Fermi-Löwdin Self Interaction Corrections (FLOSIC)

www.flosic.org

Relativistic many-body methods for atoms: Coupled-Cluster Theory, Random Phase Approximation, Many-body perturbation theory.  my_phd_thesis

Self-consistent GW theory:

It is now well known that traditional Kohn-Sham (KS) density functional theory (DFT) with local exchange-correlation (xc) functionals (LDA and GGA) highly underestimates band gaps due incomplete cancellation of the self-interaction energy and the absence of long-range polarization effect. Moreover, KS eigenvalues cannot be used to explain observed photoemission spectroscopy and optical absorption, however, such eigenvalues are used as a starting point in GW calculations. The single-shot flavor of the GW approximation (G0W0 method) is quite successful in predicting experimental bandgaps of weakly correlated s-p bonded systems. Since G0W0 lacks self-consistency, it always depends on the choice of xc functional leading to different values in the literature and making it less versatile.

There are a few flavors of fully self-consistent GW methods (e.g. scGW, QSGW approaches) that have been employed previously with partial success. It has been observed that the above approaches systematically underestimate bulk dielectric constant values, thus, yielding an overestimated bandgap. To improve bandgap values, it is now necessary to go beyond conventional GW approximation by implementing a vertex function that drastically increases computational cost. In this project, we propose to incorporate and study the importance of vertex term in the self-energy () as well as in W function. A graphical representation coupled with Hedin’s equation with vertex terms is shown in Fig. 1, vertex terms are precisely the exchange of random phase approximation (RPA) bubble diagrams. Attempts to partially include vertex corrections are being made in the form of second-order screened exchange (SOSEX) and related approximations showing improved bandgaps. A full self-consistent solution of Hedin’s equation has a lot of technical challenges, therefore, to improve computational efficiency, strategies such as diagonal G and low-rank W approximations will be explored.

Fig. 1. Diagrammatic representation of Hedin's equation. [Golze et al. Front. Chem., 09 July 2019]