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Quantum Dynamical Behaviour in Complex Systems - A Semiclassical Approach

Description: One of the biggest challenges in Chemical Dynamics is describing the behavior of complex systems accurately. Classical MD simulations have evolved to a point where calculations involving thousands of atoms are routinely carried out. Capturing coherence, tunneling and other such quantum effects for these systems, however, has proven considerably harder. Semiclassical methods such as the Initial Value Representation (SC-IVR) provide a practical way to include quantum effects while still utilizing only classical trajectory information. For smaller systems, this method has been proven to be most effective, encouraging the hope that it can be extended to deal with a large number of degrees of freedom. Several variations upon the original idea of the SCIVR have been developed to help make these larger calculations more tractable; these range from the simplest, classical limit form, the Linearized IVR (LSC-IVR) to the quantum limit form, the Exact Forward-Backward version (EFB-IVR). In this thesis a method to tune between these limits is described which allows us to choose exactly which degrees of freedom we wish to treat in a more quantum mechanical fashion and to what extent. This formulation is called the Tuning IVR (TIVR). We further describe methodology being developed to evaluate the prefactor term that appears in the IVR formalism. The regular prefactor is composed of the Monodromy matrices (jacobians of the transformation from initial to finial coordinates and momenta) which are time evolved using the Hessian. Standard MD simulations require the potential surfaces and their gradients, but very rarely is there any information on the second derivative. We would like to be able to carry out the SC-IVR calculation without this information too. With this in mind a finite difference scheme to obtain the Hessian on-the-fly is proposed. Wealso apply the IVR formalism to a few problems of current interest. A method ...
Date: May 22, 2008
Creator: Gliebe, Cheryn E & Ananth, Nandini
Partner: UNT Libraries Government Documents Department