Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

Cruz, J. César; Garza, Jorge; Yanai, Takeshi; Hirata, So

doi:10.1063/5.0091973

Title: Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

Abstract

A second-order many-body perturbation correction to the relativistic Dirac–Hartree–Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-cumulative distribution function method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with 92% strong scalability going from 64 to 4096 processors.

Authors:

^[1]; Garza, Jorge ^[1];

^[2];

^[3]

Universidad Autónoma Metropolitana-Iztapalapa, Mexico CIty (Mexico)
Nagoya Univ. (Japan)
Univ. of Illinois at Urbana-Champaign, IL (United States)

Publication Date:: Thu May 19 00:00:00 EDT 2022

Research Org.:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; Japan Society for the Promotion of Science (JSPS); USDOE

OSTI Identifier:: 1870088

Alternate Identifier(s):: OSTI ID: 1871505; OSTI ID: 1871618

Grant/Contract Number:: SC0006028; AC02-05CH11231; 620190; 21H01881; 21K18931; SPEC

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 156; Journal Issue: 22; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; Monte Carlo method; relativistic effects; perturbation theory; electron correlation; parallel computing

Citation Formats


                    Cruz, J. César, Garza, Jorge, Yanai, Takeshi, and Hirata, So. Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method.  United States: N. p., 2022. 
Web.  doi:10.1063/5.0091973.

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                    Cruz, J. César, Garza, Jorge, Yanai, Takeshi, & Hirata, So. Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method.  United States.  https://doi.org/10.1063/5.0091973

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                    Cruz, J. César, Garza, Jorge, Yanai, Takeshi, and Hirata, So. Thu .  
"Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method".  United States.  https://doi.org/10.1063/5.0091973.  https://www.osti.gov/servlets/purl/1870088.

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@article{osti_1870088,

  title        = {Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method},

  author       = {Cruz, J. César and Garza, Jorge and Yanai, Takeshi and Hirata, So},

  abstractNote = {A second-order many-body perturbation correction to the relativistic Dirac–Hartree–Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-cumulative distribution function method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with 92% strong scalability going from 64 to 4096 processors.},

  doi          = {10.1063/5.0091973},

  journal      = {Journal of Chemical Physics},

  number       = 22,

  volume       = 156,

  place        = {United States},

  year         = {Thu May 19 00:00:00 EDT 2022},

  month        = {Thu May 19 00:00:00 EDT 2022}

}

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Stochastic many-body perturbation theory for anharmonic molecular vibrations

Journal Article Hermes, Matthew R. ; Hirata, So ; CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 - Journal of Chemical Physics

A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value ofmore »« less
https://doi.org/10.1063/1.4892614
Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates

Journal Article Doran, Alexander E. ; Hirata, So - Journal of Chemical Physics

Herein, the use of many control variates is proposed as a method to accelerate the second- and third-order Monte Carlo (MC) many-body perturbation (MC-MP2 and MC-MP3) calculations. A control variate is an exactly integrable function that is strongly correlated or anti-correlated with the target function to be integrated by the MC method. Evaluating both integrals as well as their covariances in the same MC run, one can effect a mutual cancellation of the statistical uncertainties and biases in the MC integrations, thereby accelerating its convergence considerably. Six and thirty-six control variates, whose integrals are known a priori, are generated formore »« less
https://doi.org/10.1063/5.0020584

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Title: Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

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Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams journal, January 2014

Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy journal, January 2014

Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in Three Dimensions journal, March 2013

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Projector Monte Carlo method based on Slater determinants: a new sampling method for singlet state calculations journal, September 2011

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Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach journal, June 1991

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A direct MP2 gradient method journal, February 1990

Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems journal, December 2012

A Guided Stochastic Energy-Domain Formulation of the Second Order Møller–Plesset Perturbation Theory journal, December 2013

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A four-index transformation in Dirac's four-component relativistic theory journal, April 2004

Laplace transform techniques in Mo/ller–Plesset perturbation theory journal, January 1992

