International Research Experience for Undergraduates

Andrew Taube

2002 Participant

Taube

Derivation and Implementation of a Novel Semi-empirical Hamiltonian for Large Systems

This summer I have been working in the area of compuational chemistry under the direction of Dr. Rodney Bartlett. The focus of Dr. Bartlett's research is on coupled cluster methods for use in highly accurate electronic structure calculations. Unfortunately, these methods become too computationally expensive for systems larger than 10-15 atoms. To overcome this limitation, Dr. Bartlett has introduced the "transfer Hamiltonian" a similarity-transformed Hamiltonian that will return the same eigenvalues as a "normal" Hamiltonian. By use of intelligently chosen simplifications and parameterizations to the transfer Hamiltonian, a simplified version may be determined, which could allow for the fast calculation of coupled cluster level accurate electronic structures for systems that are much too larger for true coupled cluster calculations.

My work has been focused on all aspects of this project. My two main goals of this summer have been to: 1) develop consistency and limiting conditions for the transfer Hamiltonian and 2) develop a very fast self-consistent field program for the implementation of that Hamiltonian. By working with fundamental commutator relations, asymptotic conditions and boundary conditions, along with a very generalized form of the transfer Hamiltonian, I have been able to determine certain facts about the matrix elements of this Hamiltonian that should allow ready identification of possible specific functional forms. At the same time, I have written several thousand lines of FORTRAN 90 code (which I learned this summer) to build a standalone program that can be used to both implement the transfer Hamiltonian formalism and evaluate it when compared to traditional semi-empirical theory.