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

Liu, Kuan-Yu; Herbert, John M.

doi:10.1021/acs.jctc.9b01095

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

Journal Article · 25 November 2019 · Journal of Chemical Theory and Computation

DOI: https://doi.org/10.1021/acs.jctc.9b01095 · OSTI ID:1604449

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The Ohio State Univ., Columbus, OH (United States)

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.

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Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0008850

OSTI ID:: 1604449

Journal Information:: Journal of Chemical Theory and Computation, Vol. 16, Issue 1; ISSN 1549-9618

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (89)

Fantasy versus reality in fragment-based quantum chemistry Herbert, John M. The Journal of Chemical Physics, Vol. 151, Issue 17 https://doi.org/10.1063/1.5126216	journal	November 2019
The Fragment Molecular Orbital Method Fedorov, Dmitri; Kitaura, Kazuo CRC Press https://doi.org/10.1201/9781420078497	book	January 2009
Fragmentation Methods: A Route to Accurate Calculations on Large Systems Gordon, Mark S.; Fedorov, Dmitri G.; Pruitt, Spencer R. Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200093j	journal	August 2011
Energy-Based Molecular Fragmentation Methods Collins, Michael A.; Bettens, Ryan P. A. Chemical Reviews, Vol. 115, Issue 12 https://doi.org/10.1021/cr500455b	journal	April 2015
Accurate Composite and Fragment-Based Quantum Chemical Models for Large Molecules Raghavachari, Krishnan; Saha, Arjun Chemical Reviews, Vol. 115, Issue 12 https://doi.org/10.1021/cr500606e	journal	April 2015
Understanding the many-body expansion for large systems. II. Accuracy considerations Lao, Ka Un; Liu, Kuan-Yu; Richard, Ryan M. The Journal of Chemical Physics, Vol. 144, Issue 16 https://doi.org/10.1063/1.4947087	journal	April 2016
Pair–Pair Approximation to the Generalized Many-Body Expansion: An Alternative to the Four-Body Expansion for ab Initio Prediction of Protein Energetics via Molecular Fragmentation Liu, Jie; Herbert, John M. Journal of Chemical Theory and Computation, Vol. 12, Issue 2 https://doi.org/10.1021/acs.jctc.5b00955	journal	January 2016
A generalized many-body expansion and a unified view of fragment-based methods in electronic structure theory Richard, Ryan M.; Herbert, John M. The Journal of Chemical Physics, Vol. 137, Issue 6 https://doi.org/10.1063/1.4742816	journal	August 2012
Many-Body Expansion with Overlapping Fragments: Analysis of Two Approaches Richard, Ryan M.; Herbert, John M. Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct300985h	journal	February 2013
Efficient Monomer-Based Quantum Chemistry Methods for Molecular and Ionic Clusters Jacobson, Leif D.; Richard, Ryan M.; Lao, Ka Un Annual Reports in Computational Chemistry https://doi.org/10.1016/B978-0-444-62672-1.00002-9	book	January 2013
Energy benchmarks for water clusters and ice structures from an embedded many-body expansion Gillan, M. J.; Alfè, D.; Bygrave, P. J. The Journal of Chemical Physics, Vol. 139, Issue 11 https://doi.org/10.1063/1.4820906	journal	September 2013
Correlation effects and many-body interactions in water clusters Heßelmann, Andreas Beilstein Journal of Organic Chemistry, Vol. 14 https://doi.org/10.3762/bjoc.14.83	journal	January 2018
Pragmatic Many-Body Approach for Economic MP2 Energy Estimation of Molecular Clusters Khire, Subodh S.; Gadre, Shridhar R. The Journal of Physical Chemistry A, Vol. 123, Issue 23 https://doi.org/10.1021/acs.jpca.9b03481	journal	May 2019
