Effect of Geometry Optimizations on QM-Cluster and QM/MM Studies of Reaction Energies in Proteins

We have examined the effect of geometry optimization on energies calculated with the quantum mechanical (QM) cluster, combined QM and molecular mechanics (QM/MM), and big-QM approaches (very large single-point QM calculations taken from QM/MM-optimized structures, including all atoms within 4.5 angstrom of the minimal active site, all buried charged groups in the protein, and truncations moved at least three residues away from the active site). We studied a simple proton-transfer reaction between His-79 and Cys-546 in the active site of [Ni,Fe] hydrogenase and optimize QM systems of 50 different sizes (56-362 atoms). Geometries optimized with QM/MM are stable and reliable, whereas QM-cluster optimizations give larger changes in the structures and sometimes lead to large distortions in the active site if some hydrogen-bond partners to the metal ligands are omitted. Keeping 2-3 atoms for each truncated residue (rather than one) fixed in the optimization improves the results but does not solve all problems for the QM-cluster optimizations. QM-cluster energies in vacuum and a continuum solvent are insensitive to the geometry optimizations with a mean absolute change upon the optimizations of only 4-7 kJ/mol. This shows that geometry optimizations do not decrease the dependence of QM-cluster energies on how the QM system is selected; there is still a similar to 60 kJ/mol difference between calculations in which groups have been added to the QM system according to their distance to the active site or based on QM/MM free-energy components. QM/MM energies do not show such a difference, but they converge rather slowly with respect to the size of the QM system, although the convergence is improved by moving truncations away from the active site. The big-QM energies are stable over the 50 different optimized structures, 57 +/- 1 kJ/mol, although some smaller trends can be discerned. This shows that both QM-cluster geometries and energies should be interpreted with caution. Instead, we recommend QM/MM for geometry optimizations and energies calculated by the big-QM approach.