61st Annual Report on Research 2016

The goal of this proposal is to apply our quantum umbrella sampling technique to systems where it is important to be able to restrain a quantum mechanical degree of freedom. Over the past year, our focus has been on using this technique to better understand the structure of the hydrated electron. The hydrated electron is an excess electron in liquid water. The standard view of this object is that the electron repels the water and thus can be thought of as occupying a quasi-spherical cavity in the liquid. Recently, however, we challenged this view on the basis of simulations using a new pseudopotential that predicted that the electron actually occupies a region of enhanced water density, with many waters in the interior of the electron's charge density. This non-cavity eø-water potential that we derived, dubbed "LGS" in the literature, is essentially identical to that derived by Turi and Borgis (TB), which predicts a cavity electron; the only difference between LGS and TB is the analytic form chosen to represent the numerically-calculated potential. The cavity or non-cavity behavior for the hydrated eø thus depends on subtleties of how the balance of attractive and repulsive forces are represented in the potential.

Free Energies of Cavity and Non-Cavity Hydrated Electrons: Given that similarly-derived pseudopotentials, such as TB and LGS, can produce hydrated eø's with vastly different structures, one question we have recently asked is: What is the free energy difference between hydrated eø's with different structures? To answer this question, we defined a "cavity-coordinate" by integrating the number of water molecules within a certain distance of the eø's center of mass, weighted by a function that starts at 1 and drops to zero. Since the function drops smoothly with distance, our cavity coordinate can account for fractional numbers of interior waters. We then choose the average distance of the cut-off so that a TB electron has a value of zero along this coordinate and an LGS electron has an average value of 1.0.

Figure 1 shows the free energy of the two different hydrated electron models along this cavity coordinate. For TB, we see the minimum free energy lies at cavity coordinate zero, consistent with the fact that the TB potential produces a cavity eø. Moreover, we also see that putting even ~ of a water molecule into the TB eø's interior costs ~7 k_BT of energy. For the LGS non-cavity eø, on the other hand, we see that even though the minimum free energy is at cavity coordinate 1.0 (by construction), there is little free energetic cost to either removing the interior water or to adding additional water. Further analysis shows this is entirely an entropic effect: the enthalpy of the LGS potential is still net repulsive, preferring a cavity, but the LGS potential is soft enough to allow interior waters to avoid the entropic cost of creating a cavity and breaking the local water structure. Thus, the LGS model predicts that hydrated eø's become more cavity-like at lower temperatures when entropy becomes less important. It is this change in structure with temperature that leads to the observed T-dependent spectral shift.

The Behavior of Hydrated Electrons at Air/Water Interfaces: In the past few years, the experimental development of photoelectron spectroscopy from liquid jets in a vacuum has enabled a whole host of new studies, including investigations of the nature of the hydrated electrons at the air/water interface. Pioneering experiments by Abel and co-workers saw two peaks in the photo_electron spectrum, which were assigned to eø's photoejected from bulk water and eø's photoionized from states trapped at the air/water interface. Subsequently, this experiment was repeated by several groups, all of which found only a single peak with a binding energy indicative of bulk hydrated eø's. Additional photoelectron work on water cluster anions also suggests at least two types of hydrated eø's, one trapped in the cluster's interior and the other at the surface. Finally, Verlet and co-workers have performed surface-sensitive second harmonic generation (SHG) experiments on hydrated eø's, and concluded that they likely lie within 1 nm of the air/water interface, but have kinetics and spectroscopy that are similar to that of the bulk. There also has been a fair amount of simulation work trying to rationalize all these experiments, but most such work has been MQC calculations that use cavity-forming potentials, or DFT-based calculations that have a challenging time accounting for the dispersion interactions that dominate the behavior of the eø at the interface and/or cluster surface.

With our quantum umbrella sampling in hand, we can now address the question of how hydrated eø's behave at interfaces. We have calculated potentials of mean force (PMFs) for both cavity and non-cavity eø's as a function of distance from the instantaneous air/water interface (instantaneous interfaces, which depend on the positions of all the water molecules, are critical for such calculations since the eø can perturb the interfacial structure in ways that are not captured by the Gibbs' dividing surface). Figure 2 shows the results. Both types of eø's have bulk-like behavior when only 1 nm from the interface, consistent with the SHG experiment mentioned above. Not surprisingly, the LGS electron, which has a strong entropic driving force to contain interior water, prefers not to reside at the interface where water molecules are scarce; we predict a single photoelectron peak corresponding to the bulk binding energy, consistent with the majority of the photoelectron experiments. The TB cavity electron, on the other hand, shows an accessible free energy minimum only 1 nm below the instantaneous interface. It makes sense that an object that strongly repels water prefers the lower-density interface. The properties of the TB eø at the interface are quite different from that in the bulk; we predict a ~1-eV lower binding energy, a red-shift of the spectrum, and solvation kinetics faster than those seen in the bulk, none of which are consistent with the majority of the photoelectron experiments or the SHG experiment.