Importance of reference Hamiltonians containing exact exchange for accurate one-shot GW calculations of Cu ₂O

We show that a "one-shot" GW approach (denoted G ₀W ₀) can accurately calculate the photoemission/inverse- photoemission properties of Cu ₂O. As the results of any perturbative method are heavily dependent on the reference state, the appropriate reference Hamiltonian for G ₀W ₀ is identified by evaluating the performance of density-functional-theory-based input wave functions and eigenvalues generated with selected exchange-correlation functionals. It is shown that a reference Hamiltonian employing the hybrid Heyd-Scuseria-Ernzerhof functional used in conjunction with G ₀W ₀ produces an accurate photoemission/inverse-photoemission band gap and photoemission spectrum whose character is then further analyzed. The physical origin of why a hybrid functional is required for the zeroth-order wave function is discussed, giving insight into the unique electronic structure of Cu ₂O in comparison to other transition-metal oxides.