A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

doi:10.1016/J.CPLETT.2004.06.011

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A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

Journal Article•DOI•

A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

Takeshi Yanai¹, David P. Tew, Nicholas C. Handy²•Institutions (2)

Oak Ridge National Laboratory¹, University of Cambridge²

21 Jul 2004-Chemical Physics Letters (North-Holland Publishing Company)-Vol. 393, Iss: 1, pp 51-57

TL;DR: In this article, a new hybrid exchange-correlation functional named CAM-B3LYP is proposed, which combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al.

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Abstract: A new hybrid exchange–correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree–Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the standard error function with parameter 0.33.

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NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations

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Marat Valiev¹, Eric J. Bylaska¹, Niranjan Govind¹, Karol Kowalski¹, T.P. Straatsma¹, H. J. J. van Dam¹, Dunyou Wang¹, Jarek Nieplocha¹, Edoardo Aprà², Theresa L. Windus³, W. A. de Jong¹ - Show less +7 more•Institutions (3)

Environmental Molecular Sciences Laboratory¹, Oak Ridge National Laboratory², Iowa State University³

01 Sep 2010-Computer Physics Communications

TL;DR: An overview of NWChem is provided focusing primarily on the core theoretical modules provided by the code and their parallel performance, as well as Scalable parallel implementations and modular software design enable efficient utilization of current computational architectures.

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Abstract: The latest release of NWChem delivers an open-source computational chemistry package with extensive capabilities for large scale simulations of chemical and biological systems. Utilizing a common computational framework, diverse theoretical descriptions can be used to provide the best solution for a given scientific problem. Scalable parallel implementations and modular software design enable efficient utilization of current computational architectures. This paper provides an overview of NWChem focusing primarily on the core theoretical modules provided by the code and their parallel performance.

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4,666 citations

Journal Article•DOI•

Systematic optimization of long-range corrected hybrid density functionals.

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Jeng-Da Chai¹, Martin Head-Gordon•Institutions (1)

Lawrence Berkeley National Laboratory¹

27 Feb 2008-Journal of Chemical Physics

TL;DR: The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybriddensity functionals.

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Abstract: A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some “difficult problems,” such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid density functionals.

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2,852 citations

Journal Article•DOI•

Single-reference ab initio methods for the calculation of excited states of large molecules.

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Andreas Dreuw¹, Martin Head-Gordon²•Institutions (2)

Goethe University Frankfurt¹, Lawrence Berkeley National Laboratory²

06 Oct 2005-Chemical Reviews

2,353 citations

Journal Article•DOI•

Challenges for density functional theory.

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Aron J. Cohen¹, Aron J. Cohen², Aron J. Cohen³, Paula Mori-Sánchez³, Paula Mori-Sánchez², Paula Mori-Sánchez¹, Weitao Yang³, Weitao Yang², Weitao Yang¹ - Show less +5 more•Institutions (3)

Duke University¹, Autonomous University of Madrid², University of Cambridge³

11 Jan 2012-Chemical Reviews

1,908 citations

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

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Philip J. Stephens, Frank J. Devlin, Cary F. Chabalowski, Michael J. Frisch

01 Feb 1995

TL;DR: In this paper, the unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio using DFT, MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set.

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Abstract: : The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

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1,652 citations

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References

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Journal Article•DOI•

Generalized Gradient Approximation Made Simple

[...]

John P. Perdew¹, Kieron Burke¹, Matthias Ernzerhof¹•Institutions (1)

Tulane University¹

28 Oct 1996-Physical Review Letters

TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.

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Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

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146,533 citations

Journal Article•DOI•

Density‐functional thermochemistry. III. The role of exact exchange

[...]

Axel D. Becke

01 Apr 1993-Journal of Chemical Physics

TL;DR: In this article, a semi-empirical exchange correlation functional with local spin density, gradient, and exact exchange terms was proposed. But this functional performed significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

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Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

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87,732 citations

Journal Article•DOI•

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density

[...]

