Hubbard-U corrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS, TiO₂, and NiO

In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transitionmetal compounds ZnS, TiO₂, and NiO.We find that the RPA lattice constants are essentially independent of U, despite large changes in the underlying electronic structure. We further demonstrate that the non-selfconsistent RPA total energies of these materials have minima at nonzero U. Our RPA calculations find the rutile phase of TiO₂ to be more stable than anatase independent of U, a result which is consistent with experiments and qualitatively different from that found from calculations employingU-corrected (semi)local functionals.However we also find that the+U term cannot be used to correct the RPA’s poor description of the heat of formation of NiO.