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Title: Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo

Abstract

We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors.

Authors:
 [1]; ORCiD logo [2]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Physics
  2. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1567167
Alternate Identifier(s):
OSTI ID: 1529687
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Chemistry Chemical Physics. PCCP (Print)
Additional Journal Information:
Journal Name: Physical Chemistry Chemical Physics. PCCP (Print); Journal Volume: 21; Journal Issue: 27; Journal ID: ISSN 1463-9076
Publisher:
Royal Society of Chemistry
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Otis, Leon, and Neuscamman, Eric. Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo. United States: N. p., 2019. Web. doi:10.1039/c9cp02269d.
Otis, Leon, & Neuscamman, Eric. Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo. United States. doi:10.1039/c9cp02269d.
Otis, Leon, and Neuscamman, Eric. Tue . "Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo". United States. doi:10.1039/c9cp02269d. https://www.osti.gov/servlets/purl/1567167.
@article{osti_1567167,
title = {Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo},
author = {Otis, Leon and Neuscamman, Eric},
abstractNote = {We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors.},
doi = {10.1039/c9cp02269d},
journal = {Physical Chemistry Chemical Physics. PCCP (Print)},
number = 27,
volume = 21,
place = {United States},
year = {2019},
month = {1}
}

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Cited by: 4 works
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    Works referencing / citing this record:

    Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz
    journal, November 2018

    • Blunt, Nick S.; Neuscamman, Eric
    • Journal of Chemical Theory and Computation, Vol. 15, Issue 1
    • DOI: 10.1021/acs.jctc.8b00879

    Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory
    journal, March 2017

    • Sharma, Sandeep; Holmes, Adam A.; Jeanmairet, Guillaume
    • Journal of Chemical Theory and Computation, Vol. 13, Issue 4
    • DOI: 10.1021/acs.jctc.6b01028

    Optimization of quantum Monte Carlo wave functions using analytical energy derivatives
    journal, February 2000

    • Lin, Xi; Zhang, Hongkai; Rappe, Andrew M.
    • The Journal of Chemical Physics, Vol. 112, Issue 6
    • DOI: 10.1063/1.480839

    Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods
    journal, July 2007

    • Sorella, Sandro; Casula, Michele; Rocca, Dario
    • The Journal of Chemical Physics, Vol. 127, Issue 1
    • DOI: 10.1063/1.2746035

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


    Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo
    journal, November 2017

    • Blunt, N. S.; Neuscamman, Eric
    • The Journal of Chemical Physics, Vol. 147, Issue 19
    • DOI: 10.1063/1.4998197

    Energy-consistent pseudopotentials for quantum Monte Carlo calculations
    journal, June 2007

    • Burkatzki, M.; Filippi, C.; Dolg, M.
    • The Journal of Chemical Physics, Vol. 126, Issue 23
    • DOI: 10.1063/1.2741534

    The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
    journal, January 1975


    σ -SCF: A direct energy-targeting method to mean-field excited states
    journal, December 2017

    • Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D.
    • The Journal of Chemical Physics, Vol. 147, Issue 21
    • DOI: 10.1063/1.5001262

    Suppressing Ionic Terms with Number-Counting Jastrow Factors in Real Space
    journal, April 2017

    • Goetz, Brett Van Der; Neuscamman, Eric
    • Journal of Chemical Theory and Computation, Vol. 13, Issue 5
    • DOI: 10.1021/acs.jctc.7b00158

    Improved Optimization for the Cluster Jastrow Antisymmetric Geminal Power and Tests on Triple-Bond Dissociations
    journal, June 2016


    Structural Optimization by Quantum Monte Carlo: Investigating the Low-Lying Excited States of Ethylene
    journal, March 2012

    • Barborini, Matteo; Sorella, Sandro; Guidoni, Leonardo
    • Journal of Chemical Theory and Computation, Vol. 8, Issue 4
    • DOI: 10.1021/ct200724q

    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

    Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions
    journal, February 2015

    • Lüchow, Arne; Sturm, Alexander; Schulte, Christoph
    • The Journal of Chemical Physics, Vol. 142, Issue 8
    • DOI: 10.1063/1.4909554

