H. WENNERSTR~M, S. FORSBN, AND B. Roos
2430
Studies of the Ester Group. I.
A b Initio Calculations on Methyl Formate
by Hikan Wennerstrom,*'* Sture ForsBn,l* and Bjorn R O O S ~ ~ Division of Physical Chemistry 8, T h e Lund Institute of Technology, Chemical Center, S-880 07 L u n d 7, Sweden, and Institute of Theoretical Physics, University of Stockholm, S-118 46 Stockholm, Sweden (Received February 18, 2978) Publication costs assisted by T h e L u n d Institute of Technology
A6 initio LCAO-MO-SCF calculations on the s-cis, s-trans, and 90' rotated conformations of methyl formate have been performed. A gaussian basis set of a double-r type was used. With possible errors taken into account, the calculations gave the estimates AH = 8 f 3 kcal/mol and A H + = 13 k 2 kcal/mol for the strans i$ s-cis interconversion in the gas phase. In a liquid of high polarity the estimate is AH = 4 f 5 kcal/ mol and AH+ = 11 f 3 kcal/mol. All these values are in agreement with experiments. The energy difference between the s-cis and s-trans conformations is interpreted as due to an electrostatic effect. A simple model for calculating such electrostatic contributions to conformational equilibria is proposed and also applied to the conformation problem of some molecules analogous to methyl formate.
Introduction Methyl formate, the smallest carboxylic acid ester, can in many respects be regarded as a model compound for aliphatic esters. Quantum chemical calculations on methyl formate should accordingly give aspects of the structure of the ester bond. It is the main purpose of the present work to throw light on two phenomena involving this bond: the rotational barrier and the s-trans-s-cis conformation equilibrium. During recent years a large number of ab initio quantum mechanical calculations on different chemical problems have been published. The rapidly developing computer technique has made it possible to perform calculations on increasingly larger molecules. I n the present work we report the results of an ab initio LCAO-MO-SCF calculation on the three conformations of the methyl formate molecule shown in Figure 1. Forms I and I11 possess a plane of symmetry, while I1 has no symmetry at all. Several experimental determinations and estimates have been made for both AH and A H + for the s-trans-s-cis interconversion reaction I (11) Ft 111, where I1 is an assumed approximate description of the transition state (cf. Table I). The presence of a rotational barrier is generally recognized as arising from the decrease of the conjugation between one ester oxygen lone pair and the carbonyl group, but the source of the energy difference between the s-cis and s-trans conformations is less well understood. A few suggestions have been put forward on the latter question and one of the aims of present work is to scrutinize these suggestions in the light Of the culations. Schwartz, Hayes, and Rothenberg2 have recently made an ab initio calculation on formic acid very respect to to the One reported here basis set and general approach to the problem. Their results are very similar to ours, indicating that the The Journal
of
Physical Chemistry, Vol. 76, No. 2'7, 1978
carboxylic group and the corresponding ester group have many Properties in Cc"On (Cf. Table 1).
Method of calculation A single SCF-type calculation was made on each of the three conformations I, 11, and 111. A computer program, REFLECT,^^ which can make computational use of molecular symmetry, was used for I and 111, while the calculation for I1 was accomplished with IBMOL (version IV).3b Details about the gaussian basis set are given in Table 11. The basis set chosen gave 76 uncontracted and 48 contracted basis functions. Recently it has been suggested that molecular optimized orbital exponents and contraction coefficients be used in a6 initio calculation^.^ This method was not used, since a test calculation on methanol using a methane optimized set for the carbon and a water optimized set for the oxygen showed that this choice was inferior to an analogous atom optimized set. It seems that one has to limit the use of molecular optimized basis sets to calculations on molecules very similar to those on which the optimization was made. The long computer times, approximately 2 hr (IBJ*f 360/75) for each calculation, and the restricted computer time at our disposal precluded a full geometry optimization. The geometry used for the s-trans conformation I was taken from the microwave spectroscopic study made by CurL6 The geometries of 11 and I11 were obtained by a stiff rotation around the (1) (a) Lund Institute of Technology; (b) University of Stockholm. (2) M.E. Schwartz, E. F. Hayes, and S . Rothenberg, J . Chem. Phys., 52, 2011 (1970). (3) (a) P. Siegbahn, Chem. Phys. Lett., 8,245 (1971); (b) A . Veillard,
Version IV, IBM manual. (4) G. Wipff, U. Wahlgren, E. Kochanski, and J. M.Lehn, Chem. p h y s . Lett., 11, 350 (1971). (5) R. F. Curl, Jr., J . Chem. Phys., 30, 1529 (1959).
