Canonical form of the Hartree-Fock orbitals in open-shell systems

Abstract

This work compares different approaches to deriving Hartree-Fock (HF) orbitals and orbital energies for open-shell systems. We compare the basic HF equations underlying both the classic open-shell HF methods, which are the restricted open-shell HF (ROHF) and unrestricted HF (UHF) methods, and a number of the novel (amended) versions of these methods. The main attention is paid to a treatment of the validity of Brillouin's and Koopmans' theorems in the amended versions. We show that these two theorems are fully obeyed only in the special (canonical) form of the ROHF method developed by Plakhutin et al. [J. Chem. Phys. 125, 204110 (2006)] and by Davidson and Plakhutin [J. Chem. Phys. 132, 184110 (2010)], while each of the amended UHF methods suffers from some deficiencies inherent to original UHF and ROHF methods. To compare the HF orbitals derived by different methods in two different forms - DODS (different orbitals for different spins) and SODS (the same orbitals for different spins), we develop the new ROHF-DODS method which combines the use of DODS underlying amended UHF methods and the main advantage of the canonical ROHF method which is a fulfillment of the rigorous Koopmans' conditions. The main result of this work is that the orbitals and orbital energies derived with the new ROHF-DODS method appear identical to those derived with the canonical ROHF method based on the use of SODS. A discussion is presented of some related problems arising in open-shell HF methods such as a violation of the Aufbau principle.

Negative ions, molecular electron affinity and orbital structure of cata‐condensed polycyclic aromatic hydrocarbons

“…In the strict sense, the latter suggestion has no rigorous physical meaning, because the energy of electron affinity is associated with the elimination of an electron from the negative ion, not from the neutral molecule . The orbitals of the open‐shell anion should be used instead of that of the closed‐shell neutral molecule, which requires special adaption (see, e.g.,). In this connection, the widely accepted EA model based on Koopmans' theorem satisfies rather the frozen shell and adiabatic approximation, making it possible to evaluate only the vertical values of EA.…”

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

“…[10][11][12] As a result, Mayer et al transformed the EHF equations to some useful forms. [10][11][12] In future work we would like to elucidate the relation between the canonical ROHF [48][49][50][51][52] and the CObased canonical EHF methods, although we must first derive the CO-based canonical EHF equations.…”

Development of spin‐dependent relativistic open‐shell Hartree–Fock theory with time‐reversal symmetry (II): The restricted open‐shell approach

“…Two types of open‐shell Hartree–Fock (HF) methods, that is, unrestricted HF (UHF) and restricted open‐shell HF (ROHF) are fundamental tools in the quantum chemical study of paramagnetic systems. ROHF is in general applicable to arbitrary open‐shell configurations, while UHF can only be applied to half‐filled high‐spin open‐shell systems . The deficiency of ROHF is the partial arbitrariness in the construction of the Fock operator, which results in unphysical molecular orbitals (MOs) and orbital energies.…”

“…ROHF is in general applicable to arbitrary open-shell configurations, [3][4][5][6] while UHF can only be applied to half-filled high-spin open-shell systems. [7] The deficiency of ROHF is the partial arbitrariness in the construction of the Fock operator, which results in unphysical molecular orbitals (MOs) and orbital energies. Plakhutin et al [7][8][9][10] have proposed sophisticated solutions of this problem: they derived several conditions to explicitly satisfy Koopmans' theorem (KT) [11] within a simple ROHF framework.…”

“…[7] The deficiency of ROHF is the partial arbitrariness in the construction of the Fock operator, which results in unphysical molecular orbitals (MOs) and orbital energies. Plakhutin et al [7][8][9][10] have proposed sophisticated solutions of this problem: they derived several conditions to explicitly satisfy Koopmans' theorem (KT) [11] within a simple ROHF framework. Amended UHF procedures [12][13][14][15][16][17][18] have also been proposed as alternatives.Relativistic effects are vital to the study of paramagnetic systems because they often contain heavy elements.…”