ab initio study of lactonitrile: potential functions to the hydroxyl and methyl group torsions

Journal of Molecular Structure (Theochem), 205 (1990) 203-212 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

203

AB INITIO STUDY OF LACTONITRILE: POTENTIAL FUNCTIONS TO THE HYDROXYL AND METHYL GROUP TORSIONS

CLAUDIO PUEBLA and TAE-KYU HA*

Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, CH-8092 Zurich (Switzerland)

(Received 24 April 1989 )

ABSTRACT

The coupling of the OH torsion with the methyl internal rotation in lactonitrile or acetaldehyde cyanohydrin (OHCHCH,CN) was studied using the ab initio MO method. The molecular structures of three stable rotamers and of transition states as well as the barrier heights of rotations were determined. The results indicate that the two internal motions may be considered to be almost independent of each other, which is in accord with the results of a previous microwave study. Furthermore, some one-electron molecular properties and the vibrational frequencies of the three stable rotamers were determined.

INTRODUCTION

Conformational studies of a molecule in which more than one torsional group exists are of interest because the conformational equilibrium and torsional barrier of one group can be influenced by the other group. In a previous study it was shown, for example, that the internal rotation of the methyl group in methyl nitrite (CH,-ONO) rotates almost freely in its s-tram conformation while the rotational barrier in the s-cis conformer is about 2 kcal mol-’ [ 11. Previous microwave studies of lactonitrile (HOCHCH&N) have shown that the two stable gauche rotamers A and B relative to the cyan0 group (see Fig. 1) are not equivalent and the internal rotation of the methyl group might in- fluence the OH torsion [ 2,3]. The potential profile and structural relaxation indicated a repulsion of the hydroxyl hydrogen atom by the methyl group and an attraction by the cyano group. However, the rotational constants calculated for the two-dimensional model which includes CH3 and OH group motions simultaneously are practically the same as those obtained for the one-dimensional hydroxyl torsional model [ 31, indicating that both motions may be considered to be almost independent of each other.

*Author to whom correspondence should be addressed.

0166-1280/90/$03.50 0 1990 Elsevier Science Publishers B.V.

204

(b)

Fig. 1. Conformers of lactonitrile: (a) gauche 1 (rotamer A) ; (b ) gauche 2 (rotamer B ); (c ) trans (rotamer C ) .

In order to examine further the coupling of both motions ( CH3 rotation and OH torsion) in lactonitrile a detailed quantum-chemical study was carried out. As far as we are aware, there is no ab initio theoretical study available in the literature as yet. In the present paper we report ab initio results on the molecular structures of the three stable rotamers of lactonitrile, including the third one C shown in Fig. 1. The potential-energy surface of both CH3 rotation and OH torsion is also presented, from which the barrier heights of both groups and the coupling of both motions have been determined. In addition, some one- electron molecular properties and vibrational frequencies of the three rotamers were calculated and the results compared.

COMPUTATIONAL DETAILS

Ab initio SCF calculations of the structures and properties of lactonitrile were performed by employing the split-valence 4-31G [4] and split-valence plus polarization function 6-31G* [5] basis sets. Molecular geometries for the stationary points were optimized by the force method using the 4-31G basis set with analytical gradients, as implemented in the Monstergauss program system [ 61. The optimization were discontinued when the gradient length was reduced to 5 x 10m4 mdyn. Calculations of molecular properties (6-31G*) and vibrational frequencies (4-31G) for the three stable rotamers were performed using the Gaussian 82 program package [ 71.

In order to ensure that the relative stabilities obtained were not an artefact of the geometry optimization with the 4-31G set, a more extended 6-31G* basis set including d functions on C, N and 0 atoms was also used for the equilibrium structures. Furthermore, the effect of electron correlation on the relative sta- bility was studied by performing the Msller-Plesset perturbation calculation [ 81 up to fourth order (MP4).

205

RESULTS AND DISCUSSION

Energies and geometrical parameters

The optimized geometrical parameters for the three stable rotamers of lactonitrile calculated using the 4-3lG basis set are summarized in Table 1. The calculated energies at different levels of theory corresponding to the three rotamers are listed in Table 2. As shown in Table 1, changes in bond lengths and bond angles in going from the gauche 1 (A) to B and C are small. The Cl-C2 bond in B is about 0.006 A longer than that in A and the Cl-C3 bond in C is

TABLE 1

Optimized geometrical parameters for the three rotamers of lactonitrile”

Gcu~he 1 (A) Gauche 2 (B ) Truns (C)