Theoretical Characterization of the (H ₂ O) ₂₁ Cluster: Application of an n -body Decomposition Procedure ^† Cui, Jun; Liu, Hanbin; Jordan, Kenneth D. The Journal of Physical Chemistry B, Vol. 110, Issue 38 https://doi.org/10.1021/jp056416m	journal	September 2006
Benchmark Study of the Interaction Energy for an (H ₂ O) ₁₆ Cluster: Quantum Monte Carlo and Complete Basis Set Limit MP2 Results Wang, Fang-Fang; Deible, Michael J.; Jordan, Kenneth D. The Journal of Physical Chemistry A, Vol. 117, Issue 32 https://doi.org/10.1021/jp404541c	journal	June 2013
Aiming for Benchmark Accuracy with the Many-Body Expansion Richard, Ryan M.; Lao, Ka Un; Herbert, John M. Accounts of Chemical Research, Vol. 47, Issue 9 https://doi.org/10.1021/ar500119q	journal	June 2014
Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs Liu, Kuan-Yu; Herbert, John M. The Journal of Chemical Physics, Vol. 147, Issue 16 https://doi.org/10.1063/1.4986110	journal	October 2017
Understanding the many-body expansion for large systems. I. Precision considerations Richard, Ryan M.; Lao, Ka Un; Herbert, John M. The Journal of Chemical Physics, Vol. 141, Issue 1 https://doi.org/10.1063/1.4885846	journal	July 2014
Electrostatically Embedded Many-Body Expansion for Large Systems, with Applications to Water Clusters Dahlke, Erin E.; Truhlar, Donald G. Journal of Chemical Theory and Computation, Vol. 3, Issue 1 https://doi.org/10.1021/ct600253j	journal	November 2006
Fragment Quantum Mechanical Method for Large-Sized Ion–Water Clusters Liu, Jinfeng; Qi, Lian-Wen; Zhang, John Z. H. Journal of Chemical Theory and Computation, Vol. 13, Issue 5 https://doi.org/10.1021/acs.jctc.7b00149	journal	April 2017
When are Many-Body Effects Significant? Ouyang, John F.; Bettens, Ryan P. A. Journal of Chemical Theory and Computation, Vol. 12, Issue 12 https://doi.org/10.1021/acs.jctc.6b00864	journal	November 2016
Approximating quantum many-body intermolecular interactions in molecular clusters using classical polarizable force fields Beran, Gregory J. O. The Journal of Chemical Physics, Vol. 130, Issue 16 https://doi.org/10.1063/1.3121323	journal	April 2009
Predicting Organic Crystal Lattice Energies with Chemical Accuracy Beran, Gregory J. O.; Nanda, Kaushik The Journal of Physical Chemistry Letters, Vol. 1, Issue 24 https://doi.org/10.1021/jz101383z	journal	December 2010
Accurate Molecular Crystal Lattice Energies from a Fragment QM/MM Approach with On-the-Fly Ab Initio Force Field Parametrization Wen, Shuhao; Beran, Gregory J. O. Journal of Chemical Theory and Computation, Vol. 7, Issue 11 https://doi.org/10.1021/ct200541h	journal	October 2011
Prediction of organic molecular crystal geometries from MP2-level fragment quantum mechanical/molecular mechanical calculations Nanda, Kaushik D.; Beran, Gregory J. O. The Journal of Chemical Physics, Vol. 137, Issue 17 https://doi.org/10.1063/1.4764063	journal	November 2012
Practical quantum mechanics-based fragment methods for predicting molecular crystal properties Wen, Shuhao; Nanda, Kaushik; Huang, Yuanhang Physical Chemistry Chemical Physics, Vol. 14, Issue 21 https://doi.org/10.1039/c2cp23949c	journal	January 2012
Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals Hartman, Joshua D.; Beran, Gregory J. O. Journal of Chemical Theory and Computation, Vol. 10, Issue 11 https://doi.org/10.1021/ct500749h	journal	October 2014
Predicting Molecular Crystal Properties from First Principles: Finite-Temperature Thermochemistry to NMR Crystallography Beran, Gregory J. O.; Hartman, Joshua D.; Heit, Yonaton N. Accounts of Chemical Research, Vol. 49, Issue 11 https://doi.org/10.1021/acs.accounts.6b00404	journal	October 2016
The Effective Fragment Potential Method: A QM-Based MM Approach to Modeling Environmental Effects in Chemistry Gordon, Mark S.; Freitag, Mark A.; Bandyopadhyay, Pradipta The Journal of Physical Chemistry A, Vol. 105, Issue 2 https://doi.org/10.1021/jp002747h	journal	January 2001
