Joint approximate diagonalization approach to quasiparticle self-consistent GW calculations

We introduce an alternative route to quasiparticle self-consistent GW calculations (qsGW) on the basis of a joint approximate diagonalization of the one-body GW Green's functions G(epsilon(QP)(n)) taken at the input quasiparticle energies. Such an approach allows working with the full dynamical self-energy, without approximating the latter by a symmetrized static form as in the standard qsGW scheme. Calculations on the GW100 molecular test set lead, nevertheless, to a good agreement, at the 60 meV mean-absolute-error accuracy on the ionization potential, with respect to the conventional qsGW approach. We show further that constructing the density matrix from the full Green's function as in the fully self-consistent scGW scheme, and not from the occupied quasiparticle one-body orbitals, allows obtaining a scheme intermediate between the qsGW and scGW approaches, closer to coupled-cluster reference values.