Shifts in the π → π^∗ excitation energy of the cis-7-hydroxyquinoline chromophore induced by hydrogen bonding with small molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the high-level equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and noniterative triples, which provide the reference ab initio data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and the available experimental data. It is demonstrated that the spectral shifts resulting from the FDET calculations employing nonrelaxed environment densities and their EOMCC counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT approach do not agree with the EOMCC reference data. Among the discussed issues are the effects of higher-order correlations on the excitation energies and complexation-induced excitation energy shifts resulting from the EOMCC calculations, and the choice of the approximants that represent the nonadditive kinetic energy contributions to the embedding potential of FDET.

Shifts in the excitation energy of the organic chromophore, cis-7-hydroxyquinoline (cis-7HQ), corresponding to the π→π^* transition in cis-7HQ and induced by the complexation with a variety of small hydrogen-bonded molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the supermolecular equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and non-iterative triples, which provide the reference theoretical data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and experiment. Unlike in the supermolecular EOMCC and TDDFT cases, where each complexation-induced spectral shift is evaluated by performing two separate calculations, one for the complex and another one for the isolated chromophore, the FDET shifts are evaluated as the differences of the excitation energies determined for the same many-electron system, representing the chromophore fragment with two different effective potentials. By considering eight complexes of cis-7HQ with up to three small hydrogen-bonded molecules, it is shown that the spectral shifts resulting from the FDET calculations employing non-relaxed environment densities and their EOMCC reference counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT method do not agree with the EOMCC reference data. The average absolute deviation between the complexation-induced shifts, which can be as large, in absolute value, as about 2000 cm^-1, obtained using the non-relaxed FDET and supermolecular EOMCC approaches that represent two entirely different computational strategies, is only about 100 cm^-1, i.e., on the same order as the accuracy of the EOMCC calculations. This should be contrasted with the supermolecular TDDFT calculations, which produce the excitation energy shifts that differ from those resulting from the reference EOMCC calculations by about 700 cm^-1 on average. Among the discussed issues are the choice of the electronic density defining the environment with which the chromophore interacts, which is one of the key components of FDET considerations, the basis set dependence of the FDET, supermolecular TDDFT, and EOMCC results, the usefulness of the monomer vs supermolecular basis expansions in FDET considerations, and the role of approximations that are used to define the exchange-correlation potentials in FDET and supermolecular TDDFT calculations.

The relative energies of side-on versus end-on binding of molecular oxygen to a supported Cu(I) species, and the singlet versus triplet nature of the ground electronic state, are sensitive to the nature of the supporting ligands and, in particular, depend upon their geometric arrangement relative to the O₂ binding site. Highly correlated ab initio and density functional theory electronic structure calculations demonstrate that optimal overlap (and oxidative charge transfer) occurs for the side-on geometry, and this is promoted by ligands that raise the energy, thereby enhancing resonance, of the filled Cu d_xz orbital that hybridizes with the in-plane Ï€* orbital of O₂. Conversely, ligands that raise the energy of the filled Cu d_z² orbital foster a preference for end-on binding as this is the only mode that permits good overlap with the in-plane O₂ Ï€*. Because the overlap of Cu d_z² with O₂ Ï€* is reduced as compared to the overlap of Cu d_xz with the same O₂ orbital, the resonance is also reduced, leading to generally more stable triplet states relative to singlets in the end-on geometry as compared to the side-on geometry, where singlet ground states become more easily accessible once ligands are stronger donors. Biradical Cu(II)-O₂ superoxide character in the electronic structure of the supported complexes leads to significant challenges for accurate quantum chemical calculations that are best addressed by exploiting the spin-purified M06L local density functional, single-reference completely renormalized coupled-cluster theory, or multireference second-order perturbation theory, all of which provide predictions that are qualitatively and quantitatively consistent with one another.

The relative energetics of μ-η¹:η¹ (trans end-on) and μ-η²:η² (side-on) peroxo isomers of Cu₂O₂ fragments supported by 0, 2, 4, and 6 ammonia ligands have been computed with various density functional, coupled-cluster, and multiconfigurational protocols. There is substantial disagreement between the different levels for most cases, although completely renormalized coupled-cluster methods appear to offer the most reliable predictions. The significant biradical character of the end-on peroxo isomer proves problematic for the density functionals, while the demands on active space size and the need to account for interactions between different states in second-order perturbation theory prove challenging for the multireference treatments. In the latter case, it proved impossible to achieve any convincing convergence.

Accurately describing the relative energetics of alternative bis(μ-oxo) and μ-η²:η² peroxo isomers of Cu₂O₂ cores supported by 0, 2, 4, and 6 ammonia ligands is remarkably challenging for a wide variety of theoretical models, primarily owing to the difficulty of maintaining a balanced description of rapidly changing dynamical and nondynamical electron correlation effects and a varying degree of biradical character along the isomerization coordinate. The completely renormalized coupled-cluster level of theory including triple excitations and extremely efficient pure density functional levels of theory quantitatively agree with one another and also agree qualitatively with experimental results for Cu₂O₂ cores supported by analogous but larger ligands. Standard coupled-cluster methods, such as CCSD(T), are in most cases considerably less accurate and exhibit poor convergence in predicted relative energies. Hybrid density functionals significantly underestimate the stability of the bis(μ-oxo) form, with the magnitude of the error being directly proportional to the percentage Hartree−Fock exchange in the functional. Single-root CASPT2 multireference second-order perturbation theory, by contrast, significantly overestimates the stability of bis(μ-oxo) isomers. Implications of these results for modeling the mechanism of C−H bond activation by supported Cu₂O₂ cores, like that found in the active site of oxytyrosinase, are discussed.