A theoretical study of the copper–cysteine bond in blue copper proteins

The accuracy of theoretical calculations on models of the blue copper proteins is investigated using density functional theory (DFT) Becke's three-parameter hybrid method with the Lee–Yang–Parr correlation functional (B3LYP) and medium-sized basis sets. Increasing the basis set to triple-zeta quality with f-type functions on all heavy atoms and enlarging the model [up to Cu(imidazole-CH3)2(SC2H5) (CH3SC2H5)0/+] has only a limited influence on geometries and relative energies. Comparative calculations with more accurate wave-function–based methods (second-order Møller–Plesset perturbation theory, complete-active-space second-order perturbation theory, coupled-cluster method, including single and double replacement amplitudes and in addition triple replacement perturbatively) and a variety of basis sets on smaller models indicate that the DFT/B3LYP approach gives reliable results with only a small basis set dependence, whereas the former methods strongly depend on the size of the basis sets. The effect of performing the geometry optimizations in a continuum solvent is quite small, except for the flexible Cu-SMet bond. The results of this study confirm the earlier results that neither the oxidized nor the reduced copper site in the blue proteins is strained to any significant degree (in energy terms) by the protein surrounding.