Two approaches to fitting the potential energy surface
Bastiaan
Braams
Deptartment of Mathematics, Courant Institute of Mathematical Sciences
Wednesday, June 18, 2003 15:0016:00, Admin. Bldg. Lecture Room F Gaithersburg Wednesday, June 18, 2003 13:0014:00, Room 5000 Boulder
Abstract:
We discuss two distinct approaches to high dimensional interpolation
with application to fitting the potential energy surface of small
molecules. The first approach is reduced Hermite interpolation, which
requires, in the cubic case, function values and gradients on the
vertices of a box. This was implemented in a very efficient suite of
routines for use with the MULTIMODE code of Bowman and Carter for the
nuclear Schroedinger equation. The second approach is global fiting
using polynomials in terms of the inverse internuclear distances 
generally a redundant set of coordinates. This is currently being
used for molecular dynamics modelling of the CH5(+) molecule. We
discuss especially the nontrivial construction of a polynomial basis
that respects the symmetry of the potential energy surface under
permutations of like nuclei.
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