Conical intersection revisited: extension to an elliptic form

In this Letter we relate to a general 2×2 diabatic potential matrix for which is derived an analytic expression for the various non-adiabatic coupling terms. Its main advantage is in leading to a simple algorithm to determine the number and the kind of conical intersections one encounters in a (planar) region defined by a closed contour. This approach was tested with respect to two models, one of them is the elliptical linear model. This model was then, further, applied to simulate ab initio results obtained for the C2H molecule.