Electronic band gaps corrections using total energy with DFT/LDA-½ quasi-particle approximation

Abstract

The established modus operandi on the application of the LDA-½ quasi-particle approximation methodology is to optimize the cutoff radius of the electrostatic self-energy function, in order to be applied inside the infinite crystal model. Once determined, this cutoff radius properly truncates the long-ranged self-energy function originated by the procedure of removing the undesired self-energy of electrons (or holes), responsible for most of excited-states pathologies in pure LDA. However, once perturbed, this new atomic potential cannot be used to find the ground state anymore, or even to relax atomic positions. Instead, Kohn-Sham equations are now just a way to achieve a self-consistent solution to the band gap problem in DFT. In this manuscript, an ab initio study is made using VASP with PAW pseudo-potentials to analyze the energy functional (specially the total energy and the energy eigenvalues sum) and band gaps. First and second derivatives of the total energy were studied as well, concluding the optimized cutoff radius for the electrostatic self-energy in LDA-½ strongly correlates to these functions. Using first and second derivatives (with relation to the cutoff radius) of the total energy, obtained through a non-self-consistent calculation using previously converged LDA-½ charge density, resulted in average deviation of 1.7% in the determination of the optimum cutoff radius in LDA-½, if compared to the usual procedure. It was also possible to treat LDA-½ as a perturbation, to precisely identify the energy term that was excluded. One important implication of these findings is that it should be possible to derive the LDA-½ procedure of finding the correct cutoff to the self-energy function necessary for half-excitation in solids, justifying it by total energy minimization instead of searching for extreme band gap values. In other words, results point to the possibility of a decision criterion by minimum energy, not only by an extreme band gap value (maximum or minimum), for the self-energy potential to be used to correct band gaps in crystals. Finally, with the corrected ground state energy, LDA-½ could be used not only to calculate excited-states properties, but also to perform ionic relaxations and calculate other ground state properties of materials.