Solving the many-electron Schroedinger Equation accurately is extremely challenging. The simplest (yet paradoxically the most computationally demanding) method is Full Configuration Interaction (FCI), but this is possible in only the very smallest systems owing to its exponential scaling with system size.
In 2009 a great step forward in solving these equations was made by recasting them in terms of sampling, resulting in the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method[1,2], which has gone on to exactly solve systems well beyond the previous capabilities of FCI.
More commonly used than FCI, Coupled Cluster theory is said to be the ‘gold-standard’ of quantum chemistry, sitting at a sweet-spot between accuracy and computational cost. Over the past few years, building on the success of FCIQMC, we have worked out how to solve the Coupled Cluster equations stochastically[3,4] to any order of truncation. Stochastic sampling vastly reduces the storage (and time) costs for large systems allowing us to solve problems previously inaccessible through conventional methods.
In this talk I detail how the stochastic sampling works in both methods and show some applications to molecular systems.
 Fermion Monte Carlo without fixed nodes: a game of life, death, and annihilation in Slater determinant space. GH Booth, AJW Thom, A Alavi - J. Chem. Phys 131, 054106 (2009) doi:10.1063/1.3193710 .
 Breaking the carbon dimer: the challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods. GH Booth, D Cleland, AJW Thom, A Alavi – J. Chem. Phys. 135, 084105 (2011) doi: 10.1063/1.3624383 .
 Stochastic Coupled Cluster Theory. AJW Thom – Phys Rev Lett 105, 263004 (2010) doi: 10.1103/PhysRevLett.105.263004 .
 Developments in stochastic coupled cluster theory: The initiator approximation and application to the uniform electron gas. JS Spencer, AJW Thom – J. Chem. Phys. 144, 084108 (2016) doi: 10.1063/1.4942173
Dr Thom is a University Lecturer and Royal Society Fellow (URF) at the Department of Chemistry at the University of Cambridge