Density functional theory adsorption energy

Figure 6.35. Potential energy diagrams for adsorption and dissociation of N2on a Ru(0001) surface and on the same surface with a monoatomic step, as calculated with a density functional theory procedure. [Adapted from S. Dahl, A. Logadottir, R. Egberg, J. Larsen, I. Chorkendorff,...

While in previous ab initio smdies the reconstructed surface was mostly simulated as Au(lll), Feng et al. [2005] have recently performed periodic density functional theory (DFT) calculations on a realistic system in which they used a (5 x 1) unit cell and added an additional atom to the first surface layer. In their calculations, the electrode potential was included by charging the slab and placing a reference electrode (with the counter charge) in the middle of the vacuum region. From the surface free energy curves, which were evaluated on the basis of experimentally measured capacities, they concluded that there is no necessity for specific ion adsorption [Bohnen and Kolb, 1998] and that the positive surface charge alone would be sufficient to lift the reconstmction. 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

Using perturbation theory. Hammer and Nprskov developed a model for predicting molecular adsorption trends on the surfaces of transition metals (HN model). They used density functional theory (DFT) to show that molecular chemisorption energies could be predicted solely by considering interactions of a molecule s HOMO and LUMO with the center of the total d-band density of states (DOS) of the metal.In particular. 

A database of molecularly adsorbed species on various surfaces is also included (see Table 4.3). In all cases, the chemisorption energies have been calculated on stepped surfaces using density functional theory (see [56] for details). The metals have been modeled by slabs with at least three close-packed layers. The bcc metals are modeled by the bcc(210) surface and the fee and hep metals have been modeled by the fcc(211) surface. A small discrepancy between the adsorption on the hep metals in the fcc(211) structure is thus expected when the results are compared to the adsorption energies on the correct stepped hep structure instead. When mixing... 

As expected, the total interaction energies depend strongly on the van der Waals radii (of both sorbate and sorbent atoms) and the surface densities. This is true for both HK type models (Saito and Foley, 1991 Cheng and Yang, 1994) and more detailed statistical thermodynamics (or molecular simulation) approaches (such as Monte Carlo and density functional theory). Knowing the interaction potential, molecular simulation techniques enable the calculation of adsorption isotherms (see, for example, Razmus and Hall, (1991) and Cracknell etal. (1995)). 

In this chapter, we attempt to address these fundamental questions by performing extensive molecular dynamics simulations. In previous publications,15,16 we have demonstrated using ab initio molecular dynamics based on local density functional theory that H2 adsorption energies in a lattice of (9,9) armchair SWNT at a variety of temperatures with 0.4 wt. % hydrogen loading are significantly higher than in... 

An alternative approach is by the application of an approximate theory. At present, the most useful theoretical treatment for the estimation of the equilibrium properties is generally considered to be the density functional theory (DFT). This involves the derivation of the density profile, p(r), of the inhomogeneous fluid at a solid surface or within a given set of pores. Once p(r) is known, the adsorption isotherm and other thermodynamic properties, such as the energy of adsorption, can be calculated. The advantage of DFT is its speed and relative ease of calculation, but there is a risk of oversimplification through the introduction of approximate forms of the required functionals (Gubbins, 1997). 

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