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We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behavior of a coupled cluster wavefunction representation, we propose new approaches based on an intuitive, well-defined condition for sampling weights and on sampling the expansion in cluster operators of different excitation levels. We term these modifications even and truncated selections, respectively. Utilising both approaches demonstrates dramatically improved calculation stability as well as reduced computational and memory costs. These modifications are particularly effective at higher truncation levels owing to the large number of terms within the cluster expansion that can be neglected, as demonstrated by the reduction of the number of terms to be sampled when truncating at triple excitations by 77% and hextuple excitations by 98%.

We propose the use of preconditioning in FCIQMC which, in combination with perturbative estimators, greatly increases the efficiency of the algorithm. The use of preconditioning allows a time step close to unity to be used (without time-step errors), provided that multiple spawning attempts are made per walker. We show that this approach substantially reduces statistical noise on perturbative corrections to initiator error, which improve the accuracy of FCIQMC but which can suffer from significant noise in the original scheme. Therefore, the use of preconditioning and perturbatively-corrected estimators in combination leads to a significantly more efficient algorithm. In addition, a simpler approach to sampling variational and perturbative estimators in FCIQMC is presented, which also allows the variance of the energy to be calculated. These developments are investigated and applied to benzene (30e, 108o), an example where accurate treatment is not possible with the original method.

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the last decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method exact thermal density matrix, respectively. In this article we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semi-stochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker-Campbell-Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -diagCCMC -allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory.Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches. Graphical TOC EntryOver the last half-century the coupled cluster (CC) wavefunction Ansatz has proved remarkably effective at representing the solution of the Schrödinger equation in a polynomial scaling number of parameters while providing size-extensive and -consistent results. Despite reducing the full configuration interaction (FCI) N ! factorial scaling to polynomial, the computational cost of CC methods, measured in terms of both required CPU floating-point operations and memory, is still an issue. The coupled cluster with single and double substitutions (CCSD) and CCSD with perturbative triples correction (CCSD(T)) approximations provide a balance between computational cost and accuracy that has led to relatively wide adoption, but are eventually precluded for many large systems.Recent work has made great progress on this issue through application of various approximations, which enable calculations to be performed with reduced memory and computational costs. In particular, various approximations exploiting the locality of electron correlation allow calculations with costs asymptotically proportional to measures of system size.These include approaches based on orbital localisation, 1-39 molecular fragmentation, [40][41][42][43][44][45][46][47][48][49][50][51][52] and decompositions, such as resolution-of-the-identity, Cholesky or singular-value, of the two-electron integrals tensors. 19,20,[53][54][55][56][57][58] However, while providing large efficiencies in CCSD calculations, higher truncation levels will generally exceed available memory resources before such approximations are a reasonable proposition.In this letter we propose and demonstrate a coupled cluster-based projector Monte Carlo (MC) algorithm that enables automatic exploitation of the wavefunction sparsity for arbitrary excitation orders. Our met...