Noncovalent Interactions in Extended Systems Described by the Effective Fragment Potential Method: Theory and Application to Nucleobase Oligomers Ghosh, Debashree; Kosenkov, Dmytro; Vanovschi, Vitalii The Journal of Physical Chemistry A, Vol. 114, Issue 48 https://doi.org/10.1021/jp107557p	journal	December 2010
Effective Fragment Potential Method: Past, Present, and Future Slipchenko, Lyudmila V.; Gurunathan, Pradeep K. Fragmentation: Toward Accurate Calculations on Complex Molecular Systems https://doi.org/10.1002/9781119129271.ch6	book	January 2017
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 Flick, Joanna C.; Kosenkov, Dmytro; Hohenstein, Edward G. Journal of Chemical Theory and Computation, Vol. 8, Issue 8 https://doi.org/10.1021/ct200673a	journal	July 2012
Mathematical Formulation of the Fragment Molecular Orbital Method Nagata, Takeshi; Fedorov, Dmitri G.; Kitaura, Kazuo Challenges and Advances in Computational Chemistry and Physics https://doi.org/10.1007/978-90-481-2853-2_2	book	January 2011
Exploring chemistry with the fragment molecular orbital method Fedorov, Dmitri G.; Nagata, Takeshi; Kitaura, Kazuo Physical Chemistry Chemical Physics, Vol. 14, Issue 21 https://doi.org/10.1039/c2cp23784a	journal	January 2012
The fragment molecular orbital method: theoretical development, implementation in GAMESS, and applications: Fragment molecular orbital method in GAMESS Fedorov, Dmitri G. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 7, Issue 6 https://doi.org/10.1002/wcms.1322	journal	June 2017
Systematic Study of the Embedding Potential Description in the Fragment Molecular Orbital Method ^† Fedorov, Dmitri G.; Slipchenko, Lyudmila V.; Kitaura, Kazuo The Journal of Physical Chemistry A, Vol. 114, Issue 33 https://doi.org/10.1021/jp101724p	journal	August 2010
Use of an auxiliary basis set to describe the polarization in the fragment molecular orbital method Fedorov, Dmitri G.; Kitaura, Kazuo Chemical Physics Letters, Vol. 597 https://doi.org/10.1016/j.cplett.2014.02.029	journal	March 2014
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy Mardirossian, Narbe; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 16, Issue 21 https://doi.org/10.1039/c3cp54374a	journal	January 2014
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V Mardirossian, Narbe; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 142, Issue 7 https://doi.org/10.1063/1.4907719	journal	February 2015
ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation Mardirossian, Narbe; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 144, Issue 21 https://doi.org/10.1063/1.4952647	journal	June 2016
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals Mardirossian, Narbe; Head-Gordon, Martin Molecular Physics, Vol. 115, Issue 19 https://doi.org/10.1080/00268976.2017.1333644	journal	April 2017
Variational Formulation of the Generalized Many-Body Expansion with Self-Consistent Charge Embedding: Simple and Correct Analytic Energy Gradient for Fragment-Based ab Initio Molecular Dynamics Liu, Jie; Rana, Bhaskar; Liu, Kuan-Yu The Journal of Physical Chemistry Letters, Vol. 10, Issue 14 https://doi.org/10.1021/acs.jpclett.9b01214	journal	June 2019
Fully analytic energy gradient in the fragment molecular orbital method Brorsen, Kurt; Fedorov, Dmitri G. The Journal of Chemical Physics, Vol. 134, Issue 12 https://doi.org/10.1063/1.3568010	journal	March 2011
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny Molecular Physics, Vol. 113, Issue 2 https://doi.org/10.1080/00268976.2014.952696	journal	September 2014
