# 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.

## 89 Citations

### Methods for calculating forces within quantum Monte Carlo simulations

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2010

An accurate and practical method for calculating forces using the pure distribution is presented and tested for the SiH molecule and violations of the central limit theorem are found.

### Force calculation of polyatomic molecules in quantum Monte Carlo using Pulay's corrections

- Physics
- 2007

We calculated the variational and diffusion quantum Monte Carlo forces using the Hellmann–Feynman theorem and Pulay's correction for the first-row diatomic and triatomic molecules (CO, NO, CO2 and…

### Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo.

- PhysicsThe Journal of chemical physics
- 2018

An algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method based on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets is proposed.

### Calculation of interatomic forces and optimization of molecular geometry with auxiliary-ﬁeld quantum Monte Carlo: Supplementary Information

- Computer Science
- 2018

We propose an algorithm for accurate, systematic and scalable computation of interatomic forces within the auxiliary-field Quantum Monte Carlo (AFQMC) method. The algorithm relies on the…

### Discovering correlated fermions using quantum Monte Carlo

- PhysicsReports on progress in physics. Physical Society
- 2016

A summary of quantum Monte Carlo techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique.

### Accurate forces in quantum Monte Carlo calculations with nonlocal pseudopotentials.

- Physics, ChemistryPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

Equilibrium bond lengths and harmonic vibrational frequencies are calculated from the Hellmann-Feynman forces and compared with those obtained from the energies at the Hartree-Fock, VMC, and pure DMC levels.

### Accurate, efficient, and simple forces computed with quantum Monte Carlo methods.

- PhysicsPhysical review letters
- 2005

A simple procedure is introduced, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator finite, which results in very accurate geometries for the molecules H(2), LiH, CH(4), NH(3), H( 2)O, and HF.

### Efficient quantum monte carlo energies for molecular dynamics simulations.

- PhysicsPhysical review letters
- 2005

A method is presented to treat electrons within the many-body quantum Monte Carlo (QMC) approach "on-the-fly" throughout a molecular dynamics simulation, which results in highly accurate total energies for the full dynamical trajectory at a fraction of the cost of conventional, discrete sampling.

### A diffusion quantum Monte Carlo study of geometries and harmonic frequencies of molecules.

- PhysicsThe Journal of chemical physics
- 2004

An approach in determination of equilibrium geometries and harmonic frequencies of molecules by the Ornstein-Uhlenbeck diffusion quantum Monte Carlo method based on the floating spherical Gaussians, consistent with some sophisticated ab initio calculated values within reasonable statistical uncertainty.

### Minimum energy pathways via quantum Monte Carlo.

- Chemistry, PhysicsThe Journal of chemical physics
- 2013

It is suggested that a QMC approach is both viable and useful for reactions difficult to address by DFT and system sizes too large for high level quantum chemistry methods.

## References

SHOWING 1-10 OF 13 REFERENCES

### Molecular Spectra and Molecular Structure

- ChemistryNature
- 1929

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