Bond lengths (A) Cl-C2 Cl-C3 C3-N Cl-0 C2-Hl C2-H2 C2-H3 O-H4 Cl-H5

Bond angles (“) L C3C2Cl L ClC3N L H5C1C3 L OClC3 L H40Cl LHlCPCl L H2C2Cl L H3C2Cl

1.520 1.526 1.526 1.472 1.472 1.476 1.142 1.142 1.141 1.428 1.427 1.430 1.080 1.080 1.083 1.080 1.083 1.080 1.080 1.081 1.081 0.953 0.954 0.953 1.083 1.078 1.089

111.7 111.3 111.4 179.1 179.8 180.8 107.8 108.3 107.3 110.6 110.6 106.1 114.1 113.5 112.9 108.8 108.9 109.7 110.9 110.9 111.0 109.8 110.9 110.0

Dihedral angles (“) NC3ClC2 180.4 180.2 H5ClC2C3 60.0 77.2 OClC3C2 299.6 323.5 H40ClC2 183.4 60.7 HlC2ClC3 58.8 54.6 H2C2ClC3 179.1 174.5 H3C2ClC3 300.0 294.8

“Using the 4-31G basis set. See Fig 1 for numbering of atoms.

179.9 59.0

301.4 294.2

62.7 181.3 302.1

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TABLE 2

A comparison of the calculated energies (a.u.) for the three rotamers of lactonitrile”

Level of calculation Gauche 1 (A) Gauche 2 (B) TFclnS (c)

4-31G - 245.44295 - 245.44225 (0.0) (0.44)

6-31G*//4-31G - 245.80571 (0.0)

- 245.90525 (0.30)

MP2/4-3lG//4-31G - 246.52063 (0.0)

MP3/4-3lG//4-31G -246.53917 (0.0)

MP4/4-31G//4-31G - 246.55308 (0.0)

- 246.52023 (0.25)

- 246.53885 (0.20)

- 246.55275 (0.21)

- 245.43976

@.cm)

- 245.30243 (2.06)

- 246.51742 (2.01)

- 246.53601 (1.98)

- 246.54996

(1.96)

“Values in parentheses are differences in energies with respect to the most stable rotamer gauche 1 (A), in kcal mol-‘.

about 0.004 A longer than that in both A and B. In addition, the Cl-H5 bond length becomes about 0.005 A shorter in B and 0.006 A longer in C, as compared with the gauche 1 (A) rotamer. Among the bond angles, the change in both LH5ClC3 and ~H40Cl seems to be more sensitive than other parameters.

The gauche 1 (A) rotamer was calculated to be the most stable one, even though rotamer B is only about 0.44 kcal mol-’ (4-31G) or 0.21 kcal mol-l (MP4/4-31G) less stable than the former. These values agree quite well with the experimental one of 0.34 kcal mol-’ obtained by the microwave study. On the other hand, the rotamer C is calculated to lie much higher in energy than both rotamers A and B. The relative energy of about 2.0 kcal mol-’ referenced to rotamer A was obtained at all levels of theory. No experimental value has been reported as yet.

The potential energy surface for a simultaneous motion of both CH, rotation and OH torsion is shown in Fig. 2. The energy surface was obtained by com- pletely optimizing all other geometrical parameters except the two dihedral angles which determine the CH3 rotation and the OH torsion, employing the 4-31G basis set. The energy minima were located at 58.8” and 183.4” for the rotamer A, 60.7” and 54.6’ for rotamer B and 62.7” and 294.2’ for rotamer C, where the first angle represents the CH3 rotation and the second one the OH torsion. The barrier heights for the CH, rotations were calculated as 3.54,3.78 and 3.91 kcal mol-’ for rotamers A, B and C, respectively. It is also shown in Fig. 2 that the equilibrium rotational angle [ 7. (CH,) ] is not significantly

207

- 6(

OH

I

1

* 0 60 CHa 120

Fig. 2. Potential-energy surface for the CH, rotation and OH torsion in lactonitrile (two-dimensional plot). + , Energy minima.

influenced by the position of the OH group. (MM”, 60.7” and 62.7” for A, B and C, respectively). Likewise, the OH torsion is shown to be almost independent of the CH3 rotation. The barrier heights for the OH torsion were calculated as 1.85 kcal mol-’ for the A-B transition and 0.45 kcal mol-’ for the B-C transition. The three-dimensional plot for the same potential surface presented in Fig. 3 clearly shows that the CH3 rotation and the OH torsion in lactonitrile are only weakly coupled. This feature may be contrasted to the findings in methyl vinyl ether (CH,OCH=CH,) where the CHB rotation is strongly coupled with the COC bending as well as the skeletal torsion [ 91. A gearing type torsional interaction predicted by the ab initio calculation was confirmed by the three-dimensional treatment within a flexible-model study.