IBMOL,
STUDIES OF THE ESTER GROUP
2431
Table I: Experimental Determinations of AH and A H + of the s-Trans-s-Cis Conformation Change of Methyl Formate Compared with the Results of Reported Calculations AH,
AH+, s-trans
Method
koal/mol
Phase
Ref
Ir Ultrasonic relaxation U1tr asonic relaxation Ultrasonic relaxation Ab initio calculationsa Ab initio calculations on formic acid
>2.7 2.3
13.1 10.1
Gas Liquid
b
0.4
8.2
Liquid
d
6.2
11.9-12.2
Liquid
e
H
9.0
13.2
This work
S 4 S
8.1
13.0
2
kcal/mol
goo
rotated
C
numbering of atoms
T. Miyazawa, a Estimated errors not taken into account. Bull. Chem. Soc. Jap., 34, 691 (1961). c S. V. Subrahmanyan J. and J. E. Piercy, J . Acoust. Soc. Amer., 37, 340 (1965). Bailey and A. M. North, Trans. Faraday SOC.,64, 1499 (1968). 6 K. M. Burundukov and V. F. Jakovlev, J . Fiz. Chim., 42,2149 (1968).
Figure 1. The different conformations of methyl formate on which calculations were made. Included is also the numbering of atoms used in the text. (The cis-trans convention is chosen to be in accordance with the one accepted for esters of larger carboxylic acids.)
electron properties for the s-trans conformation are compared with experimentally determined values and given in Table VI.
Discussion Table I1 : Description of the Basis Set Used in the Calculations ---Atoms--
c,o
Uncontracted basis functions Contracted basis functions Exponents
7Si
Contraction coefficients
a
H
3P
3s
4s, 2~
2s
a
b (with the scale factor 1.34) b
a From B. Roos and P. Siegbahn, Theor. Chim. Acta, 17, 209 From S. Huzinaga, J. Chem. Phys., 42, 1293 (1965). (1970).
0(2)-C(1,bond of 90 and 180°, respectively, with the CH3 group staggered relative to the 0(2)-C(1) bond.
Results I n Table 111 the calculated total energy and various other energy components for the three conformations are given. The result of a Mulliken population analysis is shown in Table IV. It should be noted that due to the limited number of hydrogen basis functions the population analysis tends to underestimate the formal populations on the hydrogen atoms. This also leads to an error in the calculated dipole moments. For conformation I this error is expected to approximately cancel, since the C 30. The mean values of the energy difference agree well with experiments, especially with those of ref 13 and 14 (see Table I), which indicates that the calculations have a greater accuracy than could be predicted without reference to experiments. Several suggestions have been put forward to explain the energy difference between the s-trans and s-cis conformations of aliphatic esters. For a recent summary, see ref 10. Bailey and niorth16 conclude that the most important effect is the steric repulsion between the carbon chains in the alcohol and in the carboxylic acid forming the ester. For esters other than formate this is certainly an important factor, but for formates it is doubtful. The bulky tert-butyl formate, for example, has a higher population of the s-trans form than less bulky formates.1° The population analysis and the electron density maps furthermore show that the electron density increases on O(I) and H(*)when the methyl group is in their vicinity. The effect of a steric repulsion should be the reverse. Owen and Sheppardl'j suggest that oxygen lone-pair repulsion is an important factor in the determination of the most stable conformation. Since lone pair-lone
+
*
(8) L. Onsager, J. Amer. Chem. Soc., 58, 1486 (1936). (9) See, for example, R. J. Abraham, L. Cavalli, and K. G . R. Pachler, Mol. Phys., 11, 471 (1966). (10) iM. Oki and H. Nakanishi, Bull. Chem. SOC.Jap., 43, 2558 (1970). (11) R. J. B. Marsden and L. E. Sutton, J. Chem. SOC.,1383 (1936). (12) E. Bock, Can. J . Chem., 45, 2761 (1967). (13) T. Miyazawa, Bull. Chem. SOC.Jap., 34, 691 (1961). (14) 5. V. Subrahmanyam and J. E. Piercy, J. Acoust. SOC.Amer., 37, 340 (1965). (15) J. Bailey and A. M. North, Trans. Faraday Soc., 64, 1499 (1968). (16) L. Owen and N. Sheppard, Proc. Chem. SOC.London, 264 (1963).
