Internal rotation in nitrosomethane and acetaldehyde: incremental effect of deuterium substitution on the potential for methyl torsion

Journal of Molecular Structure, 189 (1988) 187-201 Elsevier Science Publishers B.V., Amsterdam - Printed

187 in The Netherlands

INTERNAL ROTATION IN NITROSOMETHANE AND ACETALDEHYDE: INCREMENTAL EFFECT OF DEUTERIUM SUBSTITUTION ON THE POTENTIAL FOR METHYL TORSION*

D.W. KNIGHT

and A.P. COX

Department of Physical Chemistry, University of Bristol, Bristol, BS8 1 TS, (Gt. Britain) Th. PEDERSEN Chemical Laboratory V, University of Copenhagen, The H.C. Brsted Institute, DH - 2100 Copenhagen 0 (Denmark) (Received 29 February

1988)

ABSTRACT Torsional splittings and zero-point conformational energy differences have been fitted for all forms of nitrosomethane and acetaldehyde substituted with deuterium in the methyl group. A single degree of freedom potential function, V(a) = f E V, (1 -cos ncu), has been used with the isotopic data accommodated by allowing incremental “changes in the potential according to the position of substitution. Coefficients up to and including V, have been considered. This approach has allowed rationalisation of the unusually small amount of &-gauche perturbation observed in the microwave spectrum of CHD,CHO. The incremental behaviour of the potential function relates closely to the conformational dependence of the C-H stretching force constants. The difference in C-H force constants also accounts largely for the zero-point energy differences reported here. The same ideas applied to methylamine lead to a revision of potential coefficients for CH,DNH,.

INTRODUCTION

In recent years, a large amount of data has been obtained for the methyl torsion in acetaldehyde (ethanal). In particular, the usual barrier information has been determined for several isotopic species. Less usually, the k-gauche zero-point energy difference for CH,DCHO has been obtained by matching perturbations in the rotational spectra of the two conformers [ 11. Using this information in a preliminary calculation, we found that the torsional data could be fitted by allowing the potential to undergo incremental changes upon deuterium substitution at the methyl group. More recently, we have carried out an extensive investigation of the microwave spectrum of the isoelectronic mole*Dedicated

to Professor

0022-2860/88/$03.50

D.J. Millen on the occasion of his retirement.

0 1988 Elsevier Science Publishers

B.V.

188

cule nitrosomethane. Again, we used the perturbation matching technique to find &-gauche zero-point energy differences for the CH2DN0 and CHD,NO species [2]. The purpose of this paper is to give the results of incremental calculations of the torsional potential for the deuterated species of both molecules. The incremental approach is based on an idea originally put forward by Walker and Quade [3]. In the present case, we simply assume that the effect of deuterium substitution at a given position in the methyl group is the same regardless of the state of substitution of the rest of the methyl group. Then, by equating the increments in the potential energy, which results from all of the possible substitutions, to the differences between the potentials of the various isotopic species, we obtain some interesting relationships: Using the expression: V(cu)=$

:

v, (1-cosncv)

for the potential function, and noting that, for CH,- and CDS-species, V, and V, are zero by symmetry, we obtain: ’ = v, ’ - v, ” = v, ” - v, ‘U V, - VZ3

V,, V,, (1)

v,‘+v,‘=-(v,“+v,“)

(2a)

V2’+V4’=-(V2)‘+V4”)

(2b)

The number of primes indicates the number of deuterium atoms in the methyl group of the species to which the coefficient relates. The above equations suggest that V, should change in a linear fashion according to the number of deuterium atoms, and that the difference between gauche and cis potential minima will be equal and opposite for CH2D- and CHDz-species, i.e. 3/4 (V,‘+V,‘+V,‘+V,‘)=-3/4

(v,“+V2”+V4”+V5n)

NITROSOMETHANE

There are not enough data available to determine V,’ and V, tiexperimentally. We, therefore, calculate them from V, and VS” using eqn. (1). Van Eijck [ 41 has recently re-analysed all of the available CH,- and CDS-data, eliminating some of the approximations made in earlier IAM studies. We, therefore, use his values: V,=405.3(2) cm-l and V,“‘=390.0(3) cm-‘,to obtain V,’ ~400.2 cm-’ and V,” ~395.1 cm-‘. There are no data available for the determination of V, coefficients and so, for the time being, we assume V,=O for all isotopic species. In order to apply the incremental approach further, we need to set up the torsional hamiltonian for each of the isotopic species. We, therefore, require

