Singularities in the Hamiltonian at electronic degeneracies

We discuss the singularities which arise in the Hamiltonian operator at a c rossing seam involving two potential energy surfaces of the same global sym metry. The Mead-Truhlar and our own equations are discussed and found to di ffer from each other, although leading to identical phases up to a constant factor and sign in the vicinity of the crossing seam. Also established are the relations which link the vector and scalar gauge potentials with the m ixing angle. (C) 2000 Elsevier Science B.V. All rights reserved.