In the present calculations, we also use a TB model to describe the interactions between carbon and hydrogen (H) atoms [118]. The present model is made self-consistent by the inclusion of local charge neutrality, and has been shown to be transferable to environments outside those included in the parameter fitting, like hydrocarbon molecules, diamond surfaces and amorphous diamondlike carbons [118,119]. We have paid particular attention to the Brillouin-zone sampling for convergence of the supercell calculations [120,121,104]. We use a small supercell of 64+1 atoms and a larger one of 216+1 atoms, and different sets of special k-points. For H at high symmetry sites (Bond Center (BC) and tetrahedral (T) sites), convergence in the energy is already achieved with 2 special k-points and the small supercell. For H at the ET site (to be discussed below), we use 10 special k-points for accuracy with the small supercell. The calculations with the supercell of 216+1 atoms and 2 special k-points yield quantitatively the same results as those with the small one, justifying the use of the latter.

We first consider, like others [77,78,122,79], the BC and Tinterstitial sites for H in diamond. The other possible interstitial sites (see figure (11.1)) are sites of lower energy, or even of local maximum energy, as found by us and by others [77,78,122]. All the atoms of the samples are allowed to relax by the conjugate gradient algorithm. We initially use the tight binding parametrization of Ref. [118]. We find, as found by the others, that H at the BC site is lower in energy than at the T site, however, by only 0.5 eV, a value smaller than the wide range of estimates obtained by others [77,78,122,79]. Nevertheless, our results are in full agreement with those of Ref. [122], regarding the structure of the atoms in the vicinity of the H atom at the BC site. In particular, we calculate the C-H bond length to be 1.17 Å[123] and the C-C bond to increase by 52 %, in full agreement with Ref. [122]. The nearest neighbor atoms of H at a T site are found to relax by 0.1 Å, also in very good agreement with Ref. [122]. It should be noted that these lengths are slightly shorter than those found by others [77,78]. We speculate that this is probably because in Refs. [77,78], local relaxation was applied to small H-terminated clusters, while in our work and in that of Ref. [122], full relaxation was applied to supercells.

Let us now consider the origin of the small energy difference found
here between H at the BC site and H at the T
site, and show
that this has no noticeable effects on the motion and migration
barriers of H in the crystal. The tight binding parameters for the C-H
interaction [118] were obtained from fitting to properties
of the CH_{4} molecule, as calculated by first principle models. In
the case of H in silicon, the reference molecule is SiH_{4}. However,
to extend the tight binding model to H in crystalline silicon (c-Si),
the hierarchy of energies for H at different high symmetry
interstitial sites, as obtained from *ab initio* calculations, has
to be reproduced. Boucher *et. al.* [124] found that this
hierarchy for H in c-Si is not maintained with the tight binding
parameters obtained from SiH_{4}. To properly describe H in c-Si, the
authors, therefore, suggested to decrease the strength of the Si-H
repulsive potential obtained from SiH_{4}, by using a multiplying
factor
.
The optimum
value found yielded the right
hierarchy of energies for interstitial H in c-Si.

In our case, the tight binding parameters deduced from CH_{4} lead to
the right hierarchy for interstitial H in diamond, however with
different relative energies than the ab initio data (see above). We
find that the agreement of the relative energies with *ab initio*
results can be improved by reducing the C-H repulsive energy, in the
same way as suggested by Boucher for the case of H in c-Si. In figure
(11.2), the cohesive energy of diamond with H at the BC and
T
interstitial sites is shown, as a function of the
multiplying factor .
It can be seen that the relative energy
between H at BC and H at T
can approach that obtained from
other calculations (marked in the figure by arrows) by changing the
value of .

In the rest of our investigation, the calculations of the energetics,
the energy barrier and the motion of H in diamond are carried out with
two different values for the multiplying factor: ,
which
corresponds to the initial tight binding parametrization, and
,
which yields an energy difference of 1.7 eV between H at BC
and H at T
(see figure (11.2)), well in the range of
Refs. [77,78,122,79], and close to the
*ab initio* pseudopotential result of Ref. [78]. In both
cases, the qualitative and quantitative results are similar. We thus
present below only the results obtained from the initial
parametrization (), unless stated otherwise.