Density functional theory exact exchange potential

In Kohn-Sham density functional theory, the ionization potential is the negative of the eigenvalue of the highest occupied Kohn-Sham orbital. 86-88 The IP = —sH0M0 relation holds, however, only for the exact exchange-correlation potential. Numerical confirmations for this relation exist for model systems such as the... 

Density Functional Theory (DFT) has become a powerful tool for ab-initio electronic structure calculations of atoms, molecules and solids [1, 2, 3]. The success of DFT relies on the availability of accurate approximations for the exchange-correlation (xc) energy functional Exc or, equivalently, for the xc potential vxc. Though these quantities are not known exactly, a number of properties of the exact xc potential vxc(r) are well-known and may serve as valuable criteria for the investigation of approximate xc functionals. In this contribution, we want to focus on one particular property, namely the asymptotic behavior of the xc potential For finite systems, the exact xc potential vxc(r) is known to decrease like — 1/r as r —oo, reflecting also the proper cancellation of spurious self-interaction effects induced by the Hartree potential. 

Gusarov S, Malmquist P-A, Lindh R, Roos BO (2004) Correlation potentials for a multiconfigurational-based density functional theory with exact exchange, Theor Chem Acc, 112 84-94... 

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... 

Hesselmann, A. and Jansen, G. (2003). The helium dimer potential from a combined density functional theory and symmetry-adapted perturbation theory approach using an exact exchange-correlation potential. Phys. Chem. Chem. Phys., 5, 5010-14. 

Finally, we consider density functional theory (DFT) computations of p-space properties. A naive way of calculating p-space properties is to use the Kohn-Sham orbitals obtained from a DFT computation to form a one-electron, r-space density matrix Fourier transform / according to Eq. (14), and proceed further. This approach is incorrect because the Kohn-Sham density matrix F is not the true one and, in fact, corresponds to a fictitious non-interacting system with the same p(r) as the true system. On the other hand, Hamel and coworkers [112] have shown that if the exact Kohn-Sham exchange potential is used, then the spherically averaged momentum densities of the Kohn-Sham orbitals should be very close to those of the Hartree-Fock orbitals. Of course, in practical computations the exact Kohn-Sham exchange potential is not used since it is generally not known. 

We shall see that the method of Kohn and Sham in density functional theory actually provides a sound theoretical base for this method which has been used Over the years simply as a numerical convenience. The density functional method uses a set of fictional molecular orbitals which do not themselves have any physical interpretation and whose only property is to generate an electron density which is exact. The whole of the experimental calibration procedure is thrown into the generation of a potential (the exchange/correlation potential) which can, in principle, be universal that is, not dependent on the particular molecule under study. The huge number of parameters required in earlier semi-empirical methods (some for every atom) is replaced by choice of a form for this potential and a few universal parameters (up to a dozen). 

Another important issue in density functional theory is the form of the exchange and correlation potential. In most investigations of metal surfaces, the simple local density approximation is used, again, with surprisingly successful results. In the case of a homogeneous electron gas, the effective exchange-correlation potential is given exactly by and is accurately known from quantum Monte Carlo calculations. Outside the metal, decays... 

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