  A first-principles based methodology for efficiently and accurately finding
thermodynamically stable and metastable atomic structures is introduced and
benchmarked. The approach is demonstrated for gas-phase metal-oxide clusters in
thermodynamic equilibrium with a reactive (oxygen) atmosphere at finite
pressure and temperature. It consists of two steps. At first, the
potential-energy surface is scanned by means of a global-optimization
technique, i.e., a massive-parallel first-principles cascade genetic algorithm
for which the choice of all parameters is validated against higher-level
methods. In particular, we validate a) the criteria for selection and
combination of structures used for the assemblage of new candidate structures,
and b) the choice of the exchange-correlation functional. The selection
criteria are validated against a fully unbiased method: replica-exchange
molecular dynamics. Our choice of the exchange-correlation functional, the
van-der-Waals-corrected PBE0 hybrid functional, is justified by comparisons up
to highest level currently achievable within density-functional theory, i.e.,
the renormalized second-order perturbation theory, rPT2. In the second step,
the low-energy structures are analyzed by means of ab initio atomistic
thermodynamics in order to determine compositions and structures that minimize
the Gibbs free energy at given temperature and pressure of the reactive
atmosphere.
