Correlated sampling in quantum Monte Carlo: A route to forces

@article{Filippi2000CorrelatedSI,
  title={Correlated sampling in quantum Monte Carlo: A route to forces},
  author={Claudia Filippi and C. J. Umrigar},
  journal={Physical Review B},
  year={2000},
  volume={61}
}
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate numerical forces and potential energy surfaces in diffusion Monte Carlo. This method employs a coordinate transformation, earlier used in variational Monte Carlo, to greatly reduce the statistical error. Results are presented for first-row diatomic molecules. 

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References

SHOWING 1-10 OF 13 REFERENCES

Molecular Spectra and Molecular Structure

THOSE who contributed to the recent Faraday Discussion on molecular spectra and molecular structure have now sent their written versions to the secretary for publication. Instead of the report we

Phys

  • Rev. A 33, 2786 (1986); R. M. Dickson and A. D. Becke, J. Chem. Phys. 99, 3898
  • 1993

Phys

  • Rev. B 45, 3236
  • 1992

Phys

  • 63, 1499 (1975); ibid. 65, 4121 (1976); P.J. Reynolds et al., ibid. 77, 5593
  • 1982

Phys

  • 105, 213
  • 1996

Phys

  • 99, 9790
  • 1993

Phys

  • Rev. B 36, 2092 (1987); S. Fahy, X. W. Wang, and S. G. Louie, Phys. Rev. B 42, 3503 (1990); J. C. Grossman and L. Mitas, 79, 4353 (1997); R. Q. Hood et al., Phys. Rev. Lett. 78, 3350
  • 1997

Phys

  • Rev. Lett. 60, 1719
  • 1988