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The butadiene-1,3 internal rotation potential function obtained from ab initio calculation and experimental data
Journal of Molecular Structure, 140 (1986) 87-92 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THE BUTADIENE-1,3 INTERNAL ROTATION POTENTIAL FUNCTION OBTAINED FROM AB INITIO CALCULATION AND EXPERIMENTAL DATA
YU. N. PANCHENKO and A. V. ABRAMENKOV Laboratory of Molecular Spectroscopy, Department of Chemistry, M. V. Lomonosov Moscow State University, Moscow 119899 (U.S.S.R.) Ch. W. BOCK Chemistry Department, 19144 (U.S.A.)
Philadelphia College of Textiles and Science, Philadelphia, PA
(Received 9 May 1985)
ABSTRACT Values of the Pitzer function F(G), coefficients of its Fourier expansion, and coefficients of the potential energy expansion are obtained from ab initio HF/6-311G** calculations of the potential curve for internal rotation and the optimized geometry of butadiene-1,3 (Ch. W. Bock et al., Theor. Chim. Acta, 64 (1984) 293). A correction of the theoretical coefficients in the potential energy expansion is performed on the basis of the “hot” band progression frequencies of the trans-form torsional overtones and the ab initio calculated values of the gauche-form torsional frequency of butadiene-1,3 and its two isotopomers (C,D, and cis, cis-1,4-d,-butadiene-1,3). The coefficients in the potential energy expansion are found to be: V, = 484.9, V, = 1349.1, V, = 837.2, V, = -139.3, V, = -9.8, V, = -77.5, V, = 25.8, and V, = 13.5. The advantage of using an ab initio potential curve as a starting approximation in such investigations is discussed. INTRODUCTION
The construction of a potential energy curve for the internal rotation about a bond in a molecule from experimental data is usually carried out within the framework of a rigid rotation model. Thus, when changing the dihedral angle of rotation around a bond, all other geometrical parameters are held fixed. Furthermore, various other assumptions are made to choose the starting coefficients in the potential energy Fourier expansion. These coefficients are then varied until there is good agreement with the available experimental data. In previous studies, a “non-rigid” model for conjugated systems was used for constructing the potential curve of internal rotation about the central C-C bond in butadiene-1,3 [l, 21, on the basis of ab initio calculations at the Hartree-Fock level using a (7,3) + (5,3) basis set for the C atoms and three uncontracted s functions for the H atoms with orbital exponents 4.90, 0.82, and 0.18 [3]. From the specially treated data of ref. 3 (i.e. the 0022-2860/86/$03.50
o 1986 Elsevier Science Publishers B.V.
88
so-called adjusted ab initio geometry [l] ) the values of the Pitzer function F(G), the coefficients of its Fourier expansion [4] and the values of starting coefficients Vi in the potential energy expansion were calculated. The coefficients of the potential energy expansion, refined using the experimental frequencies of the “hot” band progression of the torsional overtone 2v13 of C4H6, are given in the second column of Table 1. These coefficients turned out to be applicable for simulating analogous experimental data on the C4D6 and cis,cis-1,4-&-butadiene-1,3 molecules [2]. Recently, ab initio calculations of the potential curves for the butadiene1,3 internal rotation using more complete basis sets have been reported [ 5-81. The gauche-conformation was obtained in all cases as a second stable rotamer. Ref. 8 contains the optimized geometrical parameters and energies of butadiene-1,3 at 10 points during the rotation from O”(truns-form) to 180”(cis-form) around the C-C single bond at the HF/6-311G** level. In this connection it is of interest to reevaluate the potential curve of butadiene-1,3 on the basis of these new theoretical calculations [8], experimental data [ 1, 21, and calculated torsional frequencies of the gaucheform of three butadiene-1,3 isotopomers [ 91. TABLE
