Tunneling splittings in vibrational spectra of non-rigid molecules: VII. Globally uniform semiclassical wave functions within the instanton approach

Abstract

The perturbative instanton approach developed in the previous papers of this series (V.A. Benderskii et al., Chem. Phys. 219 (1977) 119, 143; 234 (1998) 153, 173; 244 (1999) 273, 299) is shown to reproduce tunneling splittings in low-lying excited states of multiwell 1D potentials with the same accuracy as second-order perturbation theory for anharmonic oscillators. Instanton wave functions of highly excited states in these potentials are derived using the asymptotically smooth matching of semiclassical wave functions with solutions of the Schrödinger equation for the regions near the external and internal turning points. Multidimensional, globally uniform, semiclassical wave functions of both high and low energy states are expanded over a basis set including the above 1D functions and localized functions of small-amplitude motions coupled with the tunneling coordinate. The numerical procedure for the solution of multidimensional, deep tunneling problems is discussed.