Benchmark Study for the Cysteine-Histidine Proton Transfer Reaction in a Protein Environment: Gas Phase, COSMO, QM/MM Approaches

Proton transfer reactions are of crucial interest for the investigation of proteins. We have investigated the accuracy of commonly used quantum chemical methods for the description of proton transfer reactions in different environments (gas phase, COSMO, QM/MM) using the proton transfer between the catalytic dyad residues cysteine 145 and histidine 41 of SARS coronavirus main protease as a case study. The test includes thermodynamic, kinetic, and structural properties. The study comprises computationally demanding ab initio approaches (HF, CC2, MP2, SCS-CC2, SCS-MP2, CCSD(T)), popular density functional theories (BLYP, B3LYP, M06-2X), and semiempirical methods (MNDO/d, AM1, RM1, PM3, PM6). The approximated coupled cluster approach LCCSD(T) is taken as a reference method. We find that the robustness of the tested methods with respect to the environment correlates well with the level of theory. As an example HF, CC2, MP2, and their SCS variants show similar errors for gas phase, COSMO, or QM/MM computations. In contrast for semiempirical methods, the errors strongly diversify if one goes from gas phase to COSMO or QM/MM. Particular problems are observed for the recent semiempirical methods PM6 and RM1, which show the best performance for gas phase calculations but possess larger errors in conjunction with COSMO. Finally, a combination of SCS-MP2 and B3LYP or M06-2X allows reliable estimates about remaining errors.