Conical intersections: A perspective on the computation of spectroscopic Jahn–Teller parameters and the degenerate ‘intersection space’

We present a perspective on the computation and interpretation of force constants at points of symmetry-induced (Jahn-Teller) conical intersection. Our method is based upon the projection of the 'branching space' from the full (3N - 6)-dimensional Hessian for each component of a degenerate electronic state. For Jahn-Teller active molecules, this has the effect of removing the linear Jahn-Teller coupling from all but the interstate coupling and gradient difference vectors. The quadratic coupling constants are determined by the splitting of the harmonic vibrational frequencies within degenerate vibrational normal coordinates of the 'intersection space'. The potential energy surface topology along these normal modes is analogous to the Renner-Teller effect occurring in orbitally degenerate linear molecules. Our methodology gives a straightforward theoretical analysis of the various Jahn-Teller intersections and allows the determination of the seam curvature. Thus, we are in a position to compute the various Jahn-Teller coupling constants, in a particular coordinate system, and in addition to determine the nature of the high-symmetry Jahn-Teller geometry (i.e., minimum or saddle-point on the seam). We illustrate these concepts with various examples of different Jahn-Teller conical intersections in some small molecules.