Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo

Abstract

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.

15 pages, 7 figures

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• The Shape of Full Configuration Interaction to Come
• Generalized Many-Body Expanded Full Configuration Interaction Theory
• The Adaptive Shift Method in Full Configuration Interaction Quantum Monte Carlo: Development and Applications
• Simulations of Trions and Biexcitons in Layered Hybrid Organic-Inorganic Lead Halide Perovskites
• Quantum Monte Carlo in Configuration Space with Three-Nucleon Forces
• A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo
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• Accelerating Stochastic Quantum Chemistry
• Theory and Implementation of a Novel Stochastic Approach to Coupled Cluster
• Fixed and partial-node approximations in Slater determinant space for molecules
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• Coupled-cluster pairing models for radicals with strong correlations
• Using density matrix quantum Monte Carlo for calculating exact-on-average energies for ab-initio Hamiltonians in a finite basis set
• Iterative Configuration Interaction with Selection