Einstein crystal as a reference system in free energy estimation using adiabatic switching

In this paper we investigate the behavior of an Einstein crystal as a reference system in adiabatic switching procedures. We study the canonical massive Nos\'e-Hoover chain (MNHC) dynamics [G. J. Martyna, M. L. Klein, and M. Tuckerman, J. Chem. Phys. 97, 2635 (1992)] and show it can be used to determine Helmholtz free energies within an adiabatic switching procedure. We calculate the Helmotz free energy difference between two different Einstein crystals, each consisting of 100 identical independent harmonic oscillators with different characteristic frequencies by a MNHC molecular dynamics adiabatic switching procedure. The simulations were performed using two different switching functions. Applying the quantitative error analysis of Tsao, Sheu, and Mou [J. Chem. Phys. 101, 2302 (1994)], it is found that systematic errors during the switching process can be estimated quantitatively, allowing a correction of the converged results. The corrected results obtained by adiabatic switching deviate less than 1% from the analytical value. It is observed that quantitative correction of converged results can be avoided by choosing a proper switching function. \textcopyright{} 1996 The American Physical Society.