1
Coefficients
in the butadiene-1,3
Coefficient
Adjusted ab initio geometry [l,
21
347.3 1790.0 612.8 179.8 -
V, V* V, V4 V5 V6
-
v, V*
Position of gauche-well Value of k-barrier
157”
30.0
Value of main barrier (cm-l)
energy Ab initio 6-311G** geometry
expansion Refined potential of butadiene-1,3
1111
181 489.0 1376.2 863.9 -74.2 9.4 -43.7 0.0 0.0
Refined potential of isoprene
484.9 1349.1 837.2 -139.3 -9.8 -77.5 25.8 13.5
399.9 1330.2 781.8 -175.8 -
142.5”
143.3”
140.8”
253.7
326.9
254.6
(cm-’ ) 82.8”
Position of main barrier
AH,
potential
2321.0
75.0”
75.0”
2162.4
2114.8
1108.6
1011.2
78.5”
2023.0
(cm-‘) 930.0
927.4
89 METHOD
OF CALCULATION
The Pitzer functions F(G) and their Fourier expansions are calculated from data on the variation of molecular geometrical parameters during the internal rotation around the single C-C bond [8]. In ref. 8 the geometrical parameters of butadiene-1,3 were calculated for ten different dihedral angles. We then interpolated this data also for points at 15”, 45” and 105” and calculated the reduced moments of inertia and values of the Pitzer function for all these configurations. This allowed us to calculate the coefficients of the Pitzer function Fourier expansion up to the seventh term inclusive (see Table 2). Using the data in ref. 8, the first six coefficients in the potential energy expansion were evaluated (see column 3 in Table 1). The frequencies of transitions corresponding to 2v i3 of the C4H6, C4D6, and C4H4D2 molecules were calculated with this ab initio potential (see column A in Table 3). The calculation was performed in the one-dimensional approximation by a program analogous to that of Lewis et al. [lo]. The correction of the theoretical potential was then carried out using the least-squares method from the experimental data mentioned above [ 1, 21. The values of the coefficients TABLE
2
The Pitzer function results of ref. 8.
F(o)
values
(a)
and
its Fourier
expansion
coefficients
(b)
from
(4 @(“I 0 15 30 45 60 75 90 105 120 135 150 165 180
2.7846 2.7853 2.7893 2.8053 2.8389 2.9082 3.0190 3.1810 3.4058 3.7196 4.0892 4.4105 4.5407
2.3545 2.3514 2.3443 2.3413 2.3486 2.3819 2.4472 2.5527 2.7086 2.9349 3.2087 3.4512 3.5505
1.9840 1.9829 1.9806 1.9825 1.9917 2.0187 2.0661 2.1382 2.2397 2.3827 2.5489 2.6910 2.7478
(b) FL? F, F2 F3 F4 F5 F6
3.3012 -0.7623 0.3199 -0.1035 0.0397 -0.0122 0.0017
2.6686 -0.5088 0.2509 -0.0792 0.0312 -0.0099 0.0016
2.1991 -0.3326 0.1494 -0.0445 0.0170 -0.0049 0.0003
90
TABLE 3 Comparison of experimental and calculated (with ab initio potential (A) from ref. 8 and with refined potential (B)) transition frequencies (cm-l) of overtones 2u,, in the Raman spectra of C,H,, C,H,D,, and C,D, Assignment
C,H,
tram 9-2 l-3 2-4 3-5 4-6 5-7 6-8 7-9 8-10 9-11 10-12
323.0 317.6 312.5 306.2 300.6 293.7 286.4 280.4? 271.1 263.9 256.7?
gauche O-l
155.0a
25.3 26.0 25.5 25.3 23.4 21.9 19.6 14.8 11.7 4.6 -5.2 -26.3
4.2 3.1 2.4 3.3 3.5 4.7 5.7 4.5 5.4 2.3 -2.9
302.0 297.5 292.5 286.6 280.7 276.3 271.6 269.2 262.5 255.8 250.0
-4.8
136.ga
18.6 19.2 19.5 20.1 19.9 17.5 14.6 8.5 5.7 1.6 -4.8
-0.6 -1.8 -1.8 -0.6 0.7 0.3 -0.1 -3.3 -3.0 -3.7 -6.6
-17.4
1.2
282.0 278.0 274.0 270.5 266.0 261.0 258.0 245.5 239.5 236.0 233.0
122.0a
12.8 13.6 13.9 13.1 12.8 12.4 9.4 15.2 13.9 9.2 3.1
-11.3
-4.6 -5.4 -5.8 -6.3 -5.6 -4.5 -5.5 2.3 3.7 1.7 -1.6
4.7
aThe values as calculated from the ab initio force field [ 91.
