On the Convergence of QM/MM Energies.

We have studied the convergence of QM/MM calculations with respect to the size of the QM system. We study a proton transfer between a first-sphere cysteine ligand and a second-sphere histidine group in [Ni,Fe] hydrogenase and use a 446-atom model of the protein, treated purely with QM methods as a reference. We have tested 12 different ways to redistribute charges close to the junctions (to avoid overpolarization of the QM system), but once the junctions are moved away from the active site, there is little need to redistribute the charges. We have tested 13 different variants of QM/MM approaches, including two schemes to correct errors caused by the truncation of the QM system. However, we see little gain from such correction schemes; on the contrary, they are sensitive to the charge-redistribution scheme and may cause large errors if charges are close to the junctions. In fact, the best results were obtained with a mechanical embedding approach that does not employ any correction scheme and ignores polarization. It gives a mean unsigned error for 40 QM systems of different sizes of 7 kJ/mol with a maximum error of 28 kJ/mol. The errors can be significantly decreased if bonds between the QM and MM system (junctions) are moved one residue away from all active-site residues. Then, most QM/MM variants give mean unsigned errors of 5-9 kJ/mol, maximum errors of 16-35 kJ/mol, and only five to seven residues give an error of over 5 kJ/mol. In general, QM/MM calculations converge faster with system size than pure QM calculations.