Title: Steering Orbital Optimization out of Local Minima and Saddle Points Toward Lower Energy,
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.