Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry

Abstract

We introduce an implementation of the truncated many-body expansion, MBE(n), in which the n-body corrections are screened using the effective fragment potential force field, and only those that exceed a specified energy threshold are computed at a quantum-mechanical level of theory. This energy-screened MBE(n) approach is tested at the n = 3 level for a sequence of water clusters, (H2O)N=6–34. A threshold of 0.25 kJ/mol eliminates more than 80% of the subsystem electronic structure calculations and is even more efficacious in that respect than is distance-based screening. Even so, the energy-screened MBE(3) method is faithful to a full-system quantum chemistry calculation to within 1–2 kJ/mol/monomer, even in good quality basis sets such as aug-cc-pVTZ. These errors can be reduced by means of a two-layer approach that involves a Hartree–Fock calculation for the entire cluster. Such a correction proves to be necessary in order to obtain accurate relative energies for conformational isomers of (H2O)20, but the cost of a full-system Hartree–Fock calculation remains smaller than the cost of three-body subsystem calculations at correlated levels of theory. At the level of second-order Møller–Plesset perturbation theory (MP2), a screened MBE(3) calculation plus a full-system Hartree–Fock calculation is less expensive than a full-system MP2more » calculation starting at N = 12 water molecules. This is true even if all MBE(3) subsystem calculations are performed on a single 40-core compute node, i.e., without significant parallelization. Energy-screened MBE(n) thus provides a fragment-based method that is accurate, stable in large basis sets, and low in cost, even when the latter is measured in aggregate computer time.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  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)
OSTI Identifier:
1604449
Grant/Contract Number:  
SC0008850
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 16; Journal Issue: 1; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Liu, Kuan-Yu, and Herbert, John M. Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry. United States: N. p., 2019. Web. doi:10.1021/acs.jctc.9b01095.
Copy to clipboard
Liu, Kuan-Yu, & Herbert, John M. Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry. United States. https://doi.org/10.1021/acs.jctc.9b01095
Copy to clipboard
Liu, Kuan-Yu, and Herbert, John M. Mon . "Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry". United States. https://doi.org/10.1021/acs.jctc.9b01095. https://www.osti.gov/servlets/purl/1604449.
Copy to clipboard
@article{osti_1604449,
title = {Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry},
author = {Liu, Kuan-Yu and Herbert, John M.},
abstractNote = {We introduce an implementation of the truncated many-body expansion, MBE(n), in which the n-body corrections are screened using the effective fragment potential force field, and only those that exceed a specified energy threshold are computed at a quantum-mechanical level of theory. This energy-screened MBE(n) approach is tested at the n = 3 level for a sequence of water clusters, (H2O)N=6–34. A threshold of 0.25 kJ/mol eliminates more than 80% of the subsystem electronic structure calculations and is even more efficacious in that respect than is distance-based screening. Even so, the energy-screened MBE(3) method is faithful to a full-system quantum chemistry calculation to within 1–2 kJ/mol/monomer, even in good quality basis sets such as aug-cc-pVTZ. These errors can be reduced by means of a two-layer approach that involves a Hartree–Fock calculation for the entire cluster. Such a correction proves to be necessary in order to obtain accurate relative energies for conformational isomers of (H2O)20, but the cost of a full-system Hartree–Fock calculation remains smaller than the cost of three-body subsystem calculations at correlated levels of theory. At the level of second-order Møller–Plesset perturbation theory (MP2), a screened MBE(3) calculation plus a full-system Hartree–Fock calculation is less expensive than a full-system MP2 calculation starting at N = 12 water molecules. This is true even if all MBE(3) subsystem calculations are performed on a single 40-core compute node, i.e., without significant parallelization. Energy-screened MBE(n) thus provides a fragment-based method that is accurate, stable in large basis sets, and low in cost, even when the latter is measured in aggregate computer time.},
doi = {10.1021/acs.jctc.9b01095},
journal = {Journal of Chemical Theory and Computation},
number = 1,
volume = 16,
place = {United States},
year = {2019},
month = {11}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1021/acs.jctc.9b01095
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 35 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Fantasy versus reality in fragment-based quantum chemistry
journal, November 2019

  • Herbert, John M.
  • The Journal of Chemical Physics, Vol. 151, Issue 17
  • DOI: 10.1063/1.5126216

Fragmentation Methods: A Route to Accurate Calculations on Large Systems
journal, August 2011

