Slater-Kohn-Sham potential

Here V r) is the so-called Slater-Kohn-Sham (SKS) potential involved in finding one-electron wave functions vl/i(r) yielding for an N-electron atom or molecule the ground-state density p(r) as... 

The next step in the Holas-March study was to form from the above, formally exact, theory based on the many-electron Schrodinger equation, the gradient of the exchange-correlation potential energy VXc(r). This is the many-electron part of the one-body potential to be inserted in the one-body Schrodinger equations (the so-called Slater-Kohn-Sham (SKS) equations)... 

We have anployed the parametrized DFTB method of Porezag et al. [33,34]. The approximate DFTB method is based on the density-functional theory of Hohenberg and Kohn in the formulation of Kohn and Sham [43,44]. In this method, the single particle wave functions l (r) of the Kohn-Sham equations are expanded in a set of atomic-like basis functions < > , with m being a compound index that describes the atom on which the function is centered, the angular dependence of the function, as well as its radial dependence. These functions are obtained from self-consistent density functional calculations on the isolated atoms employing a large set of Slater-type basis functions. The effective Kohn-Sham potential Feff(r) is approximated as a simple superposition of the potentials of the neutral atoms... 

Since the Fock operator is a effective one-electron operator, equation (1-29) describes a system of N electrons which do not interact among themselves but experience an effective potential VHF. In other words, the Slater determinant is the exact wave function of N noninteracting particles moving in the field of the effective potential VHF.5 It will not take long before we will meet again the idea of non-interacting systems in the discussion of the Kohn-Sham approach to density functional theory. 

Another reason for the choice of the title is the above-mentioned introduction of the Xa-method and the MS-Xa method by Slater and coworkers. There are, however, in particular two other reasons for choosing the title. The first is the formulation of the Density Functional Theory by Hohenberg and Kohn in 1964 [19], which today is probably one of the most quoted papers in electronic structure calculations. This basic work was followed by another important paper in 1965 by Kohn and Sham [20], where they showed how one could use the method for practical calculations and introduced the Kohn-Sham, KS, exchange potential. Exactly the same expression for the exchange potential had previously been derived by Caspar [21], This exchange potential is therefore often known as the Caspar-Kohn-Sham, GKS, potential. Another very important reason for choice of the title is the introduction of the three dimensional numerical integration method by Ellis and Painter in 1968-1970 [22-24]. This... 

We used the discrete variational (DV-Xa) method which uses a linear combination of atomic orbitals (LCAO) expansion of molecular orbitals to calcidate the silicate cluster electronic state. (19, 20) In this method the exchange-correlation potentials are approximated by the simple Kohn-Sham-Slater form... 

In the Kohn-Sham formalism, one assumes that there is a fictitious system of N noninteracting electrons experiencing the real external potential and this has exactly the same density as the real system. This reference system permits to treat the iV-electron system as the superposition of N one-electron systems and the corresponding iV-electron wave function of the reference system will be a Slater determinant. This is important because in this way DFT permits to handle both discrete and periodic systems. To obtain a trial density one needs to compute the energy of the real system and here it is when a model for the unknown functional is needed. To this purpose, the total energy is written as a combination of terms, all of them depending on the one-electron density only ... 

The one-electron Kohn-Sham equations were solved using the Vosko-Wilk-Nusair (VWN) functional [27] to obtain the local potential. Gradient correlations for the exchange (Becke fimctional) [28] and correlation (Perdew functional) [29] energy terms were included self-consistently. ADF represents molecular orbitals as linear combinations of Slater-type atomic orbitals. The double- basis set was employed and all calculations were spin unrestricted. Integration accuracies of 10 -10 and 10 were used during the single-point and vibrational frequency calculations, respectively. The cluster size chosen for Ag or any bimetallic was... 

By exchange, we mean the density functional definition of exchange, in which the wavefunction is a Slater determinant whose density is the exact density of the interacting system, and which minimizes the energy of the non-interacting system in the Kohn-Sham external potential, iv,a=o- Another useful concept is the pair distribution function, defined as[14]... 

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