 
Summary: Locating Multiple SelfConsistent Field Solutions: An Approach Inspired by Metadynamics
Alex J. W. Thom*
Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
Martin HeadGordon
Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
(Received 28 July 2008; published 5 November 2008)
We propose a method to locate the solutions to the selfconsistent 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 HartreeFock (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.
DOI: 10.1103/PhysRevLett.101.193001 PACS numbers: 31.10.+z, 31.15.xr
Within electronic structure theory, the solution of the
selfconsistent field (SCF) equations is a crucial matter,
both in density functional theory (DFT) and in Hartree
Fock (HF) Theory. The SCF equations are nonlinear in the
