3. Minimal Energy Conical Intersection optimisation

To optimise conical intersection geometries, the penalty function method of Levine[15] is used, removing the need for nonadiabatic coupling vectors. A function of the averaged S₁ and S₀ energies (\(\bar{E}_{1-0}\)) and the S₁-S₀ energy gap (\(\Delta E\)) is minimised:

\[F = \bar{E}_{1-0} + \sigma \frac{\Delta E^2}{|\Delta E| + \alpha}\]

\(\sigma\) is a Lagrangian multiplier and \(\alpha\) is a parameter such that \(\alpha \ll \Delta E\).