Our research interests centre around method development to tackle the electron correlation problem, specifically using concepts from quantum Monte Carlo to
solve for full CI energies of molecules, i.e. the exact energy calculated within a basis set. Specifically, our group has developed a set of techniques called Full Confinguration Interaction Quantum Monte Carlo (FCIQMC) , togther with its initiator adaptation, i-FCIQMC , which stochastically propagates a population of positive and negavtive walkers according to a simple set of rules designed to mimic the imaginary-time Schrodinger equation. The long time
limit of the distribution of walkers is FCI ground-state eigenvector, which requires
a spontaneous self-assembly of positive walkers onto the positive-amplitude determinants, and negative walkers onto the negative-amplitude determinants. The key requirement to achieve this is walker annihilation, namely that two walkers of the opposit sign instanteously located on the same determinant annihilat each other and are removed from the
simulation. The technqiue has been applied to atomic systems including cations and anions , to the first-row diatomic molecules, and to the uniform electron gas.
The movie below shows an example of an FCIQMC simulation for a model of streched N2.
This movie shows the convergence of a wavefunction obtained
using a novel stochastic method to the exact ground state
wavefunction for the stretched nitrogen molecule in a space of
379 basis functions.
The upper graph shows the contribution of each basis function
to the wavefunction (compared to the exact result) as the system
evolves. The lower graph shows the energy of the instantaneous
wavefunction and the shift (which is another measure of the
instantaneous correlation energy) compared to the exact result.
