Response to Comment on "Combined open shell Hartree-Fock theory of   atomic-molecular and nuclear systems" [I.I.Guseinov, J. Math. Chem., 42   (2007) 177] by B. N. Plakhutin and E. R. Davidson
  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. 
I.I.Guseinov