Fig. 1. The potential as a function of the rotation angle. Dashed line: ab initio quantum mechanical computations at the HF/6-311G ** level (column 3 in Table 1). Solid line: experimentally refined calculations (column 4 in Table 1).
91
obtained from the refined potential energy expansion are given in column of Table 1. The corresponding potential curves are given on Fig. 1.
4
DISCUSSION
The first three Fourier expansion coefficients for the refined potential are nearly the same as for the theoretical one (columns 3 and 4 in Table l), whereas the other three coefficients differ markedly, e.g. the values of the V4 and V, coefficients are nearly doubled and the V5 coefficient changes its sign. The deviation of frequencies of the 2~ i3 transitions as calculated with the refined potential from the experimental ones are given in columns B of Table 3. It should be noted that these deviations are very close to the residuals obtained in the case of potential for adjusted ab initio geometry [l, 21. Juxtaposition of these two potentials (columns 2 and 4 in Table 1) however, shows significant differences. It is of interest to note that the V, value is quite large in the refined potential. This shows that higher terms of the potential energy expansion should not be omitted without their preliminary evaluation. This was the reason that V, and Vg, which were not taken into account when considering the theoretical potential, were determined in the course of refinement. It is important that the V, terms are different in signs than that found in refs. 1 and 2 (see columns 2, 3, and 4 in Table 1). However, the most essential fact is that the gauche-well positions are different by about 15” (Table 1). Therefore, the two different potentials (see columns 2 and 4 in Table 1) give approximately equal calculated values of the 2v13 transition frequencies for the three butadiene-1,3 isotopomers. Consequently, the use of experimental data on the 2vi3 transition frequencies, even including the data on isotopomers (altogether 36 transitions) in the least-squares procedure, does not determine a solution which is independent of the starting approximation of the coefficients of the internal rotation potential energy expansion. In this case the role of the starting approximation is extremely important for obtaining the experimentally refined potential energy expansion. The butadiene-1,3 energy values were calculated for 5 different points during rotation around the single C-C bond with inclusion of electron correlation [8]. For four points (go”, 120”, 150”, and 180”) an approximately equal decrease in energy was obtained on going from the 6-311G** basis set to the CI/6-31G* and CI, size corr./6-31G* techniques. A little more decrease of energy was observed only for the truns-form (0”). This implies that the theoretical potential curves are of similar slope and suggests that it is not obligatory to use the CI technique for the construction of the internal rotation potential energy curve if it is to be refined by the experimental data. Evidently, it is reasonable to take as a starting approximation a potential curve calculated by the ab initio method at the Hartree-Fock level using a sufficiently complete basis set.