208

Fig. 3. Potential-energy surface for the CHs rotation and OH torsion in lactonitrile (three-dimensional plot ) .

Comparison with flexible-model calculations

In an attempt to explain the torsional data and to corroborate the assign- ments of the microwave spectra in lactonitrile, flexible-model calculations were carried out [ 31. One-dimensional model calculations were applied to the OH torsion and the results from a two-dimensional model including OH torsion and CH, rotation were reported for comparison with experiment. It was found that the rotational constants calculated for the two-dimensional model are practically the same as those obtained for the one-dimensional OH torsional model for corresponding states.

The rotational constants calculated in the present study for the two rotamers of lactonitrile are compared with the experimental values and with those from the two-dimensional model calculations in Table 3. The agreement between the calculated and observed rotational constants for both rotamers A and B is quite satisfactory, the calculated values being less than about 4-8%

209

TABLE 3

Comparison of the rotational constants and torsional parameters of lactonitrile rotamers A-C

Gauche 1 (A)

Rotational Calc. Exp. constant’l

Gauche 2 (B ) Trans (C)

2D-model CaIc. Exp. 2D-model Calc.

A 8840.30 8790.22 8809.73 8616.37 8584.20 8663.85 8735.59 B 4030.42 4005.86 4042.49 4043.73 4028.72 4067.37 4086.64 c 2999.57 2975.80 3012.60 2999.65 2987.85 3030.18 3103.36

Torsional Calc. (4-31G) Two-dimensional parameterb model

V,, (cm-‘) 1245.3 1297 V,s (cm-‘) 1334.3 1520 e(O) 64.4 57 B, (cm-‘) 649.7 400 B, (cm-‘) 708.7 1000 dE (cm-‘) 153.9 110

“In MHz. Experimental values and two-dimensional model results are from ref. 3. bThe torsional parameters are referred to ref. 3.

smaller than the experimental ones. The values from the flexible-model calculations also agree well with the ab initio values of the present study. The experimental values of the rotational constants for rotamer C have not been reported as yet. The calculation shows, however, that the B and C components in rotamer C are much larger than the corresponding values for rotamers A and B.

Some of the torsional properties obtained from the two-dimensional model in ref. 3 are also compared with those from the present ab initio study in Table 3. The calculated potential function for the OH torsion is compared with that obtained using the one-dimensional model in Fig. 4.

In the flexible-model calculations, the methyl rotational barriers were calculated as VsA= 1297 and 1520 cm-’ at the assumed OH torsional angle of 8= 257” with Bo=400 cm-l and B 1 = 1000 cm-‘. The corresponding values obtained in the present ab initio study agree quite well with these values, as Table 3 indicates. In addition, the assumed energy separation (dE) between rotamers A and B of 110 cm-l is comparable with the value of 153.9 cm-’ from the present study. As shown in Fig. 4, another very shallow minimum at - 167.6” with a high energy of about 995 cm-’ was also postulated in the previous flexible-model study. This minimum which should correspond to the rotamer C was calculated to be 700 cm-l above rotamer A in the present study, as discussed in the previous section.

Fig. 4. Potential curve for the OH group torsion. A comparison of the one-dimensional flexible model result with the present ab initio result.

TABLE 4

Molecular electronic properties of the three rotamers of lactonitrile”

Gauche 1 (A) Gauche 2 (B) Truns (C)

Dipole momentb (D ) 3.25

(3.91)

Quadrupole moment’ (a.u.)

:

- 9.9493

Q:: 2.0540 1.4953

r2> (au.) - 69.8014

Electric field gradients (a.u.) q=x (N) -0.5170 qyY (N) -0.4116 4.. (N) 0.9286 fp 0.114 4xX (0) - 1.9060 4W (0) -0.0177 Q** (0) 1.9237 rp 0.982

3.49

(4.29)

- 8.6553 7.5030 1.1523

- 70.9270

-0.5225 - 0.5207 - 0.4069 - 0.4046

0.9295 0.9253 0.124 0.125

- 1.9209 - 1.9367 0.0004 -0.0154 1.9205 1.9521 0.999 0.984

5.25

- 2.6256 0.1335 2.4921

- 68.5093

“For the most stable isomer of each species with the 6-31G* basis set. bValues in parentheses are experimental ones from ref. 3. ‘Principal-axis system of the field gradient. dAsymmetry parameter.

