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Exploiting locality in FCIQMC for fast excitation generation

Oskar Weser, Ali Alavi, Giovanni Li Manni

Published May 24, 2023• 0 citations
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Abstract

In this paper we propose an improved excitation generation algorithm for the full configuration interaction quantum monte carlo (FCIQMC) method, which is particularly effective in systems described by localized orbitals. The method is an extension of the precomputed heat-bath (PCHB) strategy of Holmes et al., with more effective sampling of double excitations and a novel approach for non-uniform sampling of single excitations. We demonstrate the effectiveness of the algorithm for a chain of 30 hydrogen atoms with atom-localized orbitals, a stack of benzene molecules, an Fe-porphyrin model complex, whereby we show an overall efficiency gain by a factor of two to four, as measured by variance reduction per wall-clock time.

DOI
10.26434/chemrxiv-2023-5b6k2

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In this paper we propose an improved excitation generation algorithm for the full configuration interaction quantum monte carlo (FCIQMC) method, which is particularly effective in systems described by localized orbitals. The method is an extension of the precomputed heat-bath (PCHB) strategy of Holmes et al., with more effective sampling of double excitations and a novel approach for non-uniform sampling of single excitations. We demonstrate the effectiveness of the algorithm for a chain of 30 hydrogen atoms with atom-localized orbitals, a stack of benzene molecules, an Fe-porphyrin model complex, whereby we show an overall efficiency gain by a factor of two to four, as measured by variance reduction per wall-clock time.
In this paper we propose an improved excitation generation algorithm for the full configuration interaction quantum monte carlo (FCIQMC) method, which is particularly effective in systems described by localized orbitals. The method is an extension of the precomputed heat-bath (PCHB) strategy of Holmes et al., with more effective sampling of double excitations and a novel approach for non-uniform sampling of single excitations. We demonstrate the effectiveness of the algorithm for a chain of 30 hydrogen atoms with atom-localized orbitals, a stack of benzene molecules, an Fe-porphyrin model complex, whereby we show an overall efficiency gain by a factor of two to four, as measured by variance reduction per wall-clock time.
In this paper, we propose an improved excitation generation algorithm for the full configuration interaction quantum Monte Carlo method, which is particularly effective in systems described by localized orbitals. The method is an extension of the precomputed heat-bath strategy of Holmes et al., with more effective sampling of double excitations and a novel approach for nonuniform sampling of single excitations. We demonstrate the effectiveness of the algorithm for a chain of 30 hydrogen atoms with atom-localized orbitals, a stack of benzene molecules, and an Fe(II)-porphyrin model complex, whereby we show an overall efficiency gain by a factor of two to four, as measured by variance reduction per wall-clock time.
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.
We present three modifications to our recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) and investigate their effects on the method’s performance for Ne, H 2 O, and N 2 . The initiator approximation, originally developed for full configuration interaction quantum Monte Carlo, significantly reduces statistical error in FCI-FRI when few samples are used in compression operations, enabling its application to larger chemical systems. The semistochastic extension, which involves exactly preserving a fixed subset of elements in each compression, improves statistical efficiency in some cases but reduces it in others. We also developed a new approach to sampling excitations that yields consistent improvements in statistical efficiency and reductions in computational cost. We discuss possible strategies based on our findings for improving the performance of stochastic quantum chemistry methods more generally.
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.
We introduce an algorithm for sampling many-body quantum states in Fock space. The algorithm efficiently samples states with probability approximately proportional to an arbitrary function of the second-quantized Hamiltonian matrix element connecting the sampled state to the current state. We apply the new sampling algorithm to the recently developed semistochastic full configuration interaction quantum Monte Carlo (S-FCIQMC) method, a semistochastic implementation of the power method for projecting out the ground state energy in a basis of Slater determinants. Our new sampling method requires modest additional computational time and memory compared to uniform sampling but results in newly spawned weights that are approximately of the same magnitude, thereby greatly improving the efficiency of projection. A comparison in efficiency between our sampling algorithm and uniform sampling is performed on the all-electron nitrogen dimer at equilibrium in Dunning's cc-pVXZ basis sets with X ∈ {D, T, Q, 5}, demonstrating a large gain in efficiency that increases with basis set size. In addition, a comparison in efficiency is performed on three all-electron first-row dimers, B2, N2, and F2, in a cc-pVQZ basis, demonstrating that the gain in efficiency compared to uniform sampling also increases dramatically with the number of electrons.