Towards an Understanding of the Activation Energies in Liquid Water

My research is focused on how the dynamical and structural prop- erties of liquids change with temperature (T) and pressure (p). Specifically, I have developed methods for calculating the derivatives of dynamical timescales with respect to T and p from molecular dynamics simulations at a single temperature and pressure.[1−8] This method provides previously unobtainable mechanistic insight via decomposition of activation energies into contributions from molecular interactions. My work has enhanced our understanding of diffusion,[1-2] reorientation,[1,3,7] viscosity,[5] and hydrogen bond exchanges[8] in liquid water, while also revealing more about the nature of activation energies.

A feature of this method is that it determines the analytical derivatives at a particular T and p rather than being calculated numerically using a range of temperatures and pressures as is done in an Arrhenius analysis. This allows activation energies to be extracted even for dynamical timescales that are non-Arrhenius (e.g., liquid water diffusion), or where the temperature ranges needed for an Arrhenius analysis are not accessible (e.g., near a phase transition).

 

We have illustrated how derivatives of the diffusion coefficient, reorientation times, and liquid structure may be used to predict the temperature dependence of these quantities deeply into the supercooled regime. For example, from room temperature simulations we used our method to predict the diffusion coefficient of water down to 125 K and found it to be in agreement with experimental measurements,[9] as shown in Figure 1.[7]

A century ago Tolman showed that the activation energy can be understood as the excess energy needed to surmount the barrier (as opposed to the common view of the height of the barrier).[10] The activation energy decompositions obtained from our method, then provide an accounting of the excess energy of a particular type (electrostatic, kinetic, etc.) required to surmount such a barrier. In every dynamical process in water that we have studied, we have found that the the Lennard-Jones and electrostatic activation energy contributions are in competition with one another, with the latter dominating. This is consistent with the energetic changes involved in breaking a hydrogen bond, as illustrated schematically in Figure 2.[8]

 

We are developing this work in a number of directions, including ongoing collaborations with Chris Mundy, Greg Schenter, Damien Laage, and Elise Diboué-Dijon. In the future, this method should allow insight into activation energies in other cases where an Arrhenius analysis is difficult, for instance a system at phase coexistence. We are also extending the decompositions to the level of individual molecular interactions (e.g., the effect of particular residues on the reorientation activation energy of a water molecule in a protein hydration shell).

References: [1] Piskulich, Z. A., Mesele, O. O. & Thompson, W. H. J. Chem. Phys. 147, 134103 (2017). [2] Piskulich, Z. A., Mesele, O. O. & Thompson, W. H. J. Chem. Phys. 148, 134105 (2018). [3] Piskulich, Z. A. & Thompson, W. H., J. Chem. Phys. 149, 164504 (2018). [4] Piskulich, Z. A., Mesele, O. O., & Thompson, W. H. J. Phys. Chem. A. 123, 7185-7194 (2019). [5] Mendis, C. H., Piskulich, Z. A. & Thompson, W. H. J. Phys. Chem. B. 123, 5857-5865 (2019). [6] Piskulich, Z.A. & Thompson, W.H. J. Chem. Phys. Commun., 152, 011102 (2020). [7] Piskulich, Z.A. & Thompson, W.H. J. Chem. Phys., 152, 074505 (2020). [8] Piskulich, Z.A., Laage, D., & Thompson, W.H. J. Chem. Phys. submitted (2020). [9] Xu, Y., Petrik, N.G., Smith, R.S., Kay, B.D. & Kimmel, G.A. Proc. Natl. Acad. Sci. 113, 14921 (2016). [10] Tolman, R. C. J. Am. Chem. Soc. 42, 2506–2528 (1920).