Benchmarking GW against exact diagonalization for semiempirical models

Abstract

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 ϳ3%. One-shot G 0 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 models͒ where correlation effects dominate over screening/ relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchangecorrelation functional by computing the exact Kohn-Sham levels of benzene.

Fully self-consistent GW calculations for molecules

“…Very similar conclusions were reached by comparing GW, G 0 W 0 , and HF to exact diagonalization for conjugated molecules described by the semiempirical PPP model. 37 …”

“…"X-eig" refers to a single-particle eigenvalue while "X-tot" refers to a total-energy difference, E͑N͒ − E͑N −1͒. 37 we showed, on the basis of GW and exact calculations for semiempirical models of conjugated molecules, that ⌬ n GW mainly describes the orbital relaxations in the final state and to a lesser extent accounts for the correlation energy of the initial and final states. This explains the negative sign of ⌬ n GW because the inclusion of orbital relaxation in the final state lowers the energy cost of removing an electron.…”

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

“…A few attempts to solve this reduced set of equations fully self-consistently have been made in the past. 37,[48][49][50][51][52][53][54][55][56][57][58][59] Although full or partially self-consistent GW calculations can give accurate ground-state total energies and are essential for particle number conservation, 60,61 the quasiparticle properties deteriorate. [49][50][51] This is a result of the successive introduction of higher order electron-electron interaction terms of certain type that are not balanced by other higher order terms contained in the vertex function.…”

Benchmark ofGWmethods for azabenzenes

“…83 It has also been suggested that scGW may provide unreliable spectra and total energies for the Hubbard model in the strong correlation regime. 84 Correcting these issues may require going beyond the GW approximation by introducing vertex corrections. Currently, such corrections are in the initial stage of exploration [85][86][87][88][89][90][91] and their implementation would come at the price of an even higher computational cost than scGW.…”