GW quasiparticle spectra from occupied states only

We introduce a method that allows for the calculation of quasiparticle spectra in the GW approximation, yet avoiding any explicit reference to empty one-electron states. This is achieved by expressing the irreducible polarizability operator and the self-energy operator through a set of linear response equations, which are solved using a Lanczos-chain algorithm. We first validate our approach by calculating the vertical ionization energies of the benzene molecule and then show its potential by addressing the spectrum of a large molecule such as free-base tetraphenylporphyrin.

Figure 1

(Color online) Calculated vertical ionization potential of the benzene molecule (disks, left scale) and dimension of the polarizability basis (triangles, right scale) versus the $q^{\ast }$ cutoff in atomic units. The polarizability basis sets have been constructed with energy cutoffs: $E^{\ast }=5\text{Ry}$ blue (black) and $E^{\ast }=10\text{Ry}$ red (gray). The lines are a guide to the eye.

Figure 2

(Color online) Differences between the calculated VIPs of benzene and experimental results. Red (solid) and green (dashed): present method using $E^{\star }=10\text{Ry}$, $q^{\star }=0.035\text{a}\text{.u}\text{.}$ and $E^{\star }=10\text{Ry}$, $q^{\star }=14.5\text{a}\text{.u}\text{.}$, respectively. Magenta (dot dashed): method of Ref. 8, upon extrapolation of the sum over virtual states. Blue (dotted): present method, but using a polarizability basis formed by PWs (see text). Experimental data are from Ref. 21. The lines are a guide to the eye.

Figure 3

(Color online) Valence electronic density of states for the ${\text{TPPH}}_2$ molecule, blue (black): theory (a Gaussian broadening of 0.25 eV has been used); red (gray): photoemission data from Ref. 23.