92
Column 5 of Table 1 contains the parameters of the internal rotation potential curve for isoprene [ 111 as obtained by an analogous procedure. The isoprene potential includes four terms only. However, good agreement is observed for the first four terms in the potential energy expansion for butadiene-1,3 and isoprene. The V, term was assumed to be zero in the case of isoprene; this will, of course, affect the values of the other coefficients in the potential energy expansion. CONCLUSIONS
The above calculations serve to emphasize that spectroscopic data alone is not sufficient for the accurate construction of molecular internal rotation curves. Furthermore, other experimental data such as the energy difference AH,, between rotational isomers or the barrier height is not generally known with sufficient accuracy to be of much help (see, for example, ref. 11). In such situations a starting approximation for the potential curve plays an important role. The agreement of the values and signs of the coefficients in the potential energy expansion of butadiene-1,3 and isoprene strongly suggests that ab initio potential curves calculated using a sufficiently complete basis set at the Hartree-Fock level can serve as a good starting approximation for an experimentally based refinement of the potential. Note added in proof. The gauche-well position (142.2”), as calculated by J. Breulet et al. (J. Am. Chem. Sot., 106 (1984) 6250), more or less agreed with the result of ref. 8. The experimental frequency of 136 cm-’ for the torsional mode of gauche-butadiene-1,3, which is given in the above paper, was obtained from the erroneous analysis of the “hot” band series of the torsional overtone 2u 13 of truns-C4H6 (L. A. Carreira, J. Chem. Phys., 62 (1975) 3851 and criticism in refs. 1 and 2). REFERENCES 1 Ch. W. Bock, P. George, M. Trachtman and M. Zanger, J. Chem. Sot., Perkin Trans. 2, (1979) 26. 2 Yu. N. Panchenko, A. V. Abramenkov, V. I. MochaIov, A. A. Zenkin, G. Keresztury and G. Jalsovszky, J. Mol. Spectrosc., 99 (1983) 288. 3 S. Skaarup, J. E. Boggs and P. N. Skancke, Tetrahedron, 32 (1976) 1179. 4 K. S. Pitzer, J. Chem. Phys., 14 (1946) 239. 5 G. De Mare, J. Mol. Struct. (Theochem), 107 (1984) 127. 6 Ch. W. Bock, P. George and M. Trachtman, J. Mol. Struct. (Theochem), 109 (1984) 1. 7 G. De Mare and D. Neisius, J. Mol. Struct. (Theochem), 109 (1984) 103. 8 Ch. W. Bock, P. George and M. Trachtman, Theor. Chim. Acta, 64 (1984) 293. 9 Ch. W. Bock, Yu. N. Panchenko, S. V. Krasnoshchiokov and V. I. Pupyshev, J. Mol. Struct., 129 (1985) 57. 10 J. D. Lewis, T. B. Malloy, Jr., T. H. Chao and J. Laane, J. Mol. Struct., 12 (1972) 427. 11 Yu. N. Panchenko, V. I. Pupyshev, A. V. Abramenkov, M. Traetteberg and S. J. Cyvin, J. Mol. Struct., 130 (1985) 355.
THE BUTADIENE-1,3 INTERNAL ROTATION POTENTIAL FUNCTION OBTAINED FROM AB INITIO CALCULATION AND EXPERIMENTAL DATA
YU. N. PANCHENKO and A. V. ABRAMENKOV Laboratory of Molecular Spectroscopy, Department of Chemistry, M. V. Lomonosov Moscow State University, Moscow 119899 (U.S.S.R.) Ch. W. BOCK Chemistry Department, 19144 (U.S.A.)
Philadelphia College of Textiles and Science, Philadelphia, PA
(Received 9 May 1985)
ABSTRACT Values of the Pitzer function F(G), coefficients of its Fourier expansion, and coefficients of the potential energy expansion are obtained from ab initio HF/6-311G** calculations of the potential curve for internal rotation and the optimized geometry of butadiene-1,3 (Ch. W. Bock et al., Theor. Chim. Acta, 64 (1984) 293). A correction of the theoretical coefficients in the potential energy expansion is performed on the basis of the “hot” band progression frequencies of the trans-form torsional overtones and the ab initio calculated values of the gauche-form torsional frequency of butadiene-1,3 and its two isotopomers (C,D, and cis, cis-1,4-d,-butadiene-1,3). The coefficients in the potential energy expansion are found to be: V, = 484.9, V, = 1349.1, V, = 837.2, V, = -139.3, V, = -9.8, V, = -77.5, V, = 25.8, and V, = 13.5. The advantage of using an ab initio potential curve as a starting approximation in such investigations is discussed. INTRODUCTION
The construction of a potential energy curve for the internal rotation about a bond in a molecule from experimental data is usually carried out within the framework of a rigid rotation model. Thus, when changing the dihedral angle of rotation around a bond, all other geometrical parameters are held fixed. Furthermore, various other assumptions are made to choose the starting coefficients in the potential energy Fourier expansion. These coefficients are then varied until there is good agreement with the available experimental data. In previous studies, a “non-rigid” model for conjugated systems was used for constructing the potential curve of internal rotation about the central C-C bond in butadiene-1,3 [l, 21, on the basis of ab initio calculations at the Hartree-Fock level using a (7,3) + (5,3) basis set for the C atoms and three uncontracted s functions for the H atoms with orbital exponents 4.90, 0.82, and 0.18 [3]. From the specially treated data of ref. 3 (i.e. the 0022-2860/86/$03.50
o 1986 Elsevier Science Publishers B.V.
