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Valence electron ionization in methane

Concepts: Restart file, vertical ionization, dynamics, dynamic electron mass

To optimize methane, we place a carbon nucleus at the origin, and surround it with four hydrogen nuclei at tetrahedral positions. A pair of core electrons sits directly on the carbon nucleus, while the remaining electrons pair to form four $ sp^{3}$ tetrahedral orbitals. As a starting point, we place the valence electrons directly on top of the hydrogen nuclei.

ch4.cfg:
  @params
  calc = minimize
  output_energy_forces = end
  @nuclei
   0  0  0  6
   1  1  1  1
  -1 -1  1  1
   1 -1 -1  1
  -1  1 -1  1
  @electrons
   0  0  0 -1 0.5
   0  0  0  1 0.5
   1  1  1 -1 1.0
   1  1  1  1 1.0
  -1 -1  1 -1 1.0
  -1 -1  1  1 1.0
   1 -1 -1 -1 1.0
   1 -1 -1  1 1.0
  -1  1 -1 -1 1.0
  -1  1 -1  1 1.0

ch4.cfg.restart:
  @nuclei
  0.000000 -0.000000 0.000000 6.000000
  1.247211 1.247211 1.247211 1.000000
  -1.247211 -1.247211 1.247211 1.000000
  1.247211 -1.247211 -1.247211 1.000000
  -1.247211 1.247211 -1.247211 1.000000
  @electrons
  -0.000000 0.000000 -0.000000 -1 0.329128
  -0.000000 0.000000 0.000000 1 0.329128
  0.979221 0.979221 0.979221 -1 1.486181
  0.979221 0.979221 0.979221 1 1.486181
  -0.979221 -0.979221 0.979221 -1 1.486181
  -0.979221 -0.979221 0.979221 1 1.486181
  0.979221 -0.979221 -0.979221 -1 1.486181
  0.979221 -0.979221 -0.979221 1 1.486181
  -0.979221 0.979221 -0.979221 -1 1.486181
  -0.979221 0.979221 -0.979221 1 1.486181

ch4.eff:
  ...
  [energy_force_elec]     1       2.528368  ...
  [energy_force_elec]     2       2.528368  ...
  [energy_force_elec]     3       0.082715  ...
  [energy_force_elec]     4       0.082715  ...
  [energy_force_elec]     5       0.082715  ...
  [energy_force_elec]     6       0.082715  ...
  [energy_force_elec]     7       0.082715  ...
  [energy_force_elec]     8       0.082715  ...
  [energy_force_elec]     9       0.082715  ...
  [energy_force_elec]     10      0.082715  ...

Figure 2.5: Methane has electron pairs in tetrahedral positions.

Once optimized, the valence electrons are centered at $ \sim$80% of the distance from the core center to the proton, reflecting the greater electronegativity of carbon over hydrogen.

In photoelectron spectroscopy, valence electrons in molecules are ionized using ultraviolet radiation. In the case of methane, this weakens the carbon-hydrogen bond, causing it to break. We would like to simulate the dynamics of this process.

The eFF orbital energies correspond roughly to how tightly individual electrons are bound to the molecule (Koopman's theorem), and in related fashion, how much energy is available to dissociative processes once they are removed. In a separate study, we found that the eFF orbital energies were similar to ones obtained from localized Hartree-Fock calculations corrected against experimental photoelectron spectroscopy measurements (14.0 eV eFF versus 16.0 eV Hartree-Fock). Hence our overall energy scale should be valid.

To study the dynamics of valence-ionized methane, we begin with the restart file from the methane optimization, delete one of the valence electrons, replace calc = minimize with calc = dynamics, and add parameters corresponding to the time step, number of steps, and how often coordinates should be output.

We also specify an electron_mass of 1.0 amu. In eFF, the time scale of electron motions is governed by this adjustable parameter, which determines how the momentum of an electron changes in response to a force. For a particle in a locally harmonic potential, this mass equals the true electron mass; however, in general the effective mass of a wave packet is difficult to calculate, whether by band theory in semiconductors or many-body theory in metals.

In the current theory, we calibrate this mass so that it reproduces a known time scale in the system we are simulating. For the Auger simulations (next section), we have found that heavy electrons are needed to reproduce experimentally observed core-hole lifetimes. In this case, we used a large effective mass purely for convenience.

ch4_ionized.cfg:
  @params
  calc = dynamics
  dt = 0.005000
  print_every = 50
  num_steps = 10000
  electron_mass = 1.000000
  @nuclei
  0.000000 -0.000000 0.000000 6.000000
  1.247211 1.247211 1.247211 1.000000
  -1.247211 -1.247211 1.247211 1.000000
  1.247211 -1.247211 -1.247211 1.000000
  -1.247211 1.247211 -1.247211 1.000000
  @electrons
  -0.000000 0.000000 -0.000000 -1 0.329128
  -0.000000 0.000000 0.000000 1 0.329128
  0.979221 0.979221 0.979221 -1 1.486181
  -0.979221 -0.979221 0.979221 -1 1.486181
  -0.979221 -0.979221 0.979221 1 1.486181
  0.979221 -0.979221 -0.979221 -1 1.486181
  0.979221 -0.979221 -0.979221 1 1.486181
  -0.979221 0.979221 -0.979221 -1 1.486181
  -0.979221 0.979221 -0.979221 1 1.486181

Figure 2.6: Dissociation of methane following removal of a CH valence electron.

We find that the $ \mathrm{CH_{4}}$ dissociates into $ \mathrm{CH_{3}^{+}}$ and $ \mathrm{H \cdot}$ and that after 50 fs, the two fragments are separated by 8.17 $ \mathrm{\AA}$.


next up previous contents index
Next: Auger dissociation of adamantane Up: Examples Previous: Hydrogen molecule   Contents   Index
Julius 2008-04-29