211

Moleculur electronic properties and vibrational frequencies

Some one-electron molecular properties calculated with the 6-31G* basis set are summarized in Table 4. The calculated dipole moments of 3.25 and 3.49 D for rotamers A and B are slightly smaller than the experimental values of 3.91 and 4.29 D, respectively. The (r”) value is a measure of the extent of electronic-charge distribution in the molecule. It is shown that the charges in rotamer B are much more widely distributed than those in rotamers A and C. The calculated asymmetry parameters (q) of the electric-field gradients, which are a measure of the deviations from the rotational symmetry of the charge distributions in the vicinity of nuclei, are shown to be relatively small in nitro- gen, while they are quite large in the oxygen of the OH group. The quadrupole coupling constants for 14N in the rotamers A and B have also been reported previously 131. While these values are given in the molecular principal-axis

TABLE 5

Calculated vibrational frequencies (cm-‘) for the three rotamers of lactonitrile”

Vibrational mode Gauche 1 (A) Gauche 2 (B) Trans (C)

VOH 3984 3973 3993

%H(CH.) 3307 3295 3298

%H(CHd 3293 3290 3270 %H(CHd 3214 3267 3204 VCH 3208 3200 3197 VCN 2573 2574 2591 s CH(CK?) 1657 1655 1657 s CH(CI3.d 1644 1651 1651 sCHWHa, 1587 1586 1586 &li/~OH 1522 1528 1561 &Hl~OH 1514 1492 1490 f&/~OH 1377 1392 1350 6 COH 1262 1254 1241 6CH(CHa) 1201 1185 1223 UC-C 1123 1144 1133 GCCH 1015 1006 1009 GCCH 872 854 866 KOH 658 655 659 GCCC 631 634 635 6Hoc 427 425 425 60H 352 343 315 GCH(CHe) 300 294 256 GCH(CHs) 244 248 237 OH torsion 213 217 221

Zero-point energy (kcal mol-‘) 53.15 53.12 53.00

‘Using the 4-31G basis set.

212

system and, therefore, a direct comparison with the present values (given in the principal-axis system of the electric-field gradients) is not possible, the calculated rl values of 0.114 and 0.124 are comparably small as compared with the value of 0.01 obtained in the previous study. Unfortunately, there are as yet no experimental values for the molecular quadrupole moments available for comparison with the calculated ones.

The calculated vibrational frequencies in lactonitrile are summarized in Ta- ble 5. The O-H and C-H stretching modes are well separated from other vibrational modes. Since the molecule does not possess any symmetry, all the other modes are combinations of more than two stretching or bending modes. The vibrational frequencies due to the bending and rotational modes of the CH, group are denoted in Table 5. The lowest vibrational frequencies, 213,217 or 221 cm-’ for rotamers A, B and C, respectively, correspond to the OH torsional mode It is interesting to note that the calculated zero-point energies are almost the same for all three rotamers. For a quantitative comparison with experimental values, which are not yet available, a careful scaling of the force field or of the calculated frequencies is necessary (cf. refs. 10 and 11).

ACKNOWLEDGEMENTS

The authors thank the computer centres of ETH Zurich and the University of Zurich for use of computer facilities.

REFERENCES

1 T.-K. Ha, R. Meyer, P.N. Gosh, A. Bauder and H.H. Gunthard, Chem. Phys. Lett., 81 (1981) 610 and references therein.

2 G. Corbelli and D.G. Lister, J. Mol. Struct., 74 (1981) 39. 3 W. Caminati, R. Meyer, M. Oldani and F. Scappini, J. Chem. Phys., 83 (1985) 3729. 4 R. Ditschfield, W.J. Hehre and J.A. Pople. J. Chem. Phys., 54 (1971) 724. 5 P.C. Hariharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. 6 N.R. Peterson and R.A. Poirier, Monstergauss, University of Toronto, Canada, 1981. 7 J.S. Binkeley, M.J. Frisch, D.J. DeFrees, K. Raghavachari, R.A. Whitehead, H.B. Schlegel,

G. Fluder and J.A. Pople, Gaussian 82, Carnegie-Mellon University, Pittsburgh, PA, 1982. 8 C. Meller and M.S. Plesset, Phys. Rev., 46 (1934) 618. J.A. Pople, J.S. Binkeley and R.

Seeger, Int. J. Quantum Chem. Symp., 10 (1979) 1. 9 R. Meyer, T.-K. Ha, M. Oldani and W. Caminati, J. Chem. Phys., 86 (1987) 1848.

10 J. Dommen, M. RodIer andT.-K. Ha, Chem. Phys., 117 (1987) 65. 11 C. Cometta-Morini, T.-K. Ha and J.F.M. Oth, J. Mol. Struct. (Theochem), 188 (1989) 79.

ab initio study of lactonitrile: potential functions to the hydroxyl and methyl group torsions

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