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

Abstract

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 Å 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 ∼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.