Improved model for the transit entropy of monatomic liquids

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This implied that the transit contribution to energy vanishes, which is incorrect. Here we develop a new formulation that corrects this deficiency. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution $S_{vib}(T/\theta_0)$, where $T$ is temperature and $\theta_0$ is the vibrational characteristic temperature, and (b) the transit contribution $S_{tr}(T/\theta_{tr})$, where $\theta_{tr}$ is a scaling temperature for each liquid. The appearance of a common functional form of $S_{tr}$ for all the liquids studied is deduced from the experimental data, when analyzed via the V-T formula. The theoretical entropy of melting is derived, in a single formula applying to normal and anomalous melting alike. An \textit{ab initio} calculation of $\theta_0$ for Na and Cu, based on density functional theory, provides verification of our analysis and V-T theory. In view of the present results, techniques currently being applied in \textit{ab initio} simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.