Page 185 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

168 C. AMOVILLI AND R. McWEENY
the neutral atom should be multiplied by a scale factor

following removal of an electron, being the recommended effective nuclear charge
for the atom in question. This value (close to the actual nuclear charge) proves to
be perfectly satisfactory. In fact, the procedure just described leads to energy values
which are not appreciably affected by further parameter optimization. The results in
the Table confirm the need to re-optimize the basis following ionization, the resultant
drop in energy being quite significant. The agreement with experiment at this level
is now probably as good as can be expected, bearing in mind the extreme simplicity
of the theoretical model on which the calculations are based.

The results for homonuclear molecules are of particular interest in so far as they ex-
hibit “symmetry breaking”. For N 2 , for example, removal of an electron from the
MO of a ground-state SCF calculation, with re-optimization of all orbitals subject to
symmetry constraints, leads to an energy value of –93.49612 hartree for the positive
ion in which the core hole is symmetrically ‘shared’ between the two atoms. But
when the symmetry constraint is relaxed the energy falls to –93.88673 hartree, cor-
responding to localization of the hole on one centre alone: this is the result expected
on physical grounds, given a sufficiently short time scale for the process of electron
removal – the valence-electron distribution responding immediately to the enhanced
attraction towards the core with the hole. Of course, as already remarked, the re-
sultant metastable state will decay rapidly: the symmetry constrained wavefunction
describes the stationary state, in a long-time limit, of a fictitious model system in
which the hole appears on either centre with equal probability. The spectroscopic