LIBEFP: A new parallel implementation of the effective fragment potential method as a portable software library Kaliman, Ilya A.; Slipchenko, Lyudmila V. Journal of Computational Chemistry, Vol. 34, Issue 26 https://doi.org/10.1002/jcc.23375	journal	July 2013
Fast determination of the optimal rotational matrix for macromolecular superpositions Liu, Pu; Agrafiotis, Dimitris K.; Theobald, Douglas L. Journal of Computational Chemistry https://doi.org/10.1002/jcc.21439	journal	January 2009
On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit Santra, Biswajit; Michaelides, Angelos; Scheffler, Matthias The Journal of Chemical Physics, Vol. 127, Issue 18 https://doi.org/10.1063/1.2790009	journal	November 2007
Evaluation of B3LYP, X3LYP, and M06-Class Density Functionals for Predicting the Binding Energies of Neutral, Protonated, and Deprotonated Water Clusters Bryantsev, Vyacheslav S.; Diallo, Mamadou S.; van Duin, Adri C. T. Journal of Chemical Theory and Computation, Vol. 5, Issue 4 https://doi.org/10.1021/ct800549f	journal	March 2009
Perspective: How good is DFT for water? Gillan, Michael J.; Alfè, Dario; Michaelides, Angelos The Journal of Chemical Physics, Vol. 144, Issue 13 https://doi.org/10.1063/1.4944633	journal	April 2016
Effective Fragment Potential Method for H-Bonding: How To Obtain Parameters for Nonrigid Fragments Dubinets, Nikita; Slipchenko, Lyudmila V. The Journal of Physical Chemistry A, Vol. 121, Issue 28 https://doi.org/10.1021/acs.jpca.7b01701	journal	July 2017
Effective Fragment Molecular Orbital Method: A Merger of the Effective Fragment Potential and Fragment Molecular Orbital Methods ^† Steinmann, Casper; Fedorov, Dmitri G.; Jensen, Jan H. The Journal of Physical Chemistry A, Vol. 114, Issue 33 https://doi.org/10.1021/jp101498m	journal	August 2010
A combined effective fragment potential–fragment molecular orbital method. II. Analytic gradient and application to the geometry optimization of solvated tetraglycine and chignolin Fedorov, Dmitri G. The Journal of Chemical Physics, Vol. 134, Issue 3 https://doi.org/10.1063/1.3517110	journal	January 2011
The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds Steinmann, Casper; Fedorov, Dmitri G.; Jensen, Jan H. PLoS ONE, Vol. 7, Issue 7 https://doi.org/10.1371/journal.pone.0041117	journal	July 2012
Fully Integrated Effective Fragment Molecular Orbital Method Pruitt, Spencer R.; Steinmann, Casper; Jensen, Jan H. Journal of Chemical Theory and Computation, Vol. 9, Issue 5 https://doi.org/10.1021/ct4001119	journal	April 2013
Analytic Gradients for the Effective Fragment Molecular Orbital Method Bertoni, Colleen; Gordon, Mark S. Journal of Chemical Theory and Computation, Vol. 12, Issue 10 https://doi.org/10.1021/acs.jctc.6b00337	journal	September 2016
Efficient and Accurate Fragmentation Methods Pruitt, Spencer R.; Bertoni, Colleen; Brorsen, Kurt R. Accounts of Chemical Research, Vol. 47, Issue 9 https://doi.org/10.1021/ar500097m	journal	May 2014
The ONIOM Method and Its Applications Chung, Lung Wa; Sameera, W. M. C.; Ramozzi, Romain Chemical Reviews, Vol. 115, Issue 12 https://doi.org/10.1021/cr5004419	journal	April 2015
A multicentered approach to integrated QM/QM calculations. Applications to multiply hydrogen bonded systems Hopkins, Brian W.; Tschumper, Gregory S. Journal of Computational Chemistry, Vol. 24, Issue 13 https://doi.org/10.1002/jcc.10319	journal	August 2003
Multicentred QM/QM methods for overlapping model systems Hopkins, Brian W.; Tschumper *, Gregory S. Molecular Physics, Vol. 103, Issue 2-3 https://doi.org/10.1080/00268970512331317291	journal	January 2005
Integrated quantum mechanical approaches for extended π systems: Multicentered QM/QM studies of the cyanogen and diacetylene trimers Hopkins, Brian W.; Tschumper, Gregory S. Chemical Physics Letters, Vol. 407, Issue 4-6 https://doi.org/10.1016/j.cplett.2005.03.115	journal	May 2005
