Using the cluster analysis of the structure population (CASP) method, error of cluster expansion (CE) can be controlled. Combining the CASP-CE with a systematic set of first-principles total energies, a model wide-gap pseudobinary system with simple crystal structures MgO-ZnO is revisited. Ground-state structures are exhaustively searched for both rocksalt and wurtzite structures. A few structures as yet unreported are found. The vibrational contribution to the Gibbs free-energy is evaluated by first-principles phonon calculations within the quasiharmonic approximation. Monte Carlo simulations are then made to compute grand potentials of two structures using the thermodynamic integration. DOI: 10.1103/PhysRevB.86.245202