(Cf. Atkins and Friedman [5], ch. 8.3, for this section).
We now apply the Rayleigh-Ritz variational method to the Hydrogen Molecule Ion
, restricting ourselves to just
real wave functions (atomic orbitals)
(
), i.e.
MO
LCAO
(3.11)
with two hydrogen groundstate
-orbitals for nuclei at
and
, respectively.