  • Gordon, Mark S.; Fedorov, Dmitri G.; Pruitt, Spencer R.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200093j

Energy-Based Molecular Fragmentation Methods
journal, April 2015

  • Collins, Michael A.; Bettens, Ryan P. A.
  • Chemical Reviews, Vol. 115, Issue 12
  • DOI: 10.1021/cr500455b

Accurate Composite and Fragment-Based Quantum Chemical Models for Large Molecules
journal, April 2015

  • Raghavachari, Krishnan; Saha, Arjun
  • Chemical Reviews, Vol. 115, Issue 12
  • DOI: 10.1021/cr500606e

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

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

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

Energy benchmarks for water clusters and ice structures from an embedded many-body expansion
journal, September 2013

  • Gillan, M. J.; Alfè, D.; Bygrave, P. J.
  • The Journal of Chemical Physics, Vol. 139, Issue 11
  • DOI: 10.1063/1.4820906

Correlation effects and many-body interactions in water clusters
journal, January 2018

  • Heßelmann, Andreas
  • Beilstein Journal of Organic Chemistry, Vol. 14
  • DOI: 10.3762/bjoc.14.83

Pragmatic Many-Body Approach for Economic MP2 Energy Estimation of Molecular Clusters
journal, May 2019

  • Khire, Subodh S.; Gadre, Shridhar R.
  • The Journal of Physical Chemistry A, Vol. 123, Issue 23
  • DOI: 10.1021/acs.jpca.9b03481

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

Benchmark Study of the Interaction Energy for an (H 2 O) 16 Cluster: Quantum Monte Carlo and Complete Basis Set Limit MP2 Results
journal, June 2013

  • Wang, Fang-Fang; Deible, Michael J.; Jordan, Kenneth D.
  • The Journal of Physical Chemistry A, Vol. 117, Issue 32
  • DOI: 10.1021/jp404541c

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

Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs
journal, October 2017

  • Liu, Kuan-Yu; Herbert, John M.
  • The Journal of Chemical Physics, Vol. 147, Issue 16
  • DOI: 10.1063/1.4986110

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

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

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

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

Approximating quantum many-body intermolecular interactions in molecular clusters using classical polarizable force fields
journal, April 2009

  • Beran, Gregory J. O.
  • The Journal of Chemical Physics, Vol. 130, Issue 16
  • DOI: 10.1063/1.3121323

Predicting Organic Crystal Lattice Energies with Chemical Accuracy
journal, December 2010

  • Beran, Gregory J. O.; Nanda, Kaushik
  • The Journal of Physical Chemistry Letters, Vol. 1, Issue 24
  • DOI: 10.1021/jz101383z

Accurate Molecular Crystal Lattice Energies from a Fragment QM/MM Approach with On-the-Fly Ab Initio Force Field Parametrization
journal, October 2011

  • Wen, Shuhao; Beran, Gregory J. O.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 11
  • DOI: 10.1021/ct200541h

Prediction of organic molecular crystal geometries from MP2-level fragment quantum mechanical/molecular mechanical calculations
journal, November 2012

  • Nanda, Kaushik D.; Beran, Gregory J. O.
  • The Journal of Chemical Physics, Vol. 137, Issue 17
  • DOI: 10.1063/1.4764063

Practical quantum mechanics-based fragment methods for predicting molecular crystal properties
journal, January 2012

  • Wen, Shuhao; Nanda, Kaushik; Huang, Yuanhang
  • Physical Chemistry Chemical Physics, Vol. 14, Issue 21
  • DOI: 10.1039/c2cp23949c

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

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

The Effective Fragment Potential Method:  A QM-Based MM Approach to Modeling Environmental Effects in Chemistry
journal, January 2001

  • Gordon, Mark S.; Freitag, Mark A.; Bandyopadhyay, Pradipta
  • The Journal of Physical Chemistry A, Vol. 105, Issue 2
  • DOI: 10.1021/jp002747h

Noncovalent Interactions in Extended Systems Described by the Effective Fragment Potential Method: Theory and Application to Nucleobase Oligomers
journal, December 2010

  • Ghosh, Debashree; Kosenkov, Dmytro; Vanovschi, Vitalii
  • The Journal of Physical Chemistry A, Vol. 114, Issue 48
  • DOI: 10.1021/jp107557p

