Comment on “Combined open shell Hartree–Fock theory of atomic-molecular and nuclear systems” [J. Math. Chem. 42 (2007) 177]

Abstract

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 orbitaldependent 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.

Highly accurate numerical solution of Hartree–Fock equation with pseudospectral method for closed-shell atoms

“…The mapping (25), previously used in the PS solution of the KS equation, [35,41,42,62] is now also applied in solving the HF and Poisson Eqs. ( 9), ( 10) and (11) with the PS method. It is accompanied by suitable scaling of the sought functions (multiplying them by (̇r) −1∕2 ) to avoid the occurrence of their first derivative over x in the scaled HF and Poisson equations which would lead to non-symmetric matrices in the final discretized forms of these equations.…”

“…The accurate numerical solution of this eigenvalue equation for atoms with closed (sub)shells is the main focus of the present paper. The extension of the restricted HF method to open-shell systems [6,10,11] results in the Hamiltonians (Fock operators) which are different for each atomic subshell. As a result, the respective HF equations include off-diagonal Lagrange multipliers so they are not eigenvalue equations.…”

On the Ordering of Orbital Energies in High-Spin ROHF†

“…For a review and bibliography on ROHF, the reader is directed to several monographs , and a review, in order to avoid any misunderstandings . For completeness we provide a short summary and introduction here.…”

Communication: ROHF theory made simple

“…Attempts to resolve these ambiguities, as well as many paradoxes resulting from them, are well documented in the literature. [3][4][5][6] On the other hand, the physical picture of unrestricted HF (UHF) is clear. 7 It is a single-determinant wave function with well-defined α and β orbital energies obeying Koopmans' theorem.…”