Multicentered integrated QM:QM methods for weakly bound clusters: An efficient and accurate 2-body:many-body treatment of hydrogen bonding and van der Waals interactions Tschumper, Gregory S. Chemical Physics Letters, Vol. 427, Issue 1-3 https://doi.org/10.1016/j.cplett.2006.06.021	journal	August 2006
Analytic gradients for the multicentred integrated QM:QM method for weakly bound clusters: efficient and accurate 2-body:many-body geometry optimizations Elsohly, Adel M.; Shaw, Cynthia L.; Guice, Marlo E. Molecular Physics, Vol. 105, Issue 19-22 https://doi.org/10.1080/00268970701633126	journal	October 2007
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} Bates, Desiree M.; Smith, Joshua R.; Janowski, Tomasz The Journal of Chemical Physics, Vol. 135, Issue 4 https://doi.org/10.1063/1.3609922	journal	July 2011
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 Bates, Desiree M.; Smith, Joshua R.; Tschumper, Gregory S. Journal of Chemical Theory and Computation, Vol. 7, Issue 9 https://doi.org/10.1021/ct200176t	journal	August 2011
N -body:Many-body QM:QM vibrational frequencies: Application to small hydrogen-bonded clusters Howard, J. Coleman; Tschumper, Gregory S. The Journal of Chemical Physics, Vol. 139, Issue 18 https://doi.org/10.1063/1.4829463	journal	November 2013
2-body:Many-body QM:QM study of structures, energetics, and vibrational frequencies for microhydrated halide ions Sexton, Thomas More; Tschumper, Gregory S. Molecular Physics, Vol. 117, Issue 9-12 https://doi.org/10.1080/00268976.2018.1554827	journal	June 2018
Molecules-in-Molecules: An Extrapolated Fragment-Based Approach for Accurate Calculations on Large Molecules and Materials Mayhall, Nicholas J.; Raghavachari, Krishnan Journal of Chemical Theory and Computation, Vol. 7, Issue 5 https://doi.org/10.1021/ct200033b	journal	April 2011
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 Saha, Arjun; Raghavachari, Krishnan Journal of Chemical Theory and Computation, Vol. 11, Issue 5 https://doi.org/10.1021/ct501045s	journal	April 2015
Evaluation of Energy Gradients and Infrared Vibrational Spectra through Molecules-in-Molecules Fragment-Based Approach Jose, K. V. Jovan; Raghavachari, Krishnan Journal of Chemical Theory and Computation, Vol. 11, Issue 3 https://doi.org/10.1021/ct501026m	journal	February 2015
Vibrational Circular Dichroism Spectra for Large Molecules through Molecules-in-Molecules Fragment-Based Approach Jose, K. V. Jovan; Beckett, Daniel; Raghavachari, Krishnan Journal of Chemical Theory and Computation, Vol. 11, Issue 9 https://doi.org/10.1021/acs.jctc.5b00647	journal	August 2015
Molecules-in-molecules fragment-based method for the calculation of chiroptical spectra of large molecules: Vibrational circular dichroism and Raman optical activity spectra of alanine polypeptides: MIM Fragment-Based Method for Calculating Chiroptical Spectra of Large Molecules Jose, K. V. Jovan; Raghavachari, Krishnan Chirality, Vol. 28, Issue 12 https://doi.org/10.1002/chir.22651	journal	November 2016
Fragment-Based Approach for the Evaluation of NMR Chemical Shifts for Large Biomolecules Incorporating the Effects of the Solvent Environment Jose, K. V. Jovan; Raghavachari, Krishnan Journal of Chemical Theory and Computation, Vol. 13, Issue 3 https://doi.org/10.1021/acs.jctc.6b00922	journal	February 2017
Theoretical Study of Protein–Ligand Interactions Using the Molecules-in-Molecules Fragmentation-Based Method Thapa, Bishnu; Beckett, Daniel; Erickson, Jon Journal of Chemical Theory and Computation, Vol. 14, Issue 10 https://doi.org/10.1021/acs.jctc.8b00531	journal	August 2018
