Exchange-correlation energy, density functionals

Because of different scaling properties, the exchange-correlation energy density functional (XCEDF) can be further decomposed into separate exchange and correlation components, ... 

In the LDA framework, the total electronic energy includes the exchange-correlation energy density functional of the form [43]... 

Although the Kohn-Sham method has been the basic procedure in DFT calculations, many exchange-correlation functionals used in conventional DFT calculations have no strict theoretical basis upon which to be used in the Kohn-Sham method. Since the Kohn-Sham method is based on the constrained search formulation, it is proven to be applicable to pure exchange-correlation energy density functionals. 

Wesolowski, T. A., Parisel, O., Ellinger, Y., Weber, J., 1997, Comparative Study of Benzene---X (X = 02, N2, CO) Complexes Using Density Functional Theory The Importance of an Accurate Exchange-Correlation Energy Density at High Reduced Density Gradients , J. Phys. Chem. A, 101, 7818. 

The term non-local is used sometimes in die literature in association with gradient-dependent (GGA) functionals. This nomenclature is not applied in this work. The LDA-, GGA-, and meta-GGA functionals are referred to as semi-local as they do not account for any long-range non-locality of the exchange-correlation energy density excseim local(r) = exc(p(r), Vp(r), V2p(r), r(r)) whereas... 

Integrals involving the exchange-correlation potential r,c or the exchange-correlation energy density cannot be evaluated analytically so that further sets of auxiliary functions are introduced. (In practice and 6,<, behave similarly so that a common set is used to fit both functions.) The exchange-correlation basis (XCB) also consists of Hermite Gaussians... 

Applications have been carried out for the correlation energy density functional E(.[p] [22,28,31,32], the kinetic and exchange energy functionals [24], the kinetic component of the correlation energy [32,33], the current-density functional theory [29], the second-order density matrix [30], and the total energy of atoms and molecules [23],... 

Fig. 5 Exact and fitted (using Eq. (21)) deviation of the RPA conventional exchange-correlation energy density from RPA-LDA, as a function of position z for the Airy gas model with force...

The quest for various approximations for the exchange-correlation energy density/(p) has spanned decades in quantum chemistry and was recently reviewed [92]. Here, we will present the red line of its implementation, as it will be further used for the current applications. The benchmark density functional stands as the Slater exchange approximation, derived within the so-called Xa theory [179] ... 

Kohout, M., Pemal, K., Wagner, F. R., Grin, Y. (2004). Electron locali2ability indicator for correlated wave functions. I. Parallel-spin pairs. Theor. Chem. Acc. 112,453 59. Lam, K. C., Cruz, F. G., Burke, K. (1998). Viral exchange-correlation energy density in Hooke s atom. Int. J. Quantum Chem. 69, 533-540. 

The major goal is to find a good functional form for the exchange-correlation energy density per particle xc where... 

The exchange-correlation kernel is thus the functional derivative of the exchange-correlation potential which in turn can be expressed in terms of the functional derivative of the exchange-correlation energy density All these... 

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