Kinetic energy functional gradient corrections

The approach initiated by Lee et al. [28], was rapidly adopted and as a consequence, several kinetic energy conjoint gradient correction functionals were generated. In order to compare the behavior of kinetic energy density functionals constructed in the context of LS-DFT and some members of the... 

For slowly varying densities, the kinetic energy functional can be represented by one of its gradient expansions. The gradient expansion of the kinetic energy density is not unique since it relies upon different derivations techniques [35], which yield or not a contibution of the laplacian of the density in the second order correction. In the following we will consider the expansion expression which does not involve V /i(r) ... 

This functional is found to be the exact LDA exchange functional. Furthermore, von Weizsacker proposed a correction term using the gradient of electron density for the Thomas-Fermi kinetic energy functional (von Weizsacker 1935),... 

Thomas-Fermi and gradient-corrected kinetic energy functionals. Response function analysis of HEG with split k-space shows that, to develop excited-state energy functionals, it is a good idea to work with densities corresponding to different regions of split -space rather than working with the total density. 

All calculations presented here are based on density-functional theory [37] (DFT) within the LDA and LSD approximations. The Kohn-Sham orbitals [38] are expanded in a plane wave (PW) basis set, with a kinetic energy cutoff of 70 Ry. The Ceperley-Alder expression for correlation and gradient corrections of the Becke-Perdew type are used [39]. We employ ah initio pseudopotentials, generated by use of the Troullier-Martins scheme [40], The coreradii used, in au, were 1.23 for the s, p atomic orbitals of carbon, 1.12 for s, p of N, 0.5 for the s of H, and 1.9, 2.0, 1.5, 1.97,... 

That is, we now aim to describe in a more appropriate way the interaction part of the kinetic energy that is introduced to the ex-change-correlation functional in the Kohn-Sham scheme. Including the kinetic energy corrections increases the computational requirements substantially, but the accuracy is also much improved compared with conventional gradient-corrected functionals. 

The improved numerical stability of the new deMon2K version also opened the possibility for accurate harmonic Franck-Condon factor calculations. Based on the combination of such calculations with experimental data from pulsed-field ionization zero-electron-kinetic energy (PFl-ZEKE) photoelectron spectroscopy, the ground state stmcture of V3 could be determined [272]. Very recently, this work has been extended to the simulation of vibrationaUy resolved negative ion photoelectron spectra [273]. In both works the use of newly developed basis sets for gradient corrected functionals was the key to success for the ground state stmcture determination. These basis sets have now been developed for aU 3d transition metal elements. With the simulation of vibrationaUy resolved photoelectron spectra of small transition metal clusters reliable stmcture and... 

Progress beyond this point becomes more difficult. The original expectation of Perdew was that c should be a number close to zero. Part of the motivation for this expectation was that the dependence of p upon R had been found extremely weak in variational density functional calculations using model electron densities [6,13]. Those variational calculations used an approximate form for the kinetic energy of the electrons the local Thomas-Fermi term plus the first density gradient correction (sec Ref. [14] for details)... 

Several authors [8,9,15-18], have recently attempted the calculation of c. All those calculations have several points in common a) The use of the density functional formalism [14] with approximate functionals for the kinetic energy of the electrons, like that of Eq. (14), or including higher order gradient corrections, b) A local density (LDA) description of exchange and correlation effects. The LDA exchange energy is... 

Lee, H., Lee, C.,and Parr, R. G. (1991) Conjoint gradient correction to the Hartree-Fock kinetic-and exchange-energy density functionals. Phys. Rev., A44, 768-771. Yang, W. (1986) Gradient correcttion in Thomas-Fermi theory. Phys. Rev., A34, 4575-4585. 

Therefore, the effect of the density Laplacian is included implicitly in the kinetic energy density. It is natural that the next step in density gradient correction is the kinetic energy density correction on Jacob s ladder (see Sect. 5.1). Major meta-GGA functionals include the van Voorhis-Scuseria 1998 (VS98) meta-GGA exchange-correlation (van Voorhis and Scuseria 1998), the Perdew-Kurt-Zupan-Blaha (PKZB) meta-GGA exchange-correlation (Perdew et al. 1999), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA exchange-correlation (Tao et al. 2003) functionals. 

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