Practical implementation of the instanton theory for the ground-state tunneling splitting

The instanton theory is reformulated with use of the path integral approach and the Wentzel-Kramers-Brillouin approximation to the Schrodinger equation. Both approaches are shown to provide the same results. A new practically useful semiclassical formula is derived for the tunneling splitting of the ground state, which can be implemented for high-dimensional systems. The theory is applicable to systems of arbitrary Riemannian metric and is also supplemented by a practical numerical recipe to evaluate the instanton trajectory, i.e., periodic orbit, in multidimensional space. Numerical examples are presented for three-dimensional (3D) and 21D systems of HO2 and malonaldehyde, respectively. (C) 2001 American Institute of Physics.