Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo
Abstract
We introduce 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 Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the technique for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. Furthermore, we perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient method for geometry optimization and molecular dynamics within AFQMC.
- Authors:
-
- California Inst. of Technology (CalTech), Pasadena, CA (United States)
- College of William and Mary, Williamsburg, VA (United States)
- Publication Date:
- Research Org.:
- College of William and Mary, Williamsburg, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1540205
- Alternate Identifier(s):
- OSTI ID: 1436372
- Grant/Contract Number:
- SC0001303; Grant no. DE-SC0001303
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 148; Journal Issue: 18; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS
Citation Formats
Motta, Mario, and Zhang, Shiwei. Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo. United States: N. p., 2018.
Web. doi:10.1063/1.5029508.
Motta, Mario, & Zhang, Shiwei. Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo. United States. doi:10.1063/1.5029508.
Motta, Mario, and Zhang, Shiwei. Tue .
"Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo". United States. doi:10.1063/1.5029508. https://www.osti.gov/servlets/purl/1540205.
@article{osti_1540205,
title = {Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo},
author = {Motta, Mario and Zhang, Shiwei},
abstractNote = {We introduce 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 Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the technique for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. Furthermore, we perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient method for geometry optimization and molecular dynamics within AFQMC.},
doi = {10.1063/1.5029508},
journal = {Journal of Chemical Physics},
number = 18,
volume = 148,
place = {United States},
year = {2018},
month = {5}
}
Web of Science
Works referenced in this record:
Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
journal, June 2006
- Al-Saidi, W. A.; Zhang, Shiwei; Krakauer, Henry
- The Journal of Chemical Physics, Vol. 124, Issue 22
Assessing weak hydrogen binding on Ca + centers: An accurate many-body study with large basis sets
journal, October 2011
- Purwanto, Wirawan; Krakauer, Henry; Virgus, Yudistira
- The Journal of Chemical Physics, Vol. 135, Issue 16
Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces
journal, November 2003
- Assaraf, Roland; Caffarel, Michel
- The Journal of Chemical Physics, Vol. 119, Issue 20
Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians
journal, June 2015
- Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei
- Physical Review Letters, Vol. 114, Issue 22
Eliminating spin contamination in auxiliary-field quantum Monte Carlo: Realistic potential energy curve of F2
journal, March 2008
- Purwanto, Wirawan; Al-Saidi, W. A.; Krakauer, Henry
- The Journal of Chemical Physics, Vol. 128, Issue 11
Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states
journal, March 2009
- Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
- The Journal of Chemical Physics, Vol. 130, Issue 9
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015
- LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico
- Physical Review X, Vol. 5, Issue 4
Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory
journal, April 1998
- El Azhary, Adel; Rauhut, Guntram; Pulay, Peter
- The Journal of Chemical Physics, Vol. 108, Issue 13
Correlated sampling in quantum Monte Carlo: A route to forces
journal, June 2000
- Filippi, Claudia; Umrigar, C. J.
- Physical Review B, Vol. 61, Issue 24
Computation of Ground-State Properties in Molecular Systems: Back-Propagation with Auxiliary-Field Quantum Monte Carlo
journal, October 2017
- Motta, Mario; Zhang, Shiwei
- Journal of Chemical Theory and Computation, Vol. 13, Issue 11
Quantum Monte Carlo method for the ground state of many-boson systems
journal, November 2004
- Purwanto, Wirawan; Zhang, Shiwei
- Physical Review E, Vol. 70, Issue 5
Electronic quantum Monte Carlo calculations of atomic forces, vibrations, and anharmonicities
journal, June 2005
- Lee, Myung Won; Mella, Massimo; Rappe, Andrew M.
- The Journal of Chemical Physics, Vol. 122, Issue 24
Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules
journal, June 2007
- Suewattana, Malliga; Purwanto, Wirawan; Zhang, Shiwei
- Physical Review B, Vol. 75, Issue 24
Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory: Analytical calculation of energy derivatives
journal, September 2013
- Pulay, Peter
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3
An auxiliary-field quantum Monte Carlo study of the chromium dimer
journal, February 2015
- Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
- The Journal of Chemical Physics, Vol. 142, Issue 6
Unified Approach for Molecular Dynamics and Density-Functional Theory
journal, November 1985
- Car, R.; Parrinello, M.
- Physical Review Letters, Vol. 55, Issue 22
Analytical energy gradients for local coupled-cluster methodsElectronic Supplementary Information available. See http://www.rsc.org/suppdata/cp/b1/b105126c/
journal, January 2001
- Rauhut, Guntram; Werner, Hans-Joachim
- Physical Chemistry Chemical Physics, Vol. 3, Issue 22
Accurate, Efficient, and Simple Forces Computed with Quantum Monte Carlo Methods
journal, January 2005
- Chiesa, Simone; Ceperley, D. M.; Zhang, Shiwei
- Physical Review Letters, Vol. 94, Issue 3
Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules : I. Theory
journal, January 1969
- Pulay, P.
