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

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.