Construction of the hamiltonian matrix in large configuration interaction calculations journal, March 1973

Stochastic evaluation of second-order Dyson self-energies journal, April 2013

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Efficient recursive computation of molecular integrals over Cartesian Gaussian functions journal, April 1986

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Equation of State Calculations by Fast Computing Machines journal, June 1953

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A fully relativistic Dirac–Hartree–Fock and second-order Mo/ller–Plesset study of the lanthanide and actinide contraction journal, December 1998

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Negative energy states in relativistic quantum chemistry journal, January 2012

Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar journal, August 1990

Exact two-component Hamiltonians revisited journal, July 2009

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space journal, January 2009

A new determinant-based full configuration interaction method journal, November 1984

Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy journal, October 2019

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Quantum Monte Carlo for Ab Initio calculations of energy-relevant materials journal, August 2013

Advances in relativistic molecular quantum mechanics journal, April 2014

Introduction to the Variational and Diffusion Monte Carlo Methods book, January 2016

Metropolis Evaluation of the Hartree–Fock Exchange Energy journal, September 2014

Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers journal, March 1996

Monte Carlo MP2 on Many Graphical Processing Units journal, September 2016

M ONTE C ARLO M ETHODS IN E LECTRONIC S TRUCTURES FOR L ARGE S YSTEMS journal, October 2000

Stochastic Self-Consistent Second-Order Green’s Function Method for Correlation Energies of Large Electronic Systems journal, October 2017

Perspective: Relativistic effects journal, April 2012

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Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo journal, January 2010

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Quantum Monte Carlo and Related Approaches journal, December 2011

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Ideas of relativistic quantum chemistry journal, July 2010

Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams
journal, January 2014

Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy
journal, January 2014

Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in Three Dimensions
journal, March 2013

Essentials of relativistic quantum chemistry
journal, May 2020

Relativistic atomic structure calculations
journal, April 1979

Communication: Explicitly correlated four-component relativistic second-order Møller-Plesset perturbation theory
journal, October 2012

Low-order scaling local electron correlation methods. I. Linear scaling local MP2
journal, October 1999

A new implementation of four-component relativistic density functional method for heavy-atom polyatomic systems
journal, November 2001

Relativistic Hamiltonians for Chemistry: A Primer
journal, November 2011

Direct relativistic MP2: properties of ground state CuF, AgF and AuF
journal, October 1997

Projector Monte Carlo method based on Slater determinants: a new sampling method for singlet state calculations
journal, September 2011

Electron correlation within the relativistic no-pair approximation
journal, August 2016

Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach
journal, June 1991

Foundations of the relativistic theory of many-electron atoms
journal, August 1980

Error estimates on averages of correlated data
journal, July 1989

Introduction to Relativistic Quantum Chemistry
January 2007

A new computational scheme for the Dirac–Hartree–Fock method employing an efficient integral algorithm
journal, April 2001

Projector Monte Carlo method based on configuration state functions. Test applications to the H4 system and dissociation of LiH
journal, October 2008

Recent Development of Relativistic Molecular Theory
journal, May 2005

The calculation of excited state properties with quantum Monte Carlo
journal, November 1988

Infinite-order quasirelativistic density functional method based on the exact matrix quasirelativistic theory
journal, July 2006

A direct MP2 gradient method
journal, February 1990

Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems
journal, December 2012

A Guided Stochastic Energy-Domain Formulation of the Second Order Møller–Plesset Perturbation Theory
journal, December 2013

Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory
journal, July 2017

A four-index transformation in Dirac's four-component relativistic theory
journal, April 2004

Laplace transform techniques in Mo/ller–Plesset perturbation theory
journal, January 1992

Construction of the hamiltonian matrix in large configuration interaction calculations
journal, March 1973

