Density Functional Theory spin potential

Keywords Spin-orbit interaction Density functional theory Spin-orbit DFT Effective core potential approach... 

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... 

Spin-potential in density functional theory framework... 

The density functional theory of Hohenberg, Kohn and Sham [173,205] has become the standard formalism for first-principles calculations of the electronic structure of extended systems. Kohn and Sham postulate a model state described by a singledeterminant wave function whose electronic density function is identical to the ground-state density of an interacting /V-clcctron system. DFT theory is based on Hohenberg-Kohn theorems, which show that the external potential function v(r) of an //-electron system is determined by its ground-state electron density. The theory can be extended to nonzero temperatures by considering a statistical electron density defined by Fermi-Dirac occupation numbers [241], The theory is also easily extended to the spin-indexed density characteristic of UHF theory and of the two-fluid model of spin-polarized metals [414],... 

For the case of a purely electrostatic external potential, P = (F , 0), the complete proof of the relativistic HK-theorem can be repeated using just the zeroth component f (x) of the four current (in the following often denoted by the more familiar n x)), i.e. the structure of the external potential determines the minimum set of basic variables for a DFT approach. As a consequence the ground state and all observables, in this case, can be understood as unique functionals of the density n only. This does, however, not imply that the spatial components of the current vanish, but rather that j(jc) = < o[w]liWI oM) has to be interpreted as a functional of n(x). Thus for standard electronic structure problems one can choose between a four current DFT description and a formulation solely in terms of n x), although one might expect the former approach to be more useful in applications to systems with j x) 0 as soon as approximations are involved. This situation is similar to the nonrelativistic case where for a spin-polarised system not subject to an external magnetic field B both the 0 limit of spin-density functional theory as well as the original pure density functional theory can be used. While the former leads in practice to more accurate results for actual spin-polarised systems (as one additional symmetry of the system is take into account explicitly), both approaches coincide for unpolarized systems. 

Eqs. (101)-(103) constitute the KS scheme of time-dependent spin-density functional theory. With the xc action functional [ t. i] defined in analogy to Eq. (43), the spin-dependent xc potentials can be represented as functional derivatives ... 

Shaik and co-workers have carried out a number studies using density functional theory based quantum chemical and QM/MM techniques to examine various aspects of the mechanism of alkane hydroxylation by cytochrome P450.178 181 These studies included, for example, calculation of the potential energy surface for the so-called rebound mechanism with methane as a substrate for two spin states, the high spin (HS) quartet state and low spin (LS) doublet state. In the rebound mechanism, Compound I initially abstracts a... 

The Kohn-Sham-Gaspar potential derived from density-functional theory has a similar expression for V c with Xa = 2/3, and only took into account exchange [20],[40]. To include correlation, several forms were proposed for / , with parameters obtained from fits to RPA calculations or more accurate Monte Carlo simulations [41] and different spin interpolations. The current version of the DVM code contains altogether nine choices of Vje, the preferred form being the Vosko, Wilk and Nusair [42] parametrization of the Ceperley and Alder Monte Carlo simulations [43]. 

While the concentration dependence of the experimental fields are reproduced rather well by the theoretical fields (a phase transition to the BCC structure occurs around 65% Fe), the later ones are obviously too small. This finding has been ascribed in the past to a shortcoming of plain spin density functional theory in dealing with the core polarization mechanism (Ebert et al. 1988a). Recent work done on the basis of the optimized potential method (OPM) gave results for the pure elements Fe, Co and Ni in very good agreement with experiment (Akai and Kotani 1999). 

Calculating xw within the framework of plain spin density functional theory (SDFT), there is no modification of the electronic potential due to the induced orbital magnetization. Working instead within the more appropriate current density functional theory, however, there would be a correction to the exchange correlation potential just as in the case of the spin susceptibility giving rise to a Stoner-like enhancement. Alternatively, this effect can be accounted for by adopting Brooks s orbital polarization formalism (Brooks 1985). 

With the exception of Ligand Field Theory, where the inclusion of atomic spin-orbit coupling is easy, a complete molecular treatment of relativity is difficult although not impossible. The work of Ellis within the Density Functional Theory DVXa framework is notable in this regard [132]. At a less rigorous level, it is relatively straightforward to develop a partial relativistic treatment. The most popular approach is to modify the potential of the core electrons to mimic the potential appropriate to the relativistically treated atom. This represents a specific use of so-called Effective Core Potentials (ECPs). Using ECPs reduces the numbers of electrons to be included explicitly in the calculation and hence reduces the execution time. Relativistic ECPs within the Hartree-Fock approximation [133] are available for all three transition series. A comparable frozen core approximation [134] scheme has been adopted for... 

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