Construction and uses of full-dimensional potential energy surfaces for small molecules

Bastiaan J. Braams (Nuclear Data Section, Division of Physical and Chemical Sciences, International Atomic Energy Agency, Vienna, Austria)
csü., 2010-04-15 15:30
062-as terem

Analytical fitted potential energy surfaces are a valuable tool for study of reaction dynamics and molecular spectroscopy. In full generality the surface depends on 3N-6 independent coordinates, where N is the number of nuclei, and the construction of such surfaces is a problem of high-dimensional approximation already for small systems, say of 5-9 atoms. In work with the Bowman group at Emory University we have used computational invariant theory and the MAGMA computer algebra system as an aid to develop representations for the potential energy and dipole moment surfaces that are fully invariant under
permutations of like nuclei. We express the potential energy in terms of internuclear distances using basis functions that are manifestly invariant, with coefficients fitted to the results of ab initio calculations. The resulting full-dimensional surface is then used for quasiclassical trajectory calculations, for diffusion Monte Carlo or path integral calculations, or for quantum mechanical calculations of a rovibrational spectrum. In the talk I will describe the mathematical background and highlights of applications.