21 30691 .67 30664.57 -.1 6 30742.32 -.0 3 30769.48 -.3 5 30736.24 -.3 2 30763.15 -.4 3 30950.66 -.0 7 30977.69 -.1 5 30824.22 -.1 0 30850.74 -.0 9 31717.83 -.3 5 31744.17** 30666.76 -.0 6 30692.80 -.04. 32212.09 -.1 8 32232.76 .00 29648.34 -.01 29676.23 + .02 30564.90 -.0 7 30586.57** 27665.78 -.0 8 27701.68 -.01 27767.70 +.23 27801.68 -.0 6 6.6 “*10 6,5 5,6 ^ 10 5,5 30647.90 30620.44** Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -.3 9 16 TABLE I (Continued) -CHO C6H5 v = 0 Transition Observed 12 5,7 5,6 12 5 . 8 5,7 12 4,8 ^ 4,7 12 4,9 - 11 4,8 12 3,9 *'11 3,8 12 S.IO*'11 3,9 12 2,io *'11 2,9 12 2 , l l ‘'11 2,10 12 l . l i 4-11 1,10 lC1,12-*-11 1,11 12 lC0,12-*-11 0,11 12 13 12,1 v = 1 Calc-Obs Observed Calc-Obs 33590.40 +.29 33620.15 -.1 9 33576.35 -.01 33605.70 -.1 8 33894.75 -.1 2 33924.55 -.4 4 33666.55 -.11 33695.75 -.5 4 34841.48 -.1 8 34869.48 -.4 9 33401.38 + .04 33429.60 + .09 35028.02 -.0 4 35049.71 + .37 32187.15 + .13 32217.77 + .23 32952.47 + .18 32977.17 + .82 30092.05 + .35 30130.48 -.01 30157.45 + .25 30195.11 .00 36114.41 + .71 36146.28 + .70 36126.83 + .6 6 36158.84 + .51 36143.28 + .54 36175.06 + .60 36165.57 + .42 36197.13** -*-12 12,0 1312,2 ^1212,1 1311,2 <'1211,1 1311,3 - 1211,2 13 10,3 ^1210,2 13 l,510,4 ^ io ^ 13 9,4 * 12 9,3 13 9,5 ^ 9,4 13 8,5 " 12 8,4 36197.13** 36228.90 13 8,6 ^ 12 8,5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. + .12 17 TABLE I (Continued) CcHcCH0 ___ Transition E L _2___ V=1 V=0 Observed 13 7,6 * 12 7 , S ' , 13 7.7 * 12 7.6 J Calc-Obs Observed + .26 36243.09 Calc-Obs + .24 36274.88 + .23 + .20 13 6,7 *"12 6,6 36315. 71* 36347.50* 13 6,8 * 12 6,7 36456.75 + .09 36488.70 -.1 5 36426.84 + .08 36458.65 -.1 8 36890.90 -.0 2 36923.44 -.5 2 36505.71 + .10 36536.95* 37960.23 -.1 8 37988.95 -.2 0 13 3,11^12 3,10 36106.17 + .09 36136.68 + .08 13 2 , n " 12 2,10 37754.81 + .08 37777.60 + .68 13 2,12^12 2,11 34698.46 + .29 34731.91 + .46 35302.17 + .28 35330.28 + .92 32511.75 + .39 32553.50 + .19 32553.24 + .31 32594.63 + .01 38891.34 + .97 38925.68 + .95 38903.36 + .95 38937.90 + .72 13 5 ,8 - 12 5,7 13 5 ,9 ^ 5 ,8 13 4 ,9 - 12 4,8 13 4.10*'12 4,9 13 3,10^12 3,9 13 1 .1 2 *12 1,11 13 1 ,1 3 -12 1,12 13 0,13^12 0,12 14 14 13.1 " 1313,0 > 13.2 " 1313,1 J 14 12,2 +13i 2, n 14 12,3 ^ 1 2 , 2 J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 TABLE I (Continued) CgHgCHO Transition V = 0 Observed ** T411,3 ^ 13l l , 2 ^ 1411,4 - 1311,3 J v = 1 Calc-Obs Observed Calc-Obs 38918.91 + .86 38953.35 + .71 38939.60 + .57 38973.83 +.62 38967.38 + .51 39001.69 + .46 39006.49 + .49 39040.93 + .27 39064.32 + .49 39098.63 + .26 1410,4 ^1310,3 1410,5 - 1310,4 i 14 9,5 " 13 9,4 ^ 14 9,6 ^ 9,5 J 14 8,6 ^ 13 8,5 ^ 14 8,7 * 13 8,6 14 7,7 J 7,6 'T 14 7,8 " 13 7,7 J 14 6,8 * 13 6,7 39155.50* 39139.43* 14 6,9 ^13 6,8 14 5,9 * 13 5,8 39344.92 + .41 39379.42 14 5 , lO^13 5,9 39286.74 + .12 39320.87* 14 4,10^13 4,9 39946.81 +.15 14 4,11^13 4,10 39336.33 14 3 , 12**13 3,11 .00 39981.91 + .40 + .14 39369.44 + .08 38777.80 + .29 38810.40 + .45 14 2 ,1 3 ^ 3 2,12 37185.62 + .39 37222.00 + .62 14 1,13^13 1,12 37638.48 + .41 37670.37 + .99 14 1,14^13 1,13 34927.57 + .48 34973.12 -.0 2 14 0,14^13 0,13 34953.50 + .38 34998.58 + .05 « Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 TABLE I (Continued) Cr HcCHQ Q—5 — - T ra n sitio n Observed Calc-Obs Observed Calc-Obs 39978.15 + .58 40013.98 +1.17 37340.88 + .53 37389.90 + .08 37356.75 + .57 37405.58 + .11 39752.52 + .62 39814.70 + .11 39762.22 + .61 39805.20 + .05 152 , u ‘ 142,13 151.14 ^ 141,13 151.15 ^ 141,14 150.15 " 140,14 161.16 ‘ 15X,15 160.16 ^ 150,15 * The lin e has a f l a t peak. th is . The reported frequency is the mid point of * * More than one assigned lines of nearly same frequency. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 TABLE I I C6H5CH0 Transition Frequencies (in MHz) fo r the second and Third Excited Torsional States va2 Transitions Observed +1.03 32254.01 - 1.12 32272.44 + .55 27753.82 + .80 27771.74 + .54 27851.32 + .24 27869.36 + .92 33964.55 - .01 33984.78 -1 .6 3 33732.65 - .21 33753.75 -1 .7 4 34905.76 + .04 34924.74 -2 .1 3 33464.98 - .63 33485.55* 35068.06 + .29 35091.36 +1.41 32257.08 + .34 32279.08 + .60 30188.54 + .41 30208.01 + .11 38026.16 - 1.10 38044.12 + .25 32613.96 -1.17 32636.01 +2.44 -f-13 1,13 35040.65 +2.28 35066.15 -1 .1 1 4-14 39745.71 - 1.21 39772.01 + .60 124 ,8 ^ 4 , 7 124 , 9 ^ 4 , 8 123 i 10"113 ,9 122, 1 0 ^ 2 , 9 122,11^112,10 <-11 1 ,1 1 13, _rt<-12_ „ 3,10 3,9 ^31 ,1 3 ^ 21,12 15 1,14 2,14 Cal c-ObJ 28170.38 " o .u ^ o .io 14 Observed + .37 1 .8 " 2 . 9 - 1 0 2 .8 1 ,1 2 Calc-Obs 28148.65 ’ ° 1 .9 * 12 v=3 2,13 * * The reported frequency is the midpoint o f a f l a t peak Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 TABLE I I I Q-branch, b-dipole Transition Frequencies (in MHz) fo r C6H5CHQ in the ground s ta te . 145,9 <~144,1o 152 s14^151,15 34172.59 -.2 0 27753.79 34093.51 -.0 1 32691.21 + .2 2 32537.48 -.5 7 175,13"174,14 34311.84 +.11 }85,1^,15 34630.88 -.0 1 194 ,1 6 *193,17 205,16^204,17 • 165 j>12'<'164,13 o 34126.32 1 35037.74 OO , 35,9 “"134,10 +.45 o 134 ,1 0 **33,11 33726.75 I 125,8 ^124,9 Calc-Obs • 125,7 Observed C\J • 1 Transition 33964.55* 35766.00 +.06 * The reported frequency is the midpoint of a f l a t peak. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE IV Rotational Coefficients o f CgH^HO fo r Ground and Excited Torsional States A (MHz) 5234.28 5214.93 5156.84 . 5174.05 B (MHz) 1564.2411 1564.9066 1565.1363 1566.1259 C (MHz) 1204.6988 1206.4753 1209.4460 1210.1345 k -0.82155 [%(B+C)]v + r [%(B+C)3, -0.82116 -0.81979 -0.82038 1.2210 1.6002* 0.8391 * The discrepancy is due to non-harmonic behavior of v * 2. The average value o f [^(B+C)] +, -[%(B+C)1 is 1.2201 which confirms harmonic behavior o f the other torsional states. V ro i\ j computer a t the University of Wyoming. This program calculates a com plete microwave spectrum fo r the frequency region o f in te re s t from the rotation al constants and includes the calculation of such special features as quadrupole s p littin g s , Stark effects and in te n s itie s . For calculation of the rotation al levels the mathematical method used is exactly th a t of King, Hainer and Cross 23 . (See Appendix A) As can be seen in Tables I and I I , the agreement between the obser ved and calculated term values is good fo r lower J gradually becomes poor fo r higher J tra n s itio n s . true fo r higher K_^ tra n s itio n s . tran sitio n s but This is p a rtic u la rly I t therefore indicates th at c e n trifu gal d is to ritio n effects become evident fo r higher values o f J. The groundstate spectrum of C,Hr CHO is a good means of studying th is e ffe c t O0 in th is molecule. For th is s ta te , (A-C) ana the asymmetry parameter values were obtained from the observed Q-branch lin es and the individual rotation al constants (see Appendix A) were determined to get the best f i t to data, with the help of the J = ll-f-10, R-branch, a type tra n s i tio n s . Thus the agreement between observed and calculated term values is best fo r J = 11^-10 series. Centrifugal d is to rtio n causes the observ ed tra n s itio n frequencies to be higher than the calculated frequencies based on the rig id rotor approximation fo r lower J tran sitio n s and causes them to be lower than the calculated value fo r higher than J = 11«-10 series. This e ffe c t increases with the excited torsional state and was observed to be the greatest fo r the second excited state of th is mole cule which does not follow the harmonic pattern of a ll the other torsion al states. For an adequate f i t to the data, however, corrections due to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 centrifugal d isto rtio n do not appear to be necessary and no such correc tions were attempted. There are a few isolated low J tran sitio n s fo r which the agreement between observed and calculated frequencies is poor. No reason fo r th is has been found. These are apparently due to an ac cidental perturbation of the energy levels concerned. I f the energy levels of a rig id asymmetric roto r are expressed as E(A, B, C) = aA + $B + yC where a , 3 and y are the derivatives o f energy defined as 6E a " 6k ’ ._ B" 6E 6B * Y _ SE " 6C on i t can be shown' th at fo r a prolate symmetric top, a-type R-branch tran sitions have a very s lig h t dependence on the A rotation al constant. How ever b-type Q-branch tran sitio ns show an appriciable dependence on th is ro tatio n al constant. Thus a ll the three rotational constants were determined accurately only fo r the ground state of benzaldehyde. In a ll the excited torsional states, B and C were determined more accurately than A since only the a-type R-branch tran sitio ns were id e n tifie d . The empirical rotation al co e ffic ie n ts w ere used to calculate the e ffe c tiv e principal moments of in e rtia and the in e rtia defects which are lis te d in Table V. These quantities were then used to calculate the d i f - frences \ , +] - 4 > e t c ., fo r successive torsional states. The small, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE V E ffe ctiv e Principal Moments o f In e r t ia * , In e rtia Defects, and Differences fo r CgBgCHO in the Ground and Excited Torsional States 0 I A(amu-A2) V=0 V=1 v-2 v=3 96.551 96.909 98.001 97.675 I B(amu»A2) 323.081 322.943 322.896 322.592 I c(amu*A2) 419.504 418.886 417.857 417.620 0 A(amu-A2) -0.128 -0.966 -3.040 -2.747 • • 0.358 1.092 -0.326 0.375 0 • -0.137 -0.047 -0.204 -0.129 • • -0.618 -1.029 -0.238 -0.628 • • -0.838 -2.074 +0.293 -0.873 * ^C^v+l“^C^v A , ..-A v+1 V The NBS-NRC recommended value o f 505376 MHz-u-A2 fo r the conversion fa cto r has been used. Average *> 26 negative in e rtia defect fo r the ground state demonstrates th at benzaldehyde is planar in its equilibrium configuration. The in e rtia defect can be w ritte n as a sum of three contributions orig inating from v ib ra tio n a l, centrifugal and electronic e ffe c ts . A = A (v ib ) + A (cent) + A (e le c t) The vib ratio nal contribution is usually the dominant term. Morino 25 Oka and have derived expressions fo r A fo r a planar molecule. Assuming th at any other vib ratio nal modes with which the torsional mode couple are a t much higher frequency, Hanyu e t . a l . 13b fo r the analysis o f the microwave spectrum fo r nitrosobenzene showed th at Av+i or ~\ ~ "h/ 2u2c“t A . - A v+l V ~ Ii>£ amu-ft2 Where u>t is the torsional frequency in cm"^. Therefore using the value -1 * 111 cm fo r the torsional frequency o f benzaldehyde obtained in the in fra -re d 11 o2 work, Ay+-j -Ay is calculated to be -0.608 amu. A . Thus the more negative in e rtia defect fo r successive excited states confirms th at the s a t e llit e lin es cbseryed do in fa c t arise from the torsional mode of v ib ra tio n . Also th is value is quite close to the value calculated by Hanyu e t . a l . using the theory o f Oka and Mori no. The r e la tiv e in te n s itie s of the ground and excited vib ratio nal Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 tran sitio ns (I- j/ I q) sre related by the Boltzman facto r i . e . to the r e la 1 tiv e populations in the two states. Thus y io = ( g ,/g 0)e sE/kT The g's are the s ta tis tic a l weights, aE is the energy separation of the vibrational state from the ground s ta te , k is Boltzman's constant and T is the temperature a t which measurements are made. ra tio of s ta tis tic a l weights is one. In benzaldehyde the Therefore a measurement of the r e l a tiv e in te n s itie s between a rotation al lin e and its s a t e llit e gives the torsional frequency. Conversely, i f another vibratio nal mode has almost the same energy displacement as one of the torsional states from the ground s ta te , the v ib ra tio n -ro ta tio n interaction w ill give ris e to lin es o f almost same in te n s ity in the two cases but displaced by d iffe re n t amounts from the ground state rotation al lin e . Since the b a rrie r to internal ro ta tio n , as determined by previous investigators, has been found to be high, one would expect several to r sional states to lie below the top o f the potential w e ll. In such a case effects due to tunneling are n e g lig ib le , and aTh almost equal spacing fo r the torsional energy levels is predicted. V ib ratio n -ro tatio n interaction then causes the tran sitio n s in excited torsional states (s a te llite s ) to be displaced from the ground state tran sitio n s by almost equal amounts^. The non-harmonic behaviour o f the second torsional state o f benzaldehyde was detected because of a greater displacement of the s a te llite s than predicted by harmonic behaviour. The s h ift from the harmonic behavior Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. suggests a Fermi resonance 26 type o f interaction of th is state with another vibratio nal mode o f the molecule. For such an in teraction the two vib ratio nal states should be nearly degenerate and have the same symmetry. Therefore the in te n s ity of the s a te llite lin es fo r th is "other vibratio nal mode" should be comparable to th at fo r lin es of the second excited torsional s tate . There have been some Tines observed below the a-type R-branch ground state lines which appear to be lin es o f th is "other mode" (See Figure 2 ) . However, a large number of lin es in these regions with considerable interference from Stark lobes o f other lin es makes id e n tific a tio n , using the in te n s ity o f the lin e as a gu ideline, rather d i f f i c u l t . Therefore, the existence o f these "other mode" lin es has not been conclusively proved. I t was possible to perform r e la tiv e in te n s ity measurements on a few selected ground and f i r s t excited torsional state lin es. These chosen lin es were the ones th at were fa r removed from any neighboring lin es and thus were lea st subject to interferen ce. Due to the ric h ness of the spectrum, only a very few lin es f e l l in th is category. resu lts o f these measurements are presented in Table V I. The S im ilar mea- % surements were not possible on the second and th ird torsional states due to n o n a v a ila b ility o f lin es on which r e lia b le measurements could be made. The C alibration arm of the spectometer allowed the determination o f the torsional frequency within ± 1 , 0 cm~* fo r a given pair o f lin e s . This was checked by performing re la tiv e in te n s ity measurements on the p a ir a number o f times. saturation 28 27 The method of slope r a tio s ' using low pressures and , and the method o f comparing unsaturated signals a t high Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 <u t— sz o •r- </l S= R3 S■M cn * <M lO" o CM CO ■a c n o 5- ra ■ & with a number of unassigned o •r* lin es zsz o Lf> DC VO O *4— O c 3 01 0 <U r* > 5- jC o CM CM UJIU 5° . .. nor <U 3 •D> ■r* s- richness of spectrum o •r* 4-1 otl is indicated Z3 s. 4J o <y cx w tc F lirthPr reDroduction prohibited w ithout permission. Reproduced with permission of the copyright owner. Further reprodu Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE VI R elative in te n s ity measurements fo r selected rotation al tran sitio ns o f CLH.CHO in the O5 ground and f i r s t excited torsional states. Transition Rel. In t . (Ground=1.00) Torsional Freq. (cm"^) 12, _ -1 1 , q 0.574 116.66 12i , i r 11i f i o ° ‘ 580 m - 39 13, Q -1 2 , 0 4,9 4,8 0.593 109.62 Z91Z 13, . , - 1 2 , . . 