Assessment of Fragmentation Strategies for Large Proteins Using the Multilayer Molecules-in-Molecules Approach Thapa, Bishnu; Beckett, Daniel; Jovan Jose, K. V. Journal of Chemical Theory and Computation, Vol. 14, Issue 3 https://doi.org/10.1021/acs.jctc.7b01198	journal	February 2018
Fragment-Based Approaches for Supramolecular Interaction Energies: Applications to Foldamers and Their Complexes with Anions Debnath, Sibali; Sengupta, Arkajyoti; Jose, K. V. Jovan Journal of Chemical Theory and Computation, Vol. 14, Issue 12 https://doi.org/10.1021/acs.jctc.8b00525	journal	November 2018
Electrostatically Embedded Many-Body Correlation Energy, with Applications to the Calculation of Accurate Second-Order Møller−Plesset Perturbation Theory Energies for Large Water Clusters Dahlke, Erin E.; Truhlar, Donald G. Journal of Chemical Theory and Computation, Vol. 3, Issue 4 https://doi.org/10.1021/ct700057x	journal	May 2007
Periodic and fragment models based on the local correlation approach Usvyat, Denis; Maschio, Lorenzo; Schütz, Martin Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 4 https://doi.org/10.1002/wcms.1357	journal	January 2018
Improved minima-hopping. TIP4P water clusters, (H2O)n with n⩽37 Kazachenko, Sergey; Thakkar, Ajit J. Chemical Physics Letters, Vol. 476, Issue 1-3 https://doi.org/10.1016/j.cplett.2009.06.026	journal	July 2009
Water nanodroplets: Predictions of five model potentials Kazachenko, Sergey; Thakkar, Ajit J. The Journal of Chemical Physics, Vol. 138, Issue 19 https://doi.org/10.1063/1.4804399	journal	May 2013
Global minima of water clusters (H2O)n, n≤21, described by an empirical potential Wales, David J.; Hodges, Matthew P. Chemical Physics Letters, Vol. 286, Issue 1-2 https://doi.org/10.1016/S0009-2614(98)00065-7	journal	April 1998
Approaching the complete-basis limit with a truncated many-body expansion Richard, Ryan M.; Lao, Ka Un; Herbert, John M. The Journal of Chemical Physics, Vol. 139, Issue 22 https://doi.org/10.1063/1.4836637	journal	December 2013
A standard grid for density functional calculations Gill, Peter M. W.; Johnson, Benny G.; Pople, John A. Chemical Physics Letters, Vol. 209, Issue 5-6 https://doi.org/10.1016/0009-2614(93)80125-9	journal	July 1993
Many-Body Basis Set Superposition Effect Ouyang, John F.; Bettens, Ryan P. A. Journal of Chemical Theory and Computation, Vol. 11, Issue 11 https://doi.org/10.1021/acs.jctc.5b00343	journal	October 2015
Optimization of parameters for semiempirical methods I. Method Stewart, James J. P. Journal of Computational Chemistry, Vol. 10, Issue 2 https://doi.org/10.1002/jcc.540100208	journal	March 1989
Optimization of parameters for semiempirical methods II. Applications Stewart, James J. P. Journal of Computational Chemistry, Vol. 10, Issue 2 https://doi.org/10.1002/jcc.540100209	journal	March 1989
Ab initio molecular dynamics of liquid water using embedded-fragment second-order many-body perturbation theory towards its accurate property prediction Willow, Soohaeng Yoo; Salim, Michael A.; Kim, Kwang S. Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep14358	journal	September 2015
Corrected small basis set Hartree-Fock method for large systems Sure, Rebecca; Grimme, Stefan Journal of Computational Chemistry, Vol. 34, Issue 19 https://doi.org/10.1002/jcc.23317	journal	May 2013
Using vibrational modes in the search for global minima of atomic and molecular clusters Kabrede, H. Chemical Physics Letters, Vol. 430, Issue 4-6 https://doi.org/10.1016/j.cplett.2006.08.136	journal	October 2006
Advances in electronic structure theory Gordon, Mark S.; Schmidt, Michael W. Theory and Applications of Computational Chemistry https://doi.org/10.1016/B978-044451719-7/50084-6	book	January 2005