Charge-density correlations in pressurized liquid lithium calculated using ab initio molecular dynamics

Static and dynamic autocorrelations of charge density, composed of positive point ions and instantaneous distribution of electron density, are studied in liquid Li in a pressure range from ambient to 186 GPa using ab initio molecular dynamics simulations. It is shown analytically that the long-wavelength limit of the charge-charge static structure factor $S_{QQ}\left(k\right)$ of liquid metals is proportional to $k^4$. Time-dependent charge-charge correlations in liquid Li at low pressures show identical relaxation as the density-density time correlation functions, in complete agreement with the linear response theory, whereas at extreme pressures we observed different relaxation of the charge and density autocorrelations. The static and dynamic properties of a part of electron density, that corresponds to the nonspherical distribution around ions, are discussed.

Figure 1

Pair distribution function in liquid Li at 1000 K at seven different pressures. A progressive vertical shift of 0.75 was applied for the sequence of pair distribution functions.

Figure 2

Left: Bond-angle distribution between the closest of the nearest neighbor atoms in the sphere $R_{\mathrm{cut}}=1.6$ Å in liquid Li at $T=1000$ K and $P=186$ GPa. Right: $l$-projected density of electronic states.

Figure 3

Ion-ion static structure factors $S_{ii}\left(k\right)$ in liquid Li at 1000 K at seven different pressures. A progressive vertical shift of 2.50 was applied for the sequence of the static structure factors.

Figure 4

Ratio of the electron-ion $S_{ei}\left(k\right)$ to ion-ion static structure factor $S_{ii}\left(k\right)$ at different pressures. In the long-wavelength limit this ratio is in perfect agreement with the sum rule (2).

Figure 5

Charge-charge static structure factor $S_{QQ}\left(k\right)$ at the seven different pressures in liquid Li at 1000 K. A progressive vertical shift of 3.00 was applied for the sequence of the static structure factors.

Figure 6

Long-wavelength asymptotes of the charge-charge static structure factors $S_{QQ}\left(k\right)$ at four pressures on double-logarithmic scale. The straight lines show the $\sim$$k^4$ dependence.

Figure 7

Dependence of the coefficent $\alpha$ at the long-wavelength limit of $S_{QQ}\left(k\right)$, Eq. (8), on the parameter $r_s$ [28]. The quadratic dependence $\sim$$r_s^2$ predicted from RPA is valid at very high pressures and is shown with the dashed line.

Figure 8

The isosurface (red shaded areas) of the ELF at the value 0.85 in snapshots of simulations at ambient pressure (left) and pressures 68 GPa (middle) and 186 GPa (right).

Figure 9

The static correlators of the electron density orthogonalized to the ionic positions (left panel), and the dependence of its peak location on the pressure together with the corresponding quantity from the ion-ion correlator (right panel).

Figure 10

Total charge and density autocorrelation functions at ambient pressure (a), 68 GPa (b), 125 GPa (c), and 186 GPa (d).

Figure 11

Relaxation of the autocorrelation between the part of the electron density orthogonalized to ionic positions. The time scale $\tau$ is equal to $0.20649$ ps.