Vibrational absorption intensities in aliphatic ring systems—I. Cyclohexane

Spectrochimica Acta, Vol. 41A, No. 9, pp. 1047-1054. 1985. OS84-8539185 53.00 + 0.00

Printed in Great Britain. 0 1985 Pergmm Press Ltd.

Vibrational absorption intensities in aliphatic ring systems-I. Cyclohexane

TIM HOGAN and DEREK STEELE*

Department of Chemistry, Royal Holloway College, Egham, Surrey TW20 OEX. U.K.

(Received for publication 29 March 1985)

Abstract-The infrared absorption intensities have been measured for cyclohexane and for cyclohexane-d, 2 in both the vapour and solution phases. There is good accord between the results and expectations for the intensity sum ratios of the two isotopic species. The data are analysed in terms of atomic polar tensors (APT) with the aid of ab initio 4-31 G computations. Problems and uncertainties arising from severely overlapping bands are discussed and it is shown that the expected similarity of the effective hydrogen atomic charges requires a particular intensity partitioning of the CH stretching bands. The ab initio calculations in conjunction with the force field of SNYDER and SCHACHTSCHNEIDER~~~ found to lead to intensities which are

within 20% of the observed for broad spectral areas, such as would be associated with given types of group motions, though the distributions within the areas are less satisfactory.

INTRODUCHON

The prediction of spectra has been the ultimate goal of vibrational spectroscopists-on academic grounds be- cause it is the most stringent test of our understanding, and on practical grounds for its analytical impli- cations. Any band is characterized by three observables-namely band centre, intensity and band shape. Although advances in the understanding of all three have been substantial in recent years none has yet reached the stage where confidence may be felt in predicting the properties of a complex molecule.

This is the first of a series of studies aimed ultimately at predicting the spectra of carbohydrates. In the current phase little attention will be focussed on the band shapes. The band contours in condensed phases are determined by the overall molecular dynamics as well as by vibrational relaxation processes [l]. Advances in this field are currently rapid, but as intensities and band centres are quite independent of the contour the latter will be disregarded at present. The prediction of band centres is also independent of the other band characteristics, but regretably this is not true for intensities, which depend both on amplitude and on the precise form of the vibration-both of which are functions of the molecular force field. It is inevitable then that studies of the force field should be a prelude to or accompany studies of absorption or Raman intensities. After the brilliant pioneering studies of CRAWFORD and his collaborators [2-4] on the theory and measurement of intensities severe difficulties were encountered in interpreting the derived dipole parameters. This was due in part to the uncertainties (or errors) in assumed force fields and in part to the well known sign indeterminacy of the experimental dipole gradient. It was not surprising then that over some two decades emphasis moved to establishing force fields. While the problem of force

*To whom correspondence should be addressed.

fields is still unsatisfactory in that the fields of few molecules with more than three atoms have as yet been reasonably established, nevertheless progress is being made in determining dipole gradients from the multip- licity of solutions possible to the intensity problem and in establishing models which may allow prediction of spectra of similar systems.

The problem may be exemplified by reference to the much studied benzene molecule. The original CRAWFORD-MILLER force field [SJ was refined by WHIFFEN [6]. Even in the quadratic approximation the number of force constants greatly exceeds the number of vibrational frequencies. (For the in-plane vibrations of benzene the numbers are 26 and 14, respectively.) Use of deuterated species and of assumptions minimizing interaction constants not established by the isotopomers yielded a field which proved satisfactory in predicting the frequencies of other aromatic molecules. It failed however to predict first order Coriolis constants adequately. DUINKER and MILLS [7] incorporated the Coriolis constants into a fitting procedure and used different assumptions where necessary based on an orbital rehybridization model. The field was substantially different. Recently ab initio calculations using Gaussian basis sets with a split valence orbital (4-21) function has been used to produce additional refinements [S]. Substantial changes in the eigenvectors result from these force constant changes and clearly this is of fundamental importance in seeking to determine a set of transition moment parameters which might be subsequently used in spectral prediction of other molecules.

RUSSELL er al. [9] showed how the statistical uncertainties in the polar parameters could be related to random errors in intensity data, molecular geometry, harmonic frequencies and force constants. Their analysis of the data on methyl fluoride, a molecule for which the data was particularly well determined, made a depressing study. It was clear that for most polyatomic molecules uncertainty in the molecular force field was going to be a major obstacle to progress.

