  The Brillouin theorem has been generalized for the extended non-relativistic
electronic Hamiltonian (Hkin+ Hne+ aHee) in relation to coupling strength
parameter (a), as well as for the configuration interactions (CI) formalism in
this respect. For a computation support, we have made a particular modification
of the SCF part in the Gaussian package: essentially a single line was changed
in an SCF algorithm, wherein the operator rij-1 was overwritten as 1/rij to
a/rij, and a was used as input. The case a=0 generates an orto-normalized set
of Slater determinants which can be used as a basis set for CI calculations for
the interesting physical case a=1, removing the known restriction by Brillouin
theorem with this trick. The latter opens a door from the theoretically
interesting subject of this work toward practice.
