Applied and Computational Mathematics Division, NIST
Tuesday, February 23, 2021, 3:00 PM EST (1:00 PM MST)
A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.
Abstract: Quantum chemists use Gaussian basis sets to expand molecular orbitals for a very good reason; all the one-and-two electron integrals can be done "analytically". However, for more general expansion sets, such as those required to represent the oscillatory basis functions required to describe the molecular continuum, these functions are inadequate. The continuum requires basis sets based on B-splines and/or finite element functions. This necessitates 3D numerical integration and the nature of the electronic density in a polyatomic molecule immediately suggests that any approach based on using a single coordinate system, is likely to be either impractical or fail completely. In this talk, I will present some background material to explain why Gaussian functions are the unique choice for standard bound state quantum chemistry calculations and then turn to our development of the 3D numerical integration approach, based on the decomposition of unity, how and why we choose the atomic weight functions as we do and show some numerical examples.