Electron Binding Energies of Open-Shell Species from Diagonal Electron-Propagator Self-Energies with Unrestricted Hartree–Fock Spin–Orbitals

For closed-shell molecules, valence electron binding
energies may
be calculated accurately and efficiently with ab initio electron-propagator methods that have surpassed their predecessors.
Advantageous combinations of accuracy and efficiency range from cubically
scaling methods with mean errors of 0.2 eV to quintically scaling
methods with mean errors of 0.1 eV or less. The diagonal self-energy
approximation in the canonical Hartree–Fock basis is responsible
for the enhanced efficiency of several methods. This work examines
the predictive capabilities of diagonal self-energy approximations
when they are generalized to the canonical spin–orbital basis
of unrestricted Hartree–Fock (UHF) theory. Experimental data
on atomic electron binding energies and high-level, correlated calculations
in a fixed basis for a set of open-shell molecules constitute standards
of comparison. A review of the underlying theory and analysis of numerical
errors lead to several recommendations for the calculation of electron
binding energies: (1) In calculations that employ the diagonal self-energy
approximation, Koopmans’s identity for UHF must be qualitatively
correct. (2) Closed-shell reference states are preferable to open-shell
reference states in calculations of molecular ionization energies
and electron affinities. (3) For molecular electron binding energies
between doublets and triplets, calculations of electron detachment
energies are more accurate and efficient than calculations of electron
attachment energies. When these recommendations are followed, mean
absolute errors increase by approximately 0.05 eV with respect to
their counterparts obtained with closed-shell reference orbitals.