Comparison of algorithms for conical intersection optimisation using semiempirical methods

We present a comparison of three previously published algorithms for optimising the minimum energy crossing point between two Born-Oppenheimer electronic states. The algorithms are implemented in a development version of the MNDO electronic structure package for use with semiempirical configuration interaction methods. The penalty function method requires only the energies and gradients of the states involved, whereas the gradient projection and Lagrange-Newton methods also require the calculation of non-adiabatic coupling terms. The performance of the algorithms is measured against a set of well-known small molecule conical intersections. The Lagrange-Newton method is found to be the most efficient, with the projected gradient method also competitive. The penalty function method can only be recommended for situations where non-adiabatic coupling terms cannot be calculated.