1047

1048 TIM HOGAN and DEREK STEELE

For small molecules the inclusion of the entire complex of vibration-rotation constants-particularly

of Coriolis constants-has led to considerable progress in their force fields. Unfortunately the properties of lower members of a series are often anomalous. An

alternative approach used was to assume transferability of fields between similar molecules and to fit simultaneously data on a range of molecules to a set of force constant parameters. The massive study of

SNYDER and SCHACHTSCHNEIDER on hydrocarbons [ 101 showed that a set or sets of parameters could be found which gave a reasonable fit to known [ll] spectral frequencies of 14 molecules. However the existence of several “acceptable” solutions was recog-

nized even at the time of publication. Such alternative solutions arise from switching the dominant mode type for two bands or sets of bands. These alternative sets would lead to different intensity parameters when intensity data were analysed.

PE 3600 data station. Resolutions varied from 2 to 0.5 cm-t. For the vapour work vapour could be introduced into the cell without disturbing the cell in any way, so percentage trans- missions could be accurately determined without any uncertainty in backgrounds. Pressures were measured on an MKS Baratron 170M with a sensitivity of 1O-3 torr and an upper pressure limit of IO+’ torr. Zero calibration was effected before use each time with a vacustat gauge. Nitrogen was employed at 1 atmosphere, as a pressure broadening agent. While this pressure appears rather low for the resolutions used of about 1 cm-’ all WILSON-WELLS [16] plots were linear or near linear within experimental error and passed through the origin. All cell background corrections and band integrations were effected under computer software control.

Solution spectra were measured in Ccl., and in the 800 cm- ’ region in CS, (0.1-l .5 M). As sample absorption is everywhere significant within the fingerprint region absorb- antes were established at weakly absorbing frequencies by the use of different cell path lengths and all absorption data subsequently corrected to comply with these absorbance requirements.

In the course of the present series of studies it has

been shown [12] that modifications of the overlay fields of hydrocarbons [lo] and ethers [ 131 permit the

determination of a set of atomic polar tensors compatible with experimental intensities and with tensors calculated using split valence orbital Gaussian basis wavefunctions. In this first paper the measured absorption intensities of cyclohexane will be reported and analysed using the SNYDER-SCHACHTSCHEIDER field. At present it has been shown only that the ab initio

results predict the correct total intensities, but that the distribution within certain frequency intervals is incorrect.

The vibrational assignments for the active vibrations of cyclohexane-d, and -d, 2 are well established [14, 15]-and need no further discussion.

EXPERIMENTAL

Due to severe overlapping of fundamentals in certain spectral ranges it is not feasible (except possibly by very high resolution data analysis) to determine the absorption intensities of the individual bands. The resultant uncertainty in the derived atomic polar tensors is discussed later. Where the bands are partially resolved in the solution spectra then a band fitting program using damped Lorentzian contours was used to measure the individual band intensities. It would be helpful if the ratio of the band intensities so derived could be assumed for the gas phase. However, bands do not all show the same enhancement factor. Experimentally we find intensity enhancements ranging from 0.72 to 2.32 compared with 1.30 predicted by the POLCFWILSON equation. The CH(CD) stretching bands have an experimental ratio of 1.03 (1.06) and whereas the CH, scissoring appears to follow expectations reasonably well, the HCC bending modes are relatively weak in the condensed.phase. Provided that one band is much more intense than the other, the error from such partitioning is unlikely to be large, especially if similar types of motion are involved. For C,H12 and C6D,3 there is only one case where such a separation is practical and needed- that is in the case of the aZU and e, bands of the d12 species at 1085 and 1068 cm-‘, respectively. Eighteen per cent of the total intensity is ascribed to the e. component.

The vapour phase i.r. spectra were measured in a Perkin- Elmer gas cell with path length variable in 1.25 m

Intensities are listed in Tables 1 and 2 and some typical intensity plots are given in Fig. 1. The curvatures of the

steps lo 10 m. Some initial spectra were obtained with a PE 325 interfaced to a Tektronix 4052 computer, but sub-

WILSON-WELLS plots [13] were very small despite the

sequently measurements were made on a PE 983 attached to a existence of several sharp strong Q branches, such as at 863 cm-’ in C6HIz and at 917 cm-’ in C6D,2, This may be

Table 1. The observed and calculated fundamental frequencies and intenstties of cyclohexane

Sym

v(cm-) Obs. Calc.

Intensity of absorption (km mol- t) Vapour Solnjgas Soln. Vapour Ab initlo APT integ. range intens.

