Efficient Real-Time Time-Dependent Density Functional Theory Method and its Application to a Collision of an Ion with a 2D Material

We have developed an efficient real-time time-dependent density functional theory (TDDFT) method that can increase the effective time step from $<1$ as in traditional methods to $0.1–0.5\mathrm{fs}$. With this algorithm, the TDDFT simulation can have comparable speed to the Born-Oppenheimer (BO) ab initio molecular dynamics (MD). As an application, we simulated the process of an energetic Cl particle colliding onto a monolayer of ${\mathrm{MoSe}}_2$. Our simulations show a significant energy transfer from the kinetic energy of the Cl particle to the electronic energy of ${\mathrm{MoSe}}_2$, and the result of TDDFT is very different from that of BO-MD simulations.

Figure 1

Model of the ${\mathrm{Cl}\text{−}\mathrm{MoSe}}_2$ collision. $a$ is the horizontal distance between nearest neighbors, $a=1.890\AA$. The region of incidence has been colored blue in (a) and zoomed in (b). Red points in (b) show the initial positions of Cl. Scattering angles $\theta$ and $\phi$ are defined as shown in (c).

Figure 2

(a) Electronic and nuclear kinetic energies during the central point penetration, and (b) the atom positions and charge density isosurfaces at 3 time steps.

Figure 3

Snapshots for density of states and occupations at 6 time steps, under different cases. Energy zero points are selected equal to the initial Fermi energies. Only states near Fermi energy are shown ($-4.5$ to 4.5 eV). Green, blue, and red states are occupied adiabatic states, Cl occupied states, and the unoccupied adiabatic state, respectively.

Figure 4

Polar plots for projectile energy loss $\mathrm{\Delta }{T}_{\mathrm{Cl}}$ from Eq. (8) under different cases. From center to the peripheral, the $\phi$ changes from 0°to 12°. A diagrammatic sketch for the incidence region has been shown in the lower left corner.