Second-order self-consistent field algorithms: from classical to quantum nuclei

TL;DR

This paper introduces a geometric framework for second-order SCF algorithms, extending the ARH method to electronic and nuclear-electronic systems, improving convergence in challenging cases.

Contribution

It develops a unified geometric approach for exact and approximate Newton SCF algorithms and extends ARH to new types of calculations, enhancing convergence stability.

Findings

ARH improves convergence stability in difficult SCF problems.

ARH overcomes slow orbital convergence in strongly-correlated molecules.

ARH significantly enhances convergence in nuclear-electronic calculations.

Abstract

This work presents a general framework for deriving exact and approximate Newton self-consistent field (SCF) orbital optimization algorithms by leveraging concepts borrowed from differential geometry. Within this framework, we extend the augmented Roothaan--Hall (ARH) algorithm to unrestricted electronic and nuclear-electronic calculations. We demonstrate that ARH yields an excellent compromise between stability and computational cost for SCF problems that are hard to converge with conventional first-order optimization strategies. In the electronic case, we show that ARH overcomes the slow convergence of orbitals in strongly-correlated molecules with the example of several iron-sulfur clusters. For nuclear-electronic calculations, ARH significantly enhances the convergence already for small molecules, as demonstrated for a series of protonated water clusters.