Studies on free energy calculations. I. Thermodynamic integration using a polynomial path Abstract: The difference in the free energy of hydration between the C₇ and a_R conformations of alanine dipeptide at infinite dilution is computed using Monte Carlo method in a canonical ensemble with the united-atom AMBER force field. The recently introduced polynomial path with different exponents for the calculation of liquid state free energies using thermodynamic integration (TI) is tested. This is achieved by separating the interaction energy between the solute and the solvent molecules into the constituent r^-12, r^-6 and Coulomb terms. The separate contribution of each term is calculated and the comparison shows that the shape of the TI integrand as a function of the coupling parameter is mainly determined by the Coulomb term. Analysis of the convergence characteristics shows that five-point Gaussian quadrature integration would be sufficient to obtain quantitatively reliable results when a polynomial path is employed.