Theoretical Models on the Cu₂O₂ Torture Track:  Mechanistic Implications for Oxytyrosinase and Small-Molecule Analogues

Abstract

Accurately describing the relative energetics of alternative bis(µ-oxo) and µ-η 2 :η 2 peroxo isomers of Cu 2 O 2 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 Cu 2 O 2 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 HartreeFock 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 Cu 2 O 2 cores, like that found in the active site of oxytyrosinase, are discussed.

Theoretical Characterization of End-On and Side-On Peroxide Coordination in Ligated Cu2O2 Models

“…As we found previously for the case of side-on peroxo versus bis(µ-oxo), 28 there is a very large variation in relative energies as a function of theoretical level. For 0 0 , a range of roughly 50 kcal mol -1 is predicted, although every level does predict the end-on isomer to be lower in energy than the side-on one.…”

“…To address the issues of convergence with respect to higher-order correlations neglected in CR-CCSD(T) and size extensivity, we also performed calculations using the recently proposed rigorously size extensive CR-CC(2,3) approach, which is based on a new, biorthogonal formulation of the method of moments of CC equations (a formalism used to design all CR-CC methods [63][64][65]67 ) employing the left eigenstates of the similarity-transformed Hamiltonian of CC theory. 77 28 and present studies confirm this. In all single-reference correlated calculations, we used the RHF determinant that we identified as the lowest-energy symmetry-adapted RHF solution as a reference.…”

“…Here, the pure functionals continue to perform well, but there is more variation in their prediction of the energy of 0 0 relative to that of 0 100 : 6.5 kcal mol -1 compared to 3.8 kcal mol -1 for side-on peroxo versus bis(µ-oxo). 28 In addition, BLYP was the most accurate functional in our prior work, while here TPSS offers the closest agreement with CR-CC(2,3),D and CR-CC-(2,3)+Q, and BLYP is least good of the pure functionals. The hybrid functionals show a systematic stabilization of 0 0 relative to 0 100 with increasing HF exchange.…”

“…[74][75][76] Third, and importantly, it does agree with other key levels of theory and experimental analogues in its predictions for the equilibrium between bis(µ-oxo) and side-on peroxo forms. 28 And finally, if we consider the CR-CC predictions for the end-on/side-on equilibrium as a function of the number of ligands, the trend is intuitively reasonable ( Figure 8). In the unligated system, there is strong Coulombic repulsion between the two copper cations, and that repulsion is reduced in the end-on structure where they are nearly 5 Å apart compared to 3.6 Å in the side-on case.…”

“…We performed a variety of standard single-reference CC calculations 56,57 using the CC method with singles and doubles (CCSD), [58][59][60] the CC method with singles, doubles, and noniterative triples (CCSD(T)), 61 and, to explore the role of higher-order correlations, the CC method with singles, doubles, and noniterative triples and quadruples (CCSD(TQ)), using variant "b" of the factorized CCSD(TQ) approximation. 62 To improve on the CC model, we performed calculations using the recently developed [62][63][64][65][66][67] completely renormalized CCSD(T) (CR-CCSD(T)) and CCSD(TQ) (CR-CCSD(TQ)) methods which can accurately and effectively deal with reactive potential energy surfaces involving bond stretching, 63-73 biradicals, 28,[74][75][76] and other cases of electronic near-degeneracies within a single-reference description employing an RHF reference. We used variant "b" of the CR-CCSD(TQ) approach, 62 which enables us to determine if the CR-CCSD(T) results are reasonably well converged with respect to higher-order correlation effects.…”