In the previous section, we showed that ionizing a valence electron can cause the bond it is participating in to break. For methane, the energy input is 20 eV. When a core electron of carbon is ionized, the energy input is a much larger 290 eV, in the resulting dynamics, several other electrons may be ionized, and several bonds may be broken. Such processes are thought to participate in the ejection of surface species in photon and electron-stimulated desorption (PSD and ESD).
In the Auger process, a valence electron falls in to fill a core hole, which releases enough energy to eject another valence electron. Thus a state with two valence holes is created. Using eFF it is possible to track, for the first time, the continuous evolution of a core-hole state into a two-valence hole state, with full electron and nuclear dynamics included. This is important because the coupled motions of nuclei and electrons during the evolution of the core hole (several femtoseconds) may influence the composition and charge of the fragments ejected from the surface following core-hole ionization.
We chose as a simple model system the hydrocarbon adamantane, . To create the input file, we used the script xyz2cfg. This script operates on hydrocarbons only, and converts a file containing the Cartesian coordinates of the atoms into an eFF input file, with reasonable initial guesses for electron positions and sizes. We generated the .xyz file using Chem3D, and the program Babel to convert between .cc1 and .xyz formats; any similar model builder would have worked just as well.
adamantane.xyz: 26 XYZ file generated by Babel. C 0.11815 1.50084 0.52678 C -0.32350 0.67631 1.74834 C -0.34174 -0.81741 1.38025 C -1.32777 -1.04800 0.22192 ... % xyz2cfg adamantane adamantane.cfg: @params calc = minimize print_every = 50 @nuclei 0.223271 2.836177 0.995470 6.000000 -0.611326 1.278041 3.303884 6.000000 -0.645795 -1.544681 2.608294 6.000000 -2.509122 -1.980433 0.419368 6.000000 ... % eff adamantane.cfg % cat adamantane.eff | grep iter [Minimize_iter_header] # iters # func evals f grad2 [Minimize_iter] 0 1 -3.260969e+02 4.201029e+01 [Minimize_iter] 50 101 -3.290854e+02 2.260760e-01 [Minimize_iter] 100 202 -3.290974e+02 3.267149e-03 [Minimize_iter] 150 302 -3.290982e+02 3.909828e-04 [Minimize_iter] 200 402 -3.290982e+02 4.024753e-06 [Minimize_iter] 250 503 -3.290982e+02 6.455939e-08 [Minimize_iter] 300 608 -3.290982e+02 2.802862e-09
To simulate the dissociation dynamics of core-ionized adamantane, we proceeded as we did in the last section, copying the restart file of the optimized geometry to a new file adamantane_ionized.cfg, deleting a core electron from the new file, and changing calc = minimize to calc = dynamics. As before, we also added dynamics parameters to the new file. In this case, a smaller time step of 0.001 fs is necessary to conserve energy, since the core-hole relaxation involves larger forces and velocities than the previously studied valence-hole relaxation.
Figure 2.8 shows the resulting dynamics trajectory. At 5 fs, the core-hole has been filled by a valence electron, and the CH bond adjacent to the ionized carbon is beginning to break. By 35 fs, an excited hydrogen atom, together with three electrons, has been ejected from the molecule, and and fragments are apparent as well.
In more advanced calculations, we took snapshots of adamantane dynamics at 300 K, then used these snapshots as starting points for vertical core-electron ionization and Auger dynamics. Thus we accounted for finite temperature effects and obtained a distribution of different trajectories.
Figure 2.9 shows a more in-depth analysis of one of these trajectories, where we have plotted the distance of all the valence electrons in the system from the nucleus of the ionized carbon. From this plot, we see that once the core electron is instantaneously removed from a carbon atom, the four surrounding valence electrons with the same spin as the ionized electron collapse inward. These four electrons fall in toward the core hole together until one electron fills the hole, causing the other three to bounce away from the core as a result of Pauli repulsion. This leads to the escape of one electron, and the excitation of the other two electrons, and at 20 fs, the fragmentation of the bonds surrounding the original core ionization.