Sampling of semiclassically quantized polyatomic molecule vibrations by an adiabatic switching method: Application to quasiclassical trajectory calculations

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Abstract
We apply the adiabatic switching (AS) method to determine the polyatomic classical motions that correspond to selected vibrational quantum states on multidimensional, anharmonic potential energy surfaces, and use these semiclassically quantized motions as initial conditions for quasiclassical trajectory (QCT) calculations of state-to-state reaction dynamics. Specifically, we calculate the classical motion corresponding to the quantum mechanical zero-point vibration of deuterated methane, CD4, and run QCT calculations on the H+CD4→HD(v′,j′)+CD3 reaction. The distribution of CD4 vibrational zero-point energy (ZPE) associated with the AS-sampled motions is compared with that from normal-mode-sampled motions. The spread of total zero-point energy in the AS calculations is much narrower than with normal-mode sampling, and the ZPE’s are appropriately shifted to lower energy due to anharmonic effects. Reverse adiabatic switching is used as an indirect check of the quantum numbers of the adiabatically sampled motion, but numerical limitations made this test inconclusive. The AS method thus appears to be superior to normal-mode sampling, but this superiority cannot be demonstrated conclusively for the fully anharmonic CD4 potential. However, the AS method is shown to perform very well for transformation from one CD4 harmonic potential to another and for transformation from an harmonic to an anharmonic, but decoupled potential in which CD4 is described by Morse oscillators. Evidence is presented that suggests the AS calculations are limited by numerical inaccuracies or intrinsic features of the potential energy surface, both of which are unavoidable. H+CD4→HD(v′,j′)+CD3 QCT calculations of state-to-state dynamics using CD4 with no ZPE, the ZPE from AS sampling, and the ZPE from normal-mode sampling are reported and compared.