Rapid Assembly of the Coulomb Matrix in Hartree-Fock Theory

Matt Challacombe
Department of Chemistry
University of Minnesota

New methods were presented for accelerating the assembly of the Coulomb matrix in Hartree-Fock theory. These methods are based on the iterative, local expansion of the electron density and its constituent distributions in atom-centered, Hermite Gaussian-type basis functions.

Two different measures that relate approximate and exact densities were considered. One is associated with the Coulomb operator, which has traditionally been used in this context, while the other involves the distance operator and results in a potential-matched approximate density. Both measures have been used to study the dependence on the size of the auxiliary basis of the error in the total energy due to approximating the Coulomb matrix in different molecular systems. These studies demonstrate that total energies accurate to better than 0.1 millihartree are readily attainable with local expansion method.