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arXiv:1305.6981 · Molecular Physics

Linear-scaling and parallelisable algorithms for stochastic quantum chemistry

George H. Booth, Simon D. Smart, Ali Alavi

Published Jan 24, 2014• 120 citations

Abstract

For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation have evolved to require the minimum amount of logic and rely heavily on computationally efficient library-based matrix algebra and optimised paging schemes. In this regard, the recent development of exact stochastic quantum chemical algorithms to reduce computational scaling and memory overhead requires a contrasting algorithmic philosophy, but one which when implemented efficiently can achieve higher accuracy/cost ratios with small random errors. Additionally, they can exploit the continuing trend for massive parallelisation which hinders the progress of deterministic high-level quantum chemical algorithms. In the Quantum Monte Carlo community, stochastic algorithms are ubiquitous but the discrete Fock space of quantum chemical methods is often unfamiliar, and the methods introduce new concepts required for algorithmic efficiency. In this paper, we explore these concepts and detail an algorithm used for Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which is implemented and available in MOLPRO and as a standalone code, and is designed for high-level parallelism and linear-scaling with walker number. Many of the algorithms are also in use in, or can be transferred to, other stochastic quantum chemical methods and implementations. We apply these algorithms to the strongly correlated chromium dimer to demonstrate their efficiency and parallelism.

DOI: 10.1080/00268976.2013.877165

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spawn

step, was improved, keeping computational and memory costs as low as possible. Furthermore, the convergence of CCMC and FCIQMC was accelerated by employing a quasi-Newton propagation. Using the model system information of what coupled cluster level is needed and having made great progress towards accelerating these methods, the computation of highly accurate energies in solid or large molecular systems should be more feasible in the future.

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We introduce a family of methods for the full configuration interaction problem in quantum chemistry, based on the fast randomized iteration (FRI) framework [Lim, L.-H.; Weare, J. SIAM Rev. 2017, 59, 547; DOI: 10.1137/15M1040827 ]. These methods, which we term “FCI-FRI”, stochastically impose sparsity during iterations of the power method and can be viewed as a generalization of full configuration interaction quantum Monte Carlo (FCIQMC) without walkers. In addition to the multinomial scheme commonly used to sample excitations in FCIQMC, we present a systematic scheme where excitations are not sampled independently. Performing ground-state calculations on five small molecules at fixed cost, we find that the systematic FCI-FRI scheme is 11–45 times more statistically efficient than the multinomial FCI-FRI scheme, which is in turn 1.4–178 times more statistically efficient than the original FCIQMC algorithm.

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