The work of our group is primarily focused on the electron correlation problem - namely how to compute the correlation energy for an atom, molecule, or even solid, starting from a mean-field (say Hartree-Fock) description of the system. Our approach is to combine quantum chemical ideas with stochastic (Monte Carlo) techniques, which enable us to tackle problems which are very difficult to solve use standard quantum chemical techniques alone.
We are developing Quantum Monte Carlo algorithms adapted for electronic (and more generally Fermionic) problems by working in Slater determinant spaces. The central problem which is encountered is the infamous "Fermion sign problem", which results from electronic wavefunctions having both positive and negative amplitudes. Currently we are working on a novel population dynamics algorithm which propagates walkers in Slater determinant space according to a type of "stochastic cellular automaton" obeying simple rules. The movie on the home page shows an evolving population of walkers of positive and negative sign settling on the FCI wavefunction of a nitrogen dimer in a minimal basis - an archetypal multireference system. The remarkable aspect of this dynamics is the spontaneous symmetry breaking caused by annhilation processes, allowing the exact nodal surface of the nitrogen molecule, as expressed by the CI coefficients, molecule to appear. No fixed-node approximation is applied.
Further animations of this method in action can be viewed here.
- Natural Orbitals for Wave Function Based Correlated Calculations Using a Plane Wave Basis Set, Andreas Grueneis, George Booth, James Spencer, Ali Alavi and Georg Kresse, J. Chem. Th. Comput., 7 , 2780-2785, (2011).
- Breaking the carbon dimer: The challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods, George Booth, Deidre Cleland, Alex Thom, and Ali Alavi, J. Chem. Phys., 135 , 084104, (2011).
- A study of electron affinites using the initiator approach to full configuration interaction quantum Monte Carlo, Deidre Cleland, George Booth, and Ali Alavi, J. Chem. Phys., 134 , 024112, (2011).
- Approaching chemical accuracy using full configuration-interaction quantum Monte Carlo: A study of ionization potentials , G.H. Booth, and Ali Alavi, J. Chem. Phys., 132 , 174104 (2010).
- Fermion Monte Carlo without fixed nodes: a Game of Life, death and annihilation in Slater Determinant space , G.H. Booth, A.J.W. Thom and Ali Alavi, J. Chem. Phys., 131 , 054106, (2009).
- Efficient calculation of the exact exchange energy in periodic systems using a truncated Coulomb potential James Spencer and Ali Alavi, Physical Review B, 77 193110 (2008)