    Approximating strongly correlated wave functions with correlator product states
    journal, December 2009


    Optimizing large parameter sets in variational quantum Monte Carlo
    journal, January 2012


    Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo
    journal, April 2015

    • Zen, Andrea; Luo, Ye; Mazzola, Guglielmo
    • The Journal of Chemical Physics, Vol. 142, Issue 14
    • DOI: 10.1063/1.4917171

    Quantum Monte Carlo simulations of solids
    journal, January 2001


    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
    • DOI: 10.1063/1.1924690

    Resonating valence bond wave function with molecular orbitals: Application to first-row molecules
    journal, October 2009

    • Marchi, Mariapia; Azadi, Sam; Casula, Michele
    • The Journal of Chemical Physics, Vol. 131, Issue 15
    • DOI: 10.1063/1.3249966

    Geminal wave functions with Jastrow correlation: A first application to atoms
    journal, October 2003

    • Casula, Michele; Sorella, Sandro
    • The Journal of Chemical Physics, Vol. 119, Issue 13
    • DOI: 10.1063/1.1604379

    Molecular hydrogen adsorbed on benzene: Insights from a quantum Monte Carlo study
    journal, October 2008

    • Beaudet, Todd D.; Casula, Michele; Kim, Jeongnim
    • The Journal of Chemical Physics, Vol. 129, Issue 16
    • DOI: 10.1063/1.2987716

    Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations
    journal, August 1997

    • Huang, Chien-Jung; Umrigar, C. J.; Nightingale, M. P.
    • The Journal of Chemical Physics, Vol. 107, Issue 8
    • DOI: 10.1063/1.474658

    Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow–Slater Expansions
    journal, October 2017

    • Assaraf, Roland; Moroni, S.; Filippi, Claudia
    • Journal of Chemical Theory and Computation, Vol. 13, Issue 11
    • DOI: 10.1021/acs.jctc.7b00648

    Size Consistent Excited States via Algorithmic Transformations between Variational Principles
    journal, November 2017

    • Shea, Jacqueline A. R.; Neuscamman, Eric
    • Journal of Chemical Theory and Computation, Vol. 13, Issue 12
    • DOI: 10.1021/acs.jctc.7b00923

    Communication: Variation after response in quantum Monte Carlo
    journal, August 2016

    • Neuscamman, Eric
    • The Journal of Chemical Physics, Vol. 145, Issue 8
    • DOI: 10.1063/1.4961686

    Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
    journal, April 2016

    • Schriber, Jeffrey B.; Evangelista, Francesco A.
    • The Journal of Chemical Physics, Vol. 144, Issue 16
    • DOI: 10.1063/1.4948308

    Wave function optimization in the variational Monte Carlo method
    journal, June 2005


    Energy and Variance Optimization of Many-Body Wave Functions
    journal, April 2005


    A full-configuration benchmark for the N2 molecule
    journal, September 1999


    Recent progresses on diarylethene based photochromic switches
    journal, January 2004

    • Tian, He; Yang, Songjie
    • Chemical Society Reviews, Vol. 33, Issue 2
    • DOI: 10.1039/b302356g

    Communication: A Jastrow factor coupled cluster theory for weak and strong electron correlation
    journal, November 2013

    • Neuscamman, Eric
    • The Journal of Chemical Physics, Vol. 139, Issue 18
    • DOI: 10.1063/1.4829536

    Correlated geminal wave function for molecules: An efficient resonating valence bond approach
    journal, October 2004

    • Casula, Michele; Attaccalite, Claudio; Sorella, Sandro
    • The Journal of Chemical Physics, Vol. 121, Issue 15
    • DOI: 10.1063/1.1794632

    Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
    journal, May 2008

    • Toulouse, Julien; Umrigar, C. J.
    • The Journal of Chemical Physics, Vol. 128, Issue 17
    • DOI: 10.1063/1.2908237

    Configuration interaction calculations on the nitrogen molecule
    journal, January 1974

    • Langhoff, Stephen R.; Davidson, Ernest R.
    • International Journal of Quantum Chemistry, Vol. 8, Issue 1
    • DOI: 10.1002/qua.560080106

    ImprovedSCF convergence acceleration
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