Stochastic evaluation of second-order Dyson self-energies
journal, April 2013

Multireference Stochastic Coupled Cluster
journal, October 2019

Large scale parallelization in stochastic coupled cluster
journal, November 2018

Monte Carlo MP2-F12 for Noncovalent Interactions: The C ₆₀ Dimer
journal, August 2021

The relativistic complete active-space second-order perturbation theory with the four-component Dirac Hamiltonian
journal, December 2006

Stochastic evaluation of second-order many-body perturbation energies
journal, November 2012

Efficient recursive computation of molecular integrals over Cartesian Gaussian functions
journal, April 1986

Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling
journal, September 2020

Equation of State Calculations by Fast Computing Machines
journal, June 1953

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models
journal, June 2012

Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates
journal, September 2020

Making four- and two-component relativistic density functional methods fully equivalent based on the idea of “from atoms to molecule”
journal, September 2007

A fully relativistic Dirac–Hartree–Fock and second-order Mo/ller–Plesset study of the lanthanide and actinide contraction
journal, December 1998

Convergence Acceleration of Parallel Monte Carlo Second-Order Many-Body Perturbation Calculations Using Redundant Walkers
journal, September 2013

Electronic structures of PtCu, PtAg, and PtAu molecules: a Dirac four-component relativistic study
journal, April 2005

Evaluating two-electron-repulsion integrals over arbitrary orbitals using zero variance Monte Carlo: Application to full configuration interaction calculations with Slater-type orbitals
journal, August 2019

Negative energy states in relativistic quantum chemistry
journal, January 2012

Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar
journal, August 1990

Exact two-component Hamiltonians revisited
journal, July 2009

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
journal, January 2009

A new determinant-based full configuration interaction method
journal, November 1984

Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy
journal, October 2019

Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states
journal, April 2013

Second-order Møller-Plesset perturbation theory for molecular Dirac-Hartree-Fock wavefunctions. Theory for up to two open-shell electrons
journal, July 1994

MP2 energy evaluation by direct methods
journal, December 1988

Quantum Monte Carlo for Ab Initio calculations of energy-relevant materials
journal, August 2013

Advances in relativistic molecular quantum mechanics
journal, April 2014

Introduction to the Variational and Diffusion Monte Carlo Methods
book, January 2016

Metropolis Evaluation of the Hartree–Fock Exchange Energy
journal, September 2014

Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers
journal, March 1996

Monte Carlo MP2 on Many Graphical Processing Units
journal, September 2016

M ONTE C ARLO M ETHODS IN E LECTRONIC S TRUCTURES FOR L ARGE S YSTEMS
journal, October 2000

Stochastic Self-Consistent Second-Order Green’s Function Method for Correlation Energies of Large Electronic Systems
journal, October 2017

Perspective: Relativistic effects
journal, April 2012

Semi-direct algorithms for the MP2 energy and gradient
journal, February 1990

Monte Carlo explicitly correlated second-order many-body perturbation theory
journal, October 2016

The zero‐order regular approximation for relativistic effects: The effect of spin–orbit coupling in closed shell molecules
journal, October 1996

Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo
journal, January 2010

Basis-set expansion calculations with the Dirac Hamiltonian
journal, March 1984

Applications of quantum Monte Carlo methods in condensed systems
journal, January 2011

Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method
journal, January 2017

Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions
journal, December 2017

A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules
journal, October 1995

Linear-scaling and parallelisable algorithms for stochastic quantum chemistry
journal, January 2014

Stochastic many-body perturbation theory for electron correlation energies
journal, December 2019

Quantum Monte Carlo and Related Approaches
journal, December 2011

Stochastic Perturbation Theory: A Low-Scaling Approach to Correlated Electronic Energies
journal, October 2007

The ZORA formalism applied to the Dirac-Fock equation
journal, December 1995

Ideas of relativistic quantum chemistry
journal, July 2010

Local Treatment of Electron Correlation
journal, October 1993

Projector Monte Carlo method based on Slater determinants: Test application to singlet excited states of H2O and LiF
journal, January 2010

Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum
journal, October 2019