2933 2914 2863 2863 1449 1449 1346 1257 1038 1015 904 862 524 241

2930 380(8) 2927 2856 108(2) 2855 1457 28.7(0.8) 1449 1350 I258 2.96(0.09) 1005 2.25

2.08 897 3.13(0.035) 860 4.20(0.04) 519 1.07(0.01) 181

370(10) 133.4 303@2894 1.03(0.03) 159.2

103(3) 269.2 28942830 1.05(0.03) 106.0

23.6(0.5) 10.0 15OG1400 1.21(0.04) 23.2

0.238(0.01) 1.2 138&1330 O.SZ(O.03) 3.60 0.6 131t&l190

2.5 I 10&970 2.18(0.01)

I.0 8.0

0.463(0.01) 0.06 56@ 480 2.32(0.04) 0.4

Vibrational absorption intensities in aliphatic rings 1049

0 45

0 4t

F! 3 f E 04i

,” x

Y 2 04E

s

5

0 45

Range 580 - 480 CM -I i 3-

I- +

+

\ a. r +

+ kz 2

,-

0 44 I +(

0, E

IO 20

Table 2. The observed and calculated fundamental frequencies and intensities of cyclohexane-dIz

Sym v(cm- 1) Intensity of absorption (km mol-‘) Vapour

Obs. Calc. Soln/gas

Soln. Vapour Ab initio APT integ. range Intens.

2221 2195 2206 2189 262.7 2111 2092 2104 2086 1160 1151 4.59(0.03) 1085 1079 7.14(0.05) 1068 1048 l.SS(O.04) 988 989 5.38(0.01) 915 885 4.65(0.05) 719 726 2.24 685 672 3.34 394 388 190 145

248.8(0.3)

6.38(0.06) 5.3(0.1) 1.2(0.1) 5.94(0.02) 3.52(0.06) 1.4 2.1 0.43 0

62.1 83.2 73.3 114.1 2300-2000 1.06

143.0 34.2 65.1 39.1

1.8 2.96 1240-1130 0.72(0.01) 9.1 5.13 1130-1045 1.35(0.02) 4.5 1.14 2.4 7.56 1045-950 0.91(0.03) 5.4 3.98 950-880 1.32(0.03) 1.0 0.0 770-600 1.6 4.6 3.38 0.05 0.30 450-350 0.2 0

Pressure (Tow 1

Range 1500 - 1400 CM - I

+ + + +

l

+

-

+

I I I I I 2 3 4

Pressure (Tom I Pressure (Torr I

- Range 970-880 CM-I

+

+ + t

I

3

Pressure I Torr )

I 4

Range 1310 - 1190 CM-I

+ + -f

I 5

Fig. 1. Plots of the integrated absorption intensities/pressure against pressure for an arbitrary selection of defined spectral areas of cyclohexane.

seen from the near horizontal plots of integrated intensity systems. The requirement that I: A/vf is invariant to isotopic + pressure vs pressure (see Fig. 1). We deduce that broaden- substitution, where the sum is taken over all vibrations of a ing is adequate. given symmetry species, is well obeyed by both vapour and

The F sum rule for intensities [3] may be used to check for solution data (see Table 3). If the CH and CD stretching internal consistency between the intensities of the two bands are excluded it is seen that the dl 2 sum is about 15 %


Table 3. A comparison of the F sums for cyclohexane-d, and -d,2 in vapour and in solution and a comparison of the ratio of intensities in

vapour and in solution with POLO-WILSON expectations

c A,/? (kmmol-’ x 1016)

Species h12 (E. + AZ”) d,,(&+Azu)

Solution inc. CH/CD 90.7 90.6 ext. CH/CD 33.1 31.3

Vapour inc. CH/CD 81.7 82.9 ext. CH/CD 25.8 30.5

Ratio (soln) inc. CH/CD 1.11 1.10

(W ext. CH/CD 1.28 1.26

PoL*WILSON ratio for (n = 1.46) = 1.30.

high. Some of this excess is probably due to the use of CS2 as a solvent for the bands at 719 and 685cm-‘. By the P~Lo-WIL~~N equation

A solutmn _ ! n2+2 * A “apO”r n c > 3

where n is the refractive index of the medium, the intensity enhancements are 1.30 and 1.48 for Ccl, and CS2, respectively (assuming the refractive indices for the NaD line). This would explain only 20 o; of the excess. Due to the overlap of thea,,and e, bands it is not possible to becertain, but it seems likely that this excess is mainly in the e, species. It is believed that this arises from increased coupling of CX stretch with XCC bending as X changes from H to D.

