Importance of van der Waals Interactions in QM/MM Simulations Demian Riccardi, Guohui Li, and Qiang Cui* Department of Chemistry and Theoretical Chemistry Institute, UniVersity of Wisconsin, Madison, 1101 UniVersity AVe, Madison, Wisconsin 53706 ReceiVed: December 23, 2003; In Final Form: March 1, 2004 The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen- bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms. 1. Introduction The analysis of chemical events in complex systems requires a potential function that can describe electronic changes in the region of interest. Current quantum mechanical approaches provide such descriptions, but there are severe limitations in the size of the systems that can be treated. 1,2 To investigate the effects of the environment on chemical events, approximations must be made with either an implicit or explicit approach. For biological systems, the inclusion of the protein and solvent environment is paramount, 3 and combined quantum mechanical and molecular mechanical (QM/MM) methods 4-6 are a popular choice for such investigations. QM/MM methods enable theo- retical computations of complex chemical events in large systems by partitioning the system into a quantum region and a molecular mechanics region. The application of the QM/MM method can provide atomistic details of catalytic mechanisms corresponding to experimental observables, which is valuable for both fundamental understanding of enzyme catalysis and realistic applications such as protein engineering. The total Hamiltonian for the molecular system under consideration in the QM/MM framework is where H ˆ QM/MM describes the interaction between the QM and MM atoms governed by H ˆ QM and H ˆ MM , respectively. The H ˆ QM/MM typically contains terms for the electrostatic, van der Waals(vdW), and bonded interactions The H ˆ bonded QM/MM is required when partitioning a single molecule into quantum and molecular mechanics regions, as is most common for applications to protein systems. For such partition- ing, the molecular mechanical bonding term is retained between the boundary QM and MM atoms, whereas the valency of the QM region is satisfied with the addition of link atoms 4 or frontier bonds. 7,8 The purpose of the vdW term is to estimate dispersion attractions that fall off as r -6 and to prevent molecular collapse being strongly repulsive at short interaction distances. In terms of the magnitudes at typical interactomic distances, electrostatic interactions usually overwhelm the vdW contributions, espe- cially in polar systems such as enzymes. Due to the rapid variation at short interatomic distances, however, the vdW interactions (therefore vdW parameters) are important to the equilibrium geometries of molecules treated by QM/MM in the gas phase. 4,9-12 In the condensed phase, on the other hand, due to averaging over a large number of configurations, the question of how important the precision of QM/MM van der Waals interactions is to the molecular properties of common interest is an interesting one, which has not been systematically explored in the past. Moreover, the vdW interaction between QM and MM atoms in the condensed phase may not only affect the enthalpy of direct interactions but also have a substantial entropic component, and the possibility of enthalpy/entropy compensation has not been analyzed in details in previous work. In the current paper, we report a systematic analysis on the * To whom the correspondence should be addressed. H ˆ) H ˆ QM + H ˆ QM/MM + H ˆ MM (1) H ˆ QM/MM ) H ˆ vdW QM/MM + H ˆ elec QM/MM + H ˆ bonded QM/MM (2) 6467 J. Phys. Chem. B 2004, 108, 6467-6478 10.1021/jp037992q CCC: $27.50 © 2004 American Chemical Society Published on Web 04/23/2004