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Unbiasing the initiator approximation in full configuration interaction quantum Monte Carlo.
Khaldoon Ghanem1, Alexander Y Lozovoi1, Ali Alavi1
1Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
The Journal of Chemical Physics
|December 16, 2019
Summary
A new method corrects bias in initiator full configuration interaction quantum Monte Carlo (i-FCI QMC) by adjusting walker acceptance probabilities. This significantly improves energy accuracy and reduces reliance on the initiator threshold for complex molecular systems.
Area of Science:
- Computational Quantum Chemistry
- Stochastic Quantum Many-Body Methods
Background:
- Initiator full configuration interaction quantum Monte Carlo (i-FCI QMC) is a powerful method for electronic structure calculations.
- A systematic undersampling bias affects noninitiator determinants in i-FCI QMC, particularly in large systems with insufficient walkers.
- This bias leads to inaccurate energy estimations, limiting the method's applicability.
Purpose of the Study:
- To identify and rectify the source of bias in the initiator full configuration interaction quantum Monte Carlo algorithm.
- To develop a more accurate and robust i-FCI QMC method that minimizes systematic errors.
- To enable highly accurate quantum chemical calculations for larger and more complex molecular systems.
Main Methods:
- Introduced a bias correction scheme based on the acceptance probability (pacc) of noninitiator determinants.
- Reduced the shift applied to noninitiator determinants proportionally to their acceptance probability.
- Validated the method on butadiene and benzene systems, correlating up to 30 electrons in large Hilbert spaces.
Main Results:
- The proposed method effectively unbiases the initiator approximation by adjusting the shift based on pacc.
- Demonstrated rapid convergence to the full configuration interaction limit with respect to walker number.
- Achieved millihartree accuracy relative to coupled cluster singles doubles triples and perturbative quadruples [CCSDT(Q)] with manageable walker counts (107-108).
Conclusions:
- The developed algorithm largely solves the initiator bias problem in i-FCI QMC for medium-sized molecules.
- The method significantly reduces dependence on the initiator threshold, allowing for accurate results even with large threshold values.
- Highly accurate and converged energies, slightly lower than CCSDT(Q), were obtained for butadiene and benzene, showcasing the method's potential.
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