Diabatic and adiabatic representations: Electronic structure caveats

In this Viewpoint issues in the construction and use of adiabatic and diabatic representations in describing spin-conserving electronically nonadiabatic processes using the Born-Huang ansatz are reviewed and illustrated. We address issues which limit the accuracy of commonly used approximate equations of motion. The following caveats are discussed. (i) The use of adiabatic states for N-state > 2 is complicated by the fact that if states (I, J) and (J, K) have conical intersections then the derivative coupling f((a),I,J )(R) may well be double-valued, rendering it inappropriate for nuclear dynamics. (ii) In the nonadiabatic tunneling regime, nuclear motion can be restricted to a single adiabatic potential energy surface on the basis of total energy. However, energetically inaccessible conical intersections make it necessary to take into account the geometric phase and the induced vector potential when formulating the nuclear Schrodinger equation. We review how a diabatization approach which takes explicit account of the derivative couplings can be used to accurately include these factors. (iii) Finally, we review how a commonly used class of two-state diabatizations based on smooth molecular properties can be subject to ruinous singularities inherent in equations defining the diabatization.