Steering Orbital Optimization out of Local Minima and Saddle Points Toward Lower Energy

TL;DR

This paper presents a fast, automated method to detect and correct incorrect orbital convergence in electronic structure calculations, helping to find lower-energy solutions and improve accuracy in high-throughput computational chemistry.

Contribution

The authors introduce a randomized perturbation technique to escape local minima and saddle points, ensuring convergence to the true lowest-energy solution in orbital optimization.

Findings

Effective detection of incorrect convergence in orbital calculations.

Ability to find lower-energy solutions by perturbing electron density.

Improved reliability in automated electronic structure computations.

Abstract

The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored that multiple self-consistent solutions can exist, several of which may correspond to minima of the energy functional. In addition to the difficulty sometimes encountered to converge the calculation to a self-consistent solution, one must ensure that the correct self-consistent solution was found, typically the one with the lowest electronic energy. Convergence to an unwanted solution is in general not trivial to detect and will deliver incorrect energy and molecular properties, and accordingly a misleading description of chemical reactivity. Wrong conclusions based on incorrect self-consistent field convergence are particularly cumbersome in automated calculations met in high-throughput virtual screening, structure optimizations, ab initio molecular dynamics, and in real-time explorations of chemical reactivity, where the vast amount of data can hardly be manually inspected. Here, we introduce a fast and automated approach to detect and cure incorrect orbital convergence, which is especially suited for electronic structure calculations on sequences of molecular structures. Our approach consists of a randomized perturbation of the converged electron density (matrix) intended to push orbital convergence to solutions that correspond to another stationary point (of potentially lower electronic energy) in the variational parameter space of an electronic wave function approximation.