88
so-called adjusted ab initio geometry [l] ) the values of the Pitzer function F(G), the coefficients of its Fourier expansion [4] and the values of starting coefficients Vi in the potential energy expansion were calculated. The coefficients of the potential energy expansion, refined using the experimental frequencies of the “hot” band progression of the torsional overtone 2v13 of C4H6, are given in the second column of Table 1. These coefficients turned out to be applicable for simulating analogous experimental data on the C4D6 and cis,cis-1,4-&-butadiene-1,3 molecules [2]. Recently, ab initio calculations of the potential curves for the butadiene1,3 internal rotation using more complete basis sets have been reported [ 5-81. The gauche-conformation was obtained in all cases as a second stable rotamer. Ref. 8 contains the optimized geometrical parameters and energies of butadiene-1,3 at 10 points during the rotation from O”(truns-form) to 180”(cis-form) around the C-C single bond at the HF/6-311G** level. In this connection it is of interest to reevaluate the potential curve of butadiene-1,3 on the basis of these new theoretical calculations [8], experimental data [ 1, 21, and calculated torsional frequencies of the gaucheform of three butadiene-1,3 isotopomers [ 91. TABLE
1
Coefficients
in the butadiene-1,3
Coefficient
Adjusted ab initio geometry [l,
21
347.3 1790.0 612.8 179.8 -
V, V* V, V4 V5 V6
-
v, V*
Position of gauche-well Value of k-barrier
157”
30.0
Value of main barrier (cm-l)
energy Ab initio 6-311G** geometry
expansion Refined potential of butadiene-1,3
1111
181 489.0 1376.2 863.9 -74.2 9.4 -43.7 0.0 0.0
Refined potential of isoprene
484.9 1349.1 837.2 -139.3 -9.8 -77.5 25.8 13.5
399.9 1330.2 781.8 -175.8 -
142.5”
143.3”
140.8”
253.7
326.9
254.6
(cm-’ ) 82.8”
Position of main barrier
AH,
potential
2321.0
75.0”
75.0”
2162.4
2114.8
1108.6
1011.2
78.5”
2023.0
(cm-‘) 930.0
927.4
89 METHOD
OF CALCULATION
The Pitzer functions F(G) and their Fourier expansions are calculated from data on the variation of molecular geometrical parameters during the internal rotation around the single C-C bond [8]. In ref. 8 the geometrical parameters of butadiene-1,3 were calculated for ten different dihedral angles. We then interpolated this data also for points at 15”, 45” and 105” and calculated the reduced moments of inertia and values of the Pitzer function for all these configurations. This allowed us to calculate the coefficients of the Pitzer function Fourier expansion up to the seventh term inclusive (see Table 2). Using the data in ref. 8, the first six coefficients in the potential energy expansion were evaluated (see column 3 in Table 1). The frequencies of transitions corresponding to 2v i3 of the C4H6, C4D6, and C4H4D2 molecules were calculated with this ab initio potential (see column A in Table 3). The calculation was performed in the one-dimensional approximation by a program analogous to that of Lewis et al. [lo]. The correction of the theoretical potential was then carried out using the least-squares method from the experimental data mentioned above [ 1, 21. The values of the coefficients TABLE
2
The Pitzer function results of ref. 8.
