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Accurate forces in quantum Monte Carlo calculations with nonlocal pseudopotentials
1Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
Calculating accurate forces in quantum Monte Carlo methods is difficult. This study derives new expressions for forces, improving accuracy for molecular properties like bond lengths in variational and diffusion Monte Carlo simulations.
Area of Science:
- Computational Quantum Chemistry
- Many-Body Quantum Physics
Background:
- Calculating forces in quantum Monte Carlo (QMC) methods, such as variational and diffusion Monte Carlo (VMC and DMC), presents significant challenges.
- Accurate force calculations are crucial for determining molecular geometries and vibrational properties.
Purpose of the Study:
- To derive and implement expressions for the Hellmann-Feynman force contribution from nonlocal pseudopotentials within VMC and DMC methods.
- To assess the accuracy of forces derived from these methods for molecular property calculations.
Main Methods:
- Derivation of Hellmann-Feynman force expressions incorporating nonlocal pseudopotentials.
- Application of these forces to calculate equilibrium bond lengths and harmonic vibrational frequencies.
- Comparison of results with energy-based calculations at Hartree-Fock, VMC, and DMC levels.
Main Results:
- The study successfully derived force expressions for VMC and DMC methods using nonlocal pseudopotentials.
- Calculations for five small molecules demonstrated good agreement between force and energy-based methods.
- Equilibrium bond lengths obtained from force and energy calculations showed a maximum difference of less than 0.007 Å at the DMC level.
Conclusions:
- The derived Hellmann-Feynman force expressions provide an accurate and efficient means for calculating molecular properties within VMC and DMC.
- These advancements facilitate reliable geometry optimization and vibrational frequency analysis in quantum Monte Carlo simulations.
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