6 research outputs found
Understanding highly excited states via parametric variations
Highly excited vibrational states of an isolated molecule encode the
vibrational energy flow pathways in the molecule. Recent studies have had
spectacular success in understanding the nature of the excited states mainly
due to the extensive studies of the classical phase space structures and their
bifurcations. Such detailed classical-quantum correspondence studies are
presently limited to two or quasi two dimensional systems. One of the main
reasons for such a constraint has to do with the problem of visualization of
relevant objects like surface of sections and Wigner or Husimi distributions
associated with an eigenstate. This neccesiates various alternative techniques
which are more algebraic than geometric in nature. In this work we introduce
one such method based on parametric variation of the eigenvalues of a
Hamiltonian. It is shown that the level velocities are correlated with the
phase space nature of the corresponding eigenstates. A semiclassical expression
for the level velocities of a single resonance Hamiltonian is derived which
provides theoretical support for the correlation. We use the level velocities
to dynamically assign the highly excited states of a model spectroscopic
Hamiltonian in the mixed phase space regime. The effect of bifurcations on the
level velocities is briefly discussed using a recently proposed spectroscopic
Hamiltonian for the HCP molecule.Comment: 12 pages, 9 figures, submitted to J. Chem. Phy
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Chemical reaction rates using the semiclassical Van-Vleck initialvalue representation
A semiclassical IVR formulation using the Van-Vleck propagator has been used to calculate the flux correlation function and thereby reaction rate constants. This Van-Vleck formulation of the flux-flux correlation function is computationally as simple as the classical Wigner model. However unlike the latter, it has the ability to capture quantum interference/coherence effects. Classical trajectories are evolved starting from the dividing surface that separates reactants and products, and are evolved negatively in time. This formulation has been tested on model problems ranging from the Eckart barrier, double well to the collinear H + H{sub 2}
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Chemical reaction rates using the semiclassical Van-Vleck initial value representation
Recommended from our members