Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Abstract

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...

Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals

“…in ref. 122. Alike the exact exchange discussed below, the meta-GGA potential turns out to depend on the l channel.…”

Ultranonlocality and accurate band gaps from a meta-generalized gradient approximation

“…These so-called meta-GGAs are well established and their development has become an impressive success story [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. They are the natural candidates for curing the abovementioned deficiencies because the explicit use of the (occupied) orbitals creates nonlocality since each ϕ i (r) depends on the density n(r ) at all points r .…”

Assessment of interaction-strength interpolation formulas for gold and silver clusters

“…the generalized gradient approximation (GGA) 65 or the meta-GGA's. 66 This is an efficient approach, 25,26,33,35,37,38,48,49,[67][68][69] but in various cases it has also shown limited accuracy, especially in the not so rare case when it is necessary to discriminate between isomers with rather similar energies (for example in the prediction of the two-to three-dimensional crossover in gold and silver clusters 38,50 ). However, unlike in the case of main group molecular calculations, the use of hybrid functionals, which include a fraction of exact exchange, is not able to provide a systematic improvement.…”