Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential

Carmona-Espíndola, Javier; Gázquez, José L.; Vela, Alberto; Trickey, S. B.

doi:10.1063/1.4906606

Title: Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential

Authors:

Carmona-Espíndola, Javier ^[1]; Gázquez, José L. ^[2]; Vela, Alberto ^[3];

^[4]

Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México
Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México, Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México
Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México
Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, P.O. Box 118435, Gainesville, Florida 32611-8435, USA

Publication Date:: Wed Feb 04 00:00:00 EST 2015

Sponsoring Org.:: USDOE

OSTI Identifier:: 1228518

Grant/Contract Number:: SC-0002139

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: The Journal of Chemical Physics

Additional Journal Information:: Journal Name: The Journal of Chemical Physics Journal Volume: 142 Journal Issue: 5; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics

Country of Publication:: United States

Language:: English

Citation Formats


                    Carmona-Espíndola, Javier, Gázquez, José L., Vela, Alberto, and Trickey, S. B. Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential.  United States: N. p., 2015. 
Web.  doi:10.1063/1.4906606.

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                    Carmona-Espíndola, Javier, Gázquez, José L., Vela, Alberto, & Trickey, S. B. Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential.  United States.  https://doi.org/10.1063/1.4906606

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                    Carmona-Espíndola, Javier, Gázquez, José L., Vela, Alberto, and Trickey, S. B. Wed .  
"Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential".  United States.  https://doi.org/10.1063/1.4906606.

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@article{osti_1228518,

  title        = {Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential},

  author       = {Carmona-Espíndola, Javier and Gázquez, José L. and Vela, Alberto and Trickey, S. B.},

  abstractNote = {},

  doi          = {10.1063/1.4906606},

  journal      = {The Journal of Chemical Physics},

  number       = 5,

  volume       = 142,

  place        = {United States},

  year         = {Wed Feb 04 00:00:00 EST 2015},

  month        = {Wed Feb 04 00:00:00 EST 2015}

}

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Zhao, Yan; Truhlar, Donald G.
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Pair interactions of rare-gas atoms as a test of exchange-energy-density functionals in regions of large density gradients
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Density functional calculations of molecular polarizabilities and hyperpolarizabilities
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DOI: 10.1063/1.477421

Similar Records in DOE PAGES and OSTI.GOV collections:

Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential

Journal Article Carmona-Espíndola, Javier ; Gázquez, José L., E-mail: jlgm@xanum.uam.mx ; Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México ; ... - Journal of Chemical Physics

A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potentialmore »« less
https://doi.org/10.1063/1.4906606
Multiresolution Quantum Chemistry in Multiwavelet Bases: Time-Dependent Density Functional Theory with Asymptotically Corrected Potentials in Local Density and Generalized Gradient Approximations

Journal Article Yanai, Takeshi ; Harrison, Robert J ; Handy, Nicholas C - Molecular Physics

No abstract prepared.
https://doi.org/10.1080/00268970412331319236
Density-functional exchange-energy approximation with correct asymptotic behavior

Journal Article Becke, A D - Phys. Rev. A; (United States)

Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
https://doi.org/10.1103/PhysRevA.38.3098
Explicit density-functional exchange potential with correct asymptotic behavior

Journal Article Umezawa, Naoto - Physical Review. A

In this paper, a density-functional exchange potential is proposed. The suggested exchange potential reproduces the correct asymptotic behavior of finite systems: -1/r, without significant increase in computational costs over a local-density approximation. Our model exchange potential, which is an explicit functional of a density and the gradient of the density, is given by a hybridization procedure of a Hartree potential and the homogeneous electron gas limit of the exchange potential. Since the Hartree potential behaves as N/r in an asymptotic region with N number of electrons, it is utilized for achieving the correct -1/r asymptotic behavior in our model exchangemore »« less
https://doi.org/10.1103/PHYSREVA.74.032505
Exploring the limit of accuracy for density functionals based on the generalized gradient approximation: Local, global hybrid, and range-separated hybrid functionals with and without dispersion corrections

Journal Article Mardirossian, Narbe ; Head-Gordon, Martin - Journal of Chemical Physics

