Economical Models for Electron Densities.

We discuss a new theoretical framework for modeling molecular electron densities. Our approach decomposes the total density into contributions from basis function products and then approximates each product using constrained least-squares approximation in a tailored local basis of functions with adjustable non-linear parameters. We show how to solve directly for the expansion coefficients and Lagrange multipliers and present an iterative method to optimize the non-linear parameters. Example products from the Dunning cc-pVTZ basis set are discussed.

Avoiding Negligible Shell Pairs and Quartets in Electronic Structure Calculations.

We define a significant shell pair in an electronic structure calculation as one that generates at least one two-electron integral larger than a preset threshold. We define a significant shell quartet similarly. We then explore several methods for identifying nonsignificant pairs and quartets so that they can be avoided and computational efficiency improved. We find that the widely used Cauchy-Schwarz bound identifies most nonsignificant quartets but that the Hölder bound is slightly more powerful for identifying nonsignificant pairs.