DFT Calculations for Surfaces of Solids

Computational solid-state physics and chemistry are vibrant areas of research. The all-electron methods for high-accuracy electronic stnicture calculations mentioned in section B3.2.3.2 are in active development, and with PAW, an efficient new all-electron method has recently been introduced. Ever more powerfiil computers enable more detailed predictions on systems of increasing size. At the same time, new, more complex materials require methods that are able to describe their large unit cells and diverse atomic make-up. Here, the new orbital-free DFT method may lead the way. More powerful teclmiques are also necessary for the accurate treatment of surfaces and their interaction with atoms and, possibly complex, molecules. Combined with recent progress in embedding theory, these developments make possible increasingly sophisticated predictions of the quantum structural properties of solids and solid surfaces. 

The last decade has seen enormous developments in SS NMR, and techniques that were used only in soluhon have become available also for solid samples. Nowadays, even conformers can be identified by solid-state NMR [22]. Therefore, this section outlines these improvements as well as their application to the characterization of selected surface organometallic species. An application of EXAFS to the characterization of surface organometallic tantalum species is also shown. Structural data obtained through EXAFS (such as that in Table 11.1) are often essential for comparisons with data obtained by DFT calