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Title: Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs

Abstract

Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H2O)37, four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H2O)20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculationsmore » can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500–1800 basis functions.« less

Authors:
 [1]; ORCiD logo [1]
  1. The Ohio State Univ., Columbus, OH (United States)
Publication Date:
Research Org.:
The Ohio State Univ., Columbus, OH (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division
OSTI Identifier:
1604463
Alternate Identifier(s):
OSTI ID: 1389890
Grant/Contract Number:  
SC0008850; SC0008550
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 16; 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

Liu, Kuan-Yu, and Herbert, John M. Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs. United States: N. p., 2017. Web. doi:10.1063/1.4986110.
Liu, Kuan-Yu, & Herbert, John M. Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs. United States. doi:10.1063/1.4986110.
Liu, Kuan-Yu, and Herbert, John M. Wed . "Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs". United States. doi:10.1063/1.4986110. https://www.osti.gov/servlets/purl/1604463.
@article{osti_1604463,
title = {Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs},
author = {Liu, Kuan-Yu and Herbert, John M.},
abstractNote = {Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H2O)37, four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H2O)20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500–1800 basis functions.},
doi = {10.1063/1.4986110},
journal = {Journal of Chemical Physics},
number = 16,
volume = 147,
place = {United States},
year = {2017},
month = {9}
}

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Works referenced in this record:

Massively parallel algorithm and implementation of RI-MP2 energy calculation for peta-scale many-core supercomputers
journal, September 2016

  • Katouda, Michio; Naruse, Akira; Hirano, Yukihiko
  • Journal of Computational Chemistry, Vol. 37, Issue 30
  • DOI: 10.1002/jcc.24491

Protein-protein interactions from linear-scaling first-principles quantum-mechanical calculations
journal, August 2010


Density functional theory calculations on entire proteins for free energies of binding: Application to a model polar binding site: Free Energies of Binding from DFT Calculations on Entire Proteins
journal, October 2014

  • Fox, Stephen J.; Dziedzic, Jacek; Fox, Thomas
  • Proteins: Structure, Function, and Bioinformatics, Vol. 82, Issue 12
  • DOI: 10.1002/prot.24686

Cluster-in-molecule local correlation method for post-Hartree–Fock calculations of large systems
journal, February 2016


Ab Initio Quantum Chemistry for Protein Structures
journal, October 2012

  • Kulik, Heather J.; Luehr, Nathan; Ufimtsev, Ivan S.
  • The Journal of Physical Chemistry B, Vol. 116, Issue 41
  • DOI: 10.1021/jp307741u

Large-Scale MP2 Calculations on the Blue Gene Architecture Using the Fragment Molecular Orbital Method
journal, December 2011

  • Fletcher, Graham D.; Fedorov, Dmitri G.; Pruitt, Spencer R.
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 1
  • DOI: 10.1021/ct200548v

The Fragment Molecular Orbital Method for Geometry Optimizations of Polypeptides and Proteins
journal, April 2007

  • Fedorov, Dmitri G.; Ishida, Toyokazu; Uebayasi, Masami
  • The Journal of Physical Chemistry A, Vol. 111, Issue 14
  • DOI: 10.1021/jp0671042

Geometry Optimization of the Active Site of a Large System with the Fragment Molecular Orbital Method
journal, January 2011

  • Fedorov, Dmitri G.; Alexeev, Yuri; Kitaura, Kazuo
  • The Journal of Physical Chemistry Letters, Vol. 2, Issue 4
  • DOI: 10.1021/jz1016894

Appraisal of molecular tailoring approach for large clusters
journal, March 2013

  • Sahu, Nityananda; Yeole, Sachin D.; Gadre, Shridhar R.
  • The Journal of Chemical Physics, Vol. 138, Issue 10
  • DOI: 10.1063/1.4793706

Molecular Tailoring Approach: A Route for ab Initio Treatment of Large Clusters
journal, May 2014

  • Sahu, Nityananda; Gadre, Shridhar R.
  • Accounts of Chemical Research, Vol. 47, Issue 9
  • DOI: 10.1021/ar500079b

Generalized Energy-Based Fragmentation Approach and Its Applications to Macromolecules and Molecular Aggregates
journal, May 2014

  • Li, Shuhua; Li, Wei; Ma, Jing
  • Accounts of Chemical Research, Vol. 47, Issue 9
  • DOI: 10.1021/ar500038z

Fragment Quantum Mechanical Calculation of Proteins and Its Applications
journal, May 2014

  • He, Xiao; Zhu, Tong; Wang, Xianwei
  • Accounts of Chemical Research, Vol. 47, Issue 9
  • DOI: 10.1021/ar500077t

Analysis of Different Fragmentation Strategies on a Variety of Large Peptides: Implementation of a Low Level of Theory in Fragment-Based Methods Can Be a Crucial Factor
journal, April 2015

  • Saha, Arjun; Raghavachari, Krishnan
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 5
  • DOI: 10.1021/ct501045s

Efficient Geometry Optimization of Large Molecular Systems in Solution Using the Fragment Molecular Orbital Method
journal, December 2016

  • Nakata, Hiroya; Fedorov, Dmitri G.
  • The Journal of Physical Chemistry A, Vol. 120, Issue 49
  • DOI: 10.1021/acs.jpca.6b09743

Molecules-in-molecules fragment-based method for the evaluation of Raman spectra of large molecules
journal, September 2015


Fragment-Based Approach for the Evaluation of NMR Chemical Shifts for Large Biomolecules Incorporating the Effects of the Solvent Environment
journal, February 2017

  • Jose, K. V. Jovan; Raghavachari, Krishnan
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 3
  • DOI: 10.1021/acs.jctc.6b00922

Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals
journal, October 2014

  • Hartman, Joshua D.; Beran, Gregory J. O.
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 11
  • DOI: 10.1021/ct500749h

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions
journal, October 2016

  • Hartman, Joshua D.; Day, Graeme M.; Beran, Gregory J. O.
  • Crystal Growth & Design, Vol. 16, Issue 11
  • DOI: 10.1021/acs.cgd.6b01157

Predicting Molecular Crystal Properties from First Principles: Finite-Temperature Thermochemistry to NMR Crystallography
journal, October 2016

  • Beran, Gregory J. O.; Hartman, Joshua D.; Heit, Yonaton N.
  • Accounts of Chemical Research, Vol. 49, Issue 11
  • DOI: 10.1021/acs.accounts.6b00404

When are Many-Body Effects Significant?
journal, November 2016

  • Ouyang, John F.; Bettens, Ryan P. A.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 12
  • DOI: 10.1021/acs.jctc.6b00864

Fragment Quantum Mechanical Method for Large-Sized Ion–Water Clusters
journal, April 2017

  • Liu, Jinfeng; Qi, Lian-Wen; Zhang, John Z. H.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 5
  • DOI: 10.1021/acs.jctc.7b00149

A generalized many-body expansion and a unified view of fragment-based methods in electronic structure theory
journal, August 2012

  • Richard, Ryan M.; Herbert, John M.
  • The Journal of Chemical Physics, Vol. 137, Issue 6
  • DOI: 10.1063/1.4742816

Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions
journal, May 2016

  • Cisneros, Gerardo Andrés; Wikfeldt, Kjartan Thor; Ojamäe, Lars
  • Chemical Reviews, Vol. 116, Issue 13
  • DOI: 10.1021/acs.chemrev.5b00644

Theoretical Characterization of the (H 2 O) 21 Cluster:  Application of an n -body Decomposition Procedure
journal, September 2006

  • Cui, Jun; Liu, Hanbin; Jordan, Kenneth D.
  • The Journal of Physical Chemistry B, Vol. 110, Issue 38
  • DOI: 10.1021/jp056416m

Understanding the many-body expansion for large systems. I. Precision considerations
journal, July 2014

  • Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
  • The Journal of Chemical Physics, Vol. 141, Issue 1
  • DOI: 10.1063/1.4885846

Understanding the many-body expansion for large systems. II. Accuracy considerations
journal, April 2016

  • Lao, Ka Un; Liu, Kuan-Yu; Richard, Ryan M.
  • The Journal of Chemical Physics, Vol. 144, Issue 16
  • DOI: 10.1063/1.4947087

Electrostatically Embedded Many-Body Expansion for Large Systems, with Applications to Water Clusters
journal, November 2006

  • Dahlke, Erin E.; Truhlar, Donald G.
  • Journal of Chemical Theory and Computation, Vol. 3, Issue 1
  • DOI: 10.1021/ct600253j

Evaluation of the Electrostatically Embedded Many-Body Expansion and the Electrostatically Embedded Many-Body Expansion of the Correlation Energy by Application to Low-Lying Water Hexamers
journal, December 2007

  • Dahlke, Erin E.; Leverentz, Hannah R.; Truhlar, Donald G.
  • Journal of Chemical Theory and Computation, Vol. 4, Issue 1
  • DOI: 10.1021/ct700183y

Aiming for Benchmark Accuracy with the Many-Body Expansion
journal, June 2014

  • Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
  • Accounts of Chemical Research, Vol. 47, Issue 9
  • DOI: 10.1021/ar500119q

Approaching the complete-basis limit with a truncated many-body expansion
journal, December 2013

  • Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
  • The Journal of Chemical Physics, Vol. 139, Issue 22
  • DOI: 10.1063/1.4836637

