Effective quasiparticle Hamiltonian based on Loumlwdin's orthogonalization

Recently several schemes have been proposed to perform self-consistent GW calculations within a one-particle (quasiparticle) approximation. These so-called quasiparticle self-consistent GW schemes have been found to be successful in reproducing band gaps of semiconductors but there is some arbitrariness in the choice of the effective one-particle Hamiltonian in these schemes and their validity has not been assessed. To avoid ambiguity in choosing the one-particle Hamiltonian, we propose a scheme which is based on Loumlwdin's method of symmetric orthogonalization. In our approach we first calculate the true quasiparticle wave functions and energies with the real part of the frequency-dependent self-energy, and then orthonormalize these states using Loumlwdin's procedure to construct the effective quasiparticle Hamiltonian. Loumlwdin's procedure ensures that the obtained orthonormal orbitals are the closest to the original nonorthogonal quasiparticle wave functions in the least-square sense and uniquely defines the one-particle Hamiltonian. Unlike previous approaches, this approach takes into account the full frequency dependence and the off-diagonal elements of the self-energy without ambiguity. As test cases, we perform quasiparticle self-consistent GW calculations on NiO and Gd. We find that our results compare well with previous results obtained using a different effective Hamiltonian.