Free Energy of Classical Molecular Crystals by Thermodynamic Integration from a Harmonic Reference

We develop an algorithm for calculating the normal modes of vibration of mechanical systems with constraints, particularly of molecules with rigid bonds and models of rigid molecules, and use it to obtain the harmonic free energy of a crystal. The anharmonic correction is then calculated by the conventional thermodynamic integration over temperature in the NVT ensemble. Attention is paid to finite-size errors, tail corrections, thermostat choice, ergodicity, and other sources of inaccuracies. The calculated free energy of ice XIV modeled by the TIP4P/2005 potential agrees with the previously reported value and is by one order more accurate.