Application of the POLC~WILSON equation to the totality of the bands excluding the CH (CD) stretches again shows reasonable accord with expectations, but the intensity enhancements ratios of the CH stretches are about 1.1. This indicates a significant reduction in the effective stretching dipoles in solution.

DETERMlNATlON OF ATOMIC POLAR TENSORS

The procedure followed to determine a set of atomic polar tensors from the experimental intensities was

(i) Evaluate the eigenvectors in terms of internal valence distortions (L matrix) using the force field for hydrocarbons of SNYDER and SCHACHTSCHNEIDER

[lOI. (ii) Compute from ab inifio wave functions the

atomic polar tensors (APTkthat is the partial derivatives of the molecular dipole moment with respect to displacements of the atoms along a chosen system of molecule fixed Cartesian axes.

(iii) From the APT and L matrix predict the absorption intensities of the fundamentals.

(iv) On the basis of accord between experiment and predictions establish probable and possible sign choices of the dipole derivatives with respect to the normal coordinates, aP/?Q for cyclohexane-da.

(v ) Derive the APT for the experimental aP/;IQ of selected sign choices. Check these for correct symmetry behaviour and for transferability to C6Dt2.

Calculations were carried out in the valence coordinate basis without symmetry. This poses a very stringent test for accidental errors in that the slightest

input error will destroy the degeneracy. The frequencies computed are in excellent accord with these of WIBERG and SHRAKE [17]. As the phase of the eigenvectors as derived in such a calculation is com- pletely arbitrary it is necessary to define precisely both coordinate basis and chosen signs of 1 vectors for subsequent discussion on APT and ZP/aQ to be meaningful. The L matrices are given in Tables 4 and 5.

To evaluate any transferable polar derivatives in terms of either internal coordinates or Cartesian distortions the sign of the transition moment-or dP/aQ-is needed. For cyclohexane the i.r. active vibrations form the representation

5nz,+8e,.

Thus there are 2’ + 2’ = 32 + 256 possible combinations of signs compatible with the measured intensities, which in the harmonic oscillator approximation are given by

Nn tap)* =- 3c4na, (aQ)’

Experimental uncertainties and errors render it non- feasible to determine the correct signs amongst this large number of possibilities by the requirement that the APT should the same for C,HIt and C6Dr2.

Ab initio calculations using restricted basis sets have been extensively explored for both structures and force constants, but less so for intensity prediction. Minimal basis sets of Slater type Gaussian orbitals, while giving good structures, have been shown to be inadequate for prediction of force constants and even more so for intensities. For methyl fluoride force constants were about 40 7; high and total intensities about a factor of 10 low. The contracted Gaussian orbital set with split valence shell contraction, n-31, performs much better for all vibrational properties including higher order vibration rotation interaction terms. Generally reported results on intensities have been encouraging. For CH3F and COF2 it was found that the dipole derivatives for the stretching symmetry coordinates were within experimental uncertainty [ 181, though bending derivatives were less satisfactory. Some im-


Table 4. The L matrices for the molecular vibrations of cyclohexane. Contributions are given for representative internal coordinates. Others are deducible by symmetry (units amu- t12)

Coordinate v(cm- ‘) 2921 2855 1448 1035 519

Ar’7 -0.277 -0.320 sMJO7 0.002 0.001 Are8 0.327 - 0.268 0.007 -0.014 0.002 (rR)“*Ap716 0.016 -0.018 -0.178 0.101 0.137 (rR)1’2AjY816 - 0.047 0.012 -0.141 -0.222 - 0.077 RA& 0.079 - 0.069 - 0.079 0.289 -0.157 rAu71s - 0.005 0.059 0.603 - 0.005 0.012

R”

