Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets

TL;DR

This paper introduces a physics-based algorithm for generating primitive Gaussian density fitting basis sets that are accurate, robust, and applicable across the periodic table, improving electronic structure calculations.

Contribution

The MADF algorithm constructs density fitting basis sets from a contracted basis, using physical principles to minimize parameters and optimize accuracy across various elements and computational methods.

Findings

Achieved microhartree-level accuracy in energy calculations.

Applicable to a wide range of elements and basis set qualities.

Reduced the number of parameters needed for accurate density fitting.

Abstract

We present model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structure. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents followed by (b) pruning of the shells according to their contributions to the 2-body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-zeta quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree-Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 microhartree per electron, respectively.