On the Construction of Property Based Diabatizations: Diabolical Singular Points

Diabatizations achieved by diagonalization of a property operator or as the extremum of a molecular property are numerous and widely used, although for a particular system a given property method may have limited accuracy or even fail catastrophically. These failures are usually analyzed in terms of limitations of the chosen property or method. Here we introduce an alternative perspective, failure attributable to singularities in the defining equations. The singular subspace is analogous to the conical intersection seam in potential energy surfaces. Using the archetypical NH3 nonadiabatic photo-dissociation, it is shown that for two states the diabatization condition has singularities on a subspace of dimension N - 2, where N = 3N(atom) - 6, is the number of internal coordinates. This singular subspace is distinct from the N - 2-dimensional seam of conical intersections of the electronic Hamiltonian and results incorrectly, in singular derivative couplings between diabatic states in unexpected regions of nuclear coordinate space. Simple indicators are developed that provide ways to anticipate and avoid these singularities.