189

the rotational constant (F) for the torsional motion. The F values for CH,NO and CD,NO are already available from the IAM fits [4]. These constants, which appear in Table 1, were used as a guide in arriving at a structure from which to calculate F constants for CH2DN0 and CHD,NO. The structure used was as published [ 51, but with the methyl group constrained to be symmetric about the internal rotation (z) axis and adjusted to reproduce the IAM value for 1, (I,=3253 (3) uA” for CH3N0 and 6.497 (1) uA” for CD,NO) [4]. The z-axis is not coincident with the C-N bond and is defined such that the methyl group is tilted slightly away from the oxygen atom. F constants were obtained using Pitzer’s method [ 61, employing ground-state moments of inertia in the calculation. Van Eijck has also calculated F constants, from structure, for the cis partially deuterated species, and these appear in Table 1 for comparison with those obtained here. For the partially deuterated species, F is a function of cx. For these species therefore, F was also computed, purely from structure, at intervals of 30’. F(a), in both cases, underwent one cycle of smooth change in 360”. A Fourier series, adequate to reproduce F in the regions of maximum probability for the torsional oscillation, may therefore, in both cases, have the form: F(a) = F. + Fl cos a. The cis and gauche F( cu) values in Table 1 were fitted to this expression to obtain the F, coefficients also given in Table 1. The torsional data for CH2DN0 and CHD,NO, taken from our recent work [ 21 are given in Table 2. dE, is the gauche-gauche zero-point splitting. dE,_, TABLE 1 Internal rotation constants F (cm-‘) Species

This work”

Van Eijck [4]

CH,NO CD,NO cis-CH,DNO gauche-CH,DNO

7.7130 5.0176 6.7267 6.3246

7.7130 5.0272 6.735 -

cis-CHD,NO gauche-CHD,NO

5.4475 5.6968

5.431 -

Coefficients of F( cr) (cm-‘) Species

F0

F1

CH,DNO CHD,NO

6.4586 5.6137

0.2681 - 0.1662

“Nitrosomethane structure (bond lengths in A, angles in degrees) used in the calculation: r(C-H) 1.0980 H-C-z 109.15 r(C-D) 1.0977 N-C-z(tilt) 1.07 r(C-N) 1.4800 C-N=0 113.2 r(N=O) 1.2114

190 TABLE 2 Internal rotation spacings Species

AE,

(MHz)

CH,DNO CHD,NO

922.01(19) 190.16( 14)

AE,_, (cm-‘) 11.20 - 10.31

Calculated potential coefficients (cm-‘) Species

V,

V,

A V,.,

CH,DNO CHD,NO

- 17.0063 14.4353

38.3669 -31.8544

16.02 - 13.06

CHD,NO torsional spacings Predicted AE’; (MHz) AEpc (cm - ’ )

170.15

- 13.04

Observed 190.16 - 10.31

is the gauche-cis zero-point splitting. AE,_, > 0 implies gauche above cis in energy. These data, taken in conjunction with the derived F,,, F, and V, parameters were fitted to the torsional hamiltonian: X=--&(F,,+F,coscu)-&+~ZV,

n

(l-cosm)

This was expanded in a free-rotor basis and factored into odd and even blocks. The blocks were diagonalised numerically, using 40 basis functions for each block. The potential was truncated above V, for want of data. The VI and V, coefficients obtained by this procedure are given in Table 2. Given also are the energy differences between cis and gauche potential minima, denoted AV,_,. These are predicted to be equal and opposite by the incremental theory and the calculations show this to be quite closely realised. We also used the CH,DNO data, via eqn. (2) to predict the AE,_, and AET for CHD,NO. The results given in Table 2 show that, despite the approximations involved, the incremental approach works surprisingly well. We now explore possible ways of improving the calculations. The effect of V6

When the barrier to internal rotation, for a molecule with a threefold symmetric internal rotor, is determined solely from microwave data for the torsional ground-state, the derived value for V, contains a contribution arising from the neglect of V, and higher terms in the potential. This limitation on

191

TABLE 3 Potential coefficients (cm-‘) modified by the inclusion of V,: V, V, (cm-‘)

V,

V,’

v, ‘I

v, I”

(0) (-6)

405.3 409.3

400.2 404.4

395.1 399.4

390.0 394.5

V, and V, V, (cm-‘)

