Conical intersections: Diabolical and often misunderstood

This account discusses recent advances in our understanding of conical intersections. Of particular interest is the role of same-symmetry conical intersections, a class of conical intersections of emerging importance. The existence of same-symmetry conical intersections was once a matter of considerable debate. However, as a result of algorithms that locate conical intersections without prior determination of the potential energy surfaces in question, the existence and importance of this class of conical intersections is now firmly established. Here a new role for this class of conical intersections is emphasized. It is observed that symmetry-allowed conical intersections, intersections readily anticipated owing to the role played by point group symmmetry, need not be isolated features. Rather symmetry-allowed and same-symmetry conical intersections can coexist in the same region of nuclear coordinate space and can in fact intersect. A procedure to anticipate these "doubly diabolical points" based only on the knowledge of the symmetry-allowed intersection is reviewed. Doubly diabolical points are potentially quite important. Their existence means that a symmetry-allowed seam of conical intersection may not provide the complete description of nonadiabatic effects in a particular region of nuclear coordinate space. Determining their prevalence in triatomic and general polyatomic molecules will be an important area of future research. Also discussed in this work is a perturbative description of the wave functions near a conical intersection. This analysis provides a transformation to a locally diabatic basis and should facilitate representation of the ab initio potential energy, and derivative couplings, surfaces that exhibit conical intersections.