Minimum Energy Conical Intersection Optimization Using DFT/MRCI(2)

The combined density functional theory and multi-reference configuration interaction (DFT/MRCI) method is a semi-empirical electronic structure approach that is both computationally efficient and of predictive accuracy for the calculation of electronic excited states and simulation of electronic spectroscopies. However, given that the reference space is generated via a selected-CI procedure, a challenge arises in the construction of smooth potential energy surfaces. To address this issue, we treat the local discontinuities that arise as noise within the Gaussian progress regression framework and learn the surfaces by explicitly incorporating and optimizing a whitenoise kernel. The characteristic polynomial coefficient surfaces of the potential matrix, which are smooth functions of nuclear coordinates even at conical intersections, are learned in place of the adiabatic energies and are used to optimize the DFT/MRCI(2) minimum energy conical intersection geometries for representative intersection motifs in the molecules ethylene, butadiene, and fulvene. One consequence of explicitly treating the noise in the surfaces is that the energy difference cannot be made arbitrarily small at points of nominal intersection. Despite the limitations, however, we find the structures as well as the branching spaces to compare well with \textit{ab initio} MRCI and conclude that this approach is a viable method to learn a smooth representation of DFT/MRCI(2) surfaces.