VI’

V,’

v, ”

v, ‘I

(0) (-6)

- 17.0063 - 16.9127

38.3669 38.2782

14.4353 14.3892

-31.8544 - 31.8000

CHD,NO torsional splitting predictions modified by the inclusion of V, V, (cm-‘)

dE’; (MHz)

dE& (cm-‘)

(0) (-6)

170.15 170.22

- 13.04 - 13.05

the accuracy of V, has to be accepted because V, and V, always remain correlated in the absence of data for torsionally excited states. Such is the position for nitrosomethane. There is, however, good reason to believe that nitrosomethane will have V, in the region ca. -5 to ca. -20 cm-‘. This follows because experimental V, determinations for comparable molecules appear always to fall in this region [ 7-91. Furthermore, the contribution to the effective V, from the interaction between internal rotation and other vibrations, calculated in the harmonic approximation, appears always to be negative and ca. - 5 cm-’ for acetaldehyde and isovalent species [lo]. It is, therefore, important to assess the consequence of neglecting V, when applying the incremental potential theory. We investigated the V, contribution by recalculating V, for CH,NO and CD,NO, keeping V, fixed at -6 cm-’ in both cases. We then repeated the calculations of the previous section for CH,DNO and CHD2N0 with V, also fixed at - 6 cm-‘. Given in Table 3 are the V, values as they appear before and after the inclusion of V,. Also given in Table 3 are the resulting V, and V, coefficients, and the predicted CHD,NO torsional spacings. It is clear that the inclusion of a constant V, common to all isotopic species has little effect on the outcome of our calculations. The effect of V, and V5 We also tried to improve the calculations by varying V, and V,. It seems sensible that these will make some contribution to the potential. Obviously,

192 TABLE 4 The effect of V, and V, on potential coefficients (cm-‘)

VI’

V2’

38.3669 44.9173 36.1397 42.7770 40.8290 39.0701 45.8798

- 17.0063 - 17.6428 - 22.3233 - 22.9370 -28.3124 -33.7666 - 34.3229

Assumed

Assumed

V,’

V,’

0 0 +10 +10 +20 +30 +30

0 - 10 0 -10 -10 -10 -20 Target values -

Predicted A& (MHz)

Predicted AE”?Tc (cm-‘)

169.89 172.93 174.45 176.94 179.75 181.38 183.11 190.16( 14)

- 13.042 - 12.567 - 12.623 - 12.299 - 12.186 - 12.218 - 12.216 -10.31(l)

however, there are not enough data to determine them by least-squares fitting. We, therefore, tried to force the CH,DNO data to predict the CHDzNO splittings by including various trial values of V, and V,, with the constraint that V,” = - V,’ and V,” = - V,‘. The results given in Table 4 do not justify the inclusion of the additional potential constants and this line of attack was abandoned. Scaling of V, and V2 One notable property of the potential coefficients given in Table 3 is that they obey the following relationship to a good approximation: vl”=-c

V,’

(da)

V,‘)= -c

V,’

(4b)

where c is a scaling factor. This enables us to use the mono-deutero species data to predict AEz_,, by adjusting c to fit AE’$ . Using this approach gave c=O.833 and predicted AEl_, = -10.58 cm-l, compared with -10.31 cm-’ observed. This result suggested a means of refining our earlier predictions for AEi_, of acetaldehyde which was not available experimentally (see next section). ACETALDEHYDE

The microwave spectra of the gauche partially-deuterated acetaldehydes were studied by Turner et al. [ 11. The torsional data obtained from this study are reproduced in Table 5. AEi_, was not determined because no definite cis-gauche

193 TABLE 5 Internal rotation splittings (from ref. 1) Species

dE,

(MHz)

CH,DCHO CHD,CHO

804.5 (1) 183.6(l)