2fI l * 0.595 ~ 108.92 M 3.12*” 3t 11 ° - 578 1 U -94 U 0,14-130 ,13 ° - 568 118-65 ,50,15*140,1A ° - 585 112-64 160,16"150,15 ° - 583 113- 45 CO o pressures were used. 31 Due to the low power available and the d if f ic u lt y in saturating the tra n s itio n s , the results o f the la t t e r method are con sidered more re lia b le in th is case. The value fo r torsional frequency was determined to be 113.8 ± 5.0 cm"^. The spread of approximately ± -1 5.0 cm is mostly due to the v a ria tio n o f r e la tiv e in te n s ity from one p a ir of lin es to another, presumably due to interference from other lin e s . Deuterated Benzaldehyde (C^Hg CDO) The rotation al spectrum of deuterated benzldehyde was also observed in the 25.5 - 40.0 GHz range. The torsional mode corresponding to in te r nal ro tatio n of the aldehyde (-CD0) group around the C-C bond, as fo r normal benzaldehyde was expected to be the lowest frequency mode. As fo r normal benzaldehyde, most intense vibratio nal s a te llite s were observ ed a t frequencies somewhat above those o f the ground-state tra n s itio n s . W ell-defined progressions, related both by e s s e n tia lly constant f r e quency increments and by steady diminution of in te n s ity were observed. From considerations o f in te n s ity and relationships discussed fo r normal benzadlehyde, these fam ilies were assigned to successively excited states o f the torsional mode. U nlike, benzaldehyde, the second excited state was observed a t the place predicted by the harmonic behaviour o f the potential b a rrie r. The close s im ila rity o f normal benzaldehyde and th is molecule therefore stresses the fa c t th at in normal benzaldehyde there happens to be present, another vibrational mode whose frequency is quite close to the second torsional state frequency, and the in teraction between these two vibrational states displaces the second torsional Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 state from the position dictated by harmonic behaviour. Apart from th is minor d e tail the normal and deuterated benzaldehyde spectra were found to be quite s im ila r. Table V II gives the observed tra n s itio n frequencies fo r the ground and f i r s t torsional states. Where as second and th ird torsional state tran sitio n s are reported in Table V III. In th is case no Q-branch tran sitio n s were id e n tifie d . Therefore in a ll the rotation al constants derived from the data and reported in Table IX the rotational constants B and C have been determined more accurately than A. ed in Table X. The calculated principal moments of in e rtia are l i s t I t was again possible to perform re la tiv e in te n s ity mea surements whose results are reported in Table X I. Para fluorobenzaldehyde (FC H^.CHO) This is another near prolate symmetric top benzaldehyde. tatio n al spectrum was observed in the 26.5 - 31.0 GHz range. I t ' s ro However, in th is case the value fo r (B+C) is nearly 1797 MHz as compared to the approximate value of 2769 MHz fo r the normal species o f benzaldehyde. This means th a t, i f the lowest R-branch a-type series observed fo r nor mal benzaldehyde in the range o f frequencies cohered was J ~ 10 lowest series observed fo r p - fluorobenzaldehyde was J - 15 +14. 9 , the This fu rth e r means th at compared to 19 ( i . e . 2 J + l) tran sitio n s observed fo r normal benzaldehyde in he lowest series, there were 29 tran sitio n s fo r p - fluorobenzaldehyde in the lowest series. Thus the p - fluoroben zaldehyde spectrum was a t le a s t, the ra tio of these two numbers times ( i . e . 29/19) as rich in lin e s as the normal benzaldehyde spectrum. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This TABLE V II Transition Frequencies (in MHz) of CgHgCDO fo r the Ground and F ir s t Excited Torsional States CgHgCDO Transitio n Observed Calc-Obs Observed Calc-Obs 27340.40 +.39 27358.45 + .45 27355.30 -.06 27372.52 -.22 27393.53 -.1 9 109 , l <i' 99 ,0 109,2^ 99 ,1 108 , 2^ 98 , 1 108,3'<' 98,2 1° 7 ,3^ 9 7,2 27376.65* 107 ,4 * 97 ,3 -.11 106,4^ 96 ,3 27409.55 106,5^ 96 ,4 105 ,5^ 9S ,4 27466.69 -.1 7 + .48 105,6** 95 ,5 10A ,6- 94,5 10. 4 ,7 9. , 4,6 103 , 7 - 93 ,6 103 ,8 * 93 ,7 , ^ 92 , 7 102 8 102,9^‘ 92 ,8 101,9^ 91 ,8 + .19 27426.10 + .13 27483.62 + .18 27481.49 + .45 27610.76 -.0 5 27626.66 + .15 27542.56 -.20 27559.22 -.5 5 28191.35* 28205.22* 27459.88 + .03 27476.66 -.21 28861.88 -.1 9 28872.88 -.6 2 26649.10 -.1 3 27649.51 -.16 26629.22* 27634.57 ,00 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 TABLE V II (Continued) C-.Hj.CD 0 6 5 T ra n sitio n v = 0 Observed v = 1 Calc-Obs Observed Calc-Obs -.2 9 10,1 '",tl10,0 ' 30073.58 + .10 30092.80 30087.12 + .14 30106.20** 10,2 "■1010,1 ■ 9,2 ~10 9,1 9.3 ^ 9,2 • 8,3 *10 8,2 ' 30106.20** 30125.21 -.1 3 30153.06 + .07 8,4 *10 8,3 7,4 - ,0 7,3 ' 30134.60 -.0 7 7,5 "‘10 7,4 ■ + .05 6,5 *10 6 ,4 ' 30178.70 30257.87 5,7 ~10 5,6 30251.10* 4,6 30470.97 6,8 *10 4,7 -.1 4 30197.25 -.2 7 30276.12 -.3 4 30269.52 -.5 6 +.06 30488.47 -.0 8 30338.40 -.11 30356.22 -.1 8 3,8 *‘10 3,7 31245.60 -.4 8 31260.18 -.7 3 3,9 *10 3,8 30173.52 + .03 30191.64 + .20 2,9 ‘ 10 2,8 31702.72 -.01 31714.29 + .08 2.10*10 2,9 29151.93 .00 29174.31 + .06 30035.90 + .34 30054.93 + .42 27191.53 -.0 9 27222.35 .00 27285.90 + .13 27316.52 -.0 9 V 5,6 *10 5,5 t o 6,6 *10 6,5 - -.0 8 1,10*10 1,9 1 .1 T 10 1,10 O.ll"10 0,10 - .2 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 TABLE V II (Continued) CgHgCDO T ra n sitio n 1211,1 ^ 12 v = 0 Observed Calc-Obs «-1 1 .1 1,1 J 1210,2 10,1 ^ 10,3 <-1 1 10,2 J 12 9,3 32806.32 + .20 32826.96 + .10 32819.32 + .19 32839.90 + .10 32836.94 + .19 32857.44 + .14 32882.16 + .16 9,2 1 12 9 , 4 " ’ 9,3 12 8 ,4 8,3 J 12 -<-1 ' 8,5 1 8,4 J 12 7,5 Calc-Obs 11,0 11,2 12 Observed 32861.48** + .12 7,4 \ 12 7,6 ^ J 12 6,6 ^ 6,5 "1 12 6,7 ^ 6,6 12 5 , 7 ^ 5,6 12 5,8 5,7 12 4.8 ^ A ,7 12 4,9 ^ 4,8 12 3,9 ^ 3,8 12 3 ,10*^ 3,9 12 2 , 10^ 2,9 34464.40 12 2 , 11*"^ 2,10 12 I ,!!**1 1,10 J 32898.54 + .08 32918.69 + .44 32955.96 -.1 0 + .11 + .29 32976.08 -.2 5 33062.97 -.0 2 33082.50 + .02 33047.65 -.1 0 33067.25 -.0 8 33374.96 -.1 7 33393.47 -.2 2 33135.75 -.0 7 33154.93 -.0 5 34323,20 -.2 6 34337.90 -.3 7 32881.17 + .02 +.17 34477.39 + .22 31645.00 +.05 31670.01 + .12 32377.41 + .59 32398.89 + .49 32861.48** Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 TABLE V II (Continued) CgHgCDO T ra n s itio n v = 0 Observed 12 1, 1 2 ^ 1 1,11 12 o, ^ 11 0,11 v Calc-Obs -1 Observed Calc-Obs 29574.33 .00 29608.32 +.11 29634.95 + .17 29668.78 + .09 35539.18 + .21 35561.28 + .37 35551.47 + .44 35573.49 + .63 35568.05 + .39 35590.54** 1312,1 * 1212,0 1312,2 * 1212,1 1311,2 * 12n , i 1311,3 ‘ , 2 U , 2 1310,3 * 1210,2 1310,4 * 1210,3 13 9 ,4 * 12 9 ,3 35590.54** 35612.56 + .39 13 9 ,5 * 12 9 ,4 13 8 ,5 * 12 8 ,4 35622.30 + .21 35645.27* 13 3,6 '■’ 2 8,5 + .23 13 7.6 ■"'2 7,5 35668.99 13 7,7 * 12 7,6 35690.75 + .20 + .79 13 6 ,7 * 12 6 ,6 35742.62 13 6 ,8 ^ + .19 + .23 6 .7 -.5 8 35765.11* 35886.52 -.0 2 35907.37 + .08 13 5 ,9 * 12 5 ,8 35854.45 -.02 35875.49 -.0 2 13 4,9 * 12 4 ,8 36332.13 -.16 36351.56 -.21 35929.46 + .03 35950.06 + .08 13 5 ,8 ~ 12 5 ,7 13 4 , l < f 12 4,9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 TABLE V II (Continued) C,HcCD0 6 5 Transition 13 3 ,1 0 * 12 3 ,9 13 3 ,i f 12 3,10 13 2 ,1 1 * ^ 2 2 ,1 0 13 2 ,1 2 * ^ 2 2 ,1 1 13 1 ,1 2 * 12 1 ,1 1 13 l , ^ 12 1 ,1 2 13 0 ,1 3 ^ 12 0 ,1 2 v - 0 v = 1- Observed Calc-Obs Observed Calc-Obs 37391.85 -.1 2 37406.74 -.1 7 35518.37 -.1 8 35540.02 + .25 37150.03 + .52 37135.49* 34110.68 + .30 34138.45 + .40 34683.33 + .52 34708.06 + .65 31951,68 + .16 31989.14 + .01 31990.05 + .06 32027.09 + .12 38272.43 -.1 5 38296.50 + .24 38284.25 + .18 38309.00 + .64 38299.70 +.38 38323.40 + .54 38320.55 + .18 38344.29 + .23 38348.32 + .48 38371.91 + .57 38387.94 + .43 38411.48 + .42 141 3 ,1 " 131 3 ,0 141 3 ,2 ^ 31 3 ,1 141 2 ,2 4-131 2 ,1 141 2 ,3 4'13 1 2 ,2 141 1 ,3 4-131 1 ,2 141 1 ,4 4-131 1 ,3 141 0 ,4 4-131 0 ,3 141 0 ,5 1 4 9,5 <-13 1 0 ,4 <-13 n , 9 ,4 14 9 ,6 <' 13 9 ,5 14 8 ,6 * 13 8 ,5 14 8 ,7 * 13 8 ,6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 TABLE V II (Continued) _______________C ^ C D O ____________________ _____ Transition V = Observed 146,8 - 136,7 146,9 - 136,8 145,9 +135,8 145,10^135,9 144,10^134,9 144,11^134,10 143,12*133,11 142,13^132,12 141,13*131,12 141,14^131,13 140,14-<"130,13 152,14^142,13 15l,1 4 * 14l f 13 151,15^141,14 l50,15^140,14 J v Calc-Obs ~1 Observed + .39 147,7 " 137,6 ^ 147 , 8 ^ 137,7 0 38446.55 + .29 Calc-Ob +.34 38469.90 +.24 38540.62 +.37 38563.46 38537.87 -.0 9 38560.64* 38732.85 + .16 38755.33 -.0 7 38692.84 + .1 0 38670.35* + .48 39349.82 -.1 2 39369.79 -.0 4 38713.67 + .12 38735.63 + .26 38141.49 + .42 38165.66 + .41 36552.70 + .40 36583.36 + .50 36978.35 + .63 37006.69* 34325.48 + .20 34366.06 + .18 34349.24 + .16 34389.68 + .13 38974.67 + .64 39008.48 +.57 39278.38 + .72 39310.35 + .78 36696.84 + .29 36740.71 + .22 36711.36 + .28 36755.15 + .20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 TABLE V II (Continued) _____ JW______ Transition v ~ 0 Observed v =1 Calc-Obs Observed Calc-Obs 16, ,^ 1 5 , , t 1,16 1,15 39066.70 +.34 39113.70 +.41 16n ,,-«-15_ 39075.46 +.37 39122.46 +.37 U 91 0 * U , Xj The lin e has a f l a t peak. th is . The reported frequency is the mid point of * * More than one assigned lines of nearly same frequency. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 TABLE V I I I C^CDO Transition Frequencies (in MHz) fo r the Second and Third Excited Torsional States y-Z Transition 111,11*'101,1Q 123,9 ^ 3 , 8 v=3 Observed Calc-Obs Observed 27252.88 +.39 27281.03 +.56 34350.80 +.07 34363.92 +.38 32919,01 +.41 +.59 32899.40* 15,1,15 .*<-14.1,14 .. CM 140 ,1 4 *130,13 29641.90 -.2 0 29673.68 +.14 29701.40 +.43 29733.06 +.55 35664.95 +.32 35685.37 -.2 3 35561.22 +.14 35581.38** 34406.10 1 141,14^131,13 32439.09 CO CM • 133,11*‘123,10 I 138,6 **128,5 32420.18 O. ^ O .ia ^ O .ll Calc-01 34428.98 +.29 36784.06 36797.90 . 34443.43 +.63 34466.50 +.88 -.3 6 36824.65 +.37 +.14 36840.30 - 1.02 ** * The reported frequency is the midpoint o f a f l a t peak. **The lin e is hurried under a much stronger Tine. calculated tra n s itio n frequency. The number is the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE IX Rotational Coefficients of C6H5CD0 fo r Ground and Excited Torsional States y=0 ^1 v=2 v=3 A (MHz) 5106.54 5089.81 5073.58 5056.98 8 (MHz) 1540.6353 1540.7465 1540.8127 1540.8489 C (MHz) 1183.8888 1185.5251 1187.1244 1188.6762 k £%(B+C)3v+1 ■[%(B+C)1 -0.81811 -0.81804 -0 .8 1 79S -0.81792 -0.8738 -0.8328 -0.7940 4» Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE X E ffective principal moments o f in e r t ia , in e rtia defects, and differences fo r C6H5CDQ in the ground and excited torsional states. v=G vsl A ® I C* I B” I A v=2 v=*3 I. (arnu A2 ) A 0 98.966 99.292 99.609 99.936 I B(amu A2 ) 328.031 328.007 327.993 327.985 426.878 426.289 425.714 425.159 -0.119 - 1.010 - 1.888 -2.762 0.325 0.318 0.327 -0.024 -0.014 -0.008 -0.589 -0.574 -0.556 -0.891 -0.878 -0.874 I c (amu k) % A (amu A ) ( I a W A v+ 1 ( i a )v “A < V 4* ro Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE XI R elative in te n s ity measurements fo r selected rotation al tran sitio ns of C6'H5CD0 in the ground and f i r s t excited torsional states Transition Rel. In t . (Ground»1.00) Torsional Freq.