Irradiation damage, especially cascade modeling, is usually preferentially dealt by larger scale methods such as molecular dynamics with empirical potentials rather than ab initio calculations. However, recently ab initio studies that directly tackle irradiation pro­cesses have appeared.

1.08.3.3.1 Threshold displacement energies

First, the increase in computer power has allowed the calculations of threshold displacement energies by ab initio molecular dynamics. We are aware of studies in GaN27 and silicon carbides.28,29 The procedure is the same as that with empirical potentials: one initi­ates a series of cascades of low but increasing energy and follows the displacement of the accelerated atom. The threshold energy is reached as soon as the atom does not return to its initial position at the end of the cascade. Such calculations are very promising as empirical potentials are usually im­precise for the orders of energies and interatomic distances at stake in threshold energies. However, they should be done with care as most pseudopo­tentials and basis sets are designed to work for moderate interatomic distances, and bringing two atoms too close to each other may lead to spurious results unless the pseudopotentials are specifically designed.

1.08.3.3.2 Electronic stopping power Second, recent studies have been published in the ab initio calculations of the electronic stopping power for high-velocity atoms or ions. The framework best suited to address this issue is time-dependent DFT (TD-DFT). Two kinds of TD-DFT have been applied to stopping power studies so far.

The first approach relies on the linear response of the system to the charged particle. The key quan­tity here is the density-density response function that measures how the electronic density of the solid reacts to a change in the external charge density. This observable is usually represented in reciprocal space and frequency, so it can be confronted directly with energy loss measurements. The density — density response function describes the possible excitations of the solid that channel an energy trans­fer from the irradiating particle to the solid. Most noticeably the (imaginary part of the) function vanishes for an energy lower than the band gap and shows a peak around the plasma frequency. Integrating this function over momentum and energy transfers, one obtains the electronic stopping power. Campillo, Pitarke, Eguiluz, and Garcia have implemented this approach and applied to some simple solids, such as aluminum or silicon.3 — They showed that there is little difference between the usual approximations of TD-DFT: the random phase approximation, which means basically no exchange correlation included, or adiabatic LDA, which means that the exchange correlation is local in space and instantaneous in time. The influence of the band structure of the solid accounts for noticeable deviations from the homogeneous elec­tron gas model.

The second approach is more straightforward conceptually but more cumbersome technically. It proposes to simply monitor the slowing down of the charged irradiated particle in a large box in real space and real time. The response of the solid is hence not limited to the linear response: all orders are automat­ically included. However, the drawback is the size of the simulation box, which should be large enough to prevent interaction between the periodic images. Fol­lowing this approach, Pruneda and coworkers33 cal­culated the stopping power in a large band gap insulator, lithium fluoride, for small velocities of the impinging particle. In the small velocity regime, the nonlinear terms in the response are shown to be important.

Unfortunately, whatever the implementation of TD-DFT in use, the calculations always rely on very crude approximations for the exchange-correlation effects. The true exchange-correlation kernel (the second derivative of the exchange-correlation energy with respect to the density) is in principle nonlocal (it is indeed long ranged) and has memory. The use of novel approximations of the kernel was recently introduced by Barriga-Carrasco but for homogeneous electron gas only.34,35