Generalized-Kohn-Sham (GKS) orbital energies obtained self-consistently from the random phase approximation energy functional with a semicanonical projection (spRPA) were recently shown to rival the accuracy of GW quasiparticle energies for valence ionization potentials. Here, we extend the scope of GKS-spRPA correlated one-particle energies from frontier-orbital ionization to core orbital ionization energies, which are notoriously difficult for GW and other response methods due to strong orbital relaxation effects. For a benchmark consisting of 23 1s core electron binding energies (CEBEs) of second-row elements, chemical shifts estimated from GKS-spRPA one-particle energies yield mean absolute deviations from experiment of 0.2 eV, which are significantly more accurate than the standard GW and comparable to Δ self-consistent field theory without semiempirical adjustment of the energy functional. For small ammonia clusters and cytosine tautomers, GKS-spRPA based chemical shifts capture subtle variations in covalent and noncovalent bonding environments; GKS-spRPA 1s CEBEs for these systems agree with equation-of-motion coupled cluster singles and doubles and ADC(4) results within 0.2–0.3 eV. Two perturbative approximations to GKS-spRPA orbital energies, which reduce the scaling from O(N6) to O(N5) and O(N4), are introduced and tested. We illustrate the application of GKS-spRPA orbital energies to larger systems by using oxygen 1s CEBEs to probe solvation and packing effects in condensed phases of water. GKS-spRPA predicts a lowering of the oxygen 1s CEBE of approximately 1.6–1.7 eV in solid and liquid phases, consistent with liquid-jet X-ray photoelectron spectroscopy and gas phase cluster experiments. The results are rationalized by partitioning GKS-spRPA electron binding energies into static, relaxation, and correlation parts.

A new series of Ln3+ and Ln2+ complexes has been synthesized using the tris(aryloxide)arene ligand system, ((Ad,MeArO)3mes)3−, recently used to isolate a complex of U2+. The triphenol precursor, (Ad,MeArOH)3mes, reacts with the Ln3+ amides, Ln(NR2)3 (R = SiMe3), to form a series of [((Ad,MeArO)3mes)Ln] complexes, 1-Ln. Crystallographic characterization was achieved for Ln = Nd, Gd, Dy, and Er. The complexes 1-Ln can be reduced with potassium graphite in the presence of 2.2.2-cryptand (crypt) to form highly absorbing solutions with properties consistent with Ln2+ complexes, [K(crypt)][((Ad,MeArO)3mes)Ln], 2-Ln. The synthesis of the Nd2+ complex [K(crypt)][((Ad,MeArO)3mes)Nd], 2-Nd, was unambiguously confirmed by X-ray crystallography. In the case of the other lanthanides, crystals were found to contain mixtures of 2-Ln co-crystallized with either a Ln3+ hydride complex, [K(crypt)][((Ad,MeArO)3mes)LnH], 3-Ln, for Ln = Gd, Dy, and Er, or a hydroxide complex, [K(crypt)][((Ad,MeArO)3mes)Ln(OH)], 4-Ln, for Ln = Dy. A Dy2+ complex with 18-crown-6 as the potassium chelator, [K(18-crown-6)(THF)2][((Ad,MeArO)3mes)Dy], 5-Dy, was isolated as a co-crystallized mixture with the Dy3+ hydride complex, [K(18-crown-6)(THF)2][((Ad,MeArO)3mes)DyH], 6-Dy. Structural comparisons of 1-Ln and 2-Ln are presented with respect to their uranium analogs and correlated with density functional theory calculations on their electronic structures.

The configuration interaction, perturbation theory, coupled cluster doubles, and random phase approximation methods are applied to a system of two quantum Drude oscillators interacting through dipole–dipole coupling. It is found that the random phase approximation gives the exact excitation energies and exact interaction energy of this system even when allowing only excitations into the first excited levels of the oscillators. In contrast, to obtain the exact results from configuration interaction or coupled cluster treatments of the model requires inclusion of excitations into all accessible excited configurations.