The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored in this paper by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the trainingmore »« less
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https://doi.org/10.1063/1.4868117

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Title: Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential

Citation Formats

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region journal, January 2001

Kohn-Sham exchange potential exact to first order in ρ(K→)/ ρ 0 journal, May 1985

The ground-state spectroscopic constants of Be2 revisited journal, April 1999

Efficient and reliable numerical integration of exchange-correlation energies and potentials journal, July 2004

Accurate universal Gaussian basis set for all atoms of the Periodic Table journal, April 1998

Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis journal, August 1980

Distributions and averages of electron density parameters: Explaining the effects of gradient corrections journal, June 1997

Improved lower bound on the indirect Coulomb energy journal, March 1981

Exchange-correlation density functional beyond the gradient approximation journal, January 1998

Hyperpolarizabilities of the methanol molecule: A CCSD calculation including vibrational corrections journal, January 2010

Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities journal, April 2001

Influence of the exchange-correlation potential in methods based on time-dependent density-functional theory journal, October 2013

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules journal, May 2000

Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and Its Use to Test Theoretical Methods journal, March 2005

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal, December 1982

Evaluating density functional performance for the quasi-two-dimensional electron gas journal, February 2000

Time dependent density functional theory of core electrons excitations journal, May 2003

G n theory : G journal, June 2011

Assessment of Density Functionals for π Systems: Energy Differences between Cumulenes and Poly-ynes; Proton Affinities, Bond Length Alternation, and Torsional Potentials of Conjugated Polyenes; and Proton Affinities of Conjugated Shiff Bases journal, September 2006

Nonuniform Scaling Applied to Surface Energies of Transition Metals journal, March 2012

Self-Consistent Equations Including Exchange and Correlation Effects journal, November 1965

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory journal, May 2012

High-precision calculation of the equation of state and crystallographic phase stability for aluminum journal, February 1996

Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] journal, February 1997

Assessment of Gaussian-3 and density functional theories for a larger experimental test set journal, May 2000

Exchange-correlation energy of the non-uniformly scaled hydrogen atom journal, April 2000

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density journal, January 1988

Excitation Energies from Time-Dependent Density-Functional Theory journal, February 1996

Challenges for Density Functional Theory journal, December 2011

Explicit density-functional exchange potential with correct asymptotic behavior journal, September 2006

Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase journal, January 1994

Density Functional Theory book, January 2011

Perspective: Fifty years of density-functional theory in chemical physics journal, May 2014

Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory journal, March 2003

Quantum-Mechanical Interpretation of the Exchange-Correlation Potential of Kohn-Sham Density-Functional Theory journal, January 1989

Measurements of nonlinear optical polarizabilities for twelve small molecules journal, February 1979

Multi-coefficient extrapolated density functional theory for thermochemistry and thermochemical kinetics journal, January 2005

Static and dynamic polarizability of C540 fullerene journal, June 2012

Frequency dependent nonlinear optical properties of molecules journal, July 1986

On the required shape corrections to the local density and generalized gradient approximations to the Kohn–Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies journal, June 2002

Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes journal, December 2003

Two-Dimensional Scan of the Performance of Generalized Gradient Approximations with Perdew–Burke–Ernzerhof-Like Enhancement Factor journal, October 2011

Variable Lieb–Oxford bound satisfaction in a generalized gradient exchange-correlation functional journal, June 2009

Measurement of the dispersion in polarizability anisotropies journal, October 1975

Molecular Spectra and Molecular Structure book, January 1979

Comment on “Concerning the applicability of density functional methods to atomic and molecular negative ions” [J. Chem. Phys. 105 , 862 (1996)] journal, June 1997

Asymptotic behavior of the ground-state charge density in atoms journal, November 1978

A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements journal, January 1998

Density-functional theory calculations with correct long-range potentials journal, August 2003

Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties journal, March 2012

Perspective on density functional theory journal, April 2012

Comparison of the Auxiliary Density Perturbation Theory and the Noniterative Approximation to the Coupled Perturbed Kohn−Sham Method: Case Study of the Polarizabilities of Disubstituted Azoarene Molecules journal, February 2010

Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems journal, January 2007

Improved Electronic Excitation Energies from Shape-Corrected Semilocal Kohn-Sham Potentials journal, June 2012

A fourth-order many-body perturbation theory calculation of the first and second electric dipole hyperpolarizability of ammonia journal, July 1992

Exchange and correlation in density-functional theory journal, September 1985

Accurate optimized-potential-model solutions for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations journal, April 1993

Chemical hardness and the discontinuity of the Kohn-Sham exchange-correlation potential journal, June 2007

Polarizabilities of azabenzenes journal, April 2000

Density-functional exchange-energy approximation with correct asymptotic behavior journal, September 1988

Note on Exchange Phenomena in the Thomas Atom journal, July 1930

Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods journal, June 2003

Exact exchange functional for the hydrogen atom journal, March 1993

Exact hydrogenic density functionals journal, October 1997

Asymptotic properties of the exchange energy density and the exchange potential of finite systems: relevance for generalized gradient approximations journal, March 1992

Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation journal, June 1986

Time-dependent auxiliary density perturbation theory journal, August 2010

Exact differential equation for the density and ionization energy of a many-particle system journal, November 1984

Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential journal, February 2015

How Important are Temperature Effects for Cluster Polarizabilities? journal, November 2008

deMon2k: deMon2k journal, November 2011

Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity journal, July 2008

Investigation of Exchange Energy Density Functional Accuracy for Interacting Molecules journal, August 2009

Density-Functional Theory of the Energy Gap journal, November 1983

NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations journal, September 2010

Self-interaction correction scheme for approximate Kohn-Sham potentials journal, November 2012

Erratum: Tight bound and convexity constraint on the exchange-correlation-energy functionalsin the low-density limit, and other formal tests of generalized-gradient approximations [Phys. Rev. B 48 , 11638 (1993)] journal, May 1997

Electronic excitations and the Becke-Johnson potential: The need for and the problem of transforming model potentials to functional derivatives journal, November 2013

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region
journal, January 2001

Kohn-Sham exchange potential exact to first order in ρ(K→)/ $ρ_{0}$
journal, May 1985

The ground-state spectroscopic constants of Be2 revisited
journal, April 1999

Efficient and reliable numerical integration of exchange-correlation energies and potentials
journal, July 2004

Accurate universal Gaussian basis set for all atoms of the Periodic Table
journal, April 1998

Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis
journal, August 1980

Distributions and averages of electron density parameters: Explaining the effects of gradient corrections
journal, June 1997

Improved lower bound on the indirect Coulomb energy
journal, March 1981

Exchange-correlation density functional beyond the gradient approximation
journal, January 1998

Hyperpolarizabilities of the methanol molecule: A CCSD calculation including vibrational corrections
journal, January 2010

Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities
journal, April 2001

Influence of the exchange-correlation potential in methods based on time-dependent density-functional theory
journal, October 2013

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules
journal, May 2000

Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and Its Use to Test Theoretical Methods
journal, March 2005

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
journal, December 1982

Evaluating density functional performance for the quasi-two-dimensional electron gas
journal, February 2000

Time dependent density functional theory of core electrons excitations
journal, May 2003

G n theory : G
journal, June 2011

Assessment of Density Functionals for π Systems: Energy Differences between Cumulenes and Poly-ynes; Proton Affinities, Bond Length Alternation, and Torsional Potentials of Conjugated Polyenes; and Proton Affinities of Conjugated Shiff Bases
journal, September 2006

Nonuniform Scaling Applied to Surface Energies of Transition Metals
journal, March 2012

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory
journal, May 2012

High-precision calculation of the equation of state and crystallographic phase stability for aluminum
journal, February 1996

Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
journal, February 1997

Assessment of Gaussian-3 and density functional theories for a larger experimental test set
journal, May 2000

Exchange-correlation energy of the non-uniformly scaled hydrogen atom
journal, April 2000

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
journal, January 1988

Excitation Energies from Time-Dependent Density-Functional Theory
journal, February 1996

