Extraction of single-particle mean kinetic energy from macroscopic thermodynamic data

We have devised a simple and practical method for the extraction of single-particle mean kinetic energy from the Helmholtz free energy, when this quantity is known for a pair of isotopes of the element under investigation. This approach is originated from a property of the mass derivative of the Helmholtz free energy, but makes use of a mass incremental ratio evaluated for the aforementioned isotopes. The transformation from mass incremental ratio to mass derivative is done using a self-consistent method based on two approximations, the latter of which is quite surprising and has been thoroughly tested. Practical calculations on solid and liquid H2 and D2, where the center-of-mass mean kinetic energy is known from reliable quantum simulation techniques, are accomplished, obtaining a remarkable agreement, in spite of a slight overestimate for the calculated data set over the simulated one. The last part of the study is devoted to mixed systems, like water and ice, where thermodynamic data are abundant and proton mean kinetic energy has been measured via deep inelastic neutron scattering. Here results are less accurate than earlier, with an overestimate of about 9–10%, and, in addition, no substantial variation going from ice to liquid water. Further investigations on the H2O/D2O system are suggested.