Accurate Prediction of Noncovalent Interaction Energies with the Effective Fragment Potential Method: Comparison of Energy Components to Symmetry-Adapted Perturbation Theory for the S22 Test Set
journal, July 2012

  • Flick, Joanna C.; Kosenkov, Dmytro; Hohenstein, Edward G.
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 8
  • DOI: 10.1021/ct200673a

Exploring chemistry with the fragment molecular orbital method
journal, January 2012

  • Fedorov, Dmitri G.; Nagata, Takeshi; Kitaura, Kazuo
  • Physical Chemistry Chemical Physics, Vol. 14, Issue 21
  • DOI: 10.1039/c2cp23784a

The fragment molecular orbital method: theoretical development, implementation in GAMESS, and applications: Fragment molecular orbital method in GAMESS
journal, June 2017

  • Fedorov, Dmitri G.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 7, Issue 6
  • DOI: 10.1002/wcms.1322

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

Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V
journal, February 2015

  • Mardirossian, Narbe; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 142, Issue 7
  • DOI: 10.1063/1.4907719

ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation
journal, June 2016

  • Mardirossian, Narbe; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 144, Issue 21
  • DOI: 10.1063/1.4952647

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals
journal, April 2017

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

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

LIBEFP: A new parallel implementation of the effective fragment potential method as a portable software library
journal, July 2013

  • Kaliman, Ilya A.; Slipchenko, Lyudmila V.
  • Journal of Computational Chemistry, Vol. 34, Issue 26
  • DOI: 10.1002/jcc.23375

Fast determination of the optimal rotational matrix for macromolecular superpositions
journal, January 2009

  • Liu, Pu; Agrafiotis, Dimitris K.; Theobald, Douglas L.
  • Journal of Computational Chemistry
  • DOI: 10.1002/jcc.21439

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit
journal, November 2007

  • Santra, Biswajit; Michaelides, Angelos; Scheffler, Matthias
  • The Journal of Chemical Physics, Vol. 127, Issue 18
  • DOI: 10.1063/1.2790009

Evaluation of B3LYP, X3LYP, and M06-Class Density Functionals for Predicting the Binding Energies of Neutral, Protonated, and Deprotonated Water Clusters
journal, March 2009

  • Bryantsev, Vyacheslav S.; Diallo, Mamadou S.; van Duin, Adri C. T.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 4
  • DOI: 10.1021/ct800549f

Perspective: How good is DFT for water?
journal, April 2016

  • Gillan, Michael J.; Alfè, Dario; Michaelides, Angelos
  • The Journal of Chemical Physics, Vol. 144, Issue 13
  • DOI: 10.1063/1.4944633

Effective Fragment Potential Method for H-Bonding: How To Obtain Parameters for Nonrigid Fragments
journal, July 2017

  • Dubinets, Nikita; Slipchenko, Lyudmila V.
  • The Journal of Physical Chemistry A, Vol. 121, Issue 28
  • DOI: 10.1021/acs.jpca.7b01701

Effective Fragment Molecular Orbital Method: A Merger of the Effective Fragment Potential and Fragment Molecular Orbital Methods †
journal, August 2010

  • Steinmann, Casper; Fedorov, Dmitri G.; Jensen, Jan H.
  • The Journal of Physical Chemistry A, Vol. 114, Issue 33
  • DOI: 10.1021/jp101498m

The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds
journal, July 2012

Fully Integrated Effective Fragment Molecular Orbital Method
journal, April 2013

  • Pruitt, Spencer R.; Steinmann, Casper; Jensen, Jan H.
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 5
  • DOI: 10.1021/ct4001119

Analytic Gradients for the Effective Fragment Molecular Orbital Method
journal, September 2016

  • Bertoni, Colleen; Gordon, Mark S.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 10
  • DOI: 10.1021/acs.jctc.6b00337

Efficient and Accurate Fragmentation Methods
journal, May 2014

  • Pruitt, Spencer R.; Bertoni, Colleen; Brorsen, Kurt R.
  • Accounts of Chemical Research, Vol. 47, Issue 9
  • DOI: 10.1021/ar500097m

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

A multicentered approach to integrated QM/QM calculations. Applications to multiply hydrogen bonded systems
journal, August 2003

  • Hopkins, Brian W.; Tschumper, Gregory S.
  • Journal of Computational Chemistry, Vol. 24, Issue 13
  • DOI: 10.1002/jcc.10319