The Journal of Physical Chemistry, Vol. 76, No. 17, 197%'
H.WENNERSTR~M, S. FORS&N, AND B. Roos
2434
C
Figure 2: The electron density in the formyl part of methyl formate in a plane through the atoms: (a) total density of the the s-trans conformation, contours 3.0, 1.0, 0.3, 0.1, and 0.03; (b) difference density between I and 111, contours 0.01, 0.003, 0.001 (solid lines), d 0 . 0 (dotted lines), -0.001, -0.003, and -0.01 (dashed lines); (c) difference density between I and 11, contours as in b.
pair repulsion has no direct definition in a HartreeFock calculation, it is difficult to say if it is important or not. One would, however, expect the following consequences: (i) a decrease in electron density in the region between the two oxygen atoms, especially in the region close to the carbonyl oxygen, in the s-cis conformation (cf. Figure 2b) ; (ii) characteristic changes in overlap populations between the oxygen in some orbitals containing large coefficients at the oxygen; and (iii) characteristic changes of orbital energies of orbitals of the lone-pair type. None of these effects is found however, and it may be said that the calculations in no way support the theory of lone pair-lone pair rGpulsion. It should be remembered that the oxygen atoms in the present case are separated by two chemical bonds, and the situation can be quite different if the oxygens are directly bonded, as, for example, in hydrogen peroxide. Marsaen and Suttonl’ suggest that the energy difference between the s-trans and s-cis conformations of esters could be partially accounted for by considering the interaction between the O(I,-C(I) and 0(2)-C(2)bond dipoles. This picture is supported by the present study. It seems, however, to be both simpler and more elucidating to handle these electroThe Journal of Physical Chemistry, Vol. 76, No. 17, 1978
static interactions as forces between point charges placed at the nuclei instead of forces between bond dipoles. In the present case of methyl formate, the formal atomic charges can be obtained from the population analysis. Figure 3 shows the relevant gross atomic charges. The electrostatic energy is then simply obtained from Zt,,qtq,/rt,. Owing to the uncertainties in the individual charges in the methyl group (cf. above), the latter is treated as a single entity. The difference in Coulomb energy between I11 and I is 7.5 kcal/mol (if the atoms in the methyl group are treated separately, one gets AE = 10 kcal/ mol), in good agreement with the 9.0 kcal/mol obtained in the ab initio calculation, indicating that the electrostatic effects are of major importance in determining the most stable conformation. This conclusion is further supported by the population analysis and by the values of the electrostatic potentials a t the nuclei. Table IV shows that the effect of going from I and I11 is a drift of electrons from O(1) and C(I) toward H(4) to obtain a screening of the Hc4) nucleus from the positive methyl group. Table V shows that the methyl group nuclei have a marked higher potential in I11 than in I, which is expected from an electrostatic model. Against this electrostatic picture it can be argued that it is in a way senseless to talk about formal charges of atoms in molecules. At long distance, however, the Coulomb interactions become increasingly important and the details of the electronic distribution are then of lesser significance. The mere presence of a rotational barrier clearly shows that other factors than the electrostatic ones a,re important, and this should of course be ‘kept in mind. A more detailed picture of the difference between the s-trans and s-cis conformations in what regards the electronic densities is given in Figures 2a and 2b. Figure 2a shows the electron density for I in the symmetry plane. Only the part of the molecule which is not directly affected by the rotation is shown. Figure 2b shows the corresponding difference in electron densities between I and 111. Figure 4 illustrates the corresponding results for the n electrons 1 A above the symmetry plane. The “in-plane” picture, Figure 2b, shows a complicated pattern. In the s-trans form the methyl group seems to repel the electrons at the carbonyl oxygen, making them go to the far side of the atom. The other clear feature is that the electron density on the H(4)atom has increased in the s-cis form. From the differences between the n-electron densities in Figure 4b, it is evident that there is an increased polarization of the ?r-carbonyl bond toward the oxygen atom in the s-trans form. ( C ) The Rotational Barrier. It is usually assumed that the conversion between s-trans and s-cis conformations of esters proceeds via a rotation of the methyl group. The possibility that the conversion involves an inversion at the ester oxygen cannot be definitely
STUDIES OF
THE
ESTERGROUP
2435 -0.49
F
+0.15
H,,,
