On the Construction of Diabatic Bases Using Molecular Properties. Rigorous Results in the Vicinity of a Conical Intersection

Abstract

Smoothness of a molecular propertyachieved by diagonalization of the matrix of the corresponding property operatoris a convenient and frequently used criterion for the construction of an adiabatic to diabatic state transformation. The choice of molecular property has been a matter of considerable discussion. When conical intersections are present, the performance of this approach near that intersection is key since the derivative coupling in the adiabatic basis is singular there. Thus it is desirable to know, a priori, whether use of a particular property will remove the singularity. Here it is shown that diagonalizing the matrix of any symmetric (real-valued hermitian) electronic property operator, satisfying only certain limited restrictions, generates a transformation that removes all of the singularity of the derivative coupling at the conical intersection. The result is illustrated by considering the dipole moment operator near a point on the 11A‘−21A‘ seam of conical intersection in HeH2.