Quantum Dynamical Behaviour in Complex Systems - A Semiclassical Approach Page: 4 of 165
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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
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.
We also apply the IVR formalism to a few problems of current interest. A
method to obtain energy eigenvalues accurately for complex systems is described.
We proposed the use of a semiclassical correction term to a preliminary quantum
calculation using, for instance, a variational approach. This allows us to increase
the accuracy significantly.
Modeling Nonadiabatic dynamics has always been a challenge to classical sim-
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Gliebe, Cheryn E & Ananth, Nandini. Quantum Dynamical Behaviour in Complex Systems - A Semiclassical Approach, thesis or dissertation, May 22, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc897026/m1/4/: accessed December 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.