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Title: Third-Order Møller–Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals

Journal Article · · Journal of Chemical Theory and Computation
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]
  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States)
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The practical utility of Møller–Plesset (MP) perturbation theory is severely constrained by the use of Hartree–Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). As such, MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N6) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1779263
Journal Information:
Journal of Chemical Theory and Computation, Vol. 16, Issue 12; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (109)

Analytic Energy Gradients and Spin Multiplicities for Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting Approximation: An Efficient Implementation journal October 2014
Generalized Gradient Approximation Made Simple journal October 1996
A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions − Assessment of Common and Reparameterized ( meta -)GGA Density Functionals journal November 2009
Binding in Radical-Solvent Binary Complexes: Benchmark Energies and Performance of Approximate Methods journal February 2013
Scaled MP3 Non-Covalent Interaction Energies Agree Closely with Accurate CCSD(T) Benchmark Data journal January 2009
Self-interaction error of local density functionals for alkali–halide dissociation journal April 2006
Semiempirical hybrid density functional with perturbative second-order correlation journal January 2006
W4-11: A high-confidence benchmark dataset for computational thermochemistry derived from first-principles W4 data journal July 2011
Possible artifacts occurring in the calculation of intermolecular energies from delocalized pictures journal January 1979
Communication: xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS journal May 2018
Configuration interaction in orbital theories journal June 1955
Assessment of Orbital-Optimized Third-Order Møller–Plesset Perturbation Theory and Its Spin-Component and Spin-Opposite Scaled Variants for Thermochemistry and Kinetics journal February 2013
N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant journal December 2001
How Accurate Is Density Functional Theory at Predicting Dipole Moments? An Assessment Using a New Database of 200 Benchmark Values journal March 2018
A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces journal June 2018
Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules journal April 2007
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Why does unrestricted Mo/ller–Plesset perturbation theory converge so slowly for spin‐contaminated wave functions? journal December 1988
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon journal January 1993
New Basis Set Exchange: An Open, Up-to-Date Resource for the Molecular Sciences Community journal October 2019
Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies journal May 2003
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
Møller-Plesset perturbation theory: from small molecule methods to methods for thousands of atoms: Møller-Plesset perturbation theory journal May 2011
Scaled Opposite Spin Second Order Møller−Plesset Theory with Improved Physical Description of Long-Range Dispersion Interactions journal August 2005
Orbital-optimized third-order Møller-Plesset perturbation theory and its spin-component and spin-opposite scaled variants: Application to symmetry breaking problems journal December 2011
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Improved third-order Møller-Plesset perturbation theory: Improved MP3 journal July 2003
On the piecewise convex or concave nature of ground state energy as a function of fractional number of electrons for approximate density functionals journal February 2017
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals journal April 2017
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals journal November 2006
The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches journal October 2018
A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states journal February 2009
Development of density functionals for thermochemical kinetics journal August 2004
A second-order perturbative correction to the coupled-cluster singles and doubles method: CCSD(2) journal August 2001
Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers journal March 1996
On the calculation of multiplet energies by the hartree-fock-slater method journal January 1977
How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry journal January 2018
Assessment of the ΔSCF density functional theory approach for electronic excitations in organic dyes journal February 2011
Simple Models for Difficult Electronic Excitations journal February 2018
Slow convergence of the møller-plesset perturbation series: the dissociation energy of hydrogen cyanide and the electron affinity of the cyano radical journal July 1987
Hartree–Fock solutions as a quasidiabatic basis for nonorthogonal configuration interaction journal September 2009
Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids journal September 2003
Double-hybrid density functionals: Double-hybrid density functionals journal July 2014
Minimally Empirical Double-Hybrid Functionals Trained against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4 journal May 2019
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V journal February 2015
Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers journal August 2018
The XYG3 type of doubly hybrid density functionals: XYG3 type of doubly hybrid density functionals journal July 2016
Multi-coefficient extrapolated density functional theory for thermochemistry and thermochemical kinetics journal January 2005
Prediction of transition state barriers and enthalpies of reaction by a new hybrid density-functional approximation journal December 2001