(cm ” 2, 10* 102. » . ° - 60° 107- 27 12. *1 1 . , 4 ,8 4,7 0.599 107.56 12i , i f " i , n ° - 606 105- 35 ° : 591 110- 59 °-537 111-80 0.585 112.59 ° * 598 107‘ 95 0.609 104.13 144 , u i3 4 ,io H*,lf«2.12 ^ 0 ,1 4 * ,30,13 150,15^140,14 . -1 ) CO enhanced the problem of id en tifyin g the lin es form th at which existed in the spectrum of benzaldehyde. were id e n tifie d . Consequently only the ground state lin es However, enough tran sitio n s were observed to establish the ground state rotational constants, though, the rotational constants B, and C, again .were more accurate than A. The id e n tifie d tran sitio n s are reported in Table X II and the calculated roational constants and principal moments of in e rtia are given in Table X I I I , Parachlorobenzaldehyde (C135C6H4 CHO and C l37 CgH4 CHO) The natural isotopic abundance fo r Cl is 24.47%. Therefore fo r a 35 is 75.53% and th at fo r Cl sample of parachlorobenzaldehyde introduced into the c e ll o f the spectrometer the percentage composition o f Cl CgH4 CHO and Cl 37 37 35 CgH4 CHO w ill be in the natural abundance ra tio o f the two chlorine isotopes. Since the in te n s ity of the rotation al lines de- pends upon the number of molecules o f the species present 29 , the in ten s ity of the lines due to the two chiorobenzaldehydes would be less than the in te n s ity when 100% of the e ith e r species is present. The re la tiv e in te n s ity fo r the lines due to same tran sitio n s should be and was found to be nearly in the ra tio o f the natural abundance o f the two isotopes. Nuclei possess a spin agular momentum f which is represented by an integral or h a lf integral quantum number I . I f a nucleus possesses a spin angular momentum greater than ^ts* i t has a non spherical charge d is trib u tio n 30 and therefore has a nonvanishing nuclear quadrupole moment. In such nuclei the spin angular momentum can couple with ro tatio n al an gular momentum to produce a hyperfine structure in he rotation al Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE X II Ground State Rotational Transition Frequencies (in MHz) of Parafluorobenzaldehyde 151 2 .3 " 141 2 ,2 ' I 26978.75 -0.44 26981.88 -0.25 27000.87 -0.60 27012.80 -0.24 27031.89 - 15i 2 , 4 - 141 2 , 3 J 151 1 .4 " 141 1 ,3 ^ 1511.5 "1411,4 J 15 8 ,7 - 14 8 ,6 'I 15 8 ,8 " 14 8 ,7 J 15 7 ,8 * 14 7 ,7 ' I 15 7 ,9 ^ 7 ,8 J 15 6 ,9 - 14 6 ,8 ") 0.1 0 15 6 , l ( f 14 6 ,9 J 15 5 ,1 Q "14 5 ,9 > 27065.05* 15 5 , l l " 14 5 , 1 0 j -0.18 15 4 , 1 1 ^ 4 4 ,1 0 2 7 1 4 5 *69 15 M 2 "14 4,11 27111 .72 -0.17 15 3 ,1 2 " 14 3 ,1 1 27479.57 +0.02 15 3 ,1 3 ^ 14 3 ,1 2 27074.85 +0.04 15 2 ,1 3 ^ 14 2 ,1 2 27995.26 +0.19 15 1 , U - 14 1 ,1 3 2730S * 75 - 0.22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 TABLE X II 1 6 ,, 0 14,2 % 14,1 ^ 1614.3 ^ 5U ,2 J 1613.3 "1513,2 "t 16t13,4 j / "-15,0 13,3, } J 1612.4 ‘ 1512,3 ^ 1612.5 *1512>4 J 1611>5 *15U ,4 ^ 1611.6 " 15i i ,5 J 28774.14 -0.32 28776.30 - 28779.55 -0.14 28783.63 - 0.01 0.20 1610.6 ^15i 0 ,5 ^ .28788.69 +0.04 28795.90 +0.03 28806.02 +0.04 28820.92 +0.07 28844.38 0.0 28885.27 +0.17 5,12**15 5 ,1 1 28833.17 +0.14 4 ,1 2 ^ 5 4,11 28989.14 +0.15 4 ,1 3 "15 4,12 28936.17 +0.10 3 ,1 3 ^ 5 3,12 29404.70 0.00 28872.30 -0.04 1610.7 ^1510,6 16 16 16 16 16 16 16 16 16 16 16 16 16 16 J 9 ,7 ^ 15 9 ,6 9 ,8 *15 9 ,7 8 ,8 *"15 8 ,7 8,9 15 8,8 7,9 " 15 7,8 7,1Q*<‘15 7»9 6 , h T 15 6 ,9 6,11^15 6,10 5 , i f ' 15 5 ,1 0 3 ,1 4 "15 3,13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE X II (Continued) T ra n sitio n Frequency 163 ,1 4 '<' 153 ,1 3 162 ,1 4 ^ 152 ,1 3 162 ,1 5 ^ 152 ,1 4 Calc-Obs 28872.30 -0.04 29864.82 - 0.01 •28286.41 -0.05 28989.68 . +0.08 27115.26 -0.06 30574.59 -0.30 30577.15 +0.10 30581.13 -0.14 30586.18 -0.36 30592.26 -0.08 30600.83 - 0.01 30612.94 +0.04 30630.90 0.00 171 4 .3 ^ 161 4 ,2 'I 1?1 4 ,4 " 161 4 ,3 J 171 3 .4 * 1 6 1 3 , 3 "l 1 7 1 3 .5 ^ 161 3 ,4 J 171 2 .5 ^ 161 2 ,4 ^ 1712.6 "*1612,5 J 1711.6 ^ 611,5 'I U l l , 7 +1611,6 J 171Q,7 ^1510,6 ^ 1710,8 ^ 610,7 J 17 9,8 ^ 9,7 >| 17 9 , 9 ^ 9,8 J 17 8,9 "16 8,8 1 17 8, 10^16 8,9 J 17 7 ,1 0 4“15 7 ,9 ' I 17 7 , l l * 16 7 ,1 0 J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE X I! (Continued) Transition Frequency 76, l l ^ 166 ,io > 7 6,12 ic 6 , 11 7512^85 ,11 it ) J Calc-Obs +0*05 30658.98 n - ° - 07 30709.15 -0.02 75, 13*"165,12 30705.28 -0.32 74 i3*164 12 30842.48 +0.07 74 , 1 4 " 154 ,1 3 3 0 7 6 2 - 12 + 0 «27 73 ,15^ 63,14 30663.92 -0.09 72 , 1 6 " 162 ,1 5 2" 9 5 - 58 - ° * 10 71 1 6 * 161 ,1 5 30648.27 +0.11 71 1 7 ^161 16 28665.78 +0.11 70 ,17*^0,16 28742.98 +0.07 81 , 1 8 " 171 ,1 7 3 0 3 1 4 - 10 - ° * 14 80 ,1 8 ^ 170 ,1 7 30372.90 +0.11 Not completely resolved. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE X II I Rotational and In e r tia l Coefficients o f Parafluorobenzaldehyde A(MHz) 5097.760 B(MHz) 976.7452 C(MHz) 819.9251 k -0.92668 I.(amu-A2) 99.137 0 I„(amu*A2) 517.408 I c(amu*Az ) 616.368 A a A(amu-A2) -0.177 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 spectrum i . e . t couples with the rotation al quantum number 3 to produce a resu ltan t to ta l angular momentum F - t + 3 I and J remain good quantum numbers whose F = J + I, J + I - l .......... vector is also quantized. | J - I| Thus each rotation al level is s p lit into 21*1 le v e ls . This s p l it - ting is proportional to eqQ, the nuclear quadrupole coupling constant 31 . Here Q is the quadrupole moment, e the u n it electronic charge and q is the e le c tric fie ld gradient a t the position of the nucleus along the near symmetry axis of the extranuclear charge d is trib u tio n . A ll these quantities are expressed in units such th a t the units fo r eqQ is MHz. The selection rule observed fo r the R-branch tran sitio n s is aF = +1 and th at fo r Q-branch tran sitio n s is aF = 0. Thus each ro tatio n al tra n s itio n is also s p lit into 21+1 tra n s itio n s . The f i r s t orderhyparfine struc ture is a lin e a r function of eqQ, and the c o e ffic ie n t o f eQq is a lin e a r function of the quadrupole asymmetry parameter n. In other words, the s p littin g due to the quadrupole hyperfine structure is o f the form eQq (a + 8n) where aand p are constants depending on the tra n s itio n involved. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The 51 s p littin g s of the lower lin es are usually affected by the value of the quadrupolar asymmetry paramenter 32 which is a measure o f the asymmetry of the f ie ld a t the nucleus. The introduction of the nuclear spin does not change the to ta l inten s ity of a ro tatio n al tra n s itio n and the sum of the in te n s itie s o f the re solved components is ju s t the in te n s ity o f the unsplit lin e . Both Cl 35 and Cl 37 isotopes have a nuclear spin o f 3 /2 . th e o ra tic a lly , each ro tatio n al tra n s itio n fo r Cl CHO is s p lit into four hyperfine lin e s . 35 Therefore CgH4 CHO or Cl 37 CgH4 Thus in addition to a lower in te n s ity due to isotopic abundance, the quadrupolar s p littin g makes i t s t i l l lower. In addition to th is the (B+C) values were found to be approximately 1301 MHz and 1273 MHz fo r Cl35 CgH4 CHO and Cl37 CgH4 CHO resp ectively. Thus the J ** 21 + 20 a-type R-branch band occured around 27300 MHz fo r Cl35 CgH4 CHO and around 25700 MHz for Cl3^ CgH4 CHO. The former number is ju s t above the 1ower end o f the frequency region covered by the Wyo ming spectrometer while the la te r is below th is lower end. There w ill be 41 ( i . e . 2J+1) ro tatio n al tran sitio n s corresponding to th is change o f ro tatio n al angular momentum quantum number. These tran sitio n s th e o ra ti c a lly , fu rth e r s p lit into four hyperfine lin es each. This along with the 1ower in te n s ity gives an extremely rich spectrum o f low in te n s ity lin e s . To make the situ atio n s lig h tly b e tte r, the rotation al spectrum was observed in the 18.0 - 26.5 GHz region with the help o f a K-band spectrometer a t Hewlett Packard Company in. Palo A lto , C a lifo rn ia . The sample pressure was also increased to around 30 m -torr to increase the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 population of the molecules. I t was found th at the s p littin g s due to the nuclear quadrupole effe c ts increase with increasing K_-j value. quadrupole hyperfine s p littin g s o f the higher The lin es a re , fo r the accuracy involved, dependent only on eQq. Therefore the value o f the quadrupole coupling constant can be obtained to a high degree o f accura cy by observing the s p littin g s in the highest lin e s . However, things are complicated due to a large amount o f overlap in the region o f high lin e s and therefore there are a lo t o f unresolvable lin es in these regions. See Figure 3. into a ll four components. In fa c t none o f the tran sitio n s was resolved Thus there was an ea rly indication th a t the value o f quadrupole coupling constant was r e la tiv e ly low. The value fo r th is constant was calculated from lin es that were s u ffic ie n tly removed from the overlapping high K_-j regions but yet had s p littin g th a t was re solvable into two components. This value is therefore quite approximate. The id e n tifie d tran sitio n s are reported in Table XIV and the ro tatio n al c o e ffic ie n ts , principal moments o f in e rtia and quadrupole coupling con stants are reported in Table XV. ed fo r lin es with Since almost no s p littin g s were observ < 3 i t has not been possible to measure n. The calculated spectrum including quadrupole s p littin g s , was again obtained 22 using Beudet’ s computer program. I t is of in te re s t to note th a t the quadrupole coupling constant de termined here fo r parachlorobenzaldehyde is quite close to the value -71.10 MHz fo r C l^ and -56.10 MHz fo r C l^ obtained by Poynter^^0 in his study o f the microwave spectrum o f chlorobenzene. Townes and D a ile y ^ point out th a t, since the quadrupole coupling constant is a measure of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. * *r • ® in Figure 3. ° ^ High resolution J a 19+18 bend o f C l^ CgH^ CHO. o trt O u> The region 24721 — 735 MHz contains nine rotation al tran sitio n s each o f which is fu rth e r s p lit into four hyperfine lin e s . The exceptionally ric h spectrum near the band centers therefore made id e n tific a tio n o f individual components almost impossible. u> 54 TABLE XIV Ground State Rotational Transitions (in MHz) h Of C135C6H**CHO and C137CJLCH0 6 (a ) C135C6H1|CH0 S p littin g s Transition ^ ^ X O 18 19 19 4 ,1 4 7 .1 2 +-18 -<-18 19 7 ,13 18 Lov;er Calc. W ,l . s j 33/2 35/2 31/2 37/2 4 ,1 3 Obs. 2* g ; « | ) 429.05 4 3 i!q 0 ) « 0 .9 7 23499.56 > 499.61 ) 499.85 A 499.90 J AQQ „ 499 *33 4gg gg ^ 37/2 3 5 /2 24747.13 \ i 39/2 7,12 J 33/2 747.89 \ 747.91 ^ 748*°° 24757.68^ 757. 6 9 J 7„ 737.23 7 ,1 1 1 19 ft ft ,1io2'I1 6 .1- t3^ 18 6 35/2 3 7 /2 747J5 7 1 9 6 . 1 4 ^ 8 6 ,1 3 j 39/2 I t H V 20 9 ,XX* 19 9 ,1 0 ^ 8972 26039.55) 29 9 . u * « 9 . n ) “ Calc. ..1 2 ^ 8 .1 1 1 20 8,13^19 8, 1 2 ! .8 * 8 .1 !) »* 35/2 2” } 045! I D 747 Obs. • 0.34 0.36 0.78 0.79 0.57 0.55 0.89 0.89 ?1 '4 / . 2 1 7Ao nn 757‘ 78 ^ M ° - 75 044.74 045.63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 TABLE XIV (Continued) Obs. 183 ,1 5 ‘ 173>14 2 3 6 3 9 ' 44 + 0 ' 11 183,16<-173,15 2349K16 - ° ‘ 17 18, ,,* 1 7 , 24032.63 +0.01 182 ,1 7 " 172 ,1 6 2 3 2 3 3 ' 33 ' ° - 16 18, ,,+ 17, , , X)1 > Xj Xu 23802.47 +0.08 0.09 ,*<-18- 24988.08 -0.22 0.21 19- ...<-18- 24796.80 +0.10 0.20 192 , 1 7 - 182 ,1 6 2 5 3 8 9 - 40 19, ,,* 1 8 , , , 23602.50 -0.14 0.13 19, , o^18, , , 25073.18 -0.63 0.07 19. 1Q«-18. 23684.08 -0.26 0.08 190 ,1 9 " 180 ,1 8 2 3 8 1 6 - 05 - ° - 15 20, ,,+ 1 9 , , , 26342.75 -0.16 0.18 20. - fi«-19-' 26101.60 +0.04 0.17 “ 2 .1 S *192 . « 25768' 42 - 0 ' 02 20, ,.+ 19, 26333.38 -0.13 94911 • “ +° - ° 7 2 5 0 2 4 - 73 + 0 ' 21 2 ,1 6 3 ,1 6 3 ,1 / 2 ,1 5 3 ,1 5 3 ,1 6 /> , 1(5 1 , lo 1 ,1 ? 3 ,1 / 3 ,lo 1 ,1 .7 ,1/ 1 ,1 / l,lo 3 ,1 6 5 ,1 / 1 , lO 200 ,2 0 * 190 ,1 9 . Calc.-Obs, S p littin g s (Calculated) Transitions 0.23 0.23 0.15 0.14 0.13 211, 21*2° 1>20 26137-92 +0-02 21O,2r 20O,2O 26234' 22 +0- 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.07 0.11 0.07 0.08 0.07 0.07 0.06 56 TABLE XIV (Continued) (b) C137C H CHO ' Transition Lower 6 ' k Calc. 24174.26 ’Vs W -1 37/2 %% 2 Y4;z 3l) 174.35 35/2 175.49 ’W 1 V * / 39/2 33/2 %% fs% 175.58 ) 37/2 35/2 39/2 33/2 24177.34 " 177.40 { & * ) 178.34 178.40 ) 37/2 r 188 , i o V p 35/2 39/2 1 9 * , u r 1 8 s . i i j 33/2 -« » 24181.59 ™ ) 181.62 182.38 J88,8? ) 182.41 » M ^ 19 s V 8 ... -) 8 9 ,1 0 i » M V V 2 ’ 8 7,11 1 . l f 18 7,12 ' 37/2 1 ^2 35/2 39/2 33/2 Obs. S p littin g s Calc. . Obs. ’^ 98 1.32 1.40 1.06 1.06 0.82 0.78 0.62 0.65 1 7 5 - 38 177.00 178- 06 ,81.40 182- 18 24187.77 8 7 l 7 S 187-60 187.78 188.38 188.25 188.39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE XIV (Continued) Transitions f Obs. Calc.-Obs 19. -,-*-183 16 3 j 15 19_3,17 . 