  Using the newly developed VASP2WANNIER90 interface we have constructed
maximally localized Wannier functions (MLWFs) for the e_g states of the
prototypical Jahn-Teller magnetic perovskite LaMnO3 at different levels of
approximation for the exchange-correlation kernel. These include conventional
density functional theory (DFT) with and without additional on-site Hubbard U
term, hybrid-DFT, and partially self-consistent GW. By suitably mapping the
MLWFs onto an effective e_g tight-binding (TB) Hamiltonian we have computed a
complete set of TB parameters which should serve as guidance for more elaborate
treatments of correlation effects in effective Hamiltonian-based approaches.
The method-dependent changes of the calculated TB parameters and their
interplay with the electron-electron (el-el) interaction term are discussed and
interpreted. We discuss two alternative model parameterizations: one in which
the effects of the el-el interaction are implicitly incorporated in the
otherwise "noninteracting" TB parameters, and a second where we include an
explicit mean-field el-el interaction term in the TB Hamiltonian. Both models
yield a set of tabulated TB parameters which provide the band dispersion in
excellent agreement with the underlying ab initio and MLWF bands.
