Third-Order Møller–Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions

Bertels, Luke W.; Lee, Joonho; Head-Gordon, Martin

doi:10.1021/acs.jpclett.9b01641

Title: Third-Order Møller–Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions

Journal Article · 01 July 2019 · Journal of Physical Chemistry Letters

DOI: https://doi.org/10.1021/acs.jpclett.9b01641 · OSTI ID:1604697

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Univ. of California, Berkeley, CA (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

In this study, we develop and test methods that include second- and third-order perturbation theory (MP3) using orbitals obtained from regularized orbital-optimized second-order perturbation theory, κ-OOMP2, denoted as MP3:κ-OOMP2. Testing MP3:κ-OOMP2 shows RMS errors that are 1.7-5 times smaller than those of MP3 across 7 data sets. To do still better, empirical training of the scaling factors for the second- and third-order correlation energies and the regularization parameter on one of those data sets led to an unregularized scaled (c₂ = 1.0; c₃ = 0.8) denoted as MP2.8:κ-OOMP2. MP2.8:κ-OOMP2 yields significant additional improvement over MP3:κ-OOMP2 in 4 of 6 test data sets on thermochemistry, kinetics, and noncovalent interactions. Remarkably, these two methods outperform coupled cluster with singles and doubles in 5 of the 7 data sets considered, at greatly reduced cost (no O(N⁶) iterations).

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1604697

Journal Information:: Journal of Physical Chemistry Letters, Vol. 10, Issue 15; ISSN 1948-7185

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 32 works

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References (57)

Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers Bernholdt, David E.; Harrison, Robert J. Chemical Physics Letters, Vol. 250, Issue 5-6 https://doi.org/10.1016/0009-2614(96)00054-1	journal	March 1996
Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules Lochan, Rohini C.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 126, Issue 16 https://doi.org/10.1063/1.2718952	journal	April 2007
Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics Neese, Frank; Schwabe, Tobias; Kossmann, Simone Journal of Chemical Theory and Computation, Vol. 5, Issue 11 https://doi.org/10.1021/ct9003299	journal	October 2009
Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory Bozkaya, Uğur; Turney, Justin M.; Yamaguchi, Yukio The Journal of Chemical Physics, Vol. 135, Issue 10 https://doi.org/10.1063/1.3631129	journal	September 2011
Structural predictions for open-shell systems: a comparative assessment of ab initio procedures Farnell, Leslie; Pople, John A.; Radom, Leo The Journal of Physical Chemistry, Vol. 87, Issue 1 https://doi.org/10.1021/j100224a019	journal	January 1983
Slow convergence of the møller-plesset perturbation series: the dissociation energy of hydrogen cyanide and the electron affinity of the cyano radical Nobes, Ross H.; Pople, John A.; Radom, Leo Chemical Physics Letters, Vol. 138, Issue 5 https://doi.org/10.1016/0009-2614(87)80545-6	journal	July 1987
Why does unrestricted Mo/ller–Plesset perturbation theory converge so slowly for spin‐contaminated wave functions? Gill, Peter M. W.; Pople, John A.; Radom, Leo The Journal of Chemical Physics, Vol. 89, Issue 12 https://doi.org/10.1063/1.455312	journal	December 1988
Assessment of Orbital-Optimized MP2.5 for Thermochemistry and Kinetics: Dramatic Failures of Standard Perturbation Theory Approaches for Aromatic Bond Dissociation Energies and Barrier Heights of Radical Reactions Soydaş, Emine; Bozkaya, Uğur Journal of Chemical Theory and Computation, Vol. 11, Issue 4 https://doi.org/10.1021/ct501184w	journal	March 2015
Regularized orbital-optimized second-order perturbation theory Stück, David; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 139, Issue 24 https://doi.org/10.1063/1.4851816	journal	December 2013
Wavefunction stability analysis without analytical electronic Hessians: application to orbital-optimised second-order Møller–Plesset theory and VV10-containing density functionals Sharada, Shaama Mallikarjun; Stück, David; Sundstrom, Eric J. Molecular Physics, Vol. 113, Issue 13-14 https://doi.org/10.1080/00268976.2015.1014442	journal	March 2015
XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule Coulson, C. A.; Fischer, I. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 303 https://doi.org/10.1080/14786444908521726	journal	April 1949
Addressing first derivative discontinuities in orbital-optimised opposite-spin scaled second-order perturbation theory with regularisation Razban, Rostam M.; Stück, David; Head-Gordon, Martin Molecular Physics, Vol. 115, Issue 17-18 https://doi.org/10.1080/00268976.2017.1284355	journal	December 2016
Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers Lee, Joonho; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 14, Issue 10 https://doi.org/10.1021/acs.jctc.8b00731	journal	August 2018
W4-11: A high-confidence benchmark dataset for computational thermochemistry derived from first-principles W4 data Karton, Amir; Daon, Shauli; Martin, Jan M. L. Chemical Physics Letters, Vol. 510, Issue 4-6 https://doi.org/10.1016/j.cplett.2011.05.007	journal	July 2011
Binding in Radical-Solvent Binary Complexes: Benchmark Energies and Performance of Approximate Methods Tentscher, Peter R.; Arey, J. Samuel Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct300846m	journal	February 2013
Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theory Lee, Joonho; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 150, Issue 24 https://doi.org/10.1063/1.5097613	journal	June 2019
Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies Grimme, Stefan The Journal of Chemical Physics, Vol. 118, Issue 20 https://doi.org/10.1063/1.1569242	journal	May 2003
Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method Jung, Yousung; Lochan, Rohini C.; Dutoi, Anthony D. The Journal of Chemical Physics, Vol. 121, Issue 20 https://doi.org/10.1063/1.1809602	journal	November 2004
Accurate Calculation of the Heats of Formation for Large Main Group Compounds with Spin-Component Scaled MP2 Methods Grimme, Stefan The Journal of Physical Chemistry A, Vol. 109, Issue 13 https://doi.org/10.1021/jp050036j	journal	April 2005