7«-l8-3,16 24236.32 +0.04 24403.18 +0.30 19_ 17H8- 24794.75’ +0.23 192,18"182,17 23964'52 - ° ‘08 191 18^181 17 24523.58 +0.05 19,1 yJ.y --*-18-1) lb 23179.92 +0.10 190,19"180,18 23318' 12 +°-°5 20,4.16 .,.1 9 ,4,15 „ 25538.25 -0.09 20.4.17 ,-^19.4 ,1,6, 25523.24 +0.03 20- 25723.75 -0.09 2°3 18^-193 17 25512.24 -0.04 20x ! l9 * 19l,1 8 26761 • " - 0 - 11 201 , 2 0 ^ 1 , 1 9 24382' 55 - ° - 05 ^11 / 3 .1 7 ^ y lb <-19- , , 3 ,1 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE XV Rotational Constants, In e r tia l Coefficients and Quadrupole Coupling Constants of Parachiorobenzaldehyde Cl 35C6H1+CH0 Cl 37C6H1+CH0 A(MHz) 5058.250 5056.233 B(MHz) 691.9960 675.5286 C(MHz) 608.8328 596.0059 k -0.96262 -0.96434 IA (amu-82) 99.911 99.951 k (arnu*A2) 730.316 748.119 Ic (amu’A2) 830.074 847.938 A (anui*A2) -0.153 -0.132 eQq(MHz) 70.0 55.2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 the energy o f orien tation of the quadrupole nucleus r e la tiv e to the e le c tric fie ld o f the e n tire molecule, i t is also a measure of the elec tron d is trib u tio n o f the bond to the atom in question. Thus fo r a purely covalent halogen, eqQ is nearly th at fo r the atomic halogen which has one p electron missing from the valence s h e ll. For 100% ionic halogens, the p electron f i l l s the valence shell and the value of eqQ approaches zero. Therefore, values o f eqQ which are intermediate to the two ex tremes should be a measure of the amount o f ionic character in the bond. Almost equal values of eqQ fo r chlorobenzene and parachlorobenzaldehyde therefore indicate an almost equal ionic character fo r the C-Cl bond in the two molecules. In other words the presence of the aldehyde group in one case has almost no e ffe c t in the other when no such group is present. This might ju s tif y to some extent the assumption made la te r in the structural determination of the benzaldehyde framework. This assumption being th at the presence of chlorine or flu o rin e in a position para to the aldehyde group in parafluoro and parachlorobenzaldehydes resp ectively, does not a ffe c t the environment of the aldehyde group from th a t which existed in normal benzaldehyde. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I I I THE DYNAMICS OF THE TWOFOLD INTERNAL ROTOR Considerable work has been devoted to the studies of the microwave spectra of molecules in which one group (called the top) may execute to r sional vibrations (also known as in ternal ro tatio n ) with respect to another (called the frame). te n tia l b a rrie r. The free rotation of the group is prevented by a po Though the study of hindered internal rotation in mole cules has been a subject of in te re s t fo r nearly fo rty years and numerous methods have been devised fo r investigating the phenomenon, i t is in te r esting to note that the origin of the potential b a rrie r is not completely understood. There have been two general approaches to study the dynamics o f in ternal rotation in single top molecules. < jr Hershbach a , and others 34 , /* , the set o f principal axes of the whole molecule is used as the coordinate system. axis method or PAM. In th at originated by Wilson Nielsen 37 This is referred to as the principal and Dennison development o f the a lte rn a tiv e method. 33 are credited with the i n i t i a l In this the axis about which the top exectues internal ro tation is chosen as one of the coordinate axes. The other two axes are fixed with respect to the framework and th e ir o r i entation is , in p rin c ip le , a r b itra ry , but the choice is usually determined to some extent by the symmetry of the molecule. the in ternal axis method or IAM. This is referred to as In th is representation the in teraction terms between o v er-all and in ternal ro tatio n are considerably smaller than Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 those from PAM. Thus these terms lend themselves more read ily to simple perturbation treatment. However, since the coordinate axes are, in gen e r a l, not principal axes, the ch ief disadvantage is th at the Hamiltonian is complicated by the presence of the terms containing the products of in e r tia . In order to derive the Hamiltonian function a model can be form ulated from the symmetry of the molecule being studied. The complexity of treatment depends upon the degree of lack of symmetry o f the molecule. A lack of symmetry in both the top and frame greatly complicates the problem. The molecular dynamics o f in tern al rotation is well understood fo r molecules where the in ternal roto r has the rotation al properties of a sym metric top so th at the moments of in e rtia o f the e n tire molecule do not depend e x p lic itly upon the angle o f internal ro ta tio n . This work is sum marized in an excellent review a r tic le by Lin and Swalen^. 2 Quade and Lin have developed a theory fo r molecules where neither the internal rotor nor the frame has the rotation al properties o f a sym metric top, The assumptions used in the derivation of the Hamiltonian were ( 1) the molecule is rig id except fo r the degree of freedom fo r in te r nal rotation i . e . other modes of in tern al vibration were neglected. These can become important i f the torsional and vibration modes have nearly the same frequency, ( 2) the molecular z-axis was chosen to be p a ra lle l to the axis of in ternal ro ta tio n , and (3) both the framework and top were assumed to possess planes of symmetry. In a la te r work Quade tightened assumption (3) and worked out the solutions when only one of the rig id portions of the molecule possessed a twofold axis o f symmetry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 Using the PAM approach, i t was found that the moments of in e rtia were no longer independent of the angle of internal ro ta tio n , the internal rotor now being not a symmetric top. Perturbation sums were more complicated because of additional terms in the to rs io n a l-ro ta tio n a l in teractio n . In the IAM approach i t was not possible to completely remove the cou pling between internal and o v e r-a ll angular momentum by a coordinate trans formation, as was possible in the case of three fold internal ro to rs . transformation was made to reduce this coupling. A However, th is did not prove very helpful because of the introduction of a-dependent terms into the moments of in e rtia which were both periodic and nonperiodic in 2ir. Therefore, solution to the internal ro tatio n problem using th is approach was obtained only in the high b a rrie r approximation which is applicable to cases where separations of the torsional energy levels are large com pared with the ro tatio n al energy separations. 5 Quade compared the two approaches and showed th at PAM was best for situations in which the potential b a rrie r is of intermediate height. The two methods compare favorably in the high b a rrie r approximation, but the IAM approach is easier to use because the Fourier series fo r the a-dependence of the moments of in e rtia can be replaced by a power series. Then the torsional ro tatio n al in teraction sim p lifies and a straightforward solution develops. In benzaldehyde the separation of ro tatio n al levels is o f the order o f -1% of the separation of torsional le v e ls , therefore, high b a rrie r ap proximation was used fo r the analysis of the spectra. IAM or PAM w ill be equivalent in this approximation. The results using However the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 benzaldehyde data was analyzed using Quade's IAM approach, this being more straightforw ard. To do th is , f i r s t of a ll the form of the potential func tion is discussed and then the method fo r deriving the k in e tic energy in order to obtain the Hamiltonian function for the problem is discussed. The method of calculation of approximate eigenvalues and eigenfunctions is covered in the succeeding sections. Potential Energy The origin of the potential b a rrie r not being c le a rly understood, the only requirement th at can be imposed on the potential function is th at i t be periodic in the re la tiv e angle a (called the angle o f internal ro tatio n ) between the frame and the top. I t is customary to assume the potential b a rrie r to be of a sinusoidal shape appropriate to the f i r s t term of a Fourier series expansion of the periodic p o te n tia l. I f the mol ecule has N number of equivalent configurations within the interval of a = 0 and a=2-ni . e . one complete internal revolution, the potential function also repeats i t s e l f N times i . e . this function has N potential minima. The potential energy V(a) is then expanded in a Fourier series as V(a) = I (a^, Cos Hkct + Sin Hka) k I t is possible to place an angular reference so that a ll sine terms are eliminated and the expansion becomes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 V(a) s I a, Cos kfJa k K By a s h ift in the reference level of the potential energy, this may be w ritten as V V(a) = j> In benzaldehyde, the ring (1 - Cos kNa) group has a plane of symmetry, therefore N = 2 and V(a) becomes , , v2 , V(a) = 2“ 0 “ CoS 2 a ) , + Vu , (1 “ CoS4a) + . . . . . Experience has shown th at the above series converges rapidly and re taining only the f i r s t term in the expansion serves as a very good approx imation. This has the added advantage th at such a simple potential func tion leads to solutions fo r the torsional wave equation in terms of Mathieu functions 39 . For a higher accuracy, hijgher terms in the expansion can be included and corrections to the energy levels can be calculated using perturbation methods. used. In the present case only the f i r s t term was Thus V (a ) = jf v2 (1 - Cos 2a) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (3 -1 ) 65 where V2 is the b a rrie r height, intervening the potential minima. I t is not known from f i r s t principles and is a parameter to be determined from the experimental data. In the high b a rrie r approximation, the internal motion degenerates into small o s c illa tio n s and the potential energy can be sim plified using the harmonic o s c illa to r approximation. Thus expanding the cosine potential function V(a) = V2 (a2 -'g- a1* .+ <x6 - ........ ) I f a is sm all, a ll terms beyond a2 can be dropped. (3 -2 ) This shows th at i f the b a rrie r is high, the lower torsional energy levels w ill be spaced at nearly equal increments. K inetic Energy and Coordinate Transformations fo r IAM I n i t i a l l y , in the derivation of the k in e tic energy the molecular axes are chosen to be fixed in the framework o f the molecule. If ^ , ft. and a . are the position vectors of an atom if) the frame, an atom in J J the top and the center o f mass o f the top respectively with respect to the center of mass of the whole molecule as the o rig in , then the k in etic energy of the system, trea tin g atoms as mass points can be w ritten as 2t . . + j mj r * Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 Using the relations R. = a) X R. , 1 1 and tR. =oj X R.« + at X„ ->a . vl J J Where u> is the angular velo city of the overall rotation of the molecule with respect to a set of axes ve lo c ity fixed in the molecule of the toparound the axis and o is the angular of internal ro ta tio n , the expression fo r k in e tic energy.becomes The f i r s t two terms represent the k in e tic energy of the overall rig id rotation of the molecule with angular ve lo c ity w, and can be w ritten as a) •I«U where I is the in e rtia tensor fo r the e n tire molecule. If I a is the moment o f in e rtia of the top then the th ird term can be expressed as I a&2 . The la s t term represents a coupling between internal and external Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 motions and on sim p lifica tio n becomes 21; (» •& ). a Since z-axis is chosen p a ra lle l to the internal rotation axis, this is equal to 2 Iaau)z . The ex pression fo r k in e tic energy, therefore, becomes 2T = w+* 1 • to + 21 aa2 + 21aauiz (3-3) Apart from z-axis being chosen p a ra lle l to the axis of ro ta tio n , the y-axis is chosen to be p a ra lle l to the plane of symmetry in the framework (the ring group in this case) and x-axis is perpendicular to the plane of symmetry with origin at the center of mass (CM) of the molecule. The mo lec u la r axes remain p a ra lle l to th e ir orientation fo r a = 0 as a is allowed to vary. For a = 0 benzaldehyde is planar and 1° xx But fo r af 0, = 1° + 1° Ay y zz the co efficien ts and products of in e rtia are <V x x 3 'x x ( I CM>yy - & - S i" 2 « + 51" 2 « 5 ^Wzz * l zz (Irm ).. . = " I S in ' C M 'xy a a COS a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 * W y z “ “Xx *W x z * 0 (3 -4) ! a = ^CT^zz where CT refers to the center o f top. The e ffe c tiv e moments of in e rtia are related to these as Ti j = ( I CM>ii ! ZZ = ^C M ^Z Z " ij * ZZ (3-5) !a The in e rtia tensor fo r a planar molecule with internal rotation in matrix notation can be w ritte n as I o 3 i—* ^W xy ^W yz *W zy ^Wzz i i o ■ ('W y x © ^CM^xx The k in e tic energy according to (3 -3 ) can now be expressed as 2T = (Ip t^ w wx wv +' (ViCM'yy V m) wu LCM'xx W jr z V z * wy +' (IrM), '*CM'zz“z ~^2C M 'x y V V »Z Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 Components of to ta l and conjugate internal angular momentum can now be calculated. These are Px = 9T/9“x = ^CM^xx “x " ^ W x y “y Py * 3T/3a)y = ( I CM) yy wy - ( TcM^xy “ x " ^CM^yz“ z Pz - p 3T/a«2- = 3T/3a ( I CM) ZZ «z - ( I CH) yz «y + ' I 0& 3 I (o + 0)z ) I t is c le a rly seen that p couples to P as well as to P since I yz/ 0 . J fc Jr fc In the IAM fo r asymmetric molecules with a plane of symmetry p again couples with P., and P . y z these couplings. However, Hecht and Dennison^ were able to remove In th e ir method, f i r s t a rotation is performed in order to elim inate the Py p coupling and then a modified Nielsen transformation 37 is applied to remove the Pzp coupling. In the present case, only one of the rig id portions has a plane of syrimetry and therefore the problem is more complicated. I t is only possi ble to reduce the coupling of p with P and P By applying two successive y ^ coordinate transformations. The f i r s t transformation is a rotation through an angle e about the x axis, e s a tis fie s the condition th at i t is inde pendent o f a and is determined such that in the h ig h -b arrier lim it there is no coupling of Py to p. Under this transformation, ' 3 Su» and I ' = S IS -1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The condition th at coupling of Py and p vanish in zeroth order gives Cos e - 1° N , yy 5 70 sin e = I N x where H > ( U ° y ) 2 + ( I x) 2] -1 ^2 (3 -6 ) The coupling between p and P^ is removed in the zeroth - order by transforming to a new set of molecular axes. A suitable transformation 5 corresponds to a rotation about, the z axis in the manner e" = e' ip" = <j>" = tp‘ + r a ' , , a" = a' , and Cos ra + wy' Sin. ra oj" = -to' Sin ra + toy' Cos ra y ^ wz = uz + where r = I a Cos e / I®2' = I a (NB)-i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (3 -7) 71 (3-8) B = 1° 1° - ( I ) 2 yy zz v x' and <j>, e, \pare the Euler angles which serve as the three external coor dinates *or fix in g the molecular axes in space. The parameter r does the same job as done by another parameter of sim ila r form in Nielsen tran sfo rmation, to remove the coupling o f p and ?z fo r 41 symmetrical molecules or in a modified Nielsen transformation in the case of asymmetric molecules with a plane of symmetry 42 . In this case i t is not possible to remove a ll a-dependent coupling o f P‘ , P ', P ', with p since r should be independent of a. ^ y 2 The k in e tic energy a fte r the second transformation can be w ritten as 2T = u)"+ • J . w" + J d"2 + 2J aa aa d" • 2" (3 -9 ) where Ju - with Jaa generally referred to + Ju «•> <3- 10> as the reduced moment of in e rtia fo r the torsional motion given by J° aa - I a[1 - I aI® yyB '1] and other 0?