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

Area of Science:

• Computational Chemistry
• Biophysical Chemistry
• Quantum Chemistry

Background:

• Quantum mechanics/molecular mechanics (QM/MM) simulations are crucial for studying reactions in solution and enzymes.
• Existing QM/MM-Ewald methods with periodic boundary conditions (PBC) require significant modifications to quantum mechanics (QM) codes.
• Nonperiodic treatments, like the droplet model, offer computational efficiency but their accuracy for long-range electrostatics needs validation.

Purpose of the Study:

• To introduce a general method (Gen-Ew) for periodic QM/MM calculations compatible with any QM code.
• To evaluate the accuracy of the Gen-Ew method by comparing it with the established QM/MM-Ewald approach.
• To compare periodic QM/MM methods with nonperiodic droplet models for reactions in solution and enzyme active sites.

Main Methods:

• Development of the General Ewald (Gen-Ew) method, approximating PBC potentials using virtual charges and QM density via electrostatic potential (ESP) charges.
• Implementation of Gen-Ew for QM/MM calculations, allowing its use with diverse QM methods.
• Comparative studies involving QM/MM-Ewald, Gen-Ew, and the droplet model for five reactions in water and the Claisen rearrangement in chorismate mutase.

Main Results:

• The Gen-Ew method shows small deviations compared to QM/MM-Ewald, making it a viable alternative when direct QM/MM-Ewald implementation is unavailable.
• Periodic and nonperiodic QM/MM treatments yielded similar free energy profiles for solution reactions (within ~1 kcal/mol).
• Both periodic and nonperiodic methods provided comparable energy profiles for the Claisen rearrangement in chorismate mutase, indicating effective capture of long-range electrostatic interactions by droplet models.

Conclusions:

• The Gen-Ew method provides a versatile approach for periodic QM/MM simulations, adaptable to various QM codes.
• Nonperiodic QM/MM calculations using droplet models of 15-20 Å radius are sufficient for accurately capturing long-range electrostatic interactions in condensed phases and enzyme systems.
• The computational efficiency and accuracy of the droplet model are further validated for QM/MM studies of chemical reactions.