AE,., (cm-‘) 15.55 -

perturbations were observed in the spectrum of CHD,CHO. We now use the incremental potential approach to predict dEL_, and compare it with the known experimental data. As for nitrosomethane we need to make use of V, values of CH3- and CDS-species in order to calculate V; and V;l. There are, however, a large number of barrier determinations to choose from [4,7,8,11-151. We therefore restrict ourselves to IAM studies involving direct diagonalisation of the torsion-rotation hamiltonian - with the inclusion of far-infrared data. Direct diagonalisation IAM studies of CH,CHO have been published by Bauder and Giinthard [8] and Van Eijck [4] and it is difficult to choose between them. Bauder and Giinthard restricted their data set to J<3 and reported F= 7.6408 cm-’ and the ground state E-A splitting, -A,, = 2070.025 MHz. Van Eijck appears to have fitted more data and reports V, =401.01(1.7) cm-’ . In this case, F, calculated from the IAM parameters, is 7.6405 cm-‘. The most detailed far-infrared study is that of Hollenstein and Winther [ 13 ] who (in cm-‘) v(lA-OA)=143.75(10), v(lE-OE) =142.03, report ZI(2A - 1A ) = 114.41( 10). We, therefore, combined the far-infrared data with the microwave do of Bauder and Gtinthard and fitted them to the hamiltonian: ~Y=--&F(LY)-$+;

(l-cos3a)+:

(1-cos6a!)

again using a free rotor basis and 40 basis functions per symmetry block. Details of the fit are given in Table 6. Weighting coefficients are l/o2 for the observation in question. do was assumed to have rs= 2 MHz. The F,, value obtained is comparable to the IAM results. The V, and V, results are similar to those obtained recently by Crighton and Bell [ 151, who fitted the far-infrared data of Hollenstein and Winther [ 131, but not do, and used an F constant of 7.8588 cm-’ calculated from the structure reported by Iijima and Tsuchiya [ 161. The results of Crighton and Bell correspond to V, = 415.0 (1.1) cm-’ and v,= -22.3(1.7) cm-‘. At this point, it is appropriate to comment on the physical significance of the V, term. Quade [lo] has calculated the contribution to the effective V, term from the interaction between internal rotation and other vibrations. In the harmonic approximation he finds the contribution to be -4.72 cm-l for CH&HO and - 5.50 cm-’ for CH$DO. Ab-initio calculations performed by Crighton and Bell [ 171, using structures in which the methyl group is con-

194 TABLE 6 CH,$HO data adjustment (cm-‘) Splittings

Obs.

Obs. -talc.

Weight (cm’)

OE-OA lE-OE lA-OA 2A-lA

0.06904860 142.03 143.75 114.41

0.00000015 0.018 -0.018 - 0.000

0.223 x 10’ 100 100 100

Estimated parameters (cm-‘) F,= 7.6441(8) V,=416.63(8) V,= -18.59(7) Estimated parameters (cm-‘) F,,= 7.706 F,= - 1.08 V,= 422.7 V,= -4.72 (assumed)

from CH,CHO data assuming V,= -4.72 cm-’

TABLE 7 V., coefficients for acetaldehyde Species

CH,CHO

CH,DCHO

CHD,CHO

CD&HO

V:, (cm-‘)

404.25

400.2

396.1

392.1

strained to be symmetric, indicate that the electronic contribution to V, is ca. + 1 cm-‘. The V, term obtained from the torsional data is, therefore, somewhat larger than might be expected. It is possible, therefore that a threefold dependence of the internal rotation constant has been folded into the effective V,. This can happen through a first-order linear relationship between F3 and V,, as pointed out by Lees [ 181. We therefore tried fitting the data by fixing V, at Quade’s value and allowing F3 to vary. The results are given at the bottom of Table 6. The F3 value obtained is, however, too large to be physically reasonable. It is evident that a resolution of this problem requires more data and possibly the inclusion of higher terms such as V, [ 141. While the V, term is interesting, it is not expected to have a significant effect on the determination of VI and V, coefficients for the partially deuterated species. Therefore, V, was effectively folded into V, for CHJJHO by recalculating V, using only F and do. V, for CD&HO, from the IAM fit of Van Eijck [ 41 is already in this form and so was used directly. The Vi and V;l coefficients, determined using eqn. (1) , are given in Table 7. As for nitrosomethane, the F constant from the fit to the CH&HO torsional

