Activation Energies & Volumes

How can we extract more information from moleculary dynamics simulations?

A key part of our current work is developing new methods for extracting key information from molecular dynamics (MD) simulations.  A prime example is the activation energy, Ea, that measures the temperature dependence of a rate constant or other dynamical timescale and thus provides information about the relevant barrier of the process of interest.  The activation energy is typically obtained by measuring or calculating the rate constant, k, at several temperatures to make an Arrhenius plot of ln versus 1/T, the slope of which is proportional to Ea.  Calculating at different temperatures can be problematic, e.g., near a phase transition or in a protein or assembly that unfolds or falls apart when is increased.  We have recently developed an approach by which the Ea can be obtained from simulations at a single temperature.  Moreover, the method allows the activation energy to be rigorously decomposed into the contributions from the kinetic energy and various interactions present in the system, thereby providing mechanistic information that is not available in any other way.  The approach is not limited to classical MD simulations - we have demonstrated it can be just as straightfowardly implemented in rigorous quantum mechanical calculations.  It is also not limited to rate constants but is applicable to any dynamical timescale that can be described by a time correlation function (which is essentially all of them!); we have demonstrated this for the diffusion coefficient, viscosity, and reorientational times in liquids.

The same general approach can be applied to obtain the pressure dependence of dynamical timescales.  The pressure dependence of a rate constant is often measured by the activation volume, that is given by the derivative of ln with respect to the pressure, p.  Since changes in timescales with are usually quite modest, calculating activation volumes is challenging.  It is typically done by obtaining the slope of an Arrhenius-like plot of ln versus p, where must be varied over thousands of bar to resolve the differences in k.  However, there are some key cases where ln does not vary linearly with p, the diffusion coefficient of water being a notable example.  Because our approach does not require changing the pressure, but yields the activation volumes from simulations at a single pressure, it avoids these problems.

Relevant References:

Zeke A. Piskulich, Oluwaseun O. Mesele, and Ward H. Thompson, Journal of Physical Chemistry A 123, 7185-7194 (2019). “Activation Energies and Beyond”

Camina H. Mendis, Zeke A. Piskulich, and Ward H. Thompson, Journal of Physical Chemistry B 123, 5857-5865 (2019). “Tests of the Stokes-Einstein Relation through the Shear Viscosity Activation Energy of Water”

Zeke A. Piskulich, Oluwaseun O. Mesele, and Ward H. Thompson, Journal of Chemical Physics 148, 134105 (2018). “Expanding the Calculation of Activation Volumes: Self- diffusion in Liquid Water”

Zeke A. Piskulich, Oluwaseun O. Mesele, and Ward H. Thompson, Journal of Chemical Physics 147, 134103 (2017). "Removing the Barrier to the Calculation of Activation Energies. Diffusion Coefficients and Reorientation Times in Liquid Water"

Oluwaseun O. Mesele and Ward H. Thompson, Journal of Chemical Physics 145, 134107 (2016). "Removing the Barrier to the Calculation of Activation Energies"

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