Self-interaction effects

At large distance from a neutral atom, V2(r) goes to and vi(r) decays exponentially.If a symmetric ansatz for the PCF is employed, the WDA XC potential will be symmetric automatically, just like the exact case above. Additionally, a symmetric XC potential has the exact asymptotic behavior (-1) and the spmious self-interaction effect in the HREDF J[( is mostly removed. Unfortunately, because of the nonsymmetric nature of the ansatz for the PCF in Eq. (113), the XC potential within the present WDA framework has three terms instead. 

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. 

In the nonrelativistic LDA one finds partial, but by no means satisfactory cancellation of self-interaction effects between Eh and The WDA... 

The linear photoresponse of metal clusters was successfully calculated for spherical [158-160, 163] as well as for spheroidal clusters [164] within the jellium model [188] using the LDA. The results are improved considerably by the use of self-interaction corrected functionals. In the context of response calculations, self-interaction effects occur at three different levels First of all, the static KS orbitals, which enter the response function, have a self-interaction error if calculated within LDA. This is because the LDA xc potential of finite systems shows an exponential rather than the correct — 1/r behaviour in the asymptotic region. As a consequence, the valence electrons of finite systems are too weakly bound and the effective (ground-state) potential does not support high-lying unoccupied states. Apart from the response function Xs, the xc kernel /xc[ o] no matter which approximation is used for it, also has a self-interaction error. This is because /ic[no] is evaluated at the unperturbed ground-state density no(r), and this density exhibits self-interaction errors if the KS orbitals were calculated in LDA. Finally the ALDA form of /,c itself carries another self-interaction error. 

While DFT has been used to successfully model activation barriers for some gas phase systems and well-defined organometallic complexes, there is a concern that DFT methods under-predict the barriers for some ft ee radical abstraction systems. The under-estimation is primarily due to the over-accounting of the self-interaction of electrons in the SCF procedure [75]. Surface-bound free radical intermediates demonstrate less localized unpaired spin due to their strong interaction with the surface. This is likely to reduce some of the problems related to self interaction effects. Below we summarize results for DFT computed barriers for the activation of simple adsorbates over different transition metals. A more thorough and systematic investigation is required to better understand what controls the accuracy in activation barrier predictions on metal surfaces. 

Main experimental findings both for the ground state (magic numbers for the stability of clusters [3] and the existence of supershells [4]) and for excited states (the dominance of collective states in the photoabsorption of metal clusters MeA with N > S) were predicted [5] before their experimental confirmation. Recently we were able to explain the temperature dependence of the absorption of small metal clusters as observed by Haber-land s group [6]. If the model is complemented by pseudopotential perturbation theory [7] the results obtained match qualitatively those obtained by demanding quantum-chemical methods (e.g. the photoabsorption spectra of Na6). Further improvement of the model includes the removal of self-interaction effects, the so-called SIC [8-10] (a consequence of using the local density approximation (LDA) to general density functional theory (DFT)). 

In addition we have calculated the electron affinities within the jellium model. But, as well known from experience in atomic physics, the LDA functional has to be corrected for so-called self-interaction effects (SIE) as originally proposed by Perdew and Zunger [8]. As explained in detail below, this leads to an orbital-dependent Kohn-Sham potential by the replacement [31] ... 

Encl[p] is the non-classical contribution to the electron-electron interaction containing all the effects of self-interaction correction, exchange and Coulomb correlation described previously. It will come as no surprise that finding explicit expressions for the yet unknown functionals, i. e. T[p] and Encl[p], represents the major challenge in density functional theory and a large fraction of this book will be devoted to that problem. 

Johnson, B. G., Gonzales, C. A., Gill, P. M. W., Pople, J. A., 1994, A Density Functional Study of the Simplest Hydrogen Abstraction Reaction. Effect of Self-Interaction Correction , Chem. Phys. Lett., 221, 100. 

One obvious drawback of the LDA-based band theory is that the self-interaction term in the Coulomb interaction is not completely canceled out by the approximate self-exchange term, particularly in the case of a tightly bound electron system. Next, the discrepancy is believed to be due to the DFT which is a ground-state theory, because we have to treat quasi-particle states in the calculation of CPs. To correct these drawbacks the so-called self-interaction correction (SIC) [6] and GW-approximation (GWA) [7] are introduced in the calculations of CPs and the full-potential linearized APW (FLAPW) method [8] is employed to find out the effects. No established formula is known to take into account the SIC. 

Kubo, Y., Sakurai, Y., Tanaka, Y., Nakamura, T., Kawata, H. and Shiotani, N. (1997) Effects of self-interaction correction on Compton profiles of diamond and silicon, J. Phys. Soc. Jpn., 66, Till 2780. 

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