Abstract
The very old and successful density-functional technique of half-occupation is revisited [J. C. Slater, Adv. Quant. Chem. 6, 1 (1972)]. We use it together with the modern exchange-correlation approximations to calculate atomic ionization energies and band gaps in semiconductors [L. G. Ferreira et al., Phys. Rev. B 78, 125116 (2008)]. Here we enlarge the results of the previous paper, add to its understandability, and show when the technique might fail. Even in this latter circumstance, the calculated band gaps are far better than those of simple LDA or GGA. As before, the difference between the Kohn-Sham ground state one-particle eigenvalues and the half-occupation eigenvalues is simply interpreted as the self-energy (not self-interaction) of the particle excitation. In both cases, that of atomic ionization energies and semiconductor band gaps, the technique is proven to be very worthy, because not only the results can be very precise but the calculations are fast and very simple.
Highlights
The very old half-occupation technique[1,2,3] and its formalization through the Janak theorem[4] have been continuously used since the seventies
The band structure calculations were made with the codes VASP39,40 and WIEN2k.41 band continuum for those cases when we make the standard SCF local-density approximation (LDA)-1/2, and falls outside for the cases when we use NSCF
Aside from its known usefulness to finite systems, such as atoms, molecules, and cluster, we extend its use to crystals and semiconductors
Summary
The very old half-occupation technique[1,2,3] and its formalization through the Janak theorem[4] have been continuously used since the seventies. Even we find many papers citing those authors and using their techniques in many computational problems.[5,6,7,8,9,10,11,12,13] The Janak theorem refers to the derivative of the total energy with respect to the occupation, which equals the Kohn-Sham (KS) eigenvalue.[14] If the derivative is linear with the occupation the half-occupation technique follows. Can prove that the difference between the IE and the KS eigenvalue, is about 1/2 the SIC defined by Ref. 17 This factor of 1/2, apparently first discovered by Trickey,[22] has been numerically verified by Refs. To avoid confusion we are naming the difference between the IE and the KS eigenvalue, following from Janak’s theorem, as “self-energy” because its expression is that of a self-energy
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