Locating Multiple Self-Consistent Field Solutions: An Approach Inspired by Metadynamics

We propose a method to locate the solutions to the self-consistent field (SCF) equations, using an approach based upon metadynamics. We define a distance function between density matrices. Within an SCF calculation, when a solution is found, a biasing potential based on distance from the solution is added to the energy to avoid reconvergence to the same solution. Multiple solutions can therefore be relatively easily found. Using this method we locate all known solutions and one unknown solution of the H4 model. The set of restricted Hartree-Fock (RHF) solutions for the nitrogen molecule is located, and a broken-symmetry solution lower in energy than the symmetric RHF solution is found corresponding to dissociation into doublet fragments.