TUNNELING SPLITTING IN VIBRATIONAL-SPECTRA OF NONRIGID MOLECULES .1. PERTURBATIVE INSTANTON APPROACH

A perturbative approach to calculating tunneling splittings in multidi mensional potential energy surfaces (PES) is developed. In two-dimensi onal (2D) model PES, represented by a quartic X-4 potential and a harm onic oscillator Y with frequency omega, both coupled by linear (CXY) o r gated ((CXY)-Y-2) terms, the extreme tunneling trajectories (ETT) of zero energy are determined by solving the classical equations of moti on in the inverted potential, - V(X, Y), in the form of a rapidly conv erging Taylor series of C/omega < 1. The series for X(t) and Y(t) cont ain only even or odd powers of C/omega, respectively. The semiclassica l action on the ETT expands into a series of (C/omega)(2). When C/omeg a < 0.5, second order action reproduces the exact value with an accura cy of better than 5%. On multidimensional PES with one saddle point, t he contributions to the action of mutually uncoupled transverse vibrat ions are additive, which enables us to introduce their spectral densit y, characterizing the tunneling dynamics. The semiclassical wave funct ion of the ground state is found within the approximation of small flu ctuation about the ETT, From this wave function, tunneling splittings are calculated, using the Lifshitz-Herring formula. The values obtaine d are in satisfactory agreement with the results of numerical diagonal ization of the Hamiltonian matrix. Hydrogen transfers in malonaldehyde and in formic acid dimers are treated as examples for the application of this approach. (C) 1997 Elsevier Science B.V.