195

data was used as a guide in arriving at a structure from which to calculate F constants for CH,DCHO and CHD,CHO. The structure used was that published by Niisberger et al. [ 191 but with the methyl group constrained to be symmetric about the C-C bond. For the CH,- and CD,- species, rotational constants were obtained from ref. 4. For the partially deuterated species, rotational constants were obtained from the data of ref. 1 and 20. In the case of the gauche forms, effective rotational constants were taken to be the average of those for ( + ) and ( - ) states after transformation into the principal axis system. Van Eijck [4] has also calculated F constants for cis CH2D- and cis CHD2 species (see Table 8). The resulting Fourier coefficients of F’ (LY) and F” ((w) are also given. These are in good agreement with a much earlier calculation by Knopp and Quade [ 211. The CH,DCHO torsional spacings (Table 5) were fitted to Vi and VL giving (in cm-‘) Vi = -8.0178, V; = 34.4919. We then made predictions of A?& via eqn. (4), with c= 1 and with c adjusted to fit AE: . The results are given in Table 9. In order to test these predictions, the microwave data for cis [ 201 andgauche [l] CHD,CHO were fitted to appropriate hamiltonians and the resulting constants used to calculate rotational energy levels. These energy manifolds were searched for coincidences, using assumed values for LIE:_,. Degeneracies closer than 2 cm-l were printed and examined in each case. dE!& = - 16.93 cm-’ TABLE 8 Internal rotation constant (cm-‘) Species

This work”

CH,CHO CD&HO cis-CH,DCHO gauche-CH,DCHO

7.6441 4.9740 6.6298 6.2752

7.6405 4.9380 6.679 -

cis-CHD,CHO gauche-CHD,CHO

5.4073 5.6345

5.434 -

Van Eijck [ 41

Coefficients of F(cr) (cm-‘) Species

F0

F1

CH,DCHO CHD,CHO

6.3934 5.5588

0.2364 -0.1515

“Acetaldehyde structure (bond lengths in A, angles in degrees) C-C-HM, 109.47 r(C-I-I,,) 124.72 1 1.6966 C-C=0 r(C-DMe) 113.93 1.5005 C-C-HaM r(C-C) 1.2038 r(C=O) 1.1237 r(C-H,&

196

TABLE 9 Predictions for AEi_, (acetaldehyde) C

1

0.915

v!; (cm-‘)

AE; (talc. ) (MHz)

AEi_, (talc.) (cm-‘)

- 34.4919 - 31.5600

175.1 (183.6)

- 16.93 - 15.37

8.0178 7.3363

TABLE 10 Internal rotation parameters (cm-’ except where indicated) Species

AE,/MHz

AE,_,

F,

Fl

VI

V2

V3

Avg.,

CH,DNO CHD,NO

922.01(19) 190.16( 14)

11.20 - 10.31

6.4586 5.6137

0.2681 -0.1662

- 17.01 14.44

38.37 -31.85

400.2 395.1

16.02 -13.06

CH,DCHO CHD,CHO

804.5 (1) 183.6( 1)

15.55 - 14.76

6.3934 5.5588

0.2364 -0.1515

- 8.02 7.93

34.49 -31.30

400.2 396.1

19.86 -17.53

( - 507.7 GHz) predicted one close degeneracy in the range J=O-20; 182,17(cis) with 184,15( + ). The cis 1S2,16t 182,17is unperturbed, so that this scheme fails. Reducing LIE:_, in magnitude has the property of moving this K, = 2 (cis), K,=4(guuche) degeneracy to lower J. A,?$_, = - 15.37 cm-l ( -460.7 GHz) predicted close degeneracies at: 14,,,,(cis) ++ 144,10(+ ) and 14,,,, ( - ); also 12,,,, (~1’s) - 1249( + ) and 124s( - ). The cis 142,12c142,13 is unperturbed, so this scheme also fails. There is, however, a poor residual, in the cis data set, for the 101,10+%7 transition ( + 0.44 MHz). This residual could not be eliminated by the inclusion of sextic distortion constants, whereas poor residuals for the higher J,AK, = 1 transitions could be so eliminated. This suggests a further small reduction in AEi_, to place suitable gauche I-C,=4 levels slightly above the cis gz7. Such a scheme gives: A& = -442.4 GHz ( - 14.76 cm-‘) and, as is required, predicts there to be no other perturbations in the observed data set. Perturbations are predicted to occur at J= 14, K, = 7 and J= 23, K, = 5 and J=27, K,=4 in the cis spectrum, bearing in mind that these levels are not likely to have been calculated very accurately. These levels are also not associated with transitions occurring in the frequency range covered at Bristol, and cannot easily be observed. The calculated K doubling at J=27, K,=4 is, for example, only ca. 2300 MHz. We therefore tentatively assign AlI& = - 14.76 cm-‘. V{ and Vl coefficients which fit this value are given, with the collected results of these investigations, in Table 10. DISCUSSION