Multicentred QM/QM methods for overlapping model systems
journal, January 2005

Integrated quantum mechanical approaches for extended π systems: Multicentered QM/QM studies of the cyanogen and diacetylene trimers
journal, May 2005

Analytic gradients for the multicentred integrated QM:QM method for weakly bound clusters: efficient and accurate 2-body:many-body geometry optimizations
journal, October 2007

  • Elsohly, Adel M.; Shaw, Cynthia L.; Guice, Marlo E.
  • Molecular Physics, Vol. 105, Issue 19-22
  • DOI: 10.1080/00268970701633126

Development of a 3-body:many-body integrated fragmentation method for weakly bound clusters and application to water clusters (H 2 O) n = 3 − 10, 16, 17
journal, July 2011

  • Bates, Desiree M.; Smith, Joshua R.; Janowski, Tomasz
  • The Journal of Chemical Physics, Vol. 135, Issue 4
  • DOI: 10.1063/1.3609922

Efficient and Accurate Methods for the Geometry Optimization of Water Clusters: Application of Analytic Gradients for the Two-Body:Many-Body QM:QM Fragmentation Method to (H 2 O) n , n = 3–10
journal, August 2011

  • Bates, Desiree M.; Smith, Joshua R.; Tschumper, Gregory S.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 9
  • DOI: 10.1021/ct200176t

N -body:Many-body QM:QM vibrational frequencies: Application to small hydrogen-bonded clusters
journal, November 2013

  • Howard, J. Coleman; Tschumper, Gregory S.
  • The Journal of Chemical Physics, Vol. 139, Issue 18
  • DOI: 10.1063/1.4829463

2-body:Many-body QM:QM study of structures, energetics, and vibrational frequencies for microhydrated halide ions
journal, June 2018

Molecules-in-Molecules: An Extrapolated Fragment-Based Approach for Accurate Calculations on Large Molecules and Materials
journal, April 2011

  • Mayhall, Nicholas J.; Raghavachari, Krishnan
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 5
  • DOI: 10.1021/ct200033b

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

Evaluation of Energy Gradients and Infrared Vibrational Spectra through Molecules-in-Molecules Fragment-Based Approach
journal, February 2015

  • Jose, K. V. Jovan; Raghavachari, Krishnan
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 3
  • DOI: 10.1021/ct501026m

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

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

Theoretical Study of Protein–Ligand Interactions Using the Molecules-in-Molecules Fragmentation-Based Method
journal, August 2018

  • Thapa, Bishnu; Beckett, Daniel; Erickson, Jon
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 10
  • DOI: 10.1021/acs.jctc.8b00531

Assessment of Fragmentation Strategies for Large Proteins Using the Multilayer Molecules-in-Molecules Approach
journal, February 2018

  • Thapa, Bishnu; Beckett, Daniel; Jovan Jose, K. V.
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 3
  • DOI: 10.1021/acs.jctc.7b01198

Fragment-Based Approaches for Supramolecular Interaction Energies: Applications to Foldamers and Their Complexes with Anions
journal, November 2018

  • Debnath, Sibali; Sengupta, Arkajyoti; Jose, K. V. Jovan
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 12
  • DOI: 10.1021/acs.jctc.8b00525

Periodic and fragment models based on the local correlation approach
journal, January 2018

  • Usvyat, Denis; Maschio, Lorenzo; Schütz, Martin
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 4
  • DOI: 10.1002/wcms.1357

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

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

Global minima of water clusters (H2O)n, n≤21, described by an empirical potential
journal, April 1998

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

A standard grid for density functional calculations
journal, July 1993

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

Optimization of parameters for semiempirical methods I. Method
journal, March 1989

Optimization of parameters for semiempirical methods II. Applications
journal, March 1989

Ab initio molecular dynamics of liquid water using embedded-fragment second-order many-body perturbation theory towards its accurate property prediction
journal, September 2015

  • Willow, Soohaeng Yoo; Salim, Michael A.; Kim, Kwang S.
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep14358

Corrected small basis set Hartree-Fock method for large systems
journal, May 2013

  • Sure, Rebecca; Grimme, Stefan
  • Journal of Computational Chemistry, Vol. 34, Issue 19
  • DOI: 10.1002/jcc.23317

Using vibrational modes in the search for global minima of atomic and molecular clusters
journal, October 2006

    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: