In this presentation, we report on our progress in developing a coarse-grained description of structural diffusion of protons that is implementable in computationally efficient reactive molecular dynamics (RMD) simulations.

The structural diffusion of a proton, as a reaction, can be given as           

The approach we have chosen is to modify the classical equilibrium molecular dynamics simulation algorithm based on quantum mechanical calculations to correctly reproduce the macroscopic reaction rates, thereby capturing the essential molecular and macroscopic features of structural diffusion.  The advantage of this approach is that we use a computationally efficient, non-reactive potential that already exists and has been optimized.

The RMD algorithm has three steps as follows:

1.      Reaction trigger – checks for a favorable starting configuration for the reaction to take place, satisfying a set of geometric and energetic triggers based on the quantum mechanical transition state and activation energy.

2.      Instantaneous reaction – coarse grains out the reaction path and the proton gets transported instantaneously.

3.      Local equilibration – satisfies the target heat of reaction,  and ensures the correct ending configuration for the reaction.

A number of conceptual and practical considerations that were taken into account for the specific formulation of RMD algorithm are enumerated below.

1.      The numerical values of the limits on the geometric and energetic triggers were tuned to either quantum mechanical or experimental measurements of activation energy E_a and rate constant k.

2.        The rattling of the proton between the two reacting molecules, which does not contribute to the structural diffusion of proton were not included in the calculation of the reaction rate.

3.        The local equilibration should not affect the system structurally, energetically and must be computationally inexpensive. So different scenarios of local equilibration were considered.

With a series of reasoning and elimination process, we can end up in the implementation of the algorithm that can give an insight to the actual physical process.

Using this procedure we can match the five properties that are required to describe a chemical reaction from the macroscopic point of view:  the stoichiometry, the rate law, the activation energy, the heat of reaction and the rate constant. By matching the macroscopic reaction rate, the mass transport property of the charge becomes predictable.

In this RMD algorithm, we have illustrated a coarse-grained procedure that has a valid starting point and a valid ending point for the chemical reaction. Information regarding the transition state is embedded in the triggers, but the structure of the transition state is not listed.  This enables the functional extrapolation of this reaction in bulk water to a hydrated proton exchange membrane (PEM) because the starting and ending points of the structural diffusion reaction are likely similar, whereas the details of the transition state may not be. For example, one of the geometric triggers checks for the necessary hydrogen bonding of the four non-reactive H atoms in the reacting molecules and in PEM it can accommodate hydration of the reacting molecules via sulfonic acid groups and the energetic trigger automatically registers the difference in forces due to presence of the sulfonic acid groups.