Periodic Boundary Conditions in QM/MM Calculations: Implementation and Tests

Quantum mechanics/molecular mechanics (QM/MM) simulations of reactions in solutions and in solvated enzymes can be performed using the QM/MM-Ewald approach with periodic boundary conditions (PBC) or a nonperiodic treatment with a finite solvent shell (droplet model). To avoid the changes in QM codes that are required in standard QM/MM-Ewald implementations, we present a general method (Gen-Ew) for periodic QM/MM calculations that can be used with any QM method in the QM/MM framework. The Gen-Ew approach approximates the QM/MM-Ewald method by representing the PBC potential by virtual charges on a sphere and the QM density by electrostatic potential (ESP) charges. Test calculations show that the deviations between Gen-Ew and QM/MM-Ewald results are generally small enough to justify the application of the Gen-Ew method in the absence of a suitable QM/MM-Ewald implementation. We compare the results from periodic QM/MM calculations (QM/MM-Ewald, Gen-Ew) to their nonperiodic counterparts (droplet model) for five test reactions in water and for the Claisen rearrangement in chorismate mutase. The periodic and nonperiodic QM/MM treatments give similar free energy profiles for the reactions in solution (umbrella sampling, free energy deviations of the order of 1 kcal/mol) and essentially the same energy profile (constrained geometry optimizations) for the Claisen rearrangement in chorismate mutase. In all cases considered, long-range electrostatic interactions are thus well captured by nonperiodic QM/MM calculations in a water droplet of reasonable size (radius of 15-20 angstrom). This provides further justification for the widespread use of the computationally efficient droplet model in QM/MM studies of reactions in solution and in enzymes.