Scaled Opposite Spin Second Order Møller−Plesset Theory with Improved Physical Description of Long-Range Dispersion Interactions Lochan, Rohini C.; Jung, Yousung; Head-Gordon, Martin The Journal of Physical Chemistry A, Vol. 109, Issue 33 https://doi.org/10.1021/jp0514426	journal	August 2005
Optimized spin-component scaled second-order Møller-Plesset perturbation theory for intermolecular interaction energies Distasio JR., Robert A.; Head-Gordon, Martin Molecular Physics, Vol. 105, Issue 8 https://doi.org/10.1080/00268970701283781	journal	April 2007
Quartic-Scaling Analytical Energy Gradient of Scaled Opposite-Spin Second-Order Møller−Plesset Perturbation Theory Lochan, Rohini C.; Shao, Yihan; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 3, Issue 3 https://doi.org/10.1021/ct600292h	journal	March 2007
Semiempirical hybrid density functional with perturbative second-order correlation Grimme, Stefan The Journal of Chemical Physics, Vol. 124, Issue 3 https://doi.org/10.1063/1.2148954	journal	January 2006
Long-range corrected double-hybrid density functionals Chai, Jeng-Da; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 131, Issue 17 https://doi.org/10.1063/1.3244209	journal	November 2009
DSD-PBEP86: in search of the best double-hybrid DFT with spin-component scaled MP2 and dispersion corrections Kozuch, Sebastian; Martin, Jan M. L. Physical Chemistry Chemical Physics, Vol. 13, Issue 45 https://doi.org/10.1039/c1cp22592h	journal	January 2011
Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ω B97M(2) double hybrid density functional Mardirossian, Narbe; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5025226	journal	June 2018
A Comprehensive Assessment of the Effectiveness of Orbital Optimization in Double-Hybrid Density Functionals in the Treatment of Thermochemistry, Kinetics, and Noncovalent Interactions Najibi, Asim; Goerigk, Lars The Journal of Physical Chemistry A, Vol. 122, Issue 25 https://doi.org/10.1021/acs.jpca.8b04058	journal	May 2018
Attenuating Away the Errors in Inter- and Intramolecular Interactions from Second-Order Møller–Plesset Calculations in the Small Aug-cc-pVDZ Basis Set Goldey, Matthew; Head-Gordon, Martin The Journal of Physical Chemistry Letters, Vol. 3, Issue 23 https://doi.org/10.1021/jz301694b	journal	November 2012
Attenuated second-order Møller–Plesset perturbation theory: performance within the aug-cc-pVTZ basis Goldey, Matthew; Dutoi, Anthony; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 15, Issue 38 https://doi.org/10.1039/c3cp51826d	journal	January 2013
Separate Electronic Attenuation Allowing a Spin-Component-Scaled Second-Order Møller–Plesset Theory to Be Effective for Both Thermochemistry and Noncovalent Interactions Goldey, Matthew; Head-Gordon, Martin The Journal of Physical Chemistry B, Vol. 118, Issue 24 https://doi.org/10.1021/jp4126478	journal	February 2014
Attenuated MP2 with a Long-Range Dispersion Correction for Treating Nonbonded Interactions Goldey, Matthew B.; Belzunces, Bastien; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 11, Issue 9 https://doi.org/10.1021/acs.jctc.5b00509	journal	August 2015
Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: An Efficient Implementation Bozkaya, Uğur Journal of Chemical Theory and Computation, Vol. 10, Issue 6 https://doi.org/10.1021/ct500231c	journal	May 2014
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 4 https://doi.org/10.1063/1.4732310	journal	July 2012
Improved third-order Møller-Plesset perturbation theory: Improved MP3 Grimme, Stefan Journal of Computational Chemistry, Vol. 24, Issue 13 https://doi.org/10.1002/jcc.10320	journal	July 2003
Comparative Study of Selected Wave Function and Density Functional Methods for Noncovalent Interaction Energy Calculations Using the Extended S22 Data Set Gráfová, Lucie; Pitoňák, Michal; Řezáč, Jan Journal of Chemical Theory and Computation, Vol. 6, Issue 8 https://doi.org/10.1021/ct1002253	journal	July 2010
Assessment of the Performance of MP2 and MP2 Variants for the Treatment of Noncovalent Interactions Riley, Kevin E.; Platts, James A.; Řezáč, Jan The Journal of Physical Chemistry A, Vol. 116, Issue 16 https://doi.org/10.1021/jp211997b	journal	April 2012
Scaled MP3 Non-Covalent Interaction Energies Agree Closely with Accurate CCSD(T) Benchmark Data Pitoňák, Michal; Neogrády, Pavel; Černý, Jiří ChemPhysChem, Vol. 10, Issue 1 https://doi.org/10.1002/cphc.200800718	journal	January 2009