Efficient Implementation of NOCI-MP2 Using the Resolution of the Identity Approximation with Application to Charged Dimers and Long C–C Bonds in Ethane Derivatives journal July 2018
Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: An Efficient Implementation journal May 2014
Approaching closed-shell accuracy for radicals using coupled cluster theory with perturbative triple substitutions journal January 2003
Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics journal October 2009
Revised M06-L functional for improved accuracy on chemical reaction barrier heights, noncovalent interactions, and solid-state physics journal July 2017
Note on an Approximation Treatment for Many-Electron Systems journal October 1934
Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method journal November 2004
Ions in solution: Density corrected density functional theory (DC-DFT) journal May 2014
Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals—Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions journal December 2010
Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory journal September 2011
Approximating full configuration interaction with selected configuration interaction and perturbation theory journal April 1991
Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory journal February 2020
Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM) † journal December 2008
Quantised Singularities in the Electromagnetic Field journal September 1931
Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number journal October 2018
Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ω B97M(2) double hybrid density functional journal June 2018
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals [Supplemental Data] fileset June 2017
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 journal March 2015
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Use of Improved Orbitals for CCSD(T) Calculations for Predicting Heats of Formation of Group IV and Group VI Metal Oxide Monomers and Dimers and UCl 6 journal July 2016
Second‐order perturbation theory with a complete active space self‐consistent field reference function journal January 1992
Introduction of n -electron valence states for multireference perturbation theory journal June 2001
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal May 1992
Exploring the competition between localization and delocalization of the neutral soliton defect in polyenyl chains with the orbital optimized second order opposite spin method journal February 2012
Stability conditions and nuclear rotations in the Hartree-Fock theory journal November 1960
Understanding and Reducing Errors in Density Functional Calculations journal August 2013
State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions journal July 2020
Adiabatic Connection for Kinetics journal June 2000
Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated? journal April 2017
Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics journal March 2009
Third-Order Møller–Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions journal July 2019
Excitation energies and Stokes shifts from a restricted open-shell Kohn-Sham approach journal April 2013
Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works journal January 2017
A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) journal July 2004
Violations of N-representability from spin-unrestricted orbitals in Møller–Plesset perturbation theory and related double-hybrid density functional theory journal April 2009
Surprising cases of divergent behavior in Mo/ller–Plesset perturbation theory journal September 1996
Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT? journal May 2020
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
The Stark Effect from the Point of View of Schroedinger's Quantum Theory journal October 1926
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy journal January 2014
On the performance of density functional theory for symmetry-breaking problems journal March 1999
Gaussian basis sets for use in correlated molecular calculations. V. Core‐valence basis sets for boron through neon journal September 1995
Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction journal August 2016
Orbital optimized double-hybrid density functionals journal July 2013
Many-electron self-interaction error in approximate density functionals journal November 2006
Toward reliable density functional methods without adjustable parameters: The PBE0 model journal April 1999
Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics † journal December 2008
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions journal January 2017
Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit? journal April 2013
Sixth-Order Møller−Plesset Perturbation TheoryOn the Convergence of the MP n Series journal January 1996
Accurate and simple analytic representation of the electron-gas correlation energy journal June 1992
ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation journal June 2016
Is Mo/ller–Plesset perturbation theory a convergent ab initio method? journal June 2000
Second-order perturbation theory with a CASSCF reference function journal July 1990
Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H 2 journal March 2019
Molecular dynamics in low-spin excited states journal March 1998
Basis-set convergence of correlated calculations on water journal June 1997
Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and its Use to Test Theoretical Methods journal April 2006
Gaussian-3 (G3) theory for molecules containing first and second-row atoms journal November 1998
Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations journal October 2020

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Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
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