Local spin-density functional theory

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

Local spin density functional theory (LSDFT) is an extension of regular DFT in the same way that restricted and unrestricted Hartree-Fock extensions were developed to deal with systems containing unpaired electrons. In this theory both the electron density and the spin density are fundamental quantities with the net spin density being the difference between the density of up-spin and down-spin electrons ... 

A. Kafafi and E. R. H. El-Gharkawy,/. Phys. Chem. A, 102,3202 (1998). A Simple Coupling Scheme Between Hartree-Fock and Local Spin-Density Functional Theories. 

M. A. Whitehead and S. Manoli, Phys. Rev. A, 38,630 (1988). Generalized-Exchange-Local-Spin-Density-Functional Theory Self-Interaction Correction. 

Guo, Y., Whitehead, M. A. (1989). Application of generalized exchange local-spin-density-functional theory electronegativity, hardness, ionization potential, and electron afSnity. Phys. Rev. A 39,2317-2323. 

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

Using local spin density functional (LSDF) theory, we obtain 70 kcal/mole for the rotational barrier of the ethylene molecule (35). In these calculations, we use the equivalent of a double-zeta+polarization basis set, i.e. for C two 2s functions. 

Three density functional theories (DFT), namely LDA, BLYP, and B3LYP, are included in this section. The simplest is the local spin density functional LDA (in the SVWN implementation), which uses the Slater exchange functional [59] and the Vosko, Wilk and Nusair [60] correlation functional. The BLYP functional uses the Becke 1988 exchange... 

A method to calculate J]j, based on the local approximation to spin density functional theory has been developed by Liechtenstein et al. [51, 52]. Using spherical charge and spin densities and a local force theorem, expression for Jjj is... 

It is impossible to develop a current-dependent relativistic exchange-correlation functional, which is computationally tractable and reduces to spin-density functional theory in the weakly relativistic limit. One reason is that there is no local approximation to such a functional since j vanishes for any homogeneous system. This means that the relativistic electron gas cannot serve as a starting point. More insight is gained from a Gordon decomposition of the current density j (see e.g. Refs. [7, 24]), which shows that j consists of an orbital part and the curl of a magnetisation density fh. 

G. Scalmani, M. J. Frisch. A New Approach to Noncollinear Spin Density Functional Theory beyond the Local Density Approximation. /. Chem. Theory Corn-put., 8 (2012) 2193-2196. 

Table4.4 Spectroscopic properties for Au2 q= -1,0, + 1) using ab-initio (Hartree Fock, HF, second-order Moller-Plesset, MP2, and coupled cluster, CCSD(T)) and DFT (local spin-density approximation, LSDA, Perdew-Wang CCA, PW91, and Becke three-parameter Lee-Yang-Parr functional, B3LYP) methods at the RPPA level of theory.

Let us introduce another early example by Slater, 1951, where the electron density is exploited as the central quantity. This approach was originally constructed not with density functional theory in mind, but as an approximation to the non-local and complicated exchange contribution of the Hartree-Fock scheme. We have seen in the previous chapter that the exchange contribution stemming from the antisymmetry of the wave function can be expressed as the interaction between the charge density of spin o and the Fermi hole of the same spin... 

These results, as most related results of density functional theory, have direct connections to the fundamental statement of the Hohenberg-Kohntheorem the nondegenerate ground state electron density p(r) of a molecule of n electrons in a local spin-independent external potential V, expressed in a spin-averaged form as... 

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