Marching along ridges. An extrapolatable approach to locating conical intersections

Abstract

A conical intersection is a singular point in nuclear coordinate space. As result of this singularity the parameters used to search for energy minimized conical intersections, energy gradients, energy difference gradients and coupling vectors, vary irregularly along the search path. This irregular variation precludes the efficient use of extrapolation procedures to speed convergence. In this work we show how a previously introduced orthogonalization procedure for the branching or g–h space can be used to design search algorithms in which the key parameters are slowly varying functions of the search path. From a topographical perspective this approach amounts to walking along a path parallel the ridge of conical intersections.