Multistate Reactive Molecular Dynamics Simulations of Proton Diffusion in Water Clusters and in the Bulk

Abstract

The molecular mechanics with proton transfer (MMPT) force field is combined with multi state adiabatic reactive molecular dynamics (MS-ARMD) to describe proton transport in the condensed phase. Parametrization for small protonated water clusters based on electronic structure calculations at the MP2/6-311+G(2d,2p) level of theory and refinement by comparing with infrared spectra for protonated water tetramer yields a force field which faithfully describes minimum energy structures of small protonated water clusters. In protonated water clusters up to (H 2 O) 100 H + the proton hopping rate is around 100 hops/ns. Convergence of such rates is already found for 21 ≤ n ≤ 31 and no further speedup in bulk water is found. This indicates that bulk-like behaviour requires solvation of a Zundel motif by ∼ 25 water molecules which corresponds to the second solvation sphere. For smaller cluster sizes the number of available states, i.e. the number of proton acceptors, is too small and slows down proton transfer * To whom correspondence should be addressed 1 rates. The cluster simulations confirm that the excess proton is typically located on the surface. The free energy surface as a function of the weights of the two lowest states and a configurational parameter suggest that the "special pair" plays a central role in rapid proton transport. The barriers between this minimum energy structure and the Zundel and Eigen minima are sufficiently low (∼ 1 kcal/mol, consistent with recent experiments and commensurate with a hopping rate of ∼ 100/ns or 1 every 10 ps) which lead to a highly dynamical environment. These findings are also consistent with recent experiments which find that Zundel-type hydration geometries are prevalent in bulk water.2

Protonation Dynamics in the K-Channel of Cytochrome c Oxidase Estimated from Molecular Dynamics Simulations

“…However, our approach can easily be extended to include protein residues. This, however, needs a QM/MM setting for the energy evaluation (thought not for the MD simulations) or other effective potentials that allow the comparison of different topologies such as provided by EVB [9,10] or reactive force fields [11,12].…”

“…An alternative is to circumvent quantum mechanical calculations entirely and emulate the behavior, i.e., change of bonds and protonation states, as best as possible by classical calculations. This can be achieved by employing several predefined (protonation) states, and corresponding, typically QM-derived effective potentials, and switching between those as done in empirical valence bond approaches [9,10], reactive force fields [11,12] and multiscale reactive MD simulations based thereon [13]. Other methods such as Q-hop [14] involve a Monte Carlo step in which a proton transfer to an acceptor is proposed, based on varying criteria, and accepted by, e.g., a Metropolis criterium, i.e., evaluating the relative probabilities of the end states of the transfer in the desired thermodynamic ensemble.…”

Reactive molecular dynamics: From small molecules to proteins

“…Furthermore, MS-ARMD can also be combined with MM with proton transfer (MMPT) 66 to follow proton transfer in the gas-and condensed phase. [67][68][69][70] It is instructive to briefly compare EVB and the two ARMD approaches. While all three methods start from an empirical force field perspective, the EVB constructs an n × n Hamiltonian with the force fields V nn for the pure states on the diagonal and mixing elements V mn (m 6 ¼ n) as off-diagonal elements.…”

“…A recent extension of MS‐ARMD is its combination with VALBOND, a force field that allows to describe the geometries and dynamics of metal complexes Here, the formulation is reminiscent of EVB whereby the diagonal terms are VALBOND descriptions of the states involved and the off‐diagonal elements describe the orbital overlap. Furthermore, MS‐ARMD can also be combined with MM with proton transfer (MMPT) to follow proton transfer in the gas‐ and condensed phase …”

A Reactive Force Field with Coarse-Grained Electrons for Liquid Water

“…In order to study such systems, reactive dissociable models are required. Several dedicated force fields have been developed to study proton transfer in water such as models based on the central force field 34 , molecular mechanics with proton transfer force field and reactive molecular dynamics 35 , and valence bond models such as MS-EVB 36 . However, these models are designed to solely treat proton transport and extension of these models to more complicated reactive chemistry and electrochemistry is not straightforward.…”