Density functional theory surface diffusion

Watson GW, Wells RPK, Willock DJ, Hutchings GJ. 2001. A comparison of the adsorption and diffusion of hydrogen on the 111 surfaces of Ni, Pd, and Pt from density functional theory calculations. J Phys Chem B 105 4889-4894. 

Molecular-level studies of mechanisms of proton and water transport in PEMs require quantum mechanical calculations these mechanisms determine the conductance of water-filled nanosized pathways in PEMs. Also at molecular to nanoscopic scale, elementary steps of molecular adsorption, surface diffusion, charge transfer, recombination, and desorption proceed on the surfaces of nanoscale catalyst particles these fundamental processes control the electrocatalytic activity of the accessible catalyst surface. Studies of stable conformations of supported nanoparticles as well as of the processes on their surface require density functional theory (DFT) calculations, molecular... 

Figure 6 Singly occupied molecular orbital (SOMO) of a propeller-like trimer radical anion of acetonitrile obtained using density functional theory. The structure was immersed in a polarizable dielectric continuum with the properties of liquid acetonitrile. Several surfaces (on the right) and midplane cuts (on the left) are shown. The SOMO has a diffuse halo that envelops the whole cluster within this halo, there is a more compact kernel that has nodes at the cavity center and on the molecules.

The NEB method has been applied successfiilly to a wide range of problems, for example studies of diffusion processes at metal surfaces,28 multiple atom exchange processes observed in sputter deposition simulations,29 dissociative adsorption of a molecule on a surface,25 diffusion of rigid water molecules on an ice Ih surface,30 contact formation between metal tip and a surface,31 cross-slip of screw dislocations in a metal (a simulation requiring over 100,000 atoms in the system, and a total of over 2,000,000 atoms in the MEP calculation),32 and diffusion processes at and near semiconductor surfaces (using a plane wave based Density Functional Theory method to calculate the atomic forces).33 In the last two applications the calculation was carried out on a cluster of workstations with the force on each image calculated on a separate node. 

The model (2)-(4) is referred to as the quenched solid non-local density functional theory (QSNLDFT). There are several advantages in considering the solid as a quenched component of the system rather than a source of the external field. On the one hand, this approach offers flexibility in the description of the fluid-solid boundary by varying the solid density and the thickness of the diffuse solid surface layer. On the other hand, it retains the main advantage of NLDFT computational efficiency because even a one-dimensional solid density distribution ceui include the effects of surface roughness and heterogeneity. For example, the solid density distribution can be taken from simulations of amorphous silica surfaces [29,30]. 

Therefore, when equilibrium cannot be plausibly assumed, apparent kinetic parameters (effective rate constants) must be used to express the reaction rate. The parameters that describe the electrochemical reaction rate include the above-mentioned exchange current density, the transfer coefficient, the activation enthalpy, and the pre-exponential factor as well as the reaction order of the species involved. These parameters are not necessarily related to a single rate-determining step, as is often assumed in electrochemical theory. By investigating i-ri curves as functions of electrode potential, temperature, and concentration of the reacting species, insight may be gained into the reaction mechanism and microscopic transport processes (such as surface diffusion) that... 

The charge density on the electrode a(m) is mostly found from Eq. (4.2.24) or (4.2.26) or measured directly (see Section 4.4). The differential capacity of the compact layer Cc can be calculated from Eq. (4.3.1) for known values of C and Cd. It follows from experiments that the quantity Cc for surface inactive electrolytes is a function of the potential applied to the electrode, but is not a function of the concentration of the electrolyte. Thus, if the value of Cc is known for a single concentration, it can be used to calculate the total differential capacity C at an arbitrary concentration of the surface-inactive electrolyte and the calculated values can be compared with experiment. This comparison is a test of the validity of the diffuse layer theory. Figure 4.5 provides examples of theoretical and experimental capacity curves for the non-adsorbing electrolyte NaF. Even at a concentration of 0.916 mol dm-3, the Cd value is not sufficient to permit us to set C Cc. 

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