SelfConsistent SelfInteraction Corrected DFT: The Method and Applications to Extended and Confined Systems
Abstract
We lay out a framework for the selfconsistent calculation of selfinteraction corrections (SIC) to the density functional theory (DFT). The technique implements the original method due to Perdew and Zunger and combines two procedures: construction of maximally localized Wannier functions (MLWF, procedure due to Marzari and Vanderbilt and to Silvestrelli) and direct minimization of the DFT+SIC total energy functional. In this formulation, the technique is applicable to both confined and extended systems. While construction of the Wannier functions is a useful tool in the case of molecules and clusters, it is a necessary step for extended systems since selfinteraction energies constructed on Bloch functions vanish. Construction of Wannier functions thus provides both a good initial guess and a set of functions for which calculation of nonvanishing SIC is possible. Two direct minimization schemes have been used to solve the nontrivial generalized eigenvalue problem. One of the methods, similar to CarParrinello method, makes use of the gradient proposed by Goedecker and Umrigar. The other method, uses a conjugate gradient algorithm with orthogonality constraints that is based upon the work of Edelman, Smith and Arias. The DFT+SIC method has been applied to several systems for which standard DFT methods do not work well. One of the more persistent failures of standard DFT methods has been their failure to yield accurate reaction barriers. However, pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange have shown great promise (i.e. B3LYP, PBE0, BH, and mPWH) in improving the accuracy of reaction barriers. Our studies of various chemical reactions showed that SIC can be used in much the same way as exact exchange. Studies of various chemical reactions showed that including a fractional amount of SIC (40%) into a DFT calculation improved the accuracy of calculated reaction energies and barriers considerably. Another notable failure of standard DFT methods has been their failure to reproduce band gaps. For widegap systems (insulators and molecules with large HOMOLUMO gaps), SIC appears to be working well. DFT+SIC calculations for SiO2, Al2O3, and TiO2 crystals, as well as for the CO molecule, have shown that 0.4*SIC correction predicts values for the gaps as well as for the singlettriplet splitting in reasonable agreement with the observed values. However, for systems with narrower gaps the results are more problematic, and the 0.4*SIC correction appears to overcorrect the DFT results. DFT+0.4*SIC calculations for Si crystal predicted a minimal gap of 2.25 eV compared to the experimental gap of 1.2 eV; in Ge a 1.2eV gap is predicted compared to the experimental gap of 0.8 eV.
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARL38004B