^ being given by Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ' (3-11) ' The J. .(a ) contain a ll the a-dependent contributions to the moments ■J o f in e rtia and a ll J . ^ a ) -> 0 in the lim it a -*■ 0. This can be checked •J from the expressions fo r J . .(a ) reported in Reference 5. These are not *J given here because they consist of Fourier series terms fo r the a-dependence of moment of in e r tia . These are la te r replaced by a power series. The power series expansion terms given la te r are more pertinent to the present case. A fte r these two coordinate transformations, the general a-dependence of in e rtia coefficients is small but not completely removed. This should be compared to the case of asymmetric molecules possessing a plane o f symmetry. In these, Hecht and Dennison 40 , by applying the modified N ie l sen transformation were able to completely remove the a-dependence of in e rtia c o e ffic ie n ts . Therefore, in the present case the actual solution of the problem is complicated by the introduction of these new a-dependent terms some of which are not periodic in 2 tt. Hence i t is not possible to combine terms and sim p lify the Fourier expansions o f the moments of in e r tia and ro tatio n al parameters. I t is possible to combine them only in the h ig h -b arrier approximation when the Fourier series fo r the a-dependence of moments of in e rtia can be replaced by a power series. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 Hamiltonian Operator and Basis of Representation The quantum mechanical Hamiltonian can be ea sily formulated from re sults o f the previous section. Development of the general theory has been presented in d e ta il by Wilson e t a l . ^ fo r vibration - rotation in te r 5 action. This theory has been applied by Quade fo r the present case to get the Hamiltonian of the general form H = H» ♦ H» ♦ Hj ♦ Htr , where HR and H° are the ro tatio n al and the torsional parts o f the Hamiltonian resp ectively, which are independent of the a-dependent terms in the k in e tic energy; whereas Hj contains a-dependent contributions to the k in e tic en ergy and H^r is the in teractio n of in tern al and overall ro ta tio n . The moments of in e rtia usually appear in the denominator and therefore y.j j are introduced fo r convenience and include the Fourier series fo r the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 a-dependence of moments of in e rtia , If g = iJ ^ jl and and are related as follows: y = 1 jI t then g = g- y " 1 = g° + example: yxx = y°x + y j ^ I sin2 a (-R)^ s i n ^ ^ a , e tc . k=0 The convergence o f the Fourier series is determined by the ra tio For solution of the problem using IAM, i t is most convenient to spec if y the ro tatio n al coordinates as the Euler angles 0, <|>, <pand to choose the symmetric top representation as the basis fo r perturbation calcu latio n . The form of the wave function is * ^R( e ,<{>) exp (iP z^) X exp [ i ( l - r ) P za] <j>T(a) where double primes have been dropped form the coordinates and dynamical variables fo r convenience and exp [ i ( l - r ) P z a ] <j>j(a) is the torsional part of the eignefunction. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Results in the H igh-Barrler Approximation In the pendence h ig h -b arrier approximation of the moments of in e rtia may be the leading terms sim plify considerably. indicated by the super-script on (k) the Fourier series fo r thea-de replaced by apowerseries and To the appropriate order in a the terms k j(ct) then become on expansion^ i 1- i . iw b- , k = ->„<«)• 0 . lN2lW-'a B'I]> V “J = °N2 * 4 2z ’ V * [" 2 J i 2a ’ * ll ■ S ' x 8' * ■W “> H B‘ 2 . ’ 0 J Za < “ > ■ 0- <3- 1 3 > and the d° elements are s t i l l given by Eqs. (3 -1 2 ). •* In the perturbation c a lc u la tio n , H° = HR + H° is the unperturbed Hamiltonian and H* - Htr + H' + H®- is considered as the perturbation. Here H° » H j‘ + H°" Where H®' gives that part of the torsional equation which gives a d iffe r e n tia l equation s im ila r to the extensively studied Mathieu's equation^ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 a fte r a change in variables a = .However,, X + gir, S = V2/y ° , b = E /y° (3-14) fo r S > 100..i.e . high b a rrie r approximation, theeigenfunctions correspondingto the Mathieu’s equation become the same as th at fo r a harmonic o s c illa to r . 5 Quade has calculated both the ro ta tio n al as well as the torsional energy in th is case. The torsional energy in the vth state is given by Ev = Uj [(2V+DS1/ 2 - I (2v2+2v+l)] + I y |2 ) (2v2+2v+3) (3-15) where y° = 1/2 J °a » y |2^arises from the a-dependence in the torsional k in e tic energy and S is called the reduced b a rrie r. The e ffe c tiv e moments of in e r tia in the harmonic approximation were calculated to be ( I e ff)t j = + 0 ^ > (2 v + l) / 2 S '/2 i i » xx, yy, zz; (3-16) i j * yz and the in e r tia defect was calculated to be Ay = 0 ^ } (2v + D / S 1/ 2 where Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (3-17) The e ffe c tiv e moments of in e rtia obtained above are not to be equated with the e ffe c tiv e principal moments which have been derived from the data fo r benzaldehyde. A rotation of axes is applied to these moments fo r com parison with the empirical values. A ll these ( r „ ) ,• „• and J° are to be calculated from the structure of 4 e f r 'ij aa the benzaldehyde framework. P a rtic u la rly , small changes in the structure of the aldehyde group can introduce errors in the calculated values. That is why i t is important th at a f a ir ly good structure fo r the benzaldehyde framework must be known in order to compare the values o f moments of in e rtia predicted by this one-de g re e -o f-1ntern a1-fre e dom model with the values obtained from the data and thus determine the a p p lic a b ility of the model. In the next chapter the method used fo r obtaining structural parameters is discussed and with its help a f a ir ly consistent structure has been obtained. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER IV STRUCTURE OF THE BENZALDEHYDE FRAMEWORK • For determination of the structure of a polar molecule in the vapor phase, microwave spectroscopy is unmatched by any other technique in pre cis io n , power and c e rta in ty . In p rin c ip a l, the method employed consists of calculation of moments of in e r tia from the observed spectral frequen cies. From the moments of in e r tia of several isotopic species, in te r atomic distances and angles are deduced. However, the moments o f in e rtia and structural parameters in this case are the e ffe c tiv e or average values fo r the vibrating molecule in the ground vib ratio nal s ta te . Since the structure of most asymmetric tops cannot be determined by only three stru ctu ral parameters ( i . e . the three unequal principal moments of in e r t i a ) , i t is necessary to combine data from several isotopic species in order to determine the structure of the molecule. And since the d iffe re n t isotopic species of the molecule w ill have d iffe re n t zero-point vib ratio n s, the e ffe c tiv e stru ctu ral parameters w ill d iffe r , s lig h tly fo r the various isotopic species. I f i t were possible to observe the spectrum of the mol ecule in several successive excited states of each vib ratio n al mode, then i t could have provided a means fo r extrapolating back to the hypothetical non-vibrating state of the molecule. However, this method is not p ra c ti cal f i r s t l y because the molecule has too many vib ratio nal modes and sec ondly due to the fa c t th at the population of molecules in upper vibratio nal levels fo r high frequency vib ratio n s, would be fa r too small to be observed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 Another approach would be to calculate the correction arising from the v ib ra tio n -ro ta tio n in te ra c tio n . Although the principles of this calcula tion are w ell known i t cannot be carried out in practice because the anharmonicity of the force fie ld s o f the atoms are not known. Therefore, the effects due to zero-point vibrations are usually ignored and the as sumption is made that the stru ctu ral parameters are id en tical fo r each isotopic species. Deviations that occur in the values o f structural para meters when d iffe re n t is o to p ic a lly substituted molecules are used in the calculation can be attrib u ted mainly to these zero-point vib ratio nal e ffe c ts . Kraitchman 44 has developed exact solutions fo r the molecular coor dinates in terms of the equilibrium moments of in e r tia . Thus in this form ulation, the calculated stru ctu ral parameters r g correspond to posi tions the atoms would occupy i f they were at rest in the molecule. This means that fo r a planar molecule the in e rtia defect fo r the r s structure w ill be zero. Again i t is assumed th at the value of r g does not vary with isotopic substitution and the coordinates of the substituted atom are determined in the principal axis system of the parent molecule. The other and more obvious method fo r obtaining the molecular structure is the solution of the moment equations is known as the r o stru ctu re. 45 . The structure so obtained I t is assumed th at the value of r„ and o orientation of the principal axes is not affected by isotopic su bstitu tion . I f th is is done, fiv e relationships can be imposed on 2 N atomic coordin ates of a planar molecule. These include two diagonal moment equations, one product o f in e rtia and two conditions on the center of mass o f the molecule. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 In the present case, only one isotopic substitution was made i . e . substitution of H by D in C H CDO. 6 5 Also due to presence of the isotopes C l35 and C l37 in natural chlorine, i t was possible to obtain data on two parachlorobenzaldehyde molecules. A ll the molecules chosen in this study are s im ila r in the sense that each has the aldehyde group on one side of the ring and H, F, C l35 and C l37 are substituted in turn a t the position para to the aldehyde group. However, the length of the bond from its origin on the ring to the substituted atom is appreciably d iffe re n t in each case. Therefore, the expressions of Kraitchman cannot be used fo r determining the coordinates o f any two atoms in the principal axis system o f one parent molecule. Since the o rien tation of the principal axes is d iffe re n t fo r each o f the molecules considered the r Q method also cannot be conveniently used. In the method actually used, expressions, fo r each molecule, which were equal to the sum of principal moments of in e rtia in each case were set up. The structural parameters obtained by this method are same as those calculated by the r Q method because in each case the e ffe c tiv e prin cipal moments of in e rtia obtained from the ground state rotation al spec trum are used in the expressions. With only fiv e molecular species studies in this work, a ll the struc tu ral parameters fo r the benzaldehyde framework cannot be determined. Therefore the following sim plifying assumptions were made. (1) The ring forms a regular hexagon in monosubstituted benzenes as well as in these molecules. (2) The environment of the aldehyde group and its structure is not Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. affected by the presence of H, F, C l35 or C l37 in the position para to this group. (3) aldehyde. C-F bond length is same in fluorobenzene as in parafluorobenzS im ilarly C-Cl bond length is same 'in chlorobenzene and para- ch1orobenza1dehyde. Admittedly, the ring w ill be distorted by varying amounts by d if f e r ent. substituents. However, the f i r s t o f the above assumptions allows the instantaneous determination of a large number of parameters. I t is also found th at the 'A' ro ta tio n al constants determined from the ground state rotation al spectrum of a ll monosubstituted benzenes have very nearly the same value. The 'A' ro ta tio n al constant in these cases is proportional to the moment o f in e rtia about the axis containing the C-X bond where X is the substituted atom. This shows th at the variatio n in d isto rtio n in the ring structure from molecule to molecule can be ignored as a good approximation. J u s tific a tio n fo r the second assumption to some extent is provided by the analysis o f the ground state ro tatio n al spectrum of parachioro benza 1dehy de carried out in the present work. The values o f quadrupole coupling constants obtained fo r the two molecular species in th is case are almost id en tical with the values obtained fo r the corresponding chlorobenzenes. The quadrupole coupling constant is a measure of the ionic bond character o f C-Cl bond in this case . This therefore indicates th at the C-Cl bond has the same percentage o f ionic character in the two cases and whether the aldehyde group is present or not a t one end o f the molecule, does not matter. