On-the-fly computation of frontal orbitals in density matrix expansions

TL;DR

This paper introduces a method for efficiently computing frontier molecular orbitals (HOMO and LUMO) during density matrix expansions by using recent eigenvalue estimates to optimize spectral shifts, significantly reducing computational time.

Contribution

It presents a novel approach that combines recent eigenvalue estimates with spectral transformation techniques to compute frontier orbitals efficiently during recursive density matrix expansions.

Findings

HOMO and LUMO orbitals can be computed in a small fraction of total recursive expansion time.

The method improves eigenpair accuracy and solver performance.

Demonstrated effectiveness on large-scale systems.

Abstract

Linear scaling density matrix methods typically do not provide individual eigenvectors and eigenvalues of the Fock/Kohn-Sham matrix, so additional work has to be performed if they are needed. Spectral transformation techniques facilitate computation of frontal (homo and lumo) molecular orbitals. In the purify-shift-and-square method the convergence of iterative eigenvalue solvers is improved by combining recursive density matrix expansion with the folded spectrum method [J. Chem. Phys. 128, 176101 (2008)]. However, the location of the shift in the folded spectrum method and the iteration of the recursive expansion selected for eigenpair computation may have a significant influence on the iterative eigenvalue solver performance and eigenvector accuracy. In this work, we make use of recent homo and lumo eigenvalue estimates [SIAM J. Sci. Comput. 36, B147 (2014)] for selecting shift and iteration such that homo and lumo orbitals can be computed in a small fraction of the total recursive expansion time and with sufficient accuracy. We illustrate our method by performing self-consistent field calculations for large scale systems.