First-Principles Simulation of the Active Sites and Reaction Environment in Electrocatalysis - Fuel Cell Catalysis: A Surface Science Approach - page 97

For the aqueous solvated systems discussed in this chapter, the vacuum layer between
slabs is filled with water molecules oriented in a hexagonal ice-like three-dimensional
hydrogen-bonded structure, graphically depicted in the schematic diagram in Fig. 4.2b.
The aqueous structures for each metal (111) surface are adapted from an original structure
determined by ab initio molecular dynamics simulations for eight layers of water over a
Pd(111) interface [Filhol and Neurock, 2006]. The water molecules closest to the metal
surface form a bilayer structure as a network of hexagonal rings that match the registry of
the metal surface, similar to experimental observations [Henderson, 2002; Michaelides
et al., 2003a]. In modeling a solvated adsorbate, one H 2 O molecule in the unit cell is
replaced by the adsorbate of interest, and the entire system (metal surface, adsorbate,
and water molecules) is re-optimized to account for variations in solvent - adsorbate
and solvent - solvent hydrogen bonding and changes in the electronic structure of the
metal surface. Electronic and geometric optimizations are held to the same convergence
standards as for vapor phase calculations.
4.3.3 Simulating the Electrochemical Interface
In an electrochemical system, the surface - adsorbate and surface - solvent interactions
are influenced by the resulting surface potential within the double-layer region. The
potential fat the interface induces a charge polarization in the metal (either negative
or positive, owing to an excess or deficit of electron density at the metal surface); the
magnitude of the excess charge depends on the difference between fand the potential
of zero charge f pzc of the metal. If fis more negative than f pzc , the excess surface
charge is negative. Ions, solute, and solvent molecules interact with the electron den-
sity and chemisorb or physisorb to the electrode surface. This adsorption occurs in the
inner layer region, as shown in Fig. 4.3. At the outer edge of the inner layer is the outer
Helmholtz plane (OHP), which is defined as the plane of closest approach of solvated
counter-ions with charge opposite to the excess surface charge. The sum of charge on
the counter-ions at the OHP is equal and opposite to the surface charge polarization,
generating a capacitor for which the potential drops approximately linearly, forming
an electric field with a typical magnitude of 10 8 V/ ˚ . The magnitude of the
field depends on f and the thickness of the inner layer, x il , which is governed by
the radii of the counter-ions, adsorbates, and solvent molecules (and is typically a
few ˚ ).
The ability to simulate actual electrochemical systems from first principles is
hindered by two predominant challenges. The first involves our inability to fully
capture the anode, cathode, and electron and proton transfer channels within a
single model system. The actual electrochemical system occurs at constant potential,
which is dictated by the chemistry that occurs at the anode and cathode. The anode and
cathode are connected electrically via macroscopic distances set by the conductor and
supporting electrolyte solution. Ab initio simulations of such macroscopic length
scales are currently not possible. The system, however, can be greatly simplified by
modeling the anode and cathode separately as artificially charged half-cells, which
is analogous to the electrode potential control set by a potentiostat in cyclic voltamme-
try experiments. The second major challenge involves maintaining a constant potential