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 A survey of molecular structure data derived from microwave studies indicates th at the length of a bond of a given type is less subject to variatio n from molecule to molecule than bond angles i f no unusual struc tural features are present. This provides ju s tific a tio n fo r the th ird assumption. I f m^ is the mass o f the 1 ^ atom, r^ the distance of the 1 ^ atom from the origin and i! the u n it dyadic, the in e rtia dyadic may be w ritte n as 19 I = | m. (r? The diagonal T1 - r . ^ . ) (4 -1 ) elements of 2 are knownas the moments of in e r t ia . For a cartesian coordinate system fix ed a t the center of mass of the molecule, the diagonal elements of the in e rtia tensor are ! xx = | Where I ( 4"2a) are formed by a permutation of x,y and z . * diagonal elements called products of in e rtia are given by yy and I 'xy = | m1 *1 y 1 The o f f- (4 - 2b) The in e rtia tensor is symmetric with 1.^ = 1^. leaving only s ix indepen dent tensor elements. For a planar molecule with x-axis perpendicular to the plane, 'I = I X2 *- 0. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 In the matrix notation the in e rtia dyadic fo r a planar molecule can be w ritten 0 XX 0 I 0 i yy yz 0 I i , yz zz The orientation of the coordinate system used to define the in e r tia l system w ill determine the values of the moments defined above. I t is always possible to rotate the coordinate axes so th at the matrix is diag onal. In the language of matrix algebra such a diagonalization can be obtained by means of a s im ila rity transformation. The rotated axes are called the principal axes, and the corresponding diagonal elements, I x , ly , I z> are known as the principal moments of in e r tia . Spectroscopic measurements only give information as to the values of the principal mo ments of in e rtia with respect to axes passing through the center of mass of the molecule. I f the origin of the coordinate axes is chosen a t the center of mass of the molecule and Eq. (4 -2 ) is used to compute the e le ments of the in e rtia tensor, the diagonalization procedure w ill automati* c a lly give the principal moments of in e r tia with respect, to the center of mass. However, i t is often desirable to s ta rt with an a rb itra ry o r i gin fo r the coordinate system and s t i l l make the computations with re spect to the center of mass. the p a ra lle l axis theorem. This can e a s ily be done by making use of To fin d the desired relatio n s we substitute in Eq. ( 4 - 1 ) , r . = R + r . represent the distance of th is atom from the center of mass, and ft the distance of the center of mass from the o rig in . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 Upon substitution of the center of mass relation s v iz . * = I mi V I mi and I 'V ? = 0 into Eq. (4 -1 ) the following experssion is obtained: where 2 ° is the in e rtia dyadic with respect to the center of mass. Typical elements fo r a planar molecule have the form* (I2 V } ) {I3 mi 2i ) ___ . (4 -3) With an a rb itra ry origin fo r the coordinate axes the d ia g o n a liza ti on procedure w ill autom atically give the principal moments o f in e r tia with respect to the center o f mass i f the elements of the in e rtia dyadic are computed from Eqs. (4 -3 ). The C-C and C-H bond lengths in the symmetrical ring and C-F and C-Cl Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 bond lengths were calculated from the *B* rotational constants determined in the study of microwave rotation al spectra of fluorobenzene^ and chlorobenzene 18 . In both cases the o rig in of the coordinate system was chosen at the point where the carbon halogen bond o rig in ates, with z-axis coin ciding with the carbon-halogen bond and the y-axis perpendicular to this axis such that both axes are in the plane of the molecule. Bond lengths C-C, C-H, and C-X, where X is e ith e r F or C l, are put equal to a, b and c respectively. See Figure 4. In th is orientation of the axes, z is also a principal axis as the molecule is symmetrical about i t and the product of in e rtia I y2 vanishes. Therefore, i f Eq (4 -3 ) is now used to evaluate Iy . the quantity computed w i l l be the principal moment o f in e r t ia about an axis p a ra lle l to the chosen y-axis but passing through the center of mass of the molecule i . e . another principal axis. This p rin c i pal moment of in e rtia is inversely proportional to the ro tatio n al con stant B. Thus we have 1° = Xc2 + (9C+9H)a2 + 2Hb2 + 6Hab - R^ - j | F>[X2c2 + (6C+6H)2a2 + H2b2 + 2H(6C+6H)ab - 2X(6C+6H)ac - 2XHbc] = C.F./B where X,C,H stand fo r the isotopic weights fo r the respective atoms in atomic mass u n its. '3* is the rotation al constant, Mol. Wt. denotes the molecular weight of the molecular species being considered and C.F. is the conversion facto r fo r converting the ro tatio n al constant expressed in MHz Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 oc a C-C = 1.399 o< b = C-H = 1.088 ± .001 o< c = C-C1= 1.713 ± .001 Figure 4. C-F = 1.300 ± .001 Structure of the Monosubstituted Benzene Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o<c c - 87 into the corresponding moments of in e rtia in amu-A2. The NBS-NRC recomo„ mended value o f 505376 MHz. p.A2 fo r the conversion facto r has been used. This corresponds to C12 = 12 atomic-weight scale. Using these values for the constants and the value of 18* from the respective ground state ro ta tional constants, the expressions fo r I ° fo r d iffe re n t molecules give For C6H5C135 24.052 c2 + 62.687a2 + 2.007 b2 + 4.642 ab + 48.732 ac + 0.629 be = 320.513 arnu-X2 For C H C l37 v 5 24.980 c2 + 63.640 a2 + 2.007 b2 + 4.667 ab + 50.613 ac + 0.653 be = 329.710 amu-X2 For C H F 15.240 c2 + 53.644 a2 + 2.005 b2 + 4.409 ab + 30.879 ac' + 0.399 be' = 196.595 amu-A2 The solution o f these equations fo r the determination of a ,b ,c and c' is not straightforward because of the presence of cross terms. In these equations, co efficien ts of b2 , ab and be are small and nearly the same. For the expressions fo r the two chlorobenzenes these terms were Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 converted into constants by using values of a, b and c determined by other methods and these constants were moved to the rig h t hand side of the expressions. This gave two equations in a and c with only the cross product ac and the constant present. The constants were eliminated from the two equations and a single equation, quadratic in a/c was obtained. This was solved to obtain the r a tio a /c . The values of a in terms of c and c in terns of a were plugged in one of the two orig in al equations to obtain approximate individual values o f a and c. plugged in one of the I® vv of b. These values were then expressions to obtain the approximate value Thus this procedure provided the range of values fo r the bond lengths a, b and c. The true bond lengths were obtained with the help of a computer program w ritten in Fortran and compiled fo r PHILCO 2100 computer. This program is given in Appendix B. In th is program, the a, b and c distances are varied by increments of O.OOlR w ithin th e ir respec tiv e range of values. The left-hand sides of the three I® J -J expressions fo r the three molecules are then calculated fo r a ll permutations of a, b and c values w ithin th e ir respective ranges. Values fo r a, b and c and the difference between the left-h and side and the right-hand side in the three Ie x p r e s s io n s is printed out i f this difference is less than ± 0 .1 , simultaneously in a ll the three cases. fo r a, b and c. This narrowed the range Their values correct to the fourth decimal place in 9 0 tiv e ranges and using the computer program once again. As a fin a l check Angstroms were determined by giving increments of 0.0001A in th e ir respec the value fo r the 'A' rotational constant was calculated and compared with the values obtained from the ro tatio n al spectrum o f the molecules. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The 89 values fo r a, b and c and th at fo r the observed and calculated ro tatio n al constants 'A' and *B' are shown in Table XVI. The structural parameters fo r the aldehyde group were determined with the help of ground state rotation al constants o f the fiv e molecules studied in the present work. In these benzaldehydes the orientation of the two in-plane principal axes varies from one molecule to another. Their orien ta tio n and the position of the center of mass in each molecule cannot be found unless a ll structural parameters are known. This is why individual rotation al constants cannot be used fo r structure determination. A well known theorem in m atrix-algebra is th at the trace of a matrix is in varian t under a s im ila rity transformation. Therefore i f the in e rtia tensor with respect to the center o f mass of the molecule is diagonalized, the sum of the principal moments of in e rtia thus obtained w ill be ju s t the sum of the moments of in e r tia before diagonalization. Since the ground state rotation al spectrum provides the values fo r A, B, and C which are inversely proportional to the principal moments of in e r tia , the following re la tio n is obtained: '° x + '?y + 'zz = C' F- A ll these benzaldehydes are planar in th e ir equilibrium configurations. • ‘ ’ Thus t ° xx = lyy zz i° + T° 2 ( I° y + I ° z ) = 505376 ( J- + 1 + 1 ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 TABLE XVI a , b, c and Comparison of Calculated and Observed Rotational Constants A and B fo r the Ground State of Fluorobenzene and Chlorobenzene W C H C l35 C H C l37 6 j a (A) 1.3985 1.3985 1.3994 b (A) 1.0872 1.0872 1.0875 0 c (A) 1.7129 1.7129 1.0875 6 5 CALC.'A' (MHz) 5672.64 5672.64 5665.73 OBS. 'A' (MHz) 5672.95 5672.53 5663.54 CALC.' B* (MHz) 1576.77 1532.90 2570.54 OBS. 'B' (MHz) 1576.77 1532.79 2570.64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The origin point where rin g . of the coordinate system in each case was chosen at the the C-C bond connecting the aldehyde group is attached to the The z-axis was chosen to coincide with this bond and the y-axis was chosen perpendicular to this bond such th at both the axes li e in the plane of the molecule. 