Self-interaction-corrected local spin density approximation

5 Self-interaction-corrected local spin density approximation 

Consider first a system of a single electron moving in an arbitrary external potential Vext(r)- The wavefimction, V l, is the solution to the Schrodinger equation 

This is a fundamental property of the true exchange-correlation functional, Exc, valid for any one-electron density. In the LSD, Exc is approximated, and the self-Coulomb and self-exchange do not cancel anymore. One speaks of spurious self-interactions that are introduced by the approximations in the local fimctionals (Dreizler and Gross, 1990). 

Next we consider a many-electron system. When the electron density is decomposed into one-electron orbital densities, n = it is straightforward 

Here the sums run over all the occupied orbitals ij/a, with the SIC given by 

---

Harrison, J. G. (1987). Electron afilnities in the self-interactions-corrected local spin density approximation. J. Chem. Phys. 86,2849-2853. 

Here the first part is the electrostatic self-Coulomb interaction and the second part is the analog correction for the exchange-correlation part of the effective potential. Please note that both functionals depend on the total density n, and not on the spin densities as in the case of Perdew and Zunger who corrected the LSDA (Local Spin Density Approximation). Results for Cu are reproduced in Figure 1.15 [31]. Though with this simple functional quantitative agreement with experimental data is not to be expected, the experimentally observed shell effects in the electron affinity are qualitatively well reproduced. 

Another calculation for the complete series used a local spin-density approximation with self-interaction correction. Relativistic contributions AA had a dramatic effect (for Os A = 1.5, AA=—1.52eV) [11]. SCF-Xa-SW theory was applied for Ru, Rh, Pd [12], Ir, and Pt [13]. A preliminary many-body calculation for the Pd ion in its 4d °5s S ground state confirmed a positive value of A [14]. 

---