Coordinate v(cm- ‘) 2930 2856 1457 1350 1257 897 860 181

A?7 0.384 0.348 0.004 0.001 0.018 0.010 0.000 0.000 AT’8 -0.358 0.375 0.010 0.008 -0.004 0.000 -0.008 0.000 rA%s 0.000 - 0.070 0.723 -0.102 0.087 0.049 - 0.057 -0.013 ml6 - 0.002 -0.044 0.042 0.104 0.045 0.115 -0.128 0.007 RA6216 0.045 0.045 - 0.033 - 0.059 -0.097 -0.149 0.069 0.086 (rR)“‘A$712 - 0.052 0.009 -0.179 0.107 -0.133 0.302 0.207 - 0.007 (rR)“‘A$716 -0.100 -0.004 -0.251 -0.131 0.382 0.079 0.112 0.002 (rR)“‘ArY812 0.057 0.002 -0.141 0.391 -0.042 - 0.202 -0.101 - 0.024 (rR)“‘Ap816 0.057 0.036 - 0.246 -0.197 - 0.226 -0.110 -0.210 - 0.029

Table 5. The L matrices for the molecular vibrations of cyclohexane-d rr. Contributions are given for representative internal coordinates. Others are deducible by symmetry (units are amu- *12)

Coordinate v(cm- ‘) 2189 2086 1079 885 388

Ar”7 0.186 - 0.249 0.010 -0.004 0.001 Are8 -0.257 -0.173 0.020 0.02 1 0.001 (rR)t/‘A/3@716 - 0.026 - 0.024 -0.140 - 0.024 0.108 (rR)t/‘Ap816 0.068 0.015 - 0.037 0.196 -0.066 RA6216 -0.123 -0.095 -0.170 - 0.248 -0.102 rA%s 0.018 0.084 0.427 -0.112 OHM

RU

Coordinate v(cm- ‘) 2195 2092 1151 1048 989 726 672 145

Ar”7 0.292 -0.194 -0.014 0.014 0.028 -0.006 -0.006 0.000 Are8 -0.256 - 0.232 - 0.024 0.003 -0.009 -0.005 0.008 0.000 rA%s - 0.007 0.085 -0.195 0.495 -0.095 - 0.022 0.007 -0.010 AR,, - 0.005 0.053 -0.163 0.006 0.052 -0.106 0.026 0.005 RA’& 0.066 - 0.032 0.115 -0.040 -0.114 0.099 0.031 0.068 (rR)‘/‘A@“712 -0.072 0.003 -0.017 -0.155 0.030 -0.092 -0.273 -0.004 (rR)“‘A/Y716 -0.141 0.003 0.159 - 0.022 0.348 0.028 -0.061 0.004 (rR)1’ZAjY812 0.082 - 0.039 -0.214 -0.244 - 0.043 0.114 0.131 -0.021 (rR)“‘A/P816 0.082 - 0.039 0.201 -0.144 -0.126 -0.108 0.169 - 0.025

provement was experienced on including polarization functions [ 191. For linear triatomics, generally involv- ing second and third row elements, the agreement on stretching derivatives deteriorated slightly and bending modes continued to show the need for polarization functions [20]. Ethane was studied by KOMORNICKI and MCIVER with similar results 1211. Regrettably the inclusion of polarization functions results in a considerable increase in the basis set. For carbon and oxygen, for example, the inclusion of d orbitals effec- tively doubles the order and increases computer requirements by factor of about 8. For molecules of chemical interest such expense is currently prohibitive.

Fortunately and surprisingly, as will be shown, the 4- 31 basis appears to predict thecorrect intensity in given spectral regions for cyclohexane and its related cyclic ethers irrespective of whether or not the region is dominated by stretching or bending motions.

No attempt was made to determine an ab initio force field. This is being studied by others [22]. Dipole derivatives were obtained by computing the dipole moment for movements along the Cartesian axes of 0.02 A for selected members of each non-equivalent atom set. The axes were chosen with the z axis along C3 and the x axis perpendicular to and bisecting the central CC bond.


The calculated atomic polar tensors are listed later. To obtain a predicted spectrum from these tensors the procedure first formulated by BIARCE et al. [23] is used

PQ = aP/aQ = PR L = Px AL.

The Cartesian displacement vectors AL were determined as described in Ref. [24]. Note that since cyclohexane has no molecular dipole moment in the chair conformation normally assumed then there is no rotational correction.

Due to overlap of the fundamental absorption bands it was not possible to compare predicted and experimental intensities for each band individually. In the CH stretching region the uZu and e, bands for the symmetric CH stretch overlap as do the antisymmetric. Likewise the scissoring vibrations are inseparable. At this stage we compare the experimental and predicted intensities for regions 303&2894, 28942830 and 150@1400 cm- ‘. Likewise for C6D1 2 characteristic group regions are used. The total predicted intensity shows excellent agreement with experiment though the distribution amongst nearby bands is in error. Thus in

d the total measured intensity in the range l&O-lOOOcm-’ is 12.9 km mole1 compared with a predicted of 15.4 km mol-‘, but about 50% of the intensity is in the 1160 cm-’ (e,) band compared with 12% predicted. Focussing attention solely on the e, bands it is apparent that the predicted intensities show a transfer of intensity compared with experiment from the 1160 cm- I mode to the 1068 and 988 cm - ’ modes, and to a lesser extent from the 719 to the 685cm-’ bands.

