AbstractIn this paper we propose a stochastic algorithm to investigate the real unrestricted Hartree–Fock problem. The approach is based on a global optimization method, the Generalized Simulated Annealing. The main characteristic of this method is that it enables the mapping of the electronic hyper‐surface in such a way as to guarantee that the absolute minimum of the functional in focus will be achieved. We tested this methodology by determining the Hartree–Fock ground‐state of the H2, LiH, BH, CH+, OH−, FH, CO, N2, BeH2, H2O, NH3, HCHO, CH4, CH, NH, CH2, NH2, OH and O2 molecules using minimal, double‐zeta, triple‐zeta and with polarization basis sets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006