Clusters exchange-correlation potential

The calculations were performed using the Hedin-Lundquist exchange correlation potential. When X-ray absorption spectra are calculated, a core-hole has to be present in order to mimic the photon absorption process. The calculations were performed both with and without complete core-hole screening. The optimal geometry for the clusters as derived from the ADF calculations was used as input for the FEFF8 calculations. 

The results reported here use the Xa exchange-correlation function, which has historical interest and can be compared to past calculations. Within the local density approximation, parametrizations that include the correlation effects found in a uniform electron gas often give a better account of spin-dependent properties (19). Since correlation effects generally stabilize low spin species more than high-spin states (20), one would expect correlation effects to increase J over the values reported here, and this was indeed found in our earlier studies of oxidized three-iron clusters (9). Calculations on the reduced species using improved exchange-correlation potentials are in progress. 

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... 

This is the point at which to demonstrate the intimate connection between density functional and density matrix theory. The link will be forged by expressing the exchange-correlation potential VXc(r) of DFT in terms of the 1 and 2 DMs of the atom, molecule, or finite cluster under consideration. The result for Vxc r) in terms of low-order DMs is due to Holas and March [52],... 

To obtain the basis functions, numerical Local Density calculations are performed for free atoms or ions, employing the same type of exchange-correlation potential as in the molecular (or cluster) calculation (this, of course, is not a necessary condition, but is usually done for the sake of coherence). The atomic self-consistent calculations seek to... 

An interesting aspect of the density functional calculations of Penzar and Ekardt is that these include self-interaction corrections. It is well known that the local density approximation (LDA) to exchange and correlation effects is not sufficiently accurate to give reliable electron affinities of free atoms or clusters [47,48]. This defidency is due to the fact that, in a neutral atom for instance, the LDA exchange-correlation potential Vif (f) decays exponentially at large r, while the exact behavior should be — 1/r. As a consequence, some atomic and cluster anions become unstable in LDA. The origin of this error is the incomplete cancellation of the self-interaction part of the classical coulomb energy term... 

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,... 

The impurity-state orbitals for the Cl crdculation were obtained by the spin-restricted LDA cluster calculation using the ordinary SCAT computation code. Although the Slater s Xa potential with a = 0.7 was used as the exchange-correlation potential, it has been confirmed that the results of the spin-restricted calculation is almost identical with those by the VWN potential. ... 

In subsection 3.1, we will present GGA and LDA calculations for Au clusters with 6first principles method outlined in section 2, which employs the same scalar-relativistic pseudo-potential for LDA and GGA (see Fig 1). These calculations show the crucial relevance of the level of density functional theory (DFT), namely the quality of the exchange-correlation functional, to predict the correct structures of Au clusters. Another, even more critical, example is presented in subsection 3.2, where we show that both approaches, LDA and GGA, predict the cage-like tetrahedral structure of Au2o as having lower energy than amorphous-like isomers, whereas for other Au clusters, namely Auig, Au ... 

The wave eigenfunctions and energy eigenvalues were obtained by real space electronic state calculations, which were performed by the use of the program code SCAT of the DV-Xx molecular orbital (MO) cluster method with the Hartree-Fock-Slater approximation [8,9]. In the method, the exchange-correlation term Vxc in the one-electron Hamiltonian was expressed in terms of the statistical local potential (1),... 

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