An 131 atom cluster with a neutral Au placed at its centre was fully
relaxed, keeping the H terminators fixed. The gap contains a 
level containing three electrons and the configuration is taken to be
, consistent with 
. The charge density was averaged over the three degenerate
states and the self-consistent energy and forces acting on the
atoms found. This procedure prevents a Jahn-Teller distortion
[13]. Such distortions have been investigated by breaking
the symmetry and relaxing in a specific electronic configuration
[8, 13] but the splitting is very small and of no
importance to the calculation of the donor and acceptor levels. The
Au-Si lengths were 2.76 Å.
The positions of the five innermost atoms, including the impurity,
were then inserted into a 297 atom cluster. An additional half
electron was added to the 
level and another half
added to the nearest 
empty level which is taken to be the
conduction band bottom. The difference between these levels then gave
an estimate of the (-/0) acceptor level. In a similar way, the donor
level was found by promoting half a electron to the level of the
positively charged defect from the three levels lying beneath this
defect level (and taken to represent thee valence band top). These
energies were then rescaled as described above to compensate for the
cluster band gap. With the present basis, the band gap in the 297-atom
cluster without any impurities is 3.51 eV. The scaling factor is then
0.33 and the resulting estimates for the levels are given in Table 1.
The deep acceptor level at 
eV compares well with the
experimental value of 0.54 eV. The donor level at 
eV is
deeper than than the experimental value of 0.35 eV. A second acceptor
level lay at 
eV. There is no evidence for this shallow
level and it presumably lies above the conduction band minimum. The
sum of the (0/+) and (-/0) levels is 1.08 eV which is almost equal
to the energy gap 1.16 eV, whereas the experimental sum is 0.89 eV.
The latter differs from the gap because of the Hubbard U term. It
is clearly a failing of the present theory to account for this term
properly.
Table: Comparison between experimental [10, 11]
and calculated energy levels 
for the gold centre and
Au-H complex (G complex).