F(o)
values
(a)
and
its Fourier
expansion
coefficients
(b)
from
(4 @(“I 0 15 30 45 60 75 90 105 120 135 150 165 180
2.7846 2.7853 2.7893 2.8053 2.8389 2.9082 3.0190 3.1810 3.4058 3.7196 4.0892 4.4105 4.5407
2.3545 2.3514 2.3443 2.3413 2.3486 2.3819 2.4472 2.5527 2.7086 2.9349 3.2087 3.4512 3.5505
1.9840 1.9829 1.9806 1.9825 1.9917 2.0187 2.0661 2.1382 2.2397 2.3827 2.5489 2.6910 2.7478
(b) FL? F, F2 F3 F4 F5 F6
3.3012 -0.7623 0.3199 -0.1035 0.0397 -0.0122 0.0017
2.6686 -0.5088 0.2509 -0.0792 0.0312 -0.0099 0.0016
2.1991 -0.3326 0.1494 -0.0445 0.0170 -0.0049 0.0003
90
TABLE 3 Comparison of experimental and calculated (with ab initio potential (A) from ref. 8 and with refined potential (B)) transition frequencies (cm-l) of overtones 2u,, in the Raman spectra of C,H,, C,H,D,, and C,D, Assignment
C,H,
tram 9-2 l-3 2-4 3-5 4-6 5-7 6-8 7-9 8-10 9-11 10-12
323.0 317.6 312.5 306.2 300.6 293.7 286.4 280.4? 271.1 263.9 256.7?
gauche O-l
155.0a
25.3 26.0 25.5 25.3 23.4 21.9 19.6 14.8 11.7 4.6 -5.2 -26.3
4.2 3.1 2.4 3.3 3.5 4.7 5.7 4.5 5.4 2.3 -2.9
302.0 297.5 292.5 286.6 280.7 276.3 271.6 269.2 262.5 255.8 250.0
-4.8
136.ga
18.6 19.2 19.5 20.1 19.9 17.5 14.6 8.5 5.7 1.6 -4.8
-0.6 -1.8 -1.8 -0.6 0.7 0.3 -0.1 -3.3 -3.0 -3.7 -6.6
-17.4
1.2
282.0 278.0 274.0 270.5 266.0 261.0 258.0 245.5 239.5 236.0 233.0
122.0a
12.8 13.6 13.9 13.1 12.8 12.4 9.4 15.2 13.9 9.2 3.1
-11.3
-4.6 -5.4 -5.8 -6.3 -5.6 -4.5 -5.5 2.3 3.7 1.7 -1.6
4.7
aThe values as calculated from the ab initio force field [ 91.
Fig. 1. The potential as a function of the rotation angle. Dashed line: ab initio quantum mechanical computations at the HF/6-311G ** level (column 3 in Table 1). Solid line: experimentally refined calculations (column 4 in Table 1).
91
obtained from the refined potential energy expansion are given in column of Table 1. The corresponding potential curves are given on Fig. 1.
4
DISCUSSION
The first three Fourier expansion coefficients for the refined potential are nearly the same as for the theoretical one (columns 3 and 4 in Table l), whereas the other three coefficients differ markedly, e.g. the values of the V4 and V, coefficients are nearly doubled and the V5 coefficient changes its sign. The deviation of frequencies of the 2~ i3 transitions as calculated with the refined potential from the experimental ones are given in columns B of Table 3. It should be noted that these deviations are very close to the residuals obtained in the case of potential for adjusted ab initio geometry [l, 21. Juxtaposition of these two potentials (columns 2 and 4 in Table 1) however, shows significant differences. It is of interest to note that the V, value is quite large in the refined potential. This shows that higher terms of the potential energy expansion should not be omitted without their preliminary evaluation. This was the reason that V, and Vg, which were not taken into account when considering the theoretical potential, were determined in the course of refinement. It is important that the V, terms are different in signs than that found in refs. 1 and 2 (see columns 2, 3, and 4 in Table 1). However, the most essential fact is that the gauche-well positions are different by about 15” (Table 1). Therefore, the two different potentials (see columns 2 and 4 in Table 1) give approximately equal calculated values of the 2v13 transition frequencies for the three butadiene-1,3 isotopomers. Consequently, the use of experimental data on the 2vi3 transition frequencies, even including the data on isotopomers (altogether 36 transitions) in the least-squares procedure, does not determine a solution which is independent of the starting approximation of the coefficients of the internal rotation potential energy expansion. In this case the role of the starting approximation is extremely important for obtaining the experimentally refined potential energy expansion. The butadiene-1,3 energy values were calculated for 5 different points during rotation around the single C-C bond with inclusion of electron correlation [8]. For four points (go”, 120”, 150”, and 180”) an approximately equal decrease in energy was obtained on going from the 6-311G** basis set to the CI/6-31G* and CI, size corr./6-31G* techniques. A little more decrease of energy was observed only for the truns-form (0”). This implies that the theoretical potential curves are of similar slope and suggests that it is not obligatory to use the CI technique for the construction of the internal rotation potential energy curve if it is to be refined by the experimental data. Evidently, it is reasonable to take as a starting approximation a potential curve calculated by the ab initio method at the Hartree-Fock level using a sufficiently complete basis set.
