We explore the existence and behaviour of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1 2 (3 n − 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH 2+and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a twoelectron problem, and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.

We investigate the existence of holomorphic Hartree–Fock solutions using a revised SCF algorithm. We use this algorithm to study the Hartree–Fock solutions for H2 and H42+ and report the emergence of holomorphic solutions at points of symmetry breaking. Finally, we find these holomorphic solutions for H4 and use them as a basis for Non-Orthogonal Configuration Interaction at a range of rectangular geometries and show them to produce energies in good agreement with Full Configuration Interaction.

We describe further details of the stochastic coupled cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in full configuration interaction quantum Monte Carlo. We describe an initiator modification to stochastic coupled cluster theory and show that initiator calculations can at times be extrapolated to the unbiased limit. We apply this method to the 3D 14-electron uniform electron gas and present complete basis set limit values of the coupled cluster singles and doubles (CCSD) and previously unattainable coupled cluster singles and doubles with perturbative triples (CCSDT) correlation energies for up to r(s) = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities.

Electron transfer processes are ubiquitous in chemistry and of great importance in many systems of biological and commercial interest. The ab-initio description of these processes remains arXiv:1807.04983v1 [physics.chem-ph]

We investigate the Hartree-Fock solutions to H2 in a minimal basis. We note the properties of the solutions and their disappearance with geometry and propose a new method, called Holomorphic Hartree-Fock theory, where we modify the self-consistent field (SCF) equations to avoid disappearance of the solutions. We use these solutions as a basis for a nonorthogonal configuration interaction to produce a smooth binding curve over a complete range of geometries.