Figure 1

Time series for the electron density fluctuations and currents corresponding to the volume elements ${\Omega }_I$ (see the text for a definition of the different quantities). Left column: The difference between the time evolution of $\mathrm{\Delta }{\rho }_I\left(t\right)$ and $\mathrm{\Delta }{\rho }_I^{\mathrm{abs}}\left(t\right)$ (insets) is a measure of the deviation from the Clausius-Mossotti limit. A selection of volume elements chosen according to their distance from the origin of the perturbation is shown: first (upper panel), second (middle panel), and third (lower panel) coordination sphere (different line styles indicate different representative molecules within the same coordination sphere). Right column: The currents between adjacent volume elements, $d\mathrm{\Delta }{\rho }_I\left(t\right)∕dt$, can be measured (same sequence as for the plots in the left column). In the inset of the upper plot, the total charge separation [sum over $I=1,...,32$ of the contributions $\mathrm{\Delta }{\rho }_I\left(t\right)$] (gray) is compared with the total absolute charge separation (black).Reuse & Permissions

Figure 2

(Color online) Two-dimensional density profiles for $\delta \rho \left(dt\right)=\rho \left(t_0\right)-\rho \left(t\right)$ after a sudden switch on of a point charge of $1e$ at the center of the box at time $t_0$. Positive (negative) values stand for an increase (depletion) of electronic density in units of $e$. From the top left corner, $dt=35$, 60, 85, and $120\mathrm{as}$. The molecules close to the plane are marked by a dark circle.Reuse & Permissions

Figure 3

Left panel: Radial distribution of the electronic disturbance, $\delta {\rho }_r\left(t\right)=r^2\int d{\Omega }_r\delta \rho (\mathbf{r},t)$ within a spherical shell of thickness $dr$ and radius $r$, during the first $200\mathrm{as}$ after perturbation. The displacement of the peaks during the first relaxation period $(\sim 80\mathrm{as})$ occurs at a speed of $\sim 0.035\mathrm{\AA }∕\mathrm{as}$. (Dark gray: excess electron density; light gray: electron “hole”. The contour at $0$ is shown in black.) Right panel: Corresponding radial density distribution, $\delta {\tilde{\rho }}_r\left(t\right)=\delta {\rho }_r\left(t\right)∕(4\pi r^{2}dr∕\Omega )$. The oscillation of the electronic disturbance, ${\tilde{\rho }}_r\left(t\right)$, close to the center of the box, $r=0$, occurs at a frequency ${\omega }_p\simeq 21.75\mathrm{eV}$.Reuse & Permissions

Figure 4

(Color online) Left: False color plot of $-\mathrm{Im}\tilde{\chi }(\mathbf{k},\omega )$ of water in units of $\mathrm{as}∕{\mathrm{\AA }}^3$ plotted against transferred momentum (x-ray experimental data from Ref. 6). Right: Same function computed for two equilibrated frames. Data are collected every $1.2\mathrm{as}$ for a total length of $4\mathrm{fs}$. The color code is arbitrary and is chosen to match the experimental values. The shell structure in $k$-space sampling is a consequence of the finite size of the simulation cell.Reuse & Permissions

Figure 5

(Color online) Real and imaginary parts of the dielectric function of liquid water. For comparison experimental data from Hayashi et al.[5] (dashed curves) and Heller et al.[4] (symbols) are also shown.Reuse & Permissions