Ab initio determination of the roto-torsional energy levels of trans-1,3-butadiene

In this paper, the flexible model based on relaxed ab initio calculations, which has been several times employed for vibrational calculations, is extended to the analysis of the rotational structures starting by the roto-torsional bands of trans-1,3-butadiene. For this purpose, the potential energy surface and the kinetic energy parameters of the nu(13) vibrational mode of butadiene are obtained with the Moller-Plesset perturbation theory up to the second order and the 6-31G(d, p), 6-31G(df, p), 6-311G(d, p), 6-311G(df, p), and 6-311G(df, ps) basis sets. The torsional levels of the -h(6), -d(4), and -d(6) isotopic species are calculated variationally and are compared with experimental data. It may be concluded that the one-dimensional model appears sufficiently accurate for butadiene-h(6) and -d(4), whereas a large kinetic interaction with the lowest wagging mode is observed for butadiene-d(6). The rotational levels corresponding to the first vibrational states of the -h(6) and -d(4) species are determined variationally up to J = 17 and J = 11 from the ab initio spectroscopic parameters which have been expanded as functions of the torsional coordinate using symmetry adapted series. The torsional wavefunction is contracted to reduce the size of the Hamiltonian matrix. A good agreement with the observed transitions is obtained for the first states nu = 0 and nu = 1. As is expected, the K doubling obtained is relatively small. For this reason, the quartic and sextic centrifugal distortion constants are obtained from the least-square fit of the variational levels to the perturbation theory equations for the symmetric top. (C) 1998 Academic Press.