Wigner Distribution by Adiabatic Switching in Normal Mode or Cartesian Coordinates and Molecular Applications

We recently presented a simple, classical trajectory-based method for generating the Wigner phase space density using classical trajectories evolving under an adiabatically switched potential. The adiabatically switched Wigner (ASW) distribution is an approximation to the exact Wigner function, which was found to be highly accurate on model systems. In this paper we discuss the implementation of the ASW procedure to polyatomic molecules both in normal mode coordinates and in Cartesian coordinates. We present its application to a six-degree-of-freedom model based on an ab initio quartic potential energy surface developed for formaldehyde in the normal mode representation and for butyne in Cartesian coordinates using the CHARMM force field. Comparisons of equilibrium properties against accurate quantum mechanical results indicate that the ASW is reliable and highly accurate over a wide temperature range in both the coordinate systems. Further, the ASW density is invariant under classical evolution, thus it is ideally suited to quasiclassical trajectory simulations. We also describe a very simple ASW-based procedure for obtaining complex-valued quasiclassical time correlation functions and vibrational spectra.