J. DOLBEAULT, M.J. ESTEBAN, E. SERE, M. VANBREUGEL Minimization methods for the one-particle Dirac equation. (25K, LaTeX 2E + RevTeX) ABSTRACT. Taking into account relativistic effects in quantum chemistry is crucial for accurate computations involving heavy atoms. Standard numerical methods can deal with the problem of {\rm variational collapse} and the appearance of {\rm spurious roots} only in special cases. The goal of this letter is to provide a general and robust method to compute particle bound states of the Dirac equation.