Models for excess electrons attached to water clusters

Cluster anions can be divided into (A) clusters of neutrals and anions and (B) clusters of neutrals and electrons, i.e., the extra electron is not attached to a specific (monomer) unit, but is bound in a collective manner. A prominent example of the latter class are water cluster anions. Owing to the distributed character of the excess electron, electron correlation is of far greater importance in class (B) clusters, for example, in small water clusters about 40% of the total electron binding energy stems from electron correlation (c.f. Dipole-bound anions ). Thus, from an electronic structure viewpoint class (B) clusters represent by far the greater challenge, and even moderate quality ab initio calculations are very expensive. The underlying idea of modeling these species is that the crucial correlation is that between the "excess" electron and the "monomer-attached" electrons, whereas the monomer-monomer interaction can be treated with a fairly standard force field.

Here are examples of three different binding motifs of the 28-mer water cluster anion:
Dipole-bound state Cavity state Network permeating state
The electron is essentially bound by the dipole moment of the neutral framework, and is localized on the surface. (The picture shows iso-contours enclosing 40% and 90% of the excess electron's density.) Despite the dominating electrostatic effects, electron correlation contributes typically 20-50% of the electron binding energy of dipole-bound states.

Dipole-bound surface states are clearly the most stable (lowest-energy) binding motifs for water clusters of up to 30 monomers and probably also for much larger clusters.

The electron occupies a void or cavity in the hydrogen bounding network (the 90% iso-contour is shown), with several monomers sticking an OH bond into the cavity (here six). For this motif both electrostatic effects and correlation effects are essential. Electrostatic effects due to the OH groups pointed into the cavity, correlation effects, since electrostatics alone is insufficient to create a bound state within the cavity.

Cavity states are models for the hydrated electron, but for clusters consisting of up to 30 monomers they are high-energy isomers (almost an eV above the global minimum of the anions), and consequently highly unlikely to be present in any cluster experiment.

There is no void in the hydrogen bonding network, and the electron is mostly (~60%) localized outside the cluster (90% and 40% iso-contours are shown). Note that the maxima of the excess electron distribution occur inside the cells of the hydrogen bonding network. This binding motif represents a correlation bound state; electrostatic effects play virtually no role in the binding.

Network permeating states have small electron detachment energies, but most neutral clusters have neither cavities nor large dipoles. These states may thus play a role in electron capture of neutral clusters.

A few more details for the adepts: In our models the energy of a water cluster anion E is computed as a sum of the energy of the neutral framework Entrl and the electron binding energy Ebdg. The first term, Entrl, is computed using a classical force field. Standard force fields such as SPC or TIPnP do not do a good job here, since these force fields have been fit to neutral structures or bulk properties, but the anions have structures very different from neutral water clusters. We use the new DPP force field specifically developed to describe both the structure of neutral and anion clusters. The second term,Ebdg, is computed from a model Hamiltonian for the excess electron. This Hamiltonian contains the electrostatic potential, a repulsive term (similar to an ECP), and a term describing polarization and dispersion interaction with the valence electrons. To model the last contribution we use either a quantum Drude oscillator on each water monomer leading to a one-electron many-body Hamiltonian, or we treat the Drude oscillators adiabatically (fixed electron approximation) leading to a local polarization potential in the excess electron Hamiltonian.

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