5. The fiv e unknown structural quantities are shown in Fig. The expressions fo r 1° J and 1° are J ! zz = 4Cf‘a s1n 60° ) 2 + 4H[( a+b) s1n 60° ]2 + 0d2 + H' e2 - KoTTTJtT I® [0d-H'e]2 . and » X( c-*-2a) 2 + C(2a)2 + 2 C (| a )2 + 2 H (i b + | a )2 + 2C(^- a )2 •3 J + 2H(£ a - \ b )2 + Cg2 + Of2 + H'e2 - tX(c+a) + C(2a) + 2C(^ a) + 2H(~ b + | a) + 2C(~ a) + 2H(1 a - j b) -Cg-Of-H'e]2 % Where X stands fo r the atomic mass of e ith e r C l, F or H depending on fo r which molecular species the moments o f in e rtia are being calculated. Only fo r C H CDO, atomic mass of deuterium was used fo r atoms marked H‘ . ®5 2(1® + yy ) was equated against the sum of principal moments of in e r tia fo r each molecule to obtain fiv e equations in fiv e unknowns. However, again the solution o f these equations was not straightforward because of the presence Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 Figure 5. Structure of the Aldehyde Group Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 TABLE XVII Structural Parameters of the Aldehyde Group d = z-0 = 1.003 ± 0.001 A e « z-H = 0.984 ± 0.001 A f * y-0 = 2.146 ± 0.001 A g = C-C = 1.477 ± 0.001 A h = y-H = 1.999 ± 0.001 A Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE X V III Comparison of the Calculated (from the Structure) and Observed Ground C l35C H CHO 6 *+ C137C H CHO 6 h FCH.CHO 6* r C H.CHO 65 CcHcCD0 65 CALC. I A 99.702 99.749 98.800 96.800 99.176 OBS. I A 99.911 99.951 99.137 96.551 98.966 CALC. I fi 730.371 748.187 517.569 322.701 327.950 OBS. I B 730.316 748.119 517.408 323.081 328.031 CALC. I c 830.073 847.936 616.369 419.503 427.126 OBS. I c 830.074 847.938 616.368 419.504 426.878 OBS. A -0.153 -0.132 -0.177 -0.128 -0.119 1 of the cross terms. Therefore, a procedure sim ila r to the one employed fo r the determination of a , b and c was used to convert a ll the cross terms in to constants. Structural parameters obtained fo r the aldehyde group in the acetaldehyde study 46 proved quite helpful as t r i a l values fo r d, e , f , g and h in the present case. The approximate values fo r the fiv e parameters were then determined by the usual method o f solving simultaneous equations. Again, the computer program given in Appendix B was used to determine the true values of d, e, f , g, and h. in Table X V II. These structural parameters are reported With the determination of these fiv e parameters, the structure fo r each one of the fiv e molecules was known. I t was not possible to calculate the moments and products of in e rtia so as to obtain the in er t ia tensor in each case. Diagonalization of this tensor provided a set o f calculated principal moments of in e r t ia , which are compared with the values obtained from the ground state ro tatio n al spectrum, in Table X V III. The agreement between the calculated and observed values is quite good consid ering the sim plifying assumptions and zero-point vibrations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER V ANALYSIS OF SPECTRA WITH RESPECT TO THE THEORY Only fo r benzaldehyde and deuterated benzaldehyde, was i t possible to id e n tify lin es upto the th ird excited torsional s ta te . Therefore, with the structure fo r the benzaldehyde framework obtained in the pre vious chapter, and the appropriate expressions fo r the effe c ts o f in te r nal rotation fo r molecules with two-fold barriers derived on the basis of a model with one degree of internal freedom, described in Chapter I I I , i t is now possible to analyze the observed spectrum fo r these two mole cules. To do th is , we f i r s t of a ll determine the height V2 o f the po te n tia l b a rrie r hindering internal ro ta tio n . Height o f the Potential B arrier Since the b a rrie r to internal ro tation as determined by previous in vestigators, fo r these two molecules has been found to be high, one expects several torsional states to be below the top o f the potential w e ll. Physically th is means th at to go from one excited torsional state to the next higher s ta te , the torsional angle increases by a small amount. Therefore, i t becomes ju s tifie d to reta in only the f i r s t term in the expansion given in Eq. (3 -2 ) o f the potential function equation (3 -1 ). i.e .' V(a) = V2a2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (5 -1 ) 97 This allows the use of the harmonic approximation fo r the evaluation o f the b a rrie r height Vg. The internal motion of the aldehyde group can now be compared to the motion o f a torsional pendulam. The torsional pendulam consists of a body in the form of a disk suspended by a wire attached to it s center of mass. The other end of the wire is securely fixed to a solid support such th at the disk can execute torsional motions about the axis fixed by the w ire. In both cases, fo r small tw is ts , the restoring torque is pro portional to the amount o f tw is t, or the angular displacement (Hooke's law ), so th at t " -ka (5 -2 ) the constant k in the above equation depends on the properties o f the wire in the case of the torsional pendulam and is called the torsional constant. For the torsional motion of the aldehyde group it s value de pends on the height o f the potential b a rrie r hindering internal ro ta tio n . Higher the potential b a rrie r, greater is the torque required to produce a torsional tw is t through an angle a . Eq. (5 -2 ) is known as the con d itio n fo r angular simple harmonic motion. The potential energy V(a) a t any instant is given by (5 -3 ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 Comparing ( 5 - 1 ) .and (5 -3 ) we get k = 2V2 Therefore by analogy to the case of the torsional pendulam, the ex pression fo r angular torsional frequency becomes v « t (2 V ,/J ' 2 °)h aa# 2 or v2 3 “T ^5”4 ^ where y? = 1/2 J 0 and J 0 is the reduced moment o f in e rtia fo r the to rT aa sional motion. aa Once the structure o f the benzaldehyde framework is de termined, the value of here, can be calculated from Eq. (3 -1 1 ). is expressed in inverse of amu. u n it. As given I t can be expressed in cm"* by the following expression 4 = — 8ir2c Ja a ( 5- 5) • The torsional frequencies fo r CgHg CHO and CgHg CDO determined from r e la tiv e in ten sity measurements as lis te d in Tables VI and XI are 113.8 ± 5.0 and 108.4 ± 4.25 cm"*, resp ectively. Using these values in the expression (5 -4) the value o f Vg, the b a rrie r to internal ro ta tio n is calculated to be 4.66 ± 0.41 kcal/mole fo r CgHg CHO and 5.06 ± 0.40 k c a l/ mole fo r CgHg CDO. On the other hand the value of the potential b a rrie r Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 determined fo r the internal motion of the same aldehyde group in acetaldehydef^ (CH^CHO) is approximately 1.15 kcal/mole fo r several isotopic species studied. S im ila rly , b a rrie r heights fo r the internal rotation o f the -OH group in phenol OH) 14. 1 * (CgHg OH) and methanol are 3.36 kcal/mole and 1.07 kcal/mole respectively, 47 (CHg Hanyu e t . a l . 1^ report a b a rrie r height of 3.86 kcal/mole fo r the torsional motion o f the nitroso group in nitrosobenzene. Thus in a ll these cases the usual b a rrie r to ro tatio n around a single bond is g reatly increased by conju gation o f the ro ta tin g group with the aromatic rin g . This indicates th a t in aromatic molecules, the bond jo in in g the ring and the internal roto r has a p a rtia l double-bond character. The p a rtia l double-bond is responsible fo r an increase in the value o f k in Eq. (5 -2 ) from the v a l ue i t would have i f the same rotor is attached to say, the methyl group. This increase in k leads to higher potential barriers fo r aromatic mole cules. I f the aldehyde group has a methyl group attached to i t in one case and a benzene ring in another, then the length o f the C-C bond connect ing the two parts of the molecule should be smaller in the la te r case as compared to the length o f the same bond in the'form er case. This is due to introduction o f some stra in - a cause o f p a rtia l double bond char a c te r, in the la t e r case. This has been observed to be so. The length of th is bond in acetaldehyde^ is 1,501 R compared to the value 1.477 observed fo r benzaldehyde in the present study. % This shortening o f the C-C bond therefore serves as a confirmatory te s t, to some exten t, fo r the explanation given above fo r r e la tiv e ly higher observed potential Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 barriers in aromatic compounds. Calculation of the Parameters fo r Analysis The calculated value fo r the dimension!ess b a rrie r height parameter S = V2/ y ° f is 819.63 fo r CgHg CHO and 1065.62 fo r CgHg CDO. This ju s t if ie s the use o f h ig h-barrier approximation because fo r S > 100, th is approximation is useful fo r calculating the various m atrix elements in 5 the Hamiltonian . The e ffe c tiv e moments o f in e rtia in the harmonic approximation are given by expressions (3 -1 6 ), where J.*? and J . ^ IJ Ij expressions (3 -1 2 ) and (3-13) resp ectively. are expressed in terms of I ■j J, aa can be calculated from These equations fo r J.? and •J i f, i f , yy 44 I , I , N and B. ot x The v a l- ues fo r these la te r quantities can be determined d ire c tly from the c a l culated structure using expressions (3 -4 ), (3 -5 ), (3 -6 ) and ( 3 -8 ), and the calculated values along with the values o f S and CHO and CgHg CDO are reported in Table XIX. fo r a ll torsional states. However, the The J . . values are same 2 JA ' *J ( fo r both CgHg ) values have constant in - crements fo r each successive torsional s ta te , i f i t is assumed^that S has the same value in each of the torsional tra n s itio n s . This assump tio n is same as saying th at the torsional energy levels are evenly spac ed i . e . the harmonic approximation is followed. Only th is change in (2) 7 values w ill be reflected in the values o f e ffe c tiv e moments o f in - ' J e r tia calculated from Eqs. (3 -1 6 ). The e ffe c tiv e moments o f in e rtia are not to be equated with the e ffe c tiv e principal moments which have been derived from data and given in Tables V and X fo r CgHg CHO and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 TABLE XIX Calculated Values of the Parameters fo r Comparison o f the Spectra o f CgHgCHO and CgHgCDO with the Theory CgHgCHO Q I (amu*A2) a C6H5CD° 89.36 89.36 1° (amu*A2) 419.50 426.88 1° (amu*A2) yy 315.59 321.67 1° (amu'A2 zz 103.91 105.21 I (amu*A2) 40.44 37.62 XX X N(amu*A2) -1 3.1 4x l0"3 3.09x10 31157.56 32427.64 J° (amu*A2) aa ' 8.48 10.15 y^Ccm"1) 1.99 1.66 V ^ c n r1) 1629.00 1769.30 S 819.63 1065.62 B(amu*A2) 2 * Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 CgHg CDO respectively. A rotation of axes must be applied to the mo ments in Eq. (3-16) fo r comparison With the empirical values. The com- parison o f the observed and calculated principal moments o f in e rtia is given in Table XX fo r both molecules. The observed and calculated v a l ues fo r the differences in the e ffe c tiv e principal moments o f in e r t ia , energy and in e rtia defect Eq. (3-17) are compared in Tables XXI and XXII fo r CgHg CHO and CgHg CDO respectively. physical data, two approaches were used. For comparison with the Calculation I assumed th a t values fo r the torsional frequency fo r these two molecules which were measured by infrared techniques^. The second calculation used the torsional energy difference determined from the r e la tiv e in te n s ity data in th is work. Both the approaches show c le a rly th a t there is a large difference between the observed and calculated values o f the differences o f these dynamical q u an titie s. work. This is a very s ig n ific a n t re s u lt of th is The lack o f agreement can be a ttrib u te d to the lim ite d applica- b i1it y o f the assumed model fo r determining the dependence o f the e ffe c tiv e moments of in e r tia . The rig id top and rig id framework model with degree o f freedom fo r only internal ro ta tio n ignores a ll interactions between internal torsion and other vibrations o f the molecule. This n a tu ra lly sim p lifies the problem considerably and requires much less data fo r evaluation of the fewer parameters needed. The discrepancy between observed and calculated behavior suggests the importance o f v i bration in te rn a l-ro ta tio n in te ra c tio n . I f the torsional frequency 1s well below the frequencies o f the other vibrations only then i t is ju s t if ia b le not to consider other vib ratio nal modes. However, in benzaldehyde Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE XX Comparison of the Observed and Calculated Principal Moments of In e rtia fo r C H CHO and C H CDO in 6 5 6 5 the Ground and F irs t Three Excited Torsional States v = 0 v - 1 v = 2 v = 3 Obs. Calc. Obs. Calc. Obs. Calc. Obs. Calc. I A(amu*$2) 96.551 96.484 96.909 96.558 98.001 96.632 97.675 96.705" I B(amu*$2) 323.081 323.164 322.943 323.386 322.896 323.609 322.692 323.832;. o I c(amu*A2} 419.504 419.352 418.886 419.056 417.857 418.760 417.620 418.463, -0.128 -0.296 -0.996 -0.888 -3.040 -1.481 -2.747 -2.073 IA(amu*A2) 98.966 98.886 99.292 98.942 99.609 98.998 99,936 99.054 I^Camu'A2) 328.031 328.149 328.007 328.404 327.993 328.659 327.985 328.915 I c (amu-I\2) 426.878 426.725 426.289 426.414 425.714 426.103 425.159 425.792 -0.119 -0.311 -1.010 -0.933 -1.888 -1.555 -2.762 -2.176 C,H,CH0 6 5 0 A(amu*A2) c6h 5cdo 15 o A(amu*A2) ' 104 TABLE XXI This table contains a comparison of observed and calculated para meters fo r CJ-LCHO. 6 5 Calculation I assumes th at value V„2 = 1550 cm"*1 while Calculation IT assumes the value V 2 = 1629 cm"1 from the microwave in te n s ity measurement. j ( 2) zz = 1.44 j ( 2) yy = 1.99 cm"1 = 7.04 = 6.08 Observed Calculation I Calculation I I (I K .-d ) xx v + l xx v -0.628 amu X2 -0.319 -0.296 (I ) ^ .-(1 ) yy v + l yy v -0.129 +0.242 +0.223 +0.375 +0.077 +0.073 (I ZZ V + l A . - A v+l v ZZ ) V -0.873 V2 * **• s 1/ 2 *"* vt 113.8 cm'1 -0.638 1550a cm"1 27.9 111 cm-1 -0.592 1629 cm-1 28.6 114 cm"1 aassumed value such th a t v corresponds to d ire c tly measured in fra -re d frequency. T Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 TABLE XXII Same as TABLE XXI but fo r C H CDO. 6 5 Calculation I assumes the value . V0 = 1647 cm-1 whereas Calculation I I assumes the value V„ = 1769 cm"1 2 2 from microwave in te n s ity measurements. i - 21 = mu J/ 1.66 cm"1 Observed (I (I ) ,,-(1 XX V + l XX ) V ) ^ -(I ) yy v + l yy v ( I ) .,-(1 v zz'v+1 ' A - - A v+l v 2 ZZ ) V T 3 5.68 amu X2 Calculation I Calculation I I -0.573 amu A2 -0.336 -0.311 -0.015 +0.280 +0.255 +0.323 +0.056 +0.056 -0.381 -0.672 -0.622 .... 1647a cm"1 1769 cm"1 s1/ 2 v = s -94 amu ° 2 31.5 108.4 cm” 1 104.6 cm"1 32.6 108.5 cm"1 aassumed value such th at v corresponds to d ire c tly measured in fra -re d frequency. T Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 a t le a s t, some evidence has been obtained in he present work about the presence of a vibrational mode o f very nearly the same frequency as the second torsional mode. Hanyu e t . a l . 