Exciting Determinants in Quantum Monte Carlo: Loading the Dice with Fast, Low-Memory Weights

High-quality excitation generators are crucial to the effectiveness of coupled cluster Monte Carlo (CCMC) and full configuration interaction Quantum Monte Carlo (FCIQMC) calculations. The heat bath sampling of Holmes et al. [Holmes, A. A.; Changlani, H. J.; Umrigar, C. J. J. Chem. Theory Comput. 2016, 12, 1561-1571.] dramatically increases the efficiency of the spawn step of such algorithms but requires memory storage scaling quartically with system size which can be prohibitive for large systems. Alternatively, Alavi et al. [Smart, S. D.; Booth, G. H.; Alavi, A. Unpublished results.] approximated these weights with weights based on Cauchy-Schwarz-like inequalities calculated on-the-fly. While reducing the memory cost, this algorithm scales linearly in system size computationally. We combine both of these ideas with the single-reference nature of many systems studied and introduce a spawn-sampling algorithm that has low memory requirements (quadratic in basis set size) compared to the heat bath algorithm and only scales either independently of system size (CCMC) or linearly in the number of electrons (FCIQMC) that works especially well on localized orbitals. Tests on small water chains with localized orbitals with CCMC and with an initiator point sample in FCIQMC indicate that it can be equally efficient as the other excitation generators. As the system gets larger, calculations with our new algorithm converge faster than the on-the-fly weight algorithm while having a much more favorable memory scaling than the heat bath algorithm.