The barrier to internal rotation arises out of the way in which the total energy of the molecule varies with conformation. This is often taken to be the

197

same as the variation of the total electronic energy, because the electronic contribution to the barrier is by far the greatest. If the Born-Oppenheimer (electronic-vibrational) separation holds good, however, then isotopic substitution has a negligible effect on the electronic energy. The asymmetry of the effective potential which results from deuterium substitution must, therefore, arise either through coupling between the torsion and other vibrations, in which case there will be a pseudo-potential contribution, or because the zero-point energy of the vibrations, which contributes to the total energy of the system, is a function of the conformation. Obviously, both mechanisms play a part, but it is the latter which is amenable to the incremental potential approach. The physical basis for the success of this approach may be understood by considering the effect of deuterium substitution in acetaldehyde. If we allow different force constants for C-H bonds eclipsed or staggered with respect to the C=O bond, substitution of D for H in the eclipsed position then causes a different change in zero-point energy compared to such a substitution in one of the gauche positions. Thus, taking CHzDCHO as an example, the fact that the &-conformer has two C-H bonds staggered and one C-D bond eclipsed, and the gauche conformer has C-H and C-D bonds staggered and a C-H bond eclipsed, gives rise to a genuine asymmetry in the torsional potential. The extent to which the potential increment theory is obeyed then depends on the precision with which zero-point energy changes determined from one isotopic species can be transferred to another. This in turn depends on the extent to which the effective potential parameters used reflect the physical torsional potential and are not distorted by a conformational dependence of the coupling between the torsion and other vibrations. That there will be such a conformation-dependent coupling is evident from symmetry considerations [ 221 because, in the normal-coordinate description, only A” vibrations may mix with the torsion in species having C, symmetry, whereas all vibrations may mix in the C1 asymmetric (gauche) forms. Despite the approximations involved in the potential increment theory, and the model-dependent difficulties involved in extracting potential parameters from the torsional data, the incremental approach has proved to be useful. Moreover, our results are in agreement with the suggestion, made elsewhere [ 23,241, that the asymmetry in the torsional potential is due mainly to a conformational dependence of the methyl C-H stretching force-constants. We can estimate the C-H and C-D stretching contributions to the asymmetry in a very straightforward way by extracting the appropriate force-constants from the observed vibrational spectra. We will use this idea to illustrate the point in a discussion of the conformer zero-point energy differences, for partially deuterated methyl species, which have been determined to date. Apart from nitrosomethane and acetaldehyde, only two other molecules, methylamine and methanol, have been studied in this respect.

198

Methylamine The first determination of a conformer zero-point energy difference, for a partially deuterated species, was that in CH,DNH,. In this case, Tamagake and Tsuboi [ 251 determined the trans-gauche energy separation, A&, from variations in microwave inversion splittings. There are two large-amplitude internal degrees of freedom in this molecule; rotation about the C-N bond and inversion at the nitrogen atom, and these two processes allow alternative paths between minima in the potential energy surface. The investigators were, therefore, able to calculate dE,_, from the spectroscopic inversion parameters, and subsequently to confirm it precisely by identifying perturbations due to trans - gauche interactions. They reported A?& = 7.060 cm- ’ and combining this with other microwave and far-infrared [ 221 torsional data, calculated a set of torsional parameters. They n0ted.a considerable difference between their fitted F(a) and its counterpart calculated from structure, and attributed this change to coupling between torsion and other vibrations. This interpretation may, however, require some modification, as will be shown. McKean and co-workers [26] ‘have made extensive use of isolated C-H stretching frequencies to determine properties of C-H bonds. Their work is based on the idea that the stretching frequency of a C-H bond, observed free from Fermi Resonance, corresponds closely to that of an isolated oscillator. In this approximation, the C-H stretching force-constant may be deduced directly. For our purpose, therefore, we may obtain the appropriate force-constants from the CHD,-species and, assuming that they apply regardless of the degree of isotopic substitution, calculate the methyl stretching zero-point contribution to A&,. In so doing, we also assume that the C-H and C-D bonds are harmonic oscillators. For CHD2NH2, McKean and Ellis [ 271 report the C-H stretching frequencies as 2955.5 (5) cm-’ for the gauche form and 2880.0(5) cm-’ for the trans form. From this we calculate for CH,DNH, a contribution to AS_, of + 10.62 cm-‘, but cm-‘. This is in favourable qualitative agreement with A&=7.06 not in agreement with the reported internal-rotation parameters. Tamagake and Tsuboi [ 251 give (for V;, =O, in cm -‘); Vl =37.815 and VZ= -26.006, hence de_, = -8.86 cm-l. It follows from these potential parameters that although the trans zero-point lies above the gauche, the trans potential minimum lies below the gauche. This artefact can be traced to their large value of F2 = 2.3 cm-‘. Their torsional data, corrected for nitrogen inversion effects, were therefore re-analysed with the coefficients of F( a) held constant at the rigid top-rigid frame values [ 221. This gave (in cm-’ ): Vl = 6.10 and V; = - 16.45, hence dVi_, = 7.76 cm-‘. This compares very favourably with the quantity calculated from the C-H stretching force constants and appears to indicate in this case that the observed A&, arises mainly from the conformational dependence of the C-H stretching force constants.

