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

Generalization of Brillouin theorem for the non-relativistic electronic  Schr\"odinger equation in relation to coupling strength parameter, and its  consequences in single determinant basis sets for configuration interactions