Thermodynamics and quantum corrections from molecular dynamics for liquid water

In principle, given the potential energy function, the values of thermodynamic variables can be computed from statistical mechanics for a system of molecules. In practice for the liquid state, however, two barriers must be overcome. This paper treats the first problem, how to quantum correct the classical mechanical thermodynamic values available from molecular dynamics, Monte Carlo, perturbation, or integral methods in order to compare with experimental quantum reality. A subsequent paper will focus on the second difficulty, the effective computation of free energy and entropy. A simple technique, derived from spectral analysis of the atomic velocity time histories, is presented here for the frequency domain quantum correction of classical thermodynamic values. This technique is based on the approximation that potential anharmonicities mainly affect the lower frequencies in the velocity spectrum where the system behaves essentially classically, while the higher spectral frequencies, where the deviation from classical mechanics is most pronounced, involve sufficiently harmonic atomic motions that harmonic quantum corrections apply. Thus, a harmonic quantum correction can be applied at all frequencies: at low frequencies where it is inaccurate it will be small, while at high frequencies where it is large it will also be relatively accurate. The approach is demonstrated by computation of the energy and constant volume heat capacity for water from classical molecular dynamics followed by quantum correction. The potential used to describe the interactions of the system of water molecules includes internal vibrational degrees of freedom and thus strong quantum effects. Comparison of the quantum corrected theoretical values with experimental measurements shows good agreement. The quantum corrections to classical thermodynamics (which are also derived for free energy and entropy) are shown to be important not only for internal vibrational motion, but also for intermolecular hindered rotational and translational motions in liquid water. They are presumably also important for other strongly associated molecules, including bimolecules, and thus should be included when comparing calculated and measured thermodynamic quantities. The approach illustrated here allows the calculation of thermodynamic quantum corrections for liquids, solutions, and large molecules such as polymers (including proteins and nucleic acids) with full inclusion of both intra- and intermolecular degrees of freedom.