Conical intersections are features of the potential energy surfaces of molecules that rise out of the breakdown of the Born-Oppenheimer approximation and the coupling of electronic and nuclear wavefunctions. Biologically, conical intersections govern many processes required for life as we know it; an example relevant to our work is the non-radiative relaxation of nucleobase molecules like Uracil, which reduces the dangerous photochemical reactions in DNA when relaxing from an excited state. Physically, conical intersections represent the seam space between degenerate electronic states on the potential energy surface of a molecule. The subspace around the seam, where the degeneracy is lifted, is defined by the branching or g-h space, which provides insight to the efficacy of the conical intersection to promote non-adiabatic transition. Conical intersections are particularly challenging to calculate because of the difficulty in describing the coupled states exactly equivalently. Multireference methods like MRCI and CASSCF are most accurate pertaining to multi-state calculations but are relatively costly in time and resources. Single reference methods including CIS, TDDFT, and EOM-CCSD are relatively cheap but are unable to accurately calculate derivative coupling with the reference state, commonly the ground state. All of the mentioned methods were benchmarked in ability to calculate the g and h vectors for the conical intersection between the first and second excited singlet state in Uracil. In order to benchmark the single reference methods with the ground and first excited singlet states in Uracil, the spin-flip modification of the single reference methods was used, where the first excited triplet state is used as the reference. All of the methods used gave non-zero results for the h vectors, qualitatively confirming the existence of the conical intersection, but had varying success in quantitatively agreeing with the more accurate methods.

Theoretical methods of calculating conical intersections

Macromolecular Chemistry: The Second Century

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