The bound state stability of the hydride ion in Hartree-Fock theory

Maximum Ionization in Restricted and Unrestricted Hartree-Fock Theory

“…Whether it holds for p > 1 is under investigation. We also note that this is a non-existence theorem (necessary but not sufficient) in the same way as Theorem 1 of [13] is, and so although the hydride ion satisfies Equation (13) it does not guarantee that the system holds a bound state (and all numerical calculations indicate it does not [3]).…”

“…However, even for the simplest two-electron system, the hydride ion, there remains unanswered questions regarding its stability at the Hartree-Fock level of theory, and this is the motivation for this paper. A recent review by the authors [3] detailed existing numerical/computational and theoretical works on the bound state stability of the hydride ion, where the term bound state refers to the existence of a discrete eigenvalue below the lowest continuum threshold. Numerical calculations and mathematical proofs agree that the many-body, non-relativistic, time-independent Schrödinger equation for the hydride ion supports a single bound state.…”

Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms

“…3,13,14 In particular, comparing the closed-shell HF energy to the exact energy of the ionised system shows that HF theory fails to predict a stable two-electron atom with Z c < Z < 1.031 177 528, 13 including H -. 15,16 However, interpreting exactly how correlation influences the stability of the two-electron atom is made difficult by an incomplete understanding of the HF approximation for small Z.…”

“…Alternatively, the unrestricted HF (UHF) approach allows the spin-up and spin-down electrons to occupy different spatial orbitals, 17 providing a qualitatively correct model for the dissociation of a single bound electron in Hat the expense of broken spin-symmetry. 15,16 The onset of HF symmetry breaking is marked by instability thresholds in the orbital a) Electronic mail: hugh.burton@chem.ox.ac.uk Hessian, 18 which have also been interpreted as critical charges in closed-shell atoms. 19 These sudden qualitative changes in the HF wave function can also be probed using the average radial electronic positions, providing an alternative indicator for electron ionisation that does not rely on energetic comparisons with the exact result.…”

Reparametrization of the Colle–Salvetti formula

“…However, it is known that anions are particularly difficult to calculate. In fact it has been said that anions owe their stability to electron correlation effects [8] and this is certainly true for the hydride ion [9]. Furthermore, there have been significant efforts to assess DFT methods for the prediction of the electronic structures of complex and multiply charged anions (e.g.…”