Tunneling splitting in vibrational spectra of non-rigid molecules. I. Perturbative instanton approach Original Research Article

A perturbative approach to calculating tunneling splittings in multidimensional potential energy surfaces (PES) is developed. In two-dimensional (2D) model PES, represented by a quartic X4 potential and a harmonic oscillator Y with frequency ω, both coupled by linear (CXY) or gated (CX2Y) terms, the extreme tunneling trajectories (ETT) of zero energy are determined by solving the classical equations of motion in the inverted potentia, −V(X, Y), in the form of rapidly converging Taylor series of C/ω < 1. The series for X(t) and Y(t) contain only even or odd powers of C/ω, respectively. The semiclassical action on the ETT expands into a series of (C/ω2). When C/ω < 0.5), second order action reproduces the exact value with an accuracy of better than 5%.