James J. Shepherd

EPSRC PhD student October 2009–March 2013.

My research in the Alavi group focuses on the application of full configuration interaction quantum Monte Carlo to the homogeneous electron gas (HEG). As a model system, the HEG has many properties that make it attractive to study: simplicity, analytic matrix elements, a consistent basis set (which is the exact Hartree-Fock basis set), a tunable density/interaction parameter and a wealth of well-understood physics.

The electron gas is potentially a difficult system to study because the correct physical behavior of the gas is only recovered in the limit as the particle number goes to infinity (as the density is held constant). In this limit theories that lack size-extensivity fail to retrieve any correlation energy, and perturbative approaches generally find divergent energies (which we show explicitly here - Phys. Rev. Lett. 110, 226401, 2013 & arXiv:1208.6103).

The applicaton of FCIQMC to the electron gas allows us to calcuate, in principle, exact and unbiased energies of finite systems. Basis set incompleteness error can be removed by extrapolation in a similar fashion to molecular calculations, yielding energies that are of comparable accuracy with DMC but lacking in fixed-node error. We have shown this comparison for the 54 electron cubic-cell gas (Phys. Rev. B 85, 081103, 2012 & arXiv:1109.2635).

In applying FCIQMC to the HEG, we have made several important observations about the method itself, in particular how best to manage computational cost in simulations. We were able to describe a strategy whereby the two sources of error in our energies, stochastic and initator error, can be separated and removed (J. Chem. Phys. 136, 244101 (2012) & arXiv:1201.4691).

We used the HEG as an example of a system whose Schrodinger equation is solvable by many-body plane-wave wavefunction expansions, and investigated the efficient removal of basis set incompleteness error, developing a new type of basis set truncation (Phys. Rev. B 86, 035111 (2012) & arXiv:1202.4990). This work was conducted in collaboration with Georg Kresse. This paper also contains benchmark energies for the 14-electron problem for FCIQMC, MP2, RPA+SOSEX and CCD theories.

In collaboration with Daan Frenkel, a group of us have investigated the statistical mechanical properties of FCIQMC and i-FCIQMC (arXiv:1209.4023).

To comment on any of my papers or discuss any aspect of my work please email me at this address.