Semiclassical Gaussian basis set method for molecular vibrational wave functions

We present theory and numerical results for a new method for obtaining eigenfunctions and eigenvalues of molecular vibrational wave functions. The method combines aspects of the semiclassical nature of vibrational motion and variational, ab initio techniques. Localized complex Gaussian wave functions, whose parameters are chosen according to classical phase space criteria are employed in standard numerical basis set diagonalization routines. The Gaussians are extremely convenient as regards construction of Hamiltonian matrix elements, computation of derived properties such as Franck–Condon factors, and interpretation of results in terms of classical motion. The basis set is not tied to any zeroth order Hamiltonian and is readily adaptable to arbitrary smooth potentials of any dimension.