In cyclohexane-d, overlap is more serious in the region below 1500 cm- I and it is not feasible to say how the distribution compares in nearby bands. Using the resolved liquid (solution) band intensities however the intensity distribution between the 904 and 862 cm- ’ e, bands is seen to be weighted theoretically too much to the lower band.

At this stage it is not possible to say with any certainty whether the fault lies with the calculated APT or with the eigenvectors. With 1,Cdioxan it will be shown that a force field based on an ab initio force field results in significantly improved agreement. Lacking this information on cyclohexane at present we shall proceed to establish the probable signs of the transition moments and an experimental set of APT.

SIGNS OF THE TRANSITION MOMENTS

The procedure is to calculate the APT for a given choice of signs of the input do cyclohexane dipole derivatives PQ. This is then used to calculate the corresponding set of intensities for the fully deuterated compound. Since cyclohexane possesses a zero molecular dipole moment, only the relative signs may be determined in this fashion-reversing the sign of any given sign choice will change the sign of the elements of the row of the APT, but this will yield the same calculated intensities for the d, 2 molecule and the same

fit factor,f: The fit factor is defined by

f= T{(Ai(obs)-Ri (calc)l/Ai (obs)j.

As there are five aZu bands there are 16 independent sign choices for c?P, /aQ.

Experimentally there are three spectral regions where bands of different symmetry overlap-the two CH stretching regions near 2920 and 2860 cm- ’ and the CH2 scissoring region at 1450 cm- ‘. Initially the intensity was distributed between the e, and aZu components in the following manner:

2930cm-‘: e, = 180 km mol-‘, uZu = 190 km mol-’

2860cm-‘: e, = 52 km mol-‘, aZu = 51 km mol-’

1449 cm-‘: e, = 15.8 km mol-‘, azu = 7.9 km mol-‘.

Following an investigation of the variation of the fit factor with the numerous possible sign combinations the effects of relaxing these constraints are then explored.

As there are five a,, bands, there are 16 independent sign choices for dP,/dQ. Only the a,, bands of d,, cyclohexane at 1079, 885 and 388 cm-’ were used in evaluating f; since the two u2” CD stretch band intensities are unavailable due to the extent of overlap with the corresponding e, bands. The five “best” sign combinations are the following:

+ + - - -,f=0.271

+ + + - -,j”=o.331

+ - + + +, f= 0.361

+ - - - -, j-=0.372

+ + - + + ) f= 0.394.

The same procedure is followed for the dP,/dQ and dP,/dQ derived from the do e, bands. Since a value of zero experimental intensity is assigned to the lowest skeletal frequency, these are 26 = 64 independent sign choices for the dP,/dQ. All d,, e, bands contribute to the value offexcept the CD stretches and the lowest frequency band. Again, the five best sign combinations are presented:

dP, /dQ f dP,IdQ +-++--- 0.607 +-+++-- ++++--- 0.680 +++++-- ++--+++ 0.681 ++---++ +---+++ 0.694 +----++ ++--+-+ 0.779 ++----+.

There is actually no great spread in the values obtained for the fit factor on a consideration of all possible signs; 0.271-0.574 for the uZu bands and 0.607-2.546 for the e, bands. Hence this parameter alone does not seem to provide a very sensitive criterion for determining the suitability of a given sign combination. However, an independent source of information is available in the results of the ab initio calculations-the following sets of signs are predicted


by the ab initio APTs:

dP,/dQ: ++---

dP,/dQ: +--++++

dP,/dQ: - + + - + - -.

Thus, the optimum sign choice for the dP, /dQ based on the fit factors does actually correspond to the ab initio sign combination. However, the latter for the dP,/dQ only appears 12th in the corresponding list. Further examination indicates that the 4th in the list appears to be the most appropriate choice, since this is the same as the ab initio apart from the sign of the very weak fourth (1350 cm- ‘) band. The ab initio then shows that the signs of the corresponding dP,/dQ should all be reversed.

