Time-Dependent Electron Localization Function - Fachbereich ...

2.4 Application of the TDELF
Fig. 2.6 Snapshots of the time-dependent ELF for the scattering of a fast, non-relativistic proton
(E kin = 2 keV, white dot in the mid bottom of a) by ethene (etylene). The molecule breaks in several
pieces. During this fragmentation process, the breaking of bonds and the subsequent creation of
lone pairs becomes clearly visible.
If one carefully examines the moment when the proton hits the carbon (fig. 2.7), one
observes that even before the proton hits the carbon, ionization occurs (fig. 2.7a).
This blob of localized electrons leaves the system downwards, roughly into the direction
of the approaching proton. Shortly after, another blob leaves the system
(fig. 2.7b,c) this time upwards. This is quite surprising since it seems as if the
proton repels the electrons while it attracts them in reality. We believe that this
phenomon is due to an overshooting of the electron oscillation between the approaching
proton and the ethene.
Calculation settings: We used a spherical mesh with a radius r = 7 Å and
∆ = 0.14 Å as spacing. The used bond lengths are d(C–C) = 1.339 Å and
d(C–H) = 1.085 Å. The angle between the hydrogen atoms was ∡(H–C–H) =
117.8 ◦ . Absorbing boundaries with a mask of the width of 0.5 Å were used.
The calculation was done using the local-density approximation for exchange and
Perdew and Zunger’s parametrization of the correlation part [34].
For the time-evolution the Suzuki--Trotter method [35] was used with a timestep
of ∆t = 0.0005 /eV = 0.33 × 10 −18 s for T = 150 /eV = 9.8 fs. The
ion movement used Newton dynamics with the velocity Verlet algorithm. The
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