Validation of density functional modeling protocols on experimental bis(μ-oxo)/μ-η²: η²-peroxo dicopper equilibria

The bis(μ-oxo)/μ-η²:η²-peroxo equilibria for seven supported Cu₂O₂ cores were studied with different hybrid and nonhybrid density functional theory models, namely, BLYP, mPWPW, TPSS, TPSSh, B3LYP, mPW1PW, and MPW1K. Supporting ligands 3,3′-iminobis(N,N-dimethylpropylamine), N,N,N′,N′,N″- pentamethyldipropylenetriamine, N-[2-(pyridin-2-yl)ethyl]-N,N,N′- trimethylpropane-1,3-diamine, bis[2-(2-pyridin-2-yl)ethyl]methylamine, bis[2-(4-methoxy-2-pyridin-2-yl)ethyl]methylamine, bis[2-(4-N,N-dimethylamino-2- pyridin-2-yl)ethyl]methylamine, and 1,4,7-triisopropyl-1,4,7-triazacyclononane were chosen on the basis of the availability of experimental data for comparison. Density functionals were examined with respect to their ability accurately to reproduce experimental properties, including, in particular, geometries and relative energies for the bis(μ-oxo) and side-on peroxo forms. While geometries from both hybrid and nonhybrid functionals were in good agreement with experiment, the incorporation of Hartree-Fock (HF) exchange in hybrid density functionals was found to have a large, degrading effect on predicted relative isomer energies. Specifically, hybrid functionals predicted the μ-η²:η²-peroxo isomer to be too stable by roughly 5-10 kcal mol^-1 for each 10% of HF exchange incorporated into the model. Continuum solvation calculations predict electrostatic effects to favor bis(μ-oxo) isomers by 1-4 kcal mol^-1 depending on ligand size, with larger ligands having smaller differential solvation effects. Analysis of computed molecular partition functions suggests that nonzero measured entropies of isomerization are likely to be primarily associated with interactions between molecular solutes and their first solvation shell.