  The study of tunneling splitting is fundamental to get insight into the
dynamics of a multitude of molecular systems. In this paper, a novel approach
to the analysis of the ground-state tunneling splitting is presented and
explicitly applied to one-dimensional systems. The isomorphism between the
Fokker-Planck-Smoluchowski operator and the Born-Oppenheimer quantum
Hamiltonian is the key element of this method. The localization function
approach, used in the field of stochastic processes to study the Kramers
problem, leads to a simple, yet asymptotically justified, integral
approximation for the tunneling splitting. The comparison with exact values of
the tunneling splittings shows a much better accuracy than WKB semiclassical
estimates.