Challenges for Density Functional Theory
journal, December 2011

Explicit density-functional exchange potential with correct asymptotic behavior
journal, September 2006

Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase
journal, January 1994

Density Functional Theory
book, January 2011

Perspective: Fifty years of density-functional theory in chemical physics
journal, May 2014

Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory
journal, March 2003

Quantum-Mechanical Interpretation of the Exchange-Correlation Potential of Kohn-Sham Density-Functional Theory
journal, January 1989

Measurements of nonlinear optical polarizabilities for twelve small molecules
journal, February 1979

Multi-coefficient extrapolated density functional theory for thermochemistry and thermochemical kinetics
journal, January 2005

Static and dynamic polarizability of C540 fullerene
journal, June 2012

Frequency dependent nonlinear optical properties of molecules
journal, July 1986

On the required shape corrections to the local density and generalized gradient approximations to the Kohn–Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies
journal, June 2002

Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes
journal, December 2003

Two-Dimensional Scan of the Performance of Generalized Gradient Approximations with Perdew–Burke–Ernzerhof-Like Enhancement Factor
journal, October 2011

Variable Lieb–Oxford bound satisfaction in a generalized gradient exchange-correlation functional
journal, June 2009

Measurement of the dispersion in polarizability anisotropies
journal, October 1975

Molecular Spectra and Molecular Structure
book, January 1979

Comment on “Concerning the applicability of density functional methods to atomic and molecular negative ions” [J. Chem. Phys. 105 , 862 (1996)]
journal, June 1997

Asymptotic behavior of the ground-state charge density in atoms
journal, November 1978

A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements
journal, January 1998

Density-functional theory calculations with correct long-range potentials
journal, August 2003

Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties
journal, March 2012

Perspective on density functional theory
journal, April 2012

Comparison of the Auxiliary Density Perturbation Theory and the Noniterative Approximation to the Coupled Perturbed Kohn−Sham Method: Case Study of the Polarizabilities of Disubstituted Azoarene Molecules
journal, February 2010

Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems
journal, January 2007

Improved Electronic Excitation Energies from Shape-Corrected Semilocal Kohn-Sham Potentials
journal, June 2012

A fourth-order many-body perturbation theory calculation of the first and second electric dipole hyperpolarizability of ammonia
journal, July 1992

Exchange and correlation in density-functional theory
journal, September 1985

Accurate optimized-potential-model solutions for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations
journal, April 1993

Chemical hardness and the discontinuity of the Kohn-Sham exchange-correlation potential
journal, June 2007

Polarizabilities of azabenzenes
journal, April 2000

Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988

Note on Exchange Phenomena in the Thomas Atom
journal, July 1930

Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods
journal, June 2003

Exact exchange functional for the hydrogen atom
journal, March 1993

Exact hydrogenic density functionals
journal, October 1997

Asymptotic properties of the exchange energy density and the exchange potential of finite systems: relevance for generalized gradient approximations
journal, March 1992

Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation
journal, June 1986

Time-dependent auxiliary density perturbation theory
journal, August 2010

Exact differential equation for the density and ionization energy of a many-particle system
journal, November 1984

Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential
journal, February 2015

How Important are Temperature Effects for Cluster Polarizabilities?
journal, November 2008

deMon2k: deMon2k
journal, November 2011

Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity
journal, July 2008

Investigation of Exchange Energy Density Functional Accuracy for Interacting Molecules
journal, August 2009

Density-Functional Theory of the Energy Gap
journal, November 1983

NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
journal, September 2010

Self-interaction correction scheme for approximate Kohn-Sham potentials
journal, November 2012

Erratum: Tight bound and convexity constraint on the exchange-correlation-energy functionalsin the low-density limit, and other formal tests of generalized-gradient approximations [Phys. Rev. B 48 , 11638 (1993)]
journal, May 1997

Electronic excitations and the Becke-Johnson potential: The need for and the problem of transforming model potentials to functional derivatives
journal, November 2013

Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions
journal, January 2006

Accurate density functional calculations on frequency-dependent hyperpolarizabilities of small molecules
journal, December 1998