The density of states from mode expansion of the self dynamic structure factor of a liquid metal

We show that by exploiting multi-Lorentzian fits of the self dynamic structure factor at various wavevectors it is possible to carefully perform the $Q \to 0$ extrapolation required to determine the spectrum $Z(\omega)$ of the velocity autocorrelation function of a liquid. The smooth $Q$-dependence of the fit parameters makes their extrapolation to $Q$=0 a simple procedure from which $Z(\omega)$ becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function reveals crucial to understand the whole dynamics of the liquid. In fact, we demonstrate the clear link between the collective modes frequencies and the shape of the frequency distribution. In the specific case considered in this work, i.e. liquid Au, analysis of $Z(\omega)$ revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra, and clearly identify the transverse nature of the above mentioned less energetic modes. Existence of propagating transverse excitations appears therefore to be quite a common feature of dense liquids. However, in some cases these are difficult to detect: we show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize $Z(\omega)$ and the information in it contained allow therefore to identify it with the density of states (DoS) of the liquid. Finally, as a side-output of this work, we provide our estimate of the self diffusion coefficient of liquid gold just above melting.