Non-linear eigensolver-based alternative to traditional SCF methods

TL;DR

This paper introduces a non-linear eigensolver based on an extension of the FEAST algorithm, offering a more efficient and robust alternative to traditional self-consistent field methods in electronic structure calculations.

Contribution

It presents a novel non-linear eigensolver derived from FEAST, improving convergence speed and robustness over traditional SCF methods in DFT calculations.

Findings

Faster convergence compared to traditional SCF methods

Converges regardless of initial guess

Reduces eigenvalue solve time significantly

Abstract

The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm to account for the non-linearity of the Hamiltonian with the occupied eigenvectors. Using a series of numerical examples and the DFT-Kohn/Sham model, it will be shown that our approach can outperform the traditional SCF mixing-scheme techniques by providing a higher converge rate, convergence to the correct solution regardless of the choice of the initial guess, and a significant reduction of the eigenvalue solve time in simulations.