Now is the time to return to the distribution of intensity in the 2930,286O and 1449 cm- ’ region. It is found that the relative magnitudes of the intensities of the 1449 cm-’ e, and azu bands strongly influences the value of the fit factor, whilst the chosen sign combination still remain most appropriate, retaining its position in the tables of this parameter. APTs that yield d,, intensities closest to those found experimentally are produced by the distribution: 1449 cm-‘: azu = 13.9 km mol-‘, e, = 9.8 km mol-‘. The following d12 intensities are then calculated:

Frequency Ohs. Ai Calc. Ai (cm- ‘) (km mol-‘)

1160 e, 3.2 1.4 1085 a*, 5.3 5.1 1068 e, 0.6 0.6 988 e, 3.0 3.7 915 azu 3.5 4.0 719 e, 0.7 0.0 685 e, 1.05 1.7 394 azu 0.4 0.3

(190 e,) 0.0 0.0 f = 0.357.

Varying the distribution of intensity within the 2930 and 2860 cm-’ regions has only a negligible effect on the resulting values of the fit factor. This is to be expected, since these bands only contribute to the magnitude of the dipole change along the CH bands. However, a parameter which is sensitive to these changes is the effective atomic charge for the axial and equatorial hydrogen atoms. KING [l l] defined an effective atomic charge by

xf = i Trace [P: (P,“)‘].

The value of xn has been found to remain roughly constant throughout a diverse range of compounds, and in all hydrocarbons except ethyne [25]. Thus for saturated hydrocarbons, olefins and benzene, xn = 0.100 + 0.005 e.

CRAWFORD’S intensity sum rules may be readily derived from a consideration of these effective charges, and the G sum rule stated as

C$=CAi+Q

where R is the rotational angular momentum correction. x,, then can be determined by comparison of the sum of intensities of do and dl z compounds, and in this present study of cyclohexane, xu = 0.115 e.

Once the distribution in the 2930 cm- ’ band has been fixed, it is found that the splitting in the 2860 cm-’ region actually determines the relative values of mu. and any.

Although the sum of the 1449cm-’ azu and e, predicted by the ab initio calculations is 42 % too high, the azu band is predicted to possess 70% of this sum, which compares well with the figure of 59 % derived by the fit factor computation. Now the ab initio results suggest that 54% of the total intensity in the 2930 cm-’ region should belong to the azu band. This implies that the weak peak at 2914 cm-’ is actually a scissoring combination band rather than the azu fundamental. In the absence of further information at this stage, faith is placed in the ab initio data, and accordingly the intensity distribution in the 2930 cm- ’ region fixed at azu = 212kmmol-‘, e, = 158 km mol-‘.

The ab initio x.,. and xHS are, respectively, 0.125 and 0.154.e. The average of 0.139 is 21% higher than the experimental value of xt, = O.l15e, so it is perhaps unwise to follow this differentiation between Ku”. and any. In parallel with the equality of the CH” and CH’ diagonal stretching force constants employed in the normal coordinate calculation, mu. is set equal to in.. This is achieved by the splitting in the 286Ocm-’ region of azu = 51 km mol-‘, e, = 52 km mol-‘, whence in- = xHG = 0.118e.

Thus, with the following sign choices:

dP,ldQ: + + - - -

dP,/dQ: +---+++

dP,/dQ: -++++--

and the following intensity distribution:

2930cm-‘: azu =212kmmol-‘, e, = 158kmmol-’

2860cm-‘: azu = 51 kmmol-‘, e, = 52kmmol-’

1449cm-‘: azu = 13.9kmmol-‘, e, =9.8kmmol-’

the following APTs were calculated. Ab initio APTs listed alongside for comparison (all APTs are ex- pressed in units of electron charge) as shown on next

page. A detailed discussion of these tensors is inap-

propriate until they can be compared with tensors for related compounds. These are to be published and it suffices to say that sufficiently uniform trends exist with oxygen substitution in the ring for confidence to be felt in the main features of the tensors. As the data increase then these tensors will be applied to spectral prediction.


