The vibrations and tunnelling of malonaldehyde on a Møller–Plesset surface

Abstract

The vibrations and tunnelling motion of malonaldehyde have been studied in their full dimensionality using an internal coordinate path Hamiltonian. In this representation there is one large amplitude internal coordinate s and 3N − 7 (=20) normal coordinates Q which are orthogonal to the large amplitude motion at all points. It is crucial that a high accuracy potential energy surface is used in order to obtain a good representation for the tunneling motion; we use a Møller–Plesset (MP2) surface. Our methodology is variational, that is we diagonalize a sufficiently large matrix in order to obtain the required vibrational levels, so an exact representation for the kinetic energy operator is used. In a harmonic valley representation ( s, Q ) complete convergence of the normal coordinate motions and the internal coordinate motions has been obtained; for the anharmonic valley in which we use two- and three-body terms in the surface (s, Q ₁, Q ₂), we also obtain complete convergence. Our final computed stretching fundamentals are deficient because our potential energy surface is truncated at quartic terms in the normal coordinates, but our lower fundamentals are good.