Molecular electronic structure theory, algorithms for parallel computers, dynamics of floppy molecules.
I am interested in the development of computational methods in theoretical chemistry. Although topics in the field of ab initio quantum chemistry continue to be the emphasis of this research, aspects of molecular quantum dynamics are also of current interest.
The potential energy surface (PES) plays a central role in molecular theory. A chemical reaction is viewed as proceeding along the reaction pathway on the ground state or excited state PES, and an electronic transition as a jump from one PES to another. The PES is a mathematical function of 3N-6 independent variables corresponding to the number of degrees of freedom of a collection of N atoms. In principle this function can be computed point by point by solving the Schroedinger equation in the Born Oppenheimer approximation. In practice, one uses any of the many available computer programs such as GAUSSIAN, HONDO, GAMESS, GRADSCF, COLUMBUS, ACES or MOLPRO. The usefulness of these ab initio computer programs has been greatly increased in recent years by advances in several different directions such as the ability to analytically evaluate energy derivatives for all of the major quantum chemical methodologies (SCF, MCSCF, CI, etc.), improved methods for treating solvent effects, recent advances in density functional theory, and novel approaches to the evaluation of electrostatic potentials and electron-electron repulsion integrals. Theoretical chemists at Buffalo have contributed to these advances far out of proportion to their relatively small number. HONDO and GRADSCF and the initial version of GAMESS were all written by previous Buffalo graduate students who have contributed significantly to the computational advances mentioned above and to other topics such as the theory of spin-orbit interaction and the use of parallel computers.
The two central challenges in computational quantum chemistry are to extend molecular electronic structure computations to bigger molecular systems and to greater accuracy. There is far more progress today in the first direction than in the second. Although there is no fundamental limit to the accuracy that can be achieved using traditional, orbital-based methods such as configuration interaction (CI), there is certainly a practical limit. Calculations with very big orbital and many-body basis sets can barely achieve an accuracy of one kcal/mol. A further improvement in accuracy by one or two orders of magnitude is required for countless chemical applications such as for the calculation of elementary rate constants from first principles. Highly accurate calculations would find immediate application to theoretical models of combustion or atmospheric chemistry. A major direction of research in my group is the search for a new approach to this classic problem in theoretical chemistry. We are testing a perturbation theoretic method in which the zeroth-order problem is solved using traditional orbital-based methods with a many-body Hamiltonian which has been modified to eliminate the so-called correlation cusp problem. The higher-order perturbation equations are then solved using geminal basis functions which depend explicitly on interelectron coordinates.
Implementation of the new methodology on parallel supercomputers has recently been initiated in collaboration with computational scientists at the Center for Computational Research (CCR).