The performance of MP2.5 and MP2.X methods for nonequilibrium geometries of molecular complexes Riley, Kevin E.; Řezáč, Jan; Hobza, Pavel Physical Chemistry Chemical Physics, Vol. 14, Issue 38 https://doi.org/10.1039/c2cp41874f	journal	January 2012
MP2.5 and MP2.X: Approaching CCSD(T) Quality Description of Noncovalent Interaction at the Cost of a Single CCSD Iteration Sedlak, Robert; Riley, Kevin E.; Řezáč, Jan ChemPhysChem, Vol. 14, Issue 4 https://doi.org/10.1002/cphc.201200850	journal	December 2012
Orbital-optimized third-order Møller-Plesset perturbation theory and its spin-component and spin-opposite scaled variants: Application to symmetry breaking problems Bozkaya, Uğur The Journal of Chemical Physics, Vol. 135, Issue 22 https://doi.org/10.1063/1.3665134	journal	December 2011
Assessment of Orbital-Optimized Third-Order Møller–Plesset Perturbation Theory and Its Spin-Component and Spin-Opposite Scaled Variants for Thermochemistry and Kinetics Soydaş, Emine; Bozkaya, Uğur Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct301078q	journal	February 2013
Orbital-optimized MP2.5 and its analytic gradients: Approaching CCSD(T) quality for noncovalent interactions Bozkaya, Uğur; Sherrill, C. David The Journal of Chemical Physics, Vol. 141, Issue 20 https://doi.org/10.1063/1.4902226	journal	November 2014
Orbital-Optimized MP3 and MP2.5 with Density-Fitting and Cholesky Decomposition Approximations Bozkaya, Uğur Journal of Chemical Theory and Computation, Vol. 12, Issue 3 https://doi.org/10.1021/acs.jctc.5b01128	journal	February 2016
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples Purvis, George D.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 76, Issue 4 https://doi.org/10.1063/1.443164	journal	February 1982
An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations Scuseria, Gustavo E.; Janssen, Curtis L.; Schaefer, Henry F. The Journal of Chemical Physics, Vol. 89, Issue 12 https://doi.org/10.1063/1.455269	journal	December 1988
Analytic energy gradients for the orbital-optimized third-order Møller–Plesset perturbation theory Bozkaya, Uğur The Journal of Chemical Physics, Vol. 139, Issue 10 https://doi.org/10.1063/1.4820877	journal	September 2013
Analytic energy gradients for orbital-optimized MP3 and MP2.5 with the density-fitting approximation: An efficient implementation Bozkaya, Uğur Journal of Computational Chemistry, Vol. 39, Issue 7 https://doi.org/10.1002/jcc.25122	journal	November 2017
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen Dunning, Thom H. The Journal of Chemical Physics, Vol. 90, Issue 2 https://doi.org/10.1063/1.456153	journal	January 1989
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions Kendall, Rick A.; Dunning, Thom H.; Harrison, Robert J. The Journal of Chemical Physics, Vol. 96, Issue 9 https://doi.org/10.1063/1.462569	journal	May 1992
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon Woon, David E.; Dunning, Thom H. The Journal of Chemical Physics, Vol. 98, Issue 2 https://doi.org/10.1063/1.464303	journal	January 1993
Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations Weigend, Florian; Köhn, Andreas; Hättig, Christof The Journal of Chemical Physics, Vol. 116, Issue 8 https://doi.org/10.1063/1.1445115	journal	February 2002
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
A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions − Assessment of Common and Reparameterized ( meta -)GGA Density Functionals Goerigk, Lars; Grimme, Stefan Journal of Chemical Theory and Computation, Vol. 6, Issue 1 https://doi.org/10.1021/ct900489g	journal	November 2009
Multi-coefficient extrapolated density functional theory for thermochemistry and thermochemical kinetics Zhao, Yan; Lynch, Benjamin J.; Truhlar, Donald G. Physical Chemistry Chemical Physics, Vol. 7, Issue 1 https://doi.org/10.1039/b416937a	journal	January 2005
Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and Its Use to Test Theoretical Methods Zhao, Yan; González-García, Núria; Truhlar, Donald G. The Journal of Physical Chemistry A, Vol. 109, Issue 9 https://doi.org/10.1021/jp045141s	journal	March 2005
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions Goerigk, Lars; Hansen, Andreas; Bauer, Christoph Physical Chemistry Chemical Physics, Vol. 19, Issue 48 https://doi.org/10.1039/C7CP04913G	journal	January 2017
Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit? Řezáč, Jan; Hobza, Pavel Journal of Chemical Theory and Computation, Vol. 9, Issue 5 https://doi.org/10.1021/ct400057w	journal	April 2013

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