Local hybrid functionals

Jaramillo, Juanita; Scuseria, Gustavo E.; Ernzerhof, Matthias

doi:10.1063/1.1528936

Cited by 346 publications

(403 citation statements)

References 28 publications

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“…Local rangeseparated exchange hybrids, which use make the fraction of exact exchange at each range a function of space, are also a route toward improved functionals. [53][54][55][56]…”

Section: Discussionmentioning

confidence: 99%

Assessment of a Middle-Range Hybrid Functional

Henderson

Izmaylov

Scuseria

et al. 2008

J. Chem. Theory Comput.

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While hybrid functionals are largely responsible for the utility of modern Kohn-Sham density functional theory, they are not without their weaknesses. In the solid state, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally demanding and can introduce unphysical effects. Both problems can be remedied by a screened hybrid which uses exact exchange only at short-range. Many molecular properties, in contrast, benefit from the inclusion of long-range exact exchange. Recently, the authors reconciled these two seemingly contradictory requirements by introducing the HISS functional [J. Chem. Phys. 2007, 127, 221103], which uses exact exchange only in the middle range. In this paper, we expand upon our previous work, benchmarking the performance of the HISS functional for several simple properties and applying it to the dissociation of homonuclear diatomic cations and to the polarizability of linear H 2 chains to determine the importance of middle-range exact exchange for these systems, which are expected to be sensitive to the asymptotic exchange potential.

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“…Local rangeseparated exchange hybrids, which use make the fraction of exact exchange at each range a function of space, are also a route toward improved functionals. [53][54][55][56]…”

Section: Discussionmentioning

confidence: 99%

Assessment of a Middle-Range Hybrid Functional

Henderson

Izmaylov

Scuseria

et al. 2008

J. Chem. Theory Comput.

Self Cite

159

140

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“…As we will see here, many additional constraints can be satisfied on the fourth rung, including exactness for all one-electron densities [3,12,23] and full exact exchange [12], but for the first time some empiricism becomes unavoidable (although it can be avoided again on the fifth rung [31]). …”

Section: Introductionmentioning

confidence: 99%

“…The fourth rung or hyper-GGA [12,22,23,24,25,26,27,28,29,30], with which we will be concerned here, adds a fully nonlocal (i.e., not semilocal) ingredient, the exactexchange energy per electron ǫ ex x . Unlike total energies E, energy densities nǫ xc are non-unique or gauge-dependent.…”

Section: Introductionmentioning

confidence: 99%

Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction

et al. 2008

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We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a "normal" region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to −1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. "Abnormal" regions, where nonlocality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than −1. Regions between these extremes are described by a hybrid functional mixing exact and semilocal exchange energy densities locally, i.e., with a mixing fraction that is a function of position r and a functional of the density. Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters, corresponding roughly to the four kinds of abnormal regions. Our local hybrid functional is perhaps the first accurate fourth-rung density functional or hyper-generalized gradient approximation, with full exact exchange, that is size-consistent in the way that simpler functionals are. It satisfies other known exact constraints, including exactness for all one-electron densities, and provides an excellent fit to the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids. Exact constraints, physical insights, and paradigm examples hopefully suppress "overfitting".

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“…It is used in nonempirical meta-GGA functionals [44,45,96,[137][138][139] and also in local hybrid functionals. [140] Due to Equation 24, we have 0 z KS 1. It can distinguish tail, nuclear, and single-orbital regions (where z KS % 1) from slowly varying density regions (where z KS % 0).…”

Section: Kinetic Energy Density Dependent Ingredientsmentioning

confidence: 99%

“…It is used in nonempirical meta-GGA functionals [44,45,96,[137][138][139] and also in local hybrid functionals. [140] Due Recent work has shown important limitations of this ingredient: it hides the full anisotropy of the KED, [141] such that its s KS -dependence is very weak, [142] and it can not correctly describe the bonding regions, because z KS 50 in the middle of the bond (as s W 50), see Figure 3.…”

Section: The Positive-defined Ks Kinetic Energy Densitymentioning

confidence: 99%

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Sala

Fabiano

Constantin

2016

Int J of Quantum Chemistry

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We present the theory of semilocal exchange-correlation (XC) energy functionals which depend on the Kohn-Sham kinetic energy density (KED), including the relevant class of meta-generalized gradient approximation (meta-GGA) functionals. Thanks to the KED ingredient, meta-GGA functionals can satisfy different exact constraints for XC energy and can be made one-electron selfcorrelation free. This leads to a better accuracy over a wider range of properties with respect to GGAs, often reaching the accuracy of hybrid functionals, but at much reduced computational cost.An extensive survey of the relevant literature on existing KED dependent XC functionals is provided, considering nonempirical, semi-empirical, and fully empirical ones. A deeper analysis and a wide benchmark are presented for functionals derived considering only exact constraints and parameters obtained from model and/or atomic systems. K E Y W O R D Sdensity functional theory, kinetic energy, meta-GGA | I N T R O D U C T I O NKohn-Sham (KS)-density functional theory (DFT) [1][2][3][4][5] is nowadays one of the most popular computational approaches in quantum chemistry, solid-state physics, and materials science. [6][7][8][9][10][11] While the ground-state description of a real system of interacting electrons requires a complicate N-electron wavefunction, in KS-DFT this is mapped onto an auxiliary system of noninteracting electrons having the same ground-state density, which can be easily described using N single-particle KS orbitals. [1,2] The correspondence between the many-electron problem and the KS system is in principle exact [1,3] and it is based on the so called exchange-correlation (XC) energy functional, which collects all the quantum electron-electron interaction terms beyond the Hartree one. [12] Within the constrained-search formalism, [13] the XC energy functional is:E xc ½q 5 min W!q hWjT 1V ee jWi2T s ½q 2J½q 5E x ½q 1U c ½q 1T c ½q ;(1) where W is an N-electron ground-state wavefunction yielding the electron density q,T is the kinetic energy (KE) operator,V ee is the electron-electron interaction operator, T s is the KE of the noninteracting system, J is the Coulomb energy, E x is the exact exchange energy, and U c and T c represent, respectively, the potential and the kinetic contributions to the DFT correlation energy E c 5U c 1T c . The important point of Equation1 is that it is an universal functional of the electron density. However, its explicit functional form is not known, and any practical realization of KS-DFT is based on an approximated XC functional. The latter determines in practice the overall accuracy of the KS-DFT calculation.The study of the exact properties of the XC energy functional as well as the development of new and improved approximations have been hot research topics in DFT for more than three decades, and a large number of XC approximations has been proposed. [12,14,15] The different XC functionals are usually classified, according to their complexity, on the so called Jacob's ladder of DFT [14,16] whic...

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Local hybrid functionals

Cited by 346 publications

References 28 publications

Assessment of a Middle-Range Hybrid Functional

Assessment of a Middle-Range Hybrid Functional

Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

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