Chengteh Lee¹, Weitao Yang¹, Robert G. Parr¹•Institutions (1)

University of North Carolina at Chapel Hill¹

15 Jan 1988-Physical Review B

TL;DR: Numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, show that density-functional formulas for the correlation energy and correlation potential give correlation energies within a few percent.

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Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

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84,646 citations

Journal Article•DOI•

Density-functional exchange-energy approximation with correct asymptotic behavior.

[...]

Axel D. Becke¹•Institutions (1)

Queen's University¹

15 Sep 1988-Physical Review A

TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that 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.

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Abstract: 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.

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45,683 citations

"A new hybrid exchange–correlation f..." refers background or methods in this paper

...Tsuneda and co-workers have demonstrated that their LC method for the Becke 1988 [14] or PBE [15] generalized-gradient approximation (GGA) exchange functionals in conjunction with their one-parameter progressive (OP) correlation functional [16] can address the above notorious problems in DFT....
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...The CAM-B3LYP functional comprises of 0.19 Hartree–Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range....
[...]
...We consider that due to the prevalence of hydrogen in chemical systems, the good reproduction of the total atomic energies, hydrogen in particular, is more important than the slight loss in quality of the atomization and ionization energies. molecules) with aug-cc-pVQZ Gaussian basis sets les) with aug-cc-pVQZ Gaussian basis sets Table 4 Statistical data for total atomic energies (hartree) of H–Ne with aug-cc-pVQZ Gaussian basis sets a aþ b MAE RMS Maximum deviation ( ) Maximum deviation (+) Deviation H LC-BOP 0.0 1.0 0.084 0.093 – 0.134 (Ne) 0.0091 LC-BLYP 0.0 1.0 0.085 0.128 – 0.128 (Ne) 0.0091 CAM-BOP 0.2 1.0 0.068 0.075 – 0.112 (Ne) 0.0075 0.8 0.049 0.054 – 0.080 (Ne) 0.0061 0.6 0.030 0.049 – 0.049 (Be) 0.0047 CAM-BLYP 0.2 1.0 0.069 0.075 – 0.107 (Ne) 0.0075 0.8 0.050 0.054 – 0.075 (Ne) 0.0061 0.6 0.031 0.034 – 0.043 (Ne) 0.0047 CAM-B3LYP 0.2 1.0 0.033 0.035 – 0.045 (Be) 0.0034 0.8 0.014 0.017 – 0.029 (Be) 0.0019 0.6 0.009 0.013 )0.025 (Ne) 0.013 (Be) 0.0005 B3LYP(G) 0.2 0.2 0.019 0.023 )0.040 (Ne) – )0.0024 B3LYP 0.2 0.2 0.005 0.005 )0.006 (F) 0.009 (Be) 0.0010 BLYP 0.0 0.0 0.011 0.016 )0.031 (F) 0.007 (Be) 0.0021 HCTH 0.0 0.0 0.008 0.010 )0.019 (Ne) 0.004 (C) )0.0064 Increasing the ratio of the Becke 88 exchange contribution at long-range reduces the errors of the atomization, ionization and the total atomic energies....
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...…0.005 )0.006 (F) 0.009 (Be) 0.0010 BLYP 0.0 0.0 0.011 0.016 )0.031 (F) 0.007 (Be) 0.0021 HCTH 0.0 0.0 0.008 0.010 )0.019 (Ne) 0.004 (C) )0.0064 Increasing the ratio of the Becke 88 exchange contribution at long-range reduces the errors of the atomization, ionization and the total atomic energies....
[...]
...In the CAM-B3LYP functional, we have replaced the Becke parameter a by two parameters a, b for mixing Becke 1988 exchange and HF exchange, with l describing the conversion from one to the other through Eq....
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Journal Article•DOI•

Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields

[...]

Philip J. Stephens, Frank J. Devlin, Cary F. Chabalowski, Michael J. Frisch

01 Nov 1994-The Journal of Physical Chemistry

TL;DR: In this article, the unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio using DFT, MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set.

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17,871 citations