On the Impact of Singularities in the Two-State Adiabatic to Diabatic State Transformation: A Global Treatment

Diabatizations based on molecular properties can remove the singularity in the derivative coupling at a conical intersection in the diabatic representation. Yet, they can also create new singularities in the derivative couplings because of the defining equations of the adiabatic to diabatic state transformation. In the iconic two-state case, these singularities occur at points termed diabolical singular points and form a seam of dimension N-int-2, where N-int is the number of internal degrees of freedom. This seam is of the same dimension as the conical intersection seam, but is distinct. Here, the global topography of the diabolical singularity seam of 1,2(1)A states of ammonia is reported using a Boys localization (BL) dipole-based diabatization and juxtaposed with a previously reported global representation of the coupled electronic state potential energy surfaces. The principal finding is that the seam of BL diabatization-induced singularities passes very close to the key saddle point on the 2(1)A potential energy surface which connects the 2(1)A equilibrium structure with the NH2 ((X) over tilde,(A) over tilde) + H channel. The construction and detailed study of the reported diabolical singularity seam is made possible by a recently constructed analytic representation of the dipole and transition dipole moment surfaces.