- Molecular Physics, Vol. 17, Issue 2
Analytical energy gradients for multiconfiguration self‐consistent field wave functions with frozen core orbitals
journal, May 1991
- Busch, Thilo; Esposti, Alessandra Degli; Werner, Hans‐Joachim
- The Journal of Chemical Physics, Vol. 94, Issue 10
Diffusive behavior of states in the Hubbard-Stratonovitch transformation
journal, January 1991
- Fahy, S.; Hamann, D. R.
- Physical Review B, Vol. 43, Issue 1
Geometry optimization in density functional methods: Geometry Optimization in Density Functional Methods
journal, March 2004
- Reveles, J. Ulises; Köster, Andreas M.
- Journal of Computational Chemistry, Vol. 25, Issue 9
Path integral Monte Carlo calculation of electronic forces
journal, October 1998
- Zong, Fenghua; Ceperley, D. M.
- Physical Review E, Vol. 58, Issue 4
Practical Schemes for Accurate Forces in Quantum Monte Carlo
journal, October 2014
- Moroni, S.; Saccani, S.; Filippi, C.
- Journal of Chemical Theory and Computation, Vol. 10, Issue 11
Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer
journal, June 2016
- Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
- The Journal of Chemical Physics, Vol. 144, Issue 24
Reaction path following by quadratic steepest descent
journal, November 1998
- Eckert, Frank; Werner, Hans-Joachim
- Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 100, Issue 1-4
Quantum Monte Carlo algorithms for electronic structure at the petascale; the Endstation project
journal, July 2008
- Esler, K. P.; Kim, J.; Ceperley, D. M.
- Journal of Physics: Conference Series, Vol. 125
NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
journal, September 2010
- Valiev, M.; Bylaska, E. J.; Govind, N.
- Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489
Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
journal, April 2003
- Zhang, Shiwei; Krakauer, Henry
- Physical Review Letters, Vol. 90, Issue 13
Computing forces with quantum Monte Carlo
journal, September 2000
- Assaraf, Roland; Caffarel, Michel
- The Journal of Chemical Physics, Vol. 113, Issue 10
Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods
journal, September 2017
- Motta, Mario; Ceperley, David M.; Chan, Garnet Kin-Lic
- Physical Review X, Vol. 7, Issue 3
Constrained path Monte Carlo method for fermion ground states
journal, March 1997
- Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.
- Physical Review B, Vol. 55, Issue 12
Pressure-induced diamond to -tin transition in bulk silicon: A quantum Monte Carlo study
journal, December 2009
- Purwanto, Wirawan; Krakauer, Henry; Zhang, Shiwei
- Physical Review B, Vol. 80, Issue 21
Chemical Transformations Approaching Chemical Accuracy via Correlated Sampling in Auxiliary-Field Quantum Monte Carlo
journal, May 2017
- Shee, James; Zhang, Shiwei; Reichman, David R.
- Journal of Chemical Theory and Computation, Vol. 13, Issue 6
Finite-Size Correction in Many-Body Electronic Structure Calculations
journal, March 2008
- Kwee, Hendra; Zhang, Shiwei; Krakauer, Henry
- Physical Review Letters, Vol. 100, Issue 12
Ab initio geometry optimization for large molecules
journal, September 1997
- Eckert, Frank; Pulay, Peter; Werner, Hans-Joachim
- Journal of Computational Chemistry, Vol. 18, Issue 12
Computing accurate forces in quantum Monte Carlo using Pulay’s corrections and energy minimization
journal, January 2003
- Casalegno, Mosé; Mella, Massimo; Rappe, Andrew M.
- The Journal of Chemical Physics, Vol. 118, Issue 16
Algorithmic differentiation and the calculation of forces by quantum Monte Carlo
journal, December 2010
- Sorella, Sandro; Capriotti, Luca
- The Journal of Chemical Physics, Vol. 133, Issue 23
Works referencing / citing this record:
Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
journal, May 2018
- Motta, Mario; Zhang, Shiwei
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 5
Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo
journal, October 2018
- Archibald, R.; Krogel, J. T.; Kent, P. R. C.
- The Journal of Chemical Physics, Vol. 149, Issue 16
Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide
journal, October 2018
- Zhang, Shuai; Malone, Fionn D.; Morales, Miguel A.
- The Journal of Chemical Physics, Vol. 149, Issue 16
Non-orthogonal multi-Slater determinant expansions in auxiliary field quantum Monte Carlo
journal, February 2019
- Landinez Borda, Edgar Josué; Gomez, John; Morales, Miguel A.
- The Journal of Chemical Physics, Vol. 150, Issue 7
An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions
journal, August 2019
- Lee, Joonho; Malone, Fionn D.; Morales, Miguel A.
- The Journal of Chemical Physics, Vol. 151, Issue 6
Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
journal, August 2019
- Vitali, Ettore; Rosenberg, Peter; Zhang, Shiwei
- Physical Review A, Vol. 100, Issue 2
Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure
journal, July 2019
- Motta, Mario; Zhang, Shiwei; Chan, Garnet Kin-Lic
- Physical Review B, Vol. 100, Issue 4