Experimental Ab initio

Cl 0.085 -0.034 - 0.038 0.129 -0.078 -0.023 - 0.034 0.046 0.022 - 0.078 0.039 0.013 - 0.072 0.042 0.176 - 0.028 0.016 0.171

c2 0.026 0 0 -0.006 0 . 0 0 0.105 -0.044 0 0.174 -0.027 0 - 0.083 0.177 0 - 0.032 0.171

Ha7 0.032 - 0.022 0.051 0.037 -0.018 -0.031 - 0.022 0.006 - 0.029 - 0.018 0.016 0.018

0.020 -0.011 -0.190 0.031 -0.018 -0.206

Ho10 -0.007 0 0

0 0.045 0.058

0 0.023 -0.190

H’8 -0.127 0.074 0.078

He9 0.000 0 0

0 -0.169 0.066 0 0.090 0.014

0.074 0.057

- 0.042 - 0.033 - 0.045 0.014

Acknowledgements-T. HOGAN gratefully acknowledges an iI31 SERC studentship. The ab initio calculations were performed using the Q.C.P.E. package Gaussian 76. [I41

E. B. WILSON JR. and A. J. WELLS, J. rhem. Phys. 14,578 ( 1946).

I:] c31

R. G. GORDON, J. them. Phys. 43, 1307 (1965). B. L. CRAWFORD JR. and H. L. DINSMORE, J. them. Phys. 18, 983 (1950). (a) B. L. CRAWFORD JR., J. them. Phys. 20, 977 (1952); (b) I. M. MILLS and D. H. WHIFF&J. them Phys. 30, 1619 (1959).

[41

[51

#

I?31

c91

D. F. EGGERS JR. and B. L. CRAWFORD JR., J. them Phys. 19, 1554 (1951) and later Dapers. B. i. CRAWFORD~~~ F. A. MILLER, J. them. Phys. 17. 249 (1949). D. H. WHIFFEN, Phil. Trans. R. Sot. A248, 131 (1955). 1. C. DUINKER and I. M. MILLS, Spectrochim. Acta 24A, 417 (1968).

K. B. WIBERG and A. SHRAKE, Specrrochim. Acta 27A, 1139 (1971); ibid. 29A, 567 (1973); ibid. 29A, 583 (1973). See for example D. STEELE, Molec. Phys. 38,145 (1979). T. B. LAKDAR, M. SUARD, E. TAILLANDIER and G. BERTHIER, Molec. Phys. 36, 509 (1978). W. B. PERSON, K. G. BROWN, D. STEELE~~~ D. PETERS, J. phys. Chem. 85, 1998 (1981). A. KOMORNICKI and J. W. MCIVER JR., J. them. Phys. 70, 2014 (1979). E. MATRAI, P. CSASZAR, G. FOGARASI and M. GAL, Spectrochim. Acta 41A, 425 (1985). J. F. BIARGE, J. HERRANZ~~~ J MORCILLO, Anal. Quim. A57, 81 (1961).

P. PULAY, G. FOGARASI and J. E. BOGGS, J. them. Phys. 74, 3999 (1981). J. W. RUSSELL, C. D. NEEDHAM and J. OVEREND, J.

PO1

WI

PI

c231

P41 J. MORCILLO, L. J. ZAMORANO and M. V. HEREDIA, Spectrochim. Acta 22, 1969 (1966). For exposition in current terminology see W. B. PERSON and D. STEELE,

them. Phys. 45, 3383 (1966). Molecular Spectroscopy, Vol. 2. Specialist Periodical

[IO] R. G. SNYDER and J. H. SCHACHTSCHNEIDER, Reports, Chemical Society, London (1974). Spectrochim. Acta 21, 169 (1965). [25] W. T. KING, in Vibrational Intensities in In@ared and

[I l] W. T. KING, G. B. MAST and P. P. BLANCHETTE, J. Raman Spectroscopy, Ch. 6 (edited by W. B. PERSONand them. Phys. 56, 4440 (1966).

[12] T. R. HOGAN and D. STEELE, to be published. G. ZERBI). No. 20 in Studies in Physical and Theoretical Chemistry, Elsevier, Amsterdam (1982).

REFERENCES

0.006 0 0 0 0.047 - 0.035 0 0.035 -0.206

-0.176 0.114 0.078 0.114 -0.045 -0.045 0.044 - 0.025 0.035

0.021 0 0 0 - 0.241 0.091 0 0.051 0.035

R. G. SNYDER and G. ZERBI, Specrrochim. Acta 23A, 391

(1967). F. A. MILLER and H. R. GOLOB, Spectrochim. Acta 20, 1517 (1964). J. CAILLOD, 0. SAUR and J. C. LAVALLEY, Spectrochim. Acla 36A, 185 (1980).

Documents

Vibrational absorption intensities in aliphatic ring systems—I. Cyclohexane