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

doi:10.1063/1.5029508

Title: 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:

^[1]; Zhang, Shiwei ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States)
College of William and Mary, Williamsburg, VA (United States)

Publication Date:: 2018-05-08

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.

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                    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.

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                    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.

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@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}

}

Copy to clipboard

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DOI: 10.1063/1.5029508

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Works referenced in this record:

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Al-Saidi, W. A.; Zhang, Shiwei; Krakauer, Henry
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Computing forces with quantum Monte Carlo
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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
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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
DOI: 10.1002/wcms.1364

Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo
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Archibald, R.; Krogel, J. T.; Kent, P. R. C.
The Journal of Chemical Physics, Vol. 149, Issue 16
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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
DOI: 10.1063/1.5040900

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
DOI: 10.1063/1.5049143

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
DOI: 10.1063/1.5109572

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
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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
DOI: 10.1103/physrevb.100.045127

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

Abstract

Citation Formats

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis journal, June 2006

Assessing weak hydrogen binding on Ca + centers: An accurate many-body study with large basis sets journal, October 2011

Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces journal, November 2003

Forces in Molecules journal, August 1939

Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians journal, June 2015

Eliminating spin contamination in auxiliary-field quantum Monte Carlo: Realistic potential energy curve of F2 journal, March 2008

Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states journal, March 2009

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms journal, December 2015

Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory journal, April 1998

Correlated sampling in quantum Monte Carlo: A route to forces journal, June 2000

Computation of Ground-State Properties in Molecular Systems: Back-Propagation with Auxiliary-Field Quantum Monte Carlo journal, October 2017

Quantum Monte Carlo method for the ground state of many-boson systems journal, November 2004

Electronic quantum Monte Carlo calculations of atomic forces, vibrations, and anharmonicities journal, June 2005

Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules journal, June 2007

Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory: Analytical calculation of energy derivatives journal, September 2013

An auxiliary-field quantum Monte Carlo study of the chromium dimer journal, February 2015

Unified Approach for Molecular Dynamics and Density-Functional Theory journal, November 1985

Analytical energy gradients for local coupled-cluster methodsElectronic Supplementary Information available. See http://www.rsc.org/suppdata/cp/b1/b105126c/ journal, January 2001

Accurate, Efficient, and Simple Forces Computed with Quantum Monte Carlo Methods journal, January 2005

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules : I. Theory journal, January 1969

Analytical energy gradients for multiconfiguration self‐consistent field wave functions with frozen core orbitals journal, May 1991

Diffusive behavior of states in the Hubbard-Stratonovitch transformation journal, January 1991

Geometry optimization in density functional methods: Geometry Optimization in Density Functional Methods journal, March 2004

Path integral Monte Carlo calculation of electronic forces journal, October 1998

Practical Schemes for Accurate Forces in Quantum Monte Carlo journal, October 2014

Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer journal, June 2016

Reaction path following by quadratic steepest descent journal, November 1998

Quantum Monte Carlo algorithms for electronic structure at the petascale; the Endstation project journal, July 2008

NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations journal, September 2010

Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants journal, April 2003

Computing forces with quantum Monte Carlo journal, September 2000

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

Constrained path Monte Carlo method for fermion ground states journal, March 1997

Pressure-induced diamond to β -tin transition in bulk silicon: A quantum Monte Carlo study journal, December 2009

Chemical Transformations Approaching Chemical Accuracy via Correlated Sampling in Auxiliary-Field Quantum Monte Carlo journal, May 2017

Finite-Size Correction in Many-Body Electronic Structure Calculations journal, March 2008

Ab initio geometry optimization for large molecules journal, September 1997

Computing accurate forces in quantum Monte Carlo using Pulay’s corrections and energy minimization journal, January 2003

Algorithmic differentiation and the calculation of forces by quantum Monte Carlo journal, December 2010

Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method journal, May 2018

Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo journal, October 2018

Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide journal, October 2018

Non-orthogonal multi-Slater determinant expansions in auxiliary field quantum Monte Carlo journal, February 2019

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

Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches journal, August 2019

Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure journal, July 2019

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
journal, June 2006

Assessing weak hydrogen binding on Ca ⁺ centers: An accurate many-body study with large basis sets
journal, October 2011

Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces
journal, November 2003

Forces in Molecules
journal, August 1939

Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians
journal, June 2015

Eliminating spin contamination in auxiliary-field quantum Monte Carlo: Realistic potential energy curve of F2
journal, March 2008

Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states
journal, March 2009

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015

Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory
journal, April 1998

Correlated sampling in quantum Monte Carlo: A route to forces
journal, June 2000

Computation of Ground-State Properties in Molecular Systems: Back-Propagation with Auxiliary-Field Quantum Monte Carlo
journal, October 2017

Quantum Monte Carlo method for the ground state of many-boson systems
journal, November 2004

Electronic quantum Monte Carlo calculations of atomic forces, vibrations, and anharmonicities
journal, June 2005

Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules
journal, June 2007

Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory: Analytical calculation of energy derivatives
journal, September 2013

An auxiliary-field quantum Monte Carlo study of the chromium dimer
journal, February 2015

Unified Approach for Molecular Dynamics and Density-Functional Theory
journal, November 1985

Analytical energy gradients for local coupled-cluster methodsElectronic Supplementary Information available. See http://www.rsc.org/suppdata/cp/b1/b105126c/
journal, January 2001

Accurate, Efficient, and Simple Forces Computed with Quantum Monte Carlo Methods
journal, January 2005

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules : I. Theory
journal, January 1969

Analytical energy gradients for multiconfiguration self‐consistent field wave functions with frozen core orbitals
journal, May 1991

Diffusive behavior of states in the Hubbard-Stratonovitch transformation
journal, January 1991

Geometry optimization in density functional methods: Geometry Optimization in Density Functional Methods
journal, March 2004

Path integral Monte Carlo calculation of electronic forces
journal, October 1998

Practical Schemes for Accurate Forces in Quantum Monte Carlo
journal, October 2014

Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer
journal, June 2016

Reaction path following by quadratic steepest descent
journal, November 1998

Quantum Monte Carlo algorithms for electronic structure at the petascale; the Endstation project
journal, July 2008

NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
journal, September 2010

Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
journal, April 2003

Computing forces with quantum Monte Carlo
journal, September 2000

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

Constrained path Monte Carlo method for fermion ground states
journal, March 1997

Pressure-induced diamond to $β$ -tin transition in bulk silicon: A quantum Monte Carlo study
journal, December 2009

Chemical Transformations Approaching Chemical Accuracy via Correlated Sampling in Auxiliary-Field Quantum Monte Carlo
journal, May 2017

Finite-Size Correction in Many-Body Electronic Structure Calculations
journal, March 2008

Ab initio geometry optimization for large molecules
journal, September 1997

Computing accurate forces in quantum Monte Carlo using Pulay’s corrections and energy minimization
journal, January 2003

Algorithmic differentiation and the calculation of forces by quantum Monte Carlo
journal, December 2010

Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
journal, May 2018

Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo
journal, October 2018

Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide
journal, October 2018

Non-orthogonal multi-Slater determinant expansions in auxiliary field quantum Monte Carlo
journal, February 2019

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

Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
journal, August 2019

Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure
journal, July 2019