Orbital energy analysis with respect to LDA and self-interaction correctedexchange-only potentials

The self-interaction correction of Perdew and Zunger with the optimized eff ective potential using the Krieger-Li-Iafrate approximation is analyzed for atomic and molecular systems in the exchange-only context. Including the s elf-interaction correction (SIC) orbital by orbital shows that the appropri ate asymptotic behavior of the exchange potential can be achieved if just t he contribution of the highest occupied molecular orbital (HOMO) is conside red. However, if a good description of the exchange potential in the valenc e region is required, and consequently a good description of the HOMO energ y, then all electrons of the valence shell must be taken into account. In c ontrast, the lowest unoccupied molecular orbital (LUMO) is described adequa tely if just the HOMO SIC contribution is employed. In addition, if the low est occupied orbital is also considered in the SIC approximation, there is an improvement in the description of the exchange potential in inner region s of an atom. When all electrons in an atom or in a molecule are considered in the SIC approximation, there exists a linear relationship between their occupied orbital energies and those obtained with the local density approx imation (LDA). This indicates that the SIC and LDA occupied orbital energie s are related by a shift. Furthermore, for a set of atoms or molecules ther e is a linear relationship between HOMO energies obtained with LDA and thos e obtained with the SIC approximation. Using both observations, the shift b etween the occupied orbital energies LDA and SIC is reported. We found that this shift (obtained for the occupied orbitals) cannot be applied to the v irtual orbitals, in particular to the LUMO. However, we do find an addition al linear relationship between LUMO energies obtained with LDA and those ob tained with the SIC approximation. The difference between the LUMO and HOMO energy (GAP) obtained with the LDA and SIC approximations is compared with that obtained with an exact local-multiplicative exchange potential and al l are compared with experimental vertical excitation energies. Whereas the LDA GAP underestimates the excitation energies, the GAP obtained with the S IC approximation and with an exact local-multiplicative exchange potential overestimates this quantity. From an analysis of the exchange energy for si mple molecules, and with a similar approach to the modified X-alpha method, we found a linear relationship between the SIC and Hartree-Fock (HF) metho ds. We show numerically that the nondiagonal terms of the exact orbital rep resentation of the exchange energy can be approximated by the SIC approach. (C) 2001 American Institute of Physics.