  This article is a thorough critique to the Plakhutin-Davidson's comments made
to our paper published in the recent year. A detailed critical examination of
the arguments that led to the suggested comments by Plakhutin and Davidson
reveals some serious flaws. It is demonstrated that the principle of the
indistinguishability of identical particles is not taking into account in
Roothaan's open shell theory. This principle leads to the fact that the
orbital-dependent energy functional and, therefore, the Hartree-Fock and
Hartree-Fock-Roothaan equations for open shell systems presented by Roothaan
and others are not, in general, invariant under unitary transformation of the
combined closed-open shells orbitals. From a mathematical point of view this
statement is fundamentally flawless. It is shown that the Plakhutin-Davidson's
personal views about our assumptions concerning the insufficiencies of classic
Roothaan's open-shell theory are undisputedly wrong.