92
Column 5 of Table 1 contains the parameters of the internal rotation potential curve for isoprene [ 111 as obtained by an analogous procedure. The isoprene potential includes four terms only. However, good agreement is observed for the first four terms in the potential energy expansion for butadiene-1,3 and isoprene. The V, term was assumed to be zero in the case of isoprene; this will, of course, affect the values of the other coefficients in the potential energy expansion. CONCLUSIONS
The above calculations serve to emphasize that spectroscopic data alone is not sufficient for the accurate construction of molecular internal rotation curves. Furthermore, other experimental data such as the energy difference AH,, between rotational isomers or the barrier height is not generally known with sufficient accuracy to be of much help (see, for example, ref. 11). In such situations a starting approximation for the potential curve plays an important role. The agreement of the values and signs of the coefficients in the potential energy expansion of butadiene-1,3 and isoprene strongly suggests that ab initio potential curves calculated using a sufficiently complete basis set at the Hartree-Fock level can serve as a good starting approximation for an experimentally based refinement of the potential. Note added in proof. The gauche-well position (142.2”), as calculated by J. Breulet et al. (J. Am. Chem. Sot., 106 (1984) 6250), more or less agreed with the result of ref. 8. The experimental frequency of 136 cm-’ for the torsional mode of gauche-butadiene-1,3, which is given in the above paper, was obtained from the erroneous analysis of the “hot” band series of the torsional overtone 2u 13 of truns-C4H6 (L. A. Carreira, J. Chem. Phys., 62 (1975) 3851 and criticism in refs. 1 and 2). REFERENCES 1 Ch. W. Bock, P. George, M. Trachtman and M. Zanger, J. Chem. Sot., Perkin Trans. 2, (1979) 26. 2 Yu. N. Panchenko, A. V. Abramenkov, V. I. MochaIov, A. A. Zenkin, G. Keresztury and G. Jalsovszky, J. Mol. Spectrosc., 99 (1983) 288. 3 S. Skaarup, J. E. Boggs and P. N. Skancke, Tetrahedron, 32 (1976) 1179. 4 K. S. Pitzer, J. Chem. Phys., 14 (1946) 239. 5 G. De Mare, J. Mol. Struct. (Theochem), 107 (1984) 127. 6 Ch. W. Bock, P. George and M. Trachtman, J. Mol. Struct. (Theochem), 109 (1984) 1. 7 G. De Mare and D. Neisius, J. Mol. Struct. (Theochem), 109 (1984) 103. 8 Ch. W. Bock, P. George and M. Trachtman, Theor. Chim. Acta, 64 (1984) 293. 9 Ch. W. Bock, Yu. N. Panchenko, S. V. Krasnoshchiokov and V. I. Pupyshev, J. Mol. Struct., 129 (1985) 57. 10 J. D. Lewis, T. B. Malloy, Jr., T. H. Chao and J. Laane, J. Mol. Struct., 12 (1972) 427. 11 Yu. N. Panchenko, V. I. Pupyshev, A. V. Abramenkov, M. Traetteberg and S. J. Cyvin, J. Mol. Struct., 130 (1985) 355.