Direct determination of optimal real-space orbitals for correlated electronic structure of molecules

TL;DR

This paper presents a numerical method to determine nearly exact real-space orbitals for correlated electronic states of molecules, achieving high accuracy and overcoming limitations of traditional Gaussian basis sets.

Contribution

It introduces an adaptive multiresolution spectral element basis for orbital optimization, providing a more accurate and stable alternative to Gaussian AO bases in correlated electronic structure calculations.

Findings

Achieves energies comparable to state-of-the-art CI solvers.

Provides significantly more accurate energies than Gaussian AO bases.

Enables optimization of over 100 orbitals on a single computer node.

Abstract

We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are expressed in real space using a multiresolution spectral element basis that is refined adaptively to achieve the user-specified target precision while avoiding the ill-conditioning issues that plague AO basis set expansions traditionally used for correlated models of molecular electronic structure. For light atoms, the orbital solver, in conjunction with a variational electronic structure model [selected Configuration Interaction(CI)] provides energies of comparable precision to a state-of-the-art atomic CI solver. The computed electronic energies of atoms and molecules are significantly more accurate than the counterparts obtained with the Gaussian AO bases of the same rank, and can be determined even when linear dependence issues preclude the use of the AO bases. It is feasible to optimize more than 100 fully-correlated numerical orbitals on a single computer node, and significant room exists for additional improvement. These findings suggest that the real-space orbital representations might be the preferred alternative to AO representations for high-end models of correlated electronic states of molecules and materials.