A method for constructing the Boltzmann-Gibbs distributions is presented by combining the re-weighting technique and the deterministic dynamical equation that produces the Tsallis distributions. The ability to produce the Boltzmann-Gibbs distributions is shown by calculating the distribution, the energy with higher moments, and the Helmholtz free energy. From numerical simulations of a small system that represents a fundamental chemical interaction model, correct answers were obtained within a wide range of temperatures. An application. to a peptide system is also shown. (C) 2003 Elsevier B.V. All rights reserved.