Research Associate
My primary research focusses on using multiple solutions to the Self-Consistent Field equations as a basis for Configuration Interaction (CI) correlation methods. To achieve this, I am currently involved in researching and developing Holomorphic Hartree-Fock theory. In normal Hartree-Fock theory, the energy functional is not holomorphic in it's arguments (the MO coefficients), and so there is no well defined complex derivative. Futhermore, as geometry changes cause the coefficients within the Hartree-Fock equations to change, stationary points of the functional disappear.
We define a new 'holomorphic' Hartree-Fock energy functional by removing the complex conjugation of coefficients from the expectation value of the energy. We anticipate that this new functional should have a constant number of stationary points as the geometry changes and will be well-behaved in the complex plane. For H2, these states represent the continuation of standard UHF states beyond the Coulson-Fischer point and extend in the complex direction. Whilst these stationary points' holomorphic energies are not particularly relevant, their locations vary smoothly with geometric changes.
The set of all h-UHF states provides a powerful basis for performing a non-orthogonal CI (NOCI) expansion at a much lower cost than Full-CI. In comparison to truncated CI, the NOCI wavefunction maintains the size-extensivity of the underlying h-UHF states and recovers a significant amount of the correlation energy. We are currently developing reliable methods for finding these h-UHF states whilst exploring the topology of the holomorphic energy functional.