QM/MM calculations with DFT for taking into account protein effects on the EPR and optical spectra of metalloproteins. Plastocyanin as a case study.

A detailed study of the influence of the surrounding protein on magnetic and optical spectra of metalloproteins is presented using the quantum-mechanical/molecular mechanical (QM/MM) approach. The well-studied type I copper site in plastocyanin in the cupric oxidation state is taken as a test case because its spectroscopic properties have been extensively studied and are well understood. The calculations have been performed using nonrelativistic and scalar relativistic (at the level of the zeroth order regular approximation, ZORA) calculations (B3LYP functional). Linear response theory has been used to calculate first- and second-order properties, namely the EPR g-tensor, the central metal hyperfine couplings (HFCs), the HFCs of the directly coordinating ligands, as well as superhyperfine couplings (1H, 14N) from remote nuclei, transition energies, and oscillator strengths. Two different model systems have been defined that do not and do include important amino acids from the second coordination sphere, respectively. For comparison, calculations have been carried out in the gas phase and in a dielectric continuum (conductor like screening model, COSMO) with a dielectric constant of four. The best results were obtained at the scalar relativistic ZORA level for the largest model in conjunction with explicit modeling of the protein environment through the QM/MM procedure, which is also considered to be the highest level of theory used in this work. The protein effects beyond the second coordination sphere were found to be quite substantial (up to 30% changes on some properties), and were found to require an explicit treatment of the protein beyond the second coordination sphere. In addition, the embedding water cage was found to have a nonnegligible influence on the calculated spectroscopic data, which is of the same order as the influence of the protein backbone charges. However, while qualitatively satisfactory, the errors in the calculated spectroscopic parameters are still substantial, and can all be traced back to the fact that the linear-response of the presently available functionals is "too stiff" with respect to the external perturbations at least for the model systems studied here. Ligand field-based approaches are used to correct for systematic errors in the DFT procedures. As a consequence, we propose a new breakdown of the copper hyperfine interaction into Fermi-contact, spin-dipolar and spin-orbit contributions.