Benchmarking GW against exact diagonalization for semiempirical models

We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW captures around 65% of the ground-state correlation energy. The lowest lying excitations are overscreened by GW leading to an underestimation of electron affinities and ionization potentials by 0.15 eV on average corresponding to $\sim 3$%. One-shot ${\text{G}}_0{\text{W}}_0$ calculations starting from Hartree-Fock reduce the screening and improve the low-lying excitation energies. The effect of the GW self-energy on the molecular excitation energies is shown to be similar to the inclusion of final-state relaxations in Hartree-Fock theory. We discuss the breakdown of the GW approximation in systems with short-range interactions (Hubbard models) where correlation effects dominate over screening/relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchange-correlation functional by computing the exact Kohn-Sham levels of benzene.

Figure 1

(Color online) Exact and GW correlation energies of the neutral ground state of the seven molecules.

Figure 2

Single-particle DOS of the OPV2 molecule. Note the logarithmic axis.

Figure 3

(Color online) Energy of the three highest occupied and three lowest unoccupied molecular orbitals relative to the exact values. While Hartree-Fock underestimates the occupied and overestimates the unoccupied levels, self-consistent GW shows the opposite trends but deviates on average less from the exact result.

Figure 4

(Color online) The HOMO-LUMO gap relative to the exact values. In addition to the HF and GW single-particle energies, the relaxed Hartree-Fock total-energy differences, $E_0^{\text{HF}}\left(N+1\right)+E_0^{\text{HF}}\left(N-1\right)-2E_0^{\text{HF}}\left(N\right)$ are also shown. The excellent results of HF for the three smallest molecules is a result of error cancellation between relaxation and correlation contributions.

Figure 5

Single-particle DOS for the Hubbard description of the benzene molecule (only on-site interactions from the PPP model are kept). Note the logarithmic axis.