GW(Γ) method without the Bethe-Salpeter equation for photoabsorption energies of spin-polarized systems

Abstract

The one-shot $GW$ method, beginning with the local density approximation (LDA), enables one to calculate photoemission and inverse photoemission spectra. In order to calculate photoabsorption spectra, one had to additionally solve the Bethe-Salpeter equation (BSE) for the two-particle (electron-hole) Green's function, which doubly induces evaluation errors. It has been recently reported that the $GW$+BSE method significantly underestimates the experimental photoabsorption energies (PAEs) of small molecules. In order to avoid these problems, we propose to apply the $GW(\mathrm{\ensuremath{\Gamma}})$ method not to the neutral ground state but to the cationic state to calculate PAEs without solving the BSE, which allows a rigorous one-to-one correspondence between the photoabsorption peak and the ``extended'' quasiparticle level. We applied the self-consistent linearized $GW\mathrm{\ensuremath{\Gamma}}$ method including the vertex correction $\mathrm{\ensuremath{\Gamma}}$ to our method, and found that this method gives the PAEs of B, ${\mathrm{Na}}_{3}$, and ${\mathrm{Li}}_{3}$ to within $0.1\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ accuracy.