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 the 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(Γ) method not to the neutral ground state but to the cationic state to calculate PAEs without solving the BSE, which allows the rigorous one-to-one correspondence between the photoabsorption peak and the "extended" quasiparticle level. We applied the self-consistent LGWΓ method including the vertex correction to our method, and found that this method gives the PAEs of B, Na 3 , and Li 3 within the 0.1 eV accuracy.

Extended quasiparticle approach to non-resonant and resonant X-ray emission spectroscopy

“…Available experimental values 10,[45][46][47][48][49][50] neutral GW calculation as e GW C1s À e GW HOMO = À289.4 + 13.8 eV = 275.6 eV, which is different from the experimental XES value À276.4 eV by 0.8 eV only. This again strongly supports the validity of the present theory, although this type of calculation (as well as the above-mentioned paper 56 ) does not allow us to calculate the spectral intensity. It can be used at least for the purpose of error estimation, but we think the ability is more than that.…”

“…Moreover, using an idea to calculate the photoabsorption energy only by performing the GW calculation for the cation of the target molecule without solving the BSE, 56 we can estimate the XES energies only from the result given in Table 7 of a Table 6 XES and RIXS fluorescence photon energies obtained by solving the BSE after the GW calculation for the EQP energies, which are listed in Tables 2-5. Available experimental values 10,[45][46][47][48][49][50] neutral GW calculation as e GW C1s À e GW HOMO = À289.4 + 13.8 eV = 275.6 eV, which is different from the experimental XES value À276.4 eV by 0.8 eV only.…”

“…In fact, there was a similar advantage in the spin-unpolarized calculation in cationic systems of Al, B, Na 3 , and Li 3 treated in the abovementioned paper. 56 Similarly, for RIXS, we performed GW calculation for an ammonia anion NH 3 À1 and obtained Table 8. From down spin levels, we can estimate the RIXS energies as e GW N1s À e GW n = À397.3 eV À e GW n (n = 3-6) as À385.9 eV, À385.9 eV, À390.9 eV, and À396.0 eV, which can be compared the experimental values in Table 6: À389.0 eV, À389.0 eV, À392.5 eV, and À394.3 eV.…”

Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions

“…14 There is not yet a widely adopted route to improve these shortcomings of the BSE, though developing extensions to both GW and BSE is a very active area of research. 13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28] Dynamical mean-field theory (DMFT) is a quantum embedding theory based on the electronic GF. In combination with the local density approximation (LDA), LDA+DMFT [29][30][31] has been very successful in predicting spectral properties of strongly-correlated solids.…”

Implementation of hyperfine coupling in all-electron mixed basis approach

“…25 ), photoelectron (or quasiparticle) and photoabsorption spectra using the GW(Γ) (+ Bethe-Salpeter equation) method (Refs. 26,27 ), and so on, the cubic harmonics is more tractable than the spherical harmonics.…”