Abstract

Although it is the lowest energy Hartree-Fock state that is usually most sought after, the non-linear self-consistent field (SCF) equations also admit a number of higher energy solutions that have been shown to resemble excited molecular states. Motivated by this, these states can be used as a basis set for Non-Orthogonal Configuration Interaction (NOCI) to obtain adiabatic states which show similar properties to the results of more expensive correlation techniques. However, the existence of an SCF state across all molecular geometries is not guaranteed and there are many known examples of coalescing solutions. The disappearance of a Hartree-Fock state severely hinders NOCI by leading to a sudden change in the basis set size, resulting in discontinuous energy curves. In holomorphic Hartree-Fock theory, a holomorphic analogue of the Hartree-Fock equations is constructed by removing the complex conjugation of orbital coefficients from the energy functional. By making this alteration, SCF states that usually disappear as the molecular geometry is changed are instead found to extend into the complex plane, allowing a continuous basis to be constructed for NOCI . In this talk, I present the theoretical and mathematical foundations of holomorphic Hartree-Fock theory and demonstrate its contribution to NOCI calculations.