13 in th e ir analysis o f the micro wave spectrum of nitrosobenzene obtained a simple expression fo r the change o f in e rtia defect fo r successive torsional state (Ay+j - Ay ) from 25 the complex expressions derived by Oka and Mori no , by considering only the torsional mode and ignoring a ll other vib ratio nal modes. The value fo r the change o f in e rtia defect fo r successive torsional state calcu lated from th is simple expression was less negative than the actual ob served value. They fu rth e r showed q u a lita tiv e ly th at i f the other v i brational modes are also considered the in teractio n between these other modes and the torsional mode would tend to make the change Ay+.j - Ay more negative than the value calculated by the simple expression. The value fo r Ay+-j - Ay fo r both CgHg CHO and CgHg CDO was calculated in Chapter I I using th is simple expression. These calculated values are quite close to the values calculated from Eq. (3 -1 7 ). Therefore i f the analysis o f Hanyu e t . a l . is applied to the case o f benzaldehyde, i t becomes quite cle ar th a t certain vibrational modes are present in th is molecule whose frequency is not much d iffe re n t from the torsional frequencies and the in teraction between vibration and internal rotation modes can not be ig nored . Internal ro tatio n can in te ra c t with the remaining vibrational degrees o f freedom and molecular ro tatio n s. these, in tu rn , can in te ra c t with the o v e r-a l1 Thus, there is an in d ire c t coupling between in tern al and o v e r-a ll ro tation which is due to n o n rig id ity o f the molecule. A q u an tita tive understanding w ill have to await fu rth e r theoretical Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. developments. Further Developments o f Theory The effec ts of no n rig id ity o f the two halves o f the molecule were f i r s t studied by Kivelson*8 from a semi-empirical point of view. He ob tained an approximate formula fo r the ro tatio n al tran sitio n s o f symmetric rotors and successfully applied th is formula to CHgSiHg and CHgSiDg. these symmetric tops, a Van Vleck 49 transformation was applied to remove the nondiagonality in the vib ratio nal quantum number. tend th is treatment to asymmetric rotors ber of adjustable parameters. For 50 An attempt to ex- produced an unmanageable num For th is reason, the semiempirical ap- proach to asymmetric rotors was abondoned fo r some tim e. Kirtman 51 re examined, modified and extended Kivelson's o rig in al approach and was able to discuss, in d e ta il, the o rig in o f various in teractio n terms. Over-all and internal rotation were separated in zeroth order, by means o f the Eckart 52 and Sayvetz 53 conditions. Even with the comprehensive treatment of Kirtman, i t was obvious th a t, in general, the microwave absorption frequencies o f an asymmetric roto r w ill depend upon an un wieldy number of empirical parameters. Only foY two group o f tra n s i tio n s , the frequency formula was found to be simple enough, provided the high b a rrie r approximation was used. sists o f the 0Q g ■*1Q -j* For prolate rotors one group con- the combination sum h[Ij \ q->2.j ^ + 1^ ^->-2^ 2] and the 22 ^->-32 2 tra n s itio n s . The other group corresponds to tran sitio ns * * 54 between the two members o f an asymmetry doublet. Quade has extended Kirtman's treatment to include the in teractio n of normal vibrations Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with the hindered internal rotation in molecules with asymmetric in te r nal ro to rs. A Van Vleck 49 transformation was again used to is o la te an i,L e ffe c tiv e o v e r-a ll and internal ro tation Hamiltonian fo r the V tional s ta te . vib ra The coupling between o v e r-a ll ro tation and vib ratio n and between internal ro tation and vib ratio n were treated as a perturbation a fte r these couplings had been reduced by applying the Sayvetz-Eckart conditions. However, i t was possible to apply the theory of internal ro ta tio n -v ib ra tio n interaction only to moleucles fo r which both the top and the framework possessed planes o f symmetry. S p e c ific a lly the theory was applied to the microwave spectrum o f p a r tia lly deuterated acetaldehydes. In view of lim ited experimental data availab le no conculsions were possible about the a p p lic a b ility o f the theory, only an encourag ing trend was noticed. In the present work s u ffic ie n t data has been obtained to te s t any future developments o f the theory to include a ll the vibratio nal modes in molecules in which only one part o f the com p le te ly asymmetric molecule has a twofold axis of symmetry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A ASYMMETRIC ROTOR ENERGY LEVELS IN RIGID-ROTOR APPROXIMATION The energy of a rig id asymmetric rotor is expressed as E< v v v ^ + w (A- 1) where Pa , Pb , and Pc are the components of the angular momentum along the principal in e r t ia l axes a, b, and c of the roto r with I a~ I b * I c as the corresponding moments of in e r tia . A=T>2/ 2 I a , Defining the rotation al constants B = t i 2/ 2 I b, C=T>2/ 2 I c (A -l) becomes E(A,B,C) = (A P2 + B P2 + C P2) / t\2 a D C The calculation of the energy levels is greatly fa c ilita te d by the change 53 of variables proposed by Ray . With this change of variables he obtained the expression E(A,B,C) = J}- (A-C) E(k) + \ (A+C) J(J-H) (A-2) Where J is the to ta l angular momentum quantum number and E(k) is called Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. no the reduced energy. E(k) = E ( i , k , - i ) i . e . E(k) corresponds to the energy of a hypothetical r ig id ro to r whose A, B and C rotation al constants are 1, k and -1 respectively where k is called Ray's asymmetry parameter and is given by i. „ 2B - A - C K T rn r I f B=A then k=l and we have the oblate symmetric top lim it and i f B-C, then k=-l corresponds to the prolate symmetric top lim it . With the energy level expression given in the form (A-2) the problem reduces to determining the value o f E(k) fo r a given set of quantum num bers, i f the energy level corresponding to these quantum numbers is desired to be calculated. termining E(k) in d e ta il. King e t. a l . 23 have treated the problem fo r de In th e ir method, matrix elements o f the Hamil- 56 tonian are generated in the Wang representation. This consists of a CJ lin e a r combination of symmetric ro to r basis functions % , \px (J,K,M) i.e . S(J,K,M, y ) = 2-1/2 [ /( J ,K ,M ) + H ) Y / ( J , - K , M ) ] where y is odd or even, say 1 or 0. For K=0 only y even (y = 0) exists and S (J,0 ,K ,0) = / ( J , 0 , M ) K and M being the projections of J on the molecule-fixed fig u re axis and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m the space-fixed f ie ld axis respectively fo r a symmetric ro to r. can take any of 2J + 1 possible values. K and M The matrix elements o f E(k) as derived by King e t . a l. are <JKMjE(k)|JKM> = FJ(J+1) + (G-F) k2 (A-3) <J,K+2,M|E(k)JJKM> = H [f( J,K+1)3 x/ 2 (A-4) where the f ( J , K+l) are given by f( J ,n ) * f(J ,~ n ) = -J- [ J (J + l)-n (n + l)] [J (J + l) -n ( n -l) ] (A-5) Tabulated values of f(J ,n ) are given in Table I of Reference 23. x ,y , and z axes re fe r to the prin cipal axes of the in e r t ia l dyadic. I t is customary in molecular spectroscopy to designate these axes as a , b, and c with the convention th at I fl< I b< I c. There are n! or six ways in which the a , b, c axes can be id e n tifie d with the x, y , z axes. The values of the co efficien ts F, G and H fo r the m atrix elements of E(k) depend on the way a , b and c are id e n tifie d with x, y and z. King e t . a l. showed th at the rig h t handed representation, in which x is id e n tifie d with b, y with c and z with a, in th e ir n o tatio n , is nearly diagonal fo r a near pro la te symmetric top molecule. In this representations F » 1 (k -1 ) (A-6a) S = 1 (A-6b) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 H -- \ (k + l) (A-6c) For a given J the energy m atrix E(k) in any representation based upon the if>x(J,K,M) can be obtained from expressions (A -3 ), (A -4 ), (A-5) and o f type (A -6 ). The expressions (A-6) w ill vary with the representation used to id e n tify the two set of axes. -J - K * J. The matrix fo r E(k) is o f order 2J+1 since I t may, however, be displayed as two submatrices whose indices involve, resp ectively, only odd K's. The transformation to a representa tion based upon S(J,K,M, y ) enables fu rth e r factoring of E(k) in to four submatrices i . e . X' E(k) X = E+ + E* + 0+ + 0" X is of order 2J + 1 and is referred to as the Wang transformation = X S For the form of X, X ', E+ , E", 0+ and 0" see Reference 23. With the matrix elements of E(k) known, calculation of the energy levels of a rig id asymmetric rotor becomes a purely mathematical problem involving the diagonalization o f the submatrices E+ , E", 0+ and 0". of these submatrices is of the Jacobi an or tridiagonal form. Each These can be e a s ily transformed to a form which allows the d ire c t application of con tinued- fra c tio n technique; the technique f i r s t used by King e t. a l, to di agonal ize these matrices. However, nov/adays these can be diagonalized Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 to a high degree of approximation by high-speed d ig ita l computer techniques, as done by Beaudet 22 in his computer program fo r example. In th is computer program, the mathematical method used is exactly that of King e t. a l. The matrix elements are generated fo r the Hamiltonian in the Wang representa*4* *■ tio n . Therefore, fo r each J value, the four independent blocks E , E , 0 and 0” are obtained, each one of which is diagonalized separately. The eigenvalues are then ordered w ithin each block by c a llin g another subroutine, so that they can each be labeled properly. As a check, the trace of the diagonalized matrix is compared with a sum-rule. In asymmetric ro to rs, the projection of the to ta l ro ta tio n al angular momentum is no longer constant along any axis or direction fixed in molecule, with the re s u lt th at K is no longera good quantum number. ever, the parameter K is kept to label the energy le v e ls . labelled in the notation where the How Each level is is the value K would have in the lim itin g case of an- oblate symmetric top, while K_1 is the value of K fo r the lim itin g prolate symmetric, top. values such th at -J s t I f K_1 - K = t then t takes on 20+1 - J. Dennison58 was f i r s t to derive the symmetry selection rules fo r an asymmetric ro to r. For R-branch a-dipole tra n s itio n s , the selection rule AJ = ± T, a K - 0 , ± 2 . . . and a K^ = ± 1, ± 3 . . . is followed. The fr e quency fo r a R-branch tra n s itio n calculated from (A -l) is given by v = (A+C) (0+1) + 1 (A-C) [EJ+1 (k) - EJ (k)J (A-7) For Q-branch tra n s itio n s , A 0=0 and fo r b-dipole tran sitio ns a K_x = ± 1 ,± 3 ... Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. aK = ±1, ±3 . . . The frequency o f a Q-branch tra n s itio n is given by -v = \ (A-C) A E(k) (A-8) Therefore from Q-branch tra n s itio n s , only the values fo r (A-C) and k can be determined. These values when plugged in to the expression fo r re branch tra n s itio n s , the value fo r (A+C) is also obtained. to obtain individual values of A and C and plugging I t is ro w easy these in the expression fo r k the value of B can also be obtained. A lte rn a tiv e ly , individual values o f A, B R-branch transitions alone. However, in this and C can be obtained from case, B and C w ill be c a l culated more accurately than A as explained in the te x t. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX B COMPUTER PROGRAM FOR EVALUATION OF STRUCTURAL PARAMETERS Reproduced with permission of the copyright owner. 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V y •X crT CC cc C cr crV W C3 -< -H C J r**. r*i GN O’- —i :> X iZ , Cv U J O- X o cr11 • • II • rv IK • cv 11 • • * •■ • T-* o H O 1— •C o *'C .V •cr 4 4 u 4 4 t* 4 4 U 4 + t—. .'V -r-i Cv *- .V T - i Cv rc o • sf\ M LlJ cr ac o il\ cv ir» u. ♦ u. o % • ^ U. TO K • ^ cr O • i% rv po U% V4 * cr u. * v*4 UJ la- O • CV Ul fa % ♦ - €>* • » o »4 fa r i C r fa c c c • J— sr- rr CV O *O r k: if 'S . < t <T <C II II II *< ? >— ^ • rlil z cr m :v -c<r r\ u. * x »- I- v4 s fa o <r-f it cr- fa *■* » -Y— --X. u_ • C3 s«r ;I « C? CT U. C/; (T, CT; CT • cr T. :X - I * C3 c<cc U fa *—»—*— 3* ri X I— o X c -« n u_; U..3 r Z Z n z> ~ 3 — i w; H ZZ 2 H H i Z H v— i— »— i— i—i— x x Z Z Z - Z Z Z O T O Q O O O O O O G * — Z L CL X ! UJ UJ UJ 'x— L L C f > C ^ -—I y—I tJ U. W U fl >1 3 vH r l »~4 H 3 X r c X X « > S c o c 5 c CN u N £ > ’J '3-LTi cz z . o o o o c sr C 5 •vr =r- j \ in X \ ci- cr- cr c r ♦c* ?<r ■ 2T < a 'O o ¥**.' n X* X X cr cr cr cr c c n • c. X o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. rv ~ o : 'Z TV X X vC X X X o cr o cT rr • *.. ■r. • c; REFERENCES 1. C. C. Lin and J. D. Swalen, Revs. Modern Phys, 31_, 841(1959). 2. C. R. Quade and C. C. L in, J. Chem. Phys, 3S3, 540(1963). 3. D. G. Burkhard, J. Chem Phys. 21_, 1541 (1953). 4. D. G. Burkhard and 5. C. R. Quade, J. 6. R. K. Kakar, E. A. Rinehart, C. R. Quade and Phys. 52, 3803 (1970). 7. R. K. Kakar and E. A. Rinehart (to be published). 8. T. Kojima, C. R. Quade, and C. C. Lin, B u ll. Am. Phys. Soc. 1, 44 (1962). 9. F . A. L. Anet and M. Ahmad, J. Am. Chem. Soc. 85, 119 (1964). 10. H. G. S ilv e r and 0. L. Wood, Trans. Faraday Soc. 6£, 5 (1964). 11. W. G. F ately, R.K. H arris, F.A. M ille r , and R. Spectrochim. Acta 21_, 231 (1965). 12. J. C. Irw in , J. Chem Phys. 23_,1355(1955). Chem Phys, 47, 1073 (1967). T. Kojima, J . Chem. E.Witkowski, F. A. M ille r , W. G. F ately, and R. E. 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