Acid, Base and Electrical Charge at the Water Surface

Liquid water seems simple, but there’s a lot of chemistry going on in it.
It is common knowledge that, in pure water, under ordinary conditions, 1 in every 10 million H2O molecules is dissociated into the acid ion H+ and the base ion OH. However, what preference, if any, these self-ions of water have to sit at the air water interface has been the subject of lengthy and heated debate. The question is consequential in a wide range of contexts, including on the surface of droplets in the atmosphere and at the surfaces of biomolecules.  The Herzfeld group has now bridged the gap between experiment and theory by using a model that efficiently balances three subtle features of water molecules (polarizability, H+ sharing, and H+ transfer) that control the ambient behavior of the liquid. The model predicts that OH– prefers the air-water interface while H+ avoids it, consistent with observations of the response of air bubbles in water to an applied electric field.
Bai C, Herzfeld J. Surface Propensities of the Self-Ions of Water. ACS Central Science. 2016.

Easy Come, Easy Go

Whereas the diffusion of water molecules in the bulk liquid depends entirely on breaking hydrogen bonds, the diffusion of proton defects (i.e., an excess proton in acid or a proton deficit in base) is expedited by proton hopping across hydrogen bonds.  The details of this process are well understood in acid, and the process in base was believed to occur in analogous fashion. However, theoretical studies of hydroxide have given highly divergent predictions of solvation structures and diffusion rates, depending on the chosen recipe for such simulations: some predicted the traditionally expected solvation structures and some predicted the experimentally observed diffusion trends, but none do both. Now Seyit Kale, a graduate student in Prof. Judith Herzfeld’s group, has studied proton defects using the group’s recently developed LEWIS force field.[1] The LEWIS simulations obtain the correct relative diffusion rates with hydroxide solvation structures that are analogous to those of hydronium,[2] thereby supporting the traditional picture of the “proton hole”. The authors also catch and characterize proton transfer events, identifying similar “special pairs”[3] as the intermediates in both cases (see figure).

[1]       S. Kale, J. Herzfeld, J. Chem. Phys. 2012, 136, 084109.
[2]       S. Kale, J. Herzfeld, Angew. Chem. Int. Edit. 2012 in press. DOI: 10.1002/anie.201203568.
[3]       O. Markovitch, H. Chen, S. Izvekov, F. Paesani, G. A. Voth, N. Agmon, J. Phys. Chem. B. 2008, 112, 9456-9466.


Escaping the Lattice

The next best thing to seeing real atoms is to mimic them in silico: we assign interactions between the atoms and then — pouf –They’re alive!

The number of particles in a visible sample is on the order of Avogadro’s constant, say ~1023, whereas a fairly muscular computer can only follow ~105-107 atoms at a time. To compensate, computational scientists typically replicate their simulation boxes infinitely in space. This creates a quandary for calculating forces across replication boxes. The simplest option, which is to neglect forces beyond a chosen cut-off, suffices for many interactions, is too crude for the particularly long-range interactions that occur between charges. To accurately account for these interactions, it is customary to use a clever 90-year-old (!) technique, called the Ewald sum.(1)

The problem with the Ewald sum is that it requires imposing a long-range periodicity that is inappropriately short for macromolecules.(2) To avoid artifacts, a number of alternatives have been suggested. One intuitive approach, called “force shifting”, smooths the interaction energy and its first derivative (the force) at the chosen cutoff. However, this creates new artifacts (see figure) when particles have very large or varying charges, as in some ionic liquids. Brandeis scientists Seyit Kale and Judith Herzfeld, have found that this problem can be solved by also smoothing the second derivative of the interaction energy (the acceleration).(3)  This approach performs virtually as well as the Ewald sum in a new reactive force field that they have been developing (see figure).

The neighbor frequencies for bulk water calculated with force shifting at a cutoff of 9 Å (red) and 12 Å (magenta) versus with the authors’ new approach at a 9 Å cutoff (blue) and the Ewald sum (black). The blue and black curves are virtually the same while the red and magenta curves contain artifacts. The inset shows a representation of a water molecule from the force field that the authors are developing.

  1. Ewald P (1921) The Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 369: 253-287.
  2. Hunenberger PH, McCammon JA (1999) Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: A continuum electrostatics study. Biophys. Chem. 78: 69-88.
  3. Kale S, Herzfeld J (2011) Pairwise Long-range Compensation for Strongly Ionic Systems. J. Chem. Theory Comput. 7: 3620-3624.

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