Exact exchange relations

Theory of exact exchange relations for a single excited state 13... 

Development of methods related to DFT that can treat this situation accurately is an active area of research where considerable progress is being made. Two representative examples of this kind of work are P. Rinke, A. Qteish, J. Neugebauer, and M. Scheffler, Exciting Prospects for Solids Exact Exchange Based Functional Meet Quasiparticle Energy Calculations, Phys. Stat. Sol. 245 (2008), 929, and J. Uddin, J. E. Peralta, and G. E. Scuseria, Density Functional Theory Study of Bulk Platinum Monoxide, Phys. Rev. B, 71 (2005), 155112. 

Transferability is in some ways a double problem. The first of these relates to whether an optimised exact exchange contribution able to reproduce spin-state splittings in a given compound or class of compounds will repro-... 

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... 

Subsequent to the study of Holas and March summarized above, Levy and March [56] have effected a generalization which permits a formulation as a function of the electron-electron repulsion coupling constant A. As will be discussed below, the purpose of their generalization is to allow Vxc(r) to be separated into exchange and correlation contributions. This is achieved by then developing relations which are associated with each order in A. The first-order development yields a formal expression for the exact exchange potential Vjf(r), given by... 

For finite systems and clusters in particular an important source of problems strictly related to the local and semilocal approximations is the asymptotic behavior of the potential felt by an electron that is well outside the cluster. The exact exchange-correlation potential converges asymptotically (and probably rather quickly [40]) to l)/r,... 

Since the exact functional relating the energy to the electron (or spin) density is unknown, it is necessary to design approximate functionals, and the accuracy of a DFT method depends on the suitability of the functionals employed. Many different functionals for exchange and correlation have been proposed, and it is beyond the scope of this article to outline their mathematical forms (these may... 

We elaborate on recent attempts to derive the local and energy-dependent density-functional potential v from the diagrammatic structure of many-body perturbation theory for the exact exchange-correlation energy, without explicit recourse to an extremal principle. The local v can be related to the nonlocal and dynamic self-energy E obtained from perturbation theory. 

Relation of exact exchange to Gorling-Levy perturbation theory... 

Stretched H and related systems are of course unusual. In most systems, the exact exchange-correlation hole is reasonably localized around its electron, as it is in LSD or GGA - and that fact is one of the reasons [93] why LSD and GGA work as well as they do. 

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