Potential hydrogen approaching metal surface

Figure 5.22 Lennard-Jones potential of hydrogen approaching a metallic surface. Far from the metal surface the potential of a hydrogen molecule and oftwo hydrogen atoms is separated by the dissociation energy. The first attractive interaction ofthe hydrogen molecule is the van der Waals force leading to the physisorbed state. Closer to the surface the...

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

Figure 1.2 Potential energy curves for the approach of a hydrogen molecule and of two hydrogen atoms to a metal surface E is the activation energy — AH is the heat of adsorption subscripts p and c are, respectively, physical adsorption and chemisorption.

Consider first the behaviour of hydrogen approaching a nickel surface. This was modelled in Fig. 2.5 in connection with the description of the ability of a metal catalyst such as Ni to split the hydrogen molecule into two hydrogen atoms. This process was shown to take place about 0.1 nm outside the Ni surface. It is easy to extend the calculation to see what happens if the hydrogen atoms are allowed to penetrate into the Ni lattice, simply by using the same method to calculate potential energies for H positions below the top Ni layer. The result is shown in Fig. 2.60. 

A fundamental requirement on all of the computational studies on metal surface dynamics is fhe need fo perform simulafions with realistic potentials and in a feasible amounf of fime. To this end, the temperature-accelerated dynamics method [14,74,75] has arisen as a possible approach for reaching the latter limit. With the exception of quanfum simulations, most classical simulations are based on semiempirical potentials derived either from the embedded atom method or effective medium theory [76-78]. However a recent potential energy surface for hydrogen on Cu(l 10) based on density functional theory calculations produced qualitatively different results from those of the embedded atom method including predictions of differenf preferred binding sites [79]. 

Fig. 4.14 Schematic potential energy diagram for a hydrogen molecule approaching a metal surface. In this case the metal hydride formation is endothermic. See the text for details.

Fig. 4.18 Potential energy diagram for hydrogen approaching various metal surfaces as indicated. For further details please consult the text and the literature. Adapted from (Hammer and Norskov (1995), Ref [185]).

A third model (termed model IIP below) describes the metal surface as an external potential function [37], similar to the approach taken by Berkowitz in the case of the platinum surface [3, 4]. The external potential consists of a Morse function plus a corrugation term for oxygen-surface and a repulsive term for hydrogen-surface interactions ... 

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