THE GEOMETRIC VECTOR POTENTIAL IN MOLECULAR-SYSTEMS WITH ARBITRARILY MANY IDENTICAL NUCLEI

It is known that Born-Oppenheimer electronic wave functions (in systems in which electronic spin plays no role) can acquire a double-valuedness as functions of nuclear coordinates unless the real wave function is multiplied by a phase factor that cancels the sign change that occurs when the nuclear coordinates traverse a closed path enclosing an intersection between two electronic energy levels. We show how such phase factors can be obtained in principle for systems of arbitrary complexity by making use of the cofactors of the adjusted Hamiltonian matrix H-Ej, where Ej is an eigenvalue. The method makes no direct reference to the location of the intersection, and therefore can be used when one is interested in paths that go around the intersection without approaching it closely, bypassing the necessity of costly electronic calculations near the intersection. With appropriate choice of basis functions, the phase factor will cause the electronic wave function to be not only single-valued but invariant under permutations of identical nuclei. Some simple examples are discussed. © 1995 American Institute of Physics.