Generalized Switch Functions in the Multilevel Many-Body Expansion Method and Its Application to Water Clusters
journal, April 2017

  • Chen, Guo Dong; Weng, Jingwei; Song, Guoliang
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 5
  • DOI: 10.1021/acs.jctc.7b00144

Many-Body Expansion with Overlapping Fragments: Analysis of Two Approaches
journal, February 2013

  • Richard, Ryan M.; Herbert, John M.
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 3
  • DOI: 10.1021/ct300985h

Benchmark Relative Energies for Large Water Clusters with the Generalized Energy-Based Fragmentation Method
journal, May 2017

  • Yuan, Dandan; Li, Yunzhi; Ni, Zhigang
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 6
  • DOI: 10.1021/acs.jctc.7b00284

Achieving the CCSD(T) Basis-Set Limit in Sizable Molecular Clusters: Counterpoise Corrections for the Many-Body Expansion
journal, July 2013

  • Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
  • The Journal of Physical Chemistry Letters, Vol. 4, Issue 16
  • DOI: 10.1021/jz401368u

Trouble with the Many-Body Expansion
journal, June 2014

  • Ouyang, John F.; Cvitkovic, Milan W.; Bettens, Ryan P. A.
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 9
  • DOI: 10.1021/ct500396b

Fast electron correlation methods for molecular clusters without basis set superposition errors
journal, February 2008

  • Kamiya, Muneaki; Hirata, So; Valiev, Marat
  • The Journal of Chemical Physics, Vol. 128, Issue 7
  • DOI: 10.1063/1.2828517

Many-Body Basis Set Superposition Effect
journal, October 2015

  • Ouyang, John F.; Bettens, Ryan P. A.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 11
  • DOI: 10.1021/acs.jctc.5b00343

The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors
journal, October 1970


van der Waals interaction potentials: Many-body basis set superposition effects
journal, October 1983


State of the Art in Counterpoise Theory
journal, November 1994

  • van Duijneveldt, Frans B.; van Duijneveldt-van de Rijdt, Jeanne G. C. M.; van Lenthe, Joop H.
  • Chemical Reviews, Vol. 94, Issue 7
  • DOI: 10.1021/cr00031a007

The ONIOM Method and Its Applications
journal, April 2015

  • Chung, Lung Wa; Sameera, W. M. C.; Ramozzi, Romain
  • Chemical Reviews, Vol. 115, Issue 12
  • DOI: 10.1021/cr5004419

Many-Overlapping-Body (MOB) Expansion: A Generalized Many Body Expansion for Nondisjoint Monomers in Molecular Fragmentation Calculations of Covalent Molecules
journal, July 2012

  • Mayhall, Nicholas J.; Raghavachari, Krishnan
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 8
  • DOI: 10.1021/ct300366e

Vibrational Circular Dichroism Spectra for Large Molecules through Molecules-in-Molecules Fragment-Based Approach
journal, August 2015

  • Jose, K. V. Jovan; Beckett, Daniel; Raghavachari, Krishnan
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 9
  • DOI: 10.1021/acs.jctc.5b00647

Water nanodroplets: Predictions of five model potentials
journal, May 2013

  • Kazachenko, Sergey; Thakkar, Ajit J.
  • The Journal of Chemical Physics, Vol. 138, Issue 19
  • DOI: 10.1063/1.4804399

A standard grid for density functional calculations
journal, July 1993


Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
journal, September 2014


Improved minima-hopping. TIP4P water clusters, <mml:math altimg="si3.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:msub><mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> with <mml:math altimg="si4.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mrow><mml:mi>n</mml:mi><mml:mo>⩽</mml:mo><mml:mn>37</mml:mn></mml:mrow></mml:math>
journal, July 2009


ONIOM-based QM:QM electronic embedding method using Löwdin atomic charges: Energies and analytic gradients
journal, March 2010

  • Mayhall, Nicholas J.; Raghavachari, Krishnan; Hratchian, Hrant P.
  • The Journal of Chemical Physics, Vol. 132, Issue 11
  • DOI: 10.1063/1.3315417

Fully analytic energy gradient in the fragment molecular orbital method
journal, March 2011

  • Brorsen, Kurt; Fedorov, Dmitri G.
  • The Journal of Chemical Physics, Vol. 134, Issue 12
  • DOI: 10.1063/1.3568010

Systematic Study of the Embedding Potential Description in the Fragment Molecular Orbital Method
journal, August 2010

  • Fedorov, Dmitri G.; Slipchenko, Lyudmila V.; Kitaura, Kazuo
  • The Journal of Physical Chemistry A, Vol. 114, Issue 33
  • DOI: 10.1021/jp101724p

Use of an auxiliary basis set to describe the polarization in the fragment molecular orbital method
journal, March 2014