Electronic structure of the manganese and iron oxide solids is studied by the quantum Monte Carlo (QMC) methods. The trial wavefunctions are built using orbitals from unrestricted Hartree-Fock and Density Functional Theory, and the electron-electron correlation is recovered by the fixed-node QMC. The correlation effects are significant and QMC estimations of the gap and cohesion show a very good agreement with experiment. Comparison with hybrid functional results points out the importance of the exact exchange for improvement of the Density Functional description of transition metal oxide systems. The QMC methodology have enabled us to calculate the FeO equation of state as well as the transition pressure between the low- and high-pressure FeO structures.

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