Proton Transfer in Aqueous Solution: Exploring the Boundaries of Adaptive QM/MM

In this chapter, we review the current state-of-the-art in quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in aqueous solutions, and we discuss how proton transfer poses new challenges for its successful application. In the QM/MM description of an aqueous reaction, solvent molecules in the QM region are diffusive and need to be either constrained within the region, or their description (QM versus MM) needs to be updated as they diffuse away. The latter approach is known as adaptive QM/MM. We review several constrained and adaptive QM/MM methods, and classify them in a consistent manner. Most of the adaptive methods employ a transition region, where every solvent molecule can continuously change character (from QM to MM, and vice versa), temporarily becoming partially QM and partially MM. Where a conventional QM/MM scheme partitions a system into a set of QM and a set of MM atoms, an adaptive method employs multiple QM/MM partitions, to describe the fractional QM character. We distinguish two classes of adaptive methods: Discontinuous and continuous. The former methods use at most two QM/MM partitions, and cannot completely avoid discontinuities in the energy and the forces. The more recent continuous adaptive methods employ a larger number of QM/MM partitions for a given configuration. Comparing the performance of the methods for the description of solution chemistry, we find that in certain cases the low-cost constrained methods are sufficiently accurate. For more demanding purposes, the continuous adaptive schemes provide a good balance between dynamical and structural accuracy. Finally, we challenge the adaptive approach by applying it to the difficult topic of proton transfer and diffusion. We present new results, using a well-behaved continuous adaptive method (DAS) to describe an alkaline aqueous solution of methanol. Comparison with fully QM and fully MM simulations shows that the main discrepancies are rooted in the presence of a QM/MM boundary, and not in the adaptive scheme. An anomalous confinement of the hydroxide ion to the QM part of the system stems from the mismatch between QM and MM potentials, which affects the free diffusion of the ion. We also observe an increased water density inside the QM region, which originates from the different chemical potentials of the QM and MM water molecules. The high density results in locally enhanced proton transfer rates.