199

Methanol

Conformer zero-point energy differences in the partially deuterated methanol species were investigated by Serrallach et al. [ 241 during the course of an extensive valence force-field refinement. These authors initially adjusted forceconstants from the vibrational fundamentals of the four symmetrically substituted species, CH,OH/D and CD,OH/D, and found, in the vibrational potential function, that significant deviation from local CZVsymmetry of the methyl group was required in order to reproduce the observed methyl C-H/D stretching frequencies. This initial force field predicted the fundamentals of the four partially deuterated species, CH,DOH/D and CHD,OH/D, with good accuracy, the partially deuterated data being used for subsequent refinement, and also enabled the conformer zero-point energy differences to be calculated. They predicted the trans form to be more stable than the gauche in the CH2Dspecies, and the reverse in the CHD,-species, the differences being ?9 cm-’ for -OH species and ? 10 cm-’ for - OD species. These predictions were approximately confirmed by study of rotamer interconversion rates in lowtemperature inert-gas matrices [ 281. The results were held to be consistent with the methyl in-plane (trans) C-H stretching force-constant being greater than the out-of-plane (gauche) force constants. This is also directly evident from the CHD2 species (i.e. isolated) methyl stretching frequencies which were reported (in cm- ’ ) :

vt (C-H) up (C-H)

CHD,OH

CHDzOD

2978.8 2919.3

2980.2 2919.5

Note, incidentally, that the trans-gauche splitting of v (C-H ) is in the opposite sense to that found for methylamine (lone-pair trans effect [ 271). Nitrosomethane

and acetaldehyde

McKean [26] has reported the methyl C-H stretching frequencies of CHD,CHO as 3002 cm-’ for the cis form and 2945 cm-’ for the gauche form. Using these data, as before, gives a contribution to A& of +8.12 cm-l. This is in good agreement with an estimate of -f&33 cm-’ obtained from a more complete normal coordinate analysis [ 11. It is also in agreement with the direction of shift obtained from the microwave analysis of CH,DCHO data (A?& = 15.55 cm-‘). The C-H stretching contribution is, of course, not expected to account completely for the observed torsional spacing, but it is probably the main single contributor. Moreover, the same situation should be expected to prevail in nitrosomethane since there is some indication that, in

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general, for a CH,-group adjacent to a double bond, the C-H bond in the plane of the double bond is stronger than the out-of-plane bond [ 261. CONCLUSION

It is clear that a major contribution to the conformer zero-point energy differences, in molecules with a partially deuterated methyl group, is attributable to asymmetry in the C-H stretching force-constants. Such a conclusion is consistent with the observation that isolated C-H stretching frequencies differ between conformers of the same molecule and is also a further indication that, in general, the methyl group does not possess C,, symmetry, but has only the symmetry of the molecule as a whole. This asymmetry, in the case of acetaldehyde, has also been predicted by the high-level ab-initio calculations of Pulay [29]. Furthermore, the ordering of the torsional spacings in partially deuterated species is dictated by the resulting vibrational contribution, unless changes in torsion-vibration coupling, or the (Y dependence of the internal rotation constant, make contributions which offset this effect. ACKNOWLEDGEMENTS

We thank SERC for a research studentship. It is a great pleasure to be able to contribute a paper concerning the nitroso group in this ‘Festschrift’ edition for Professor D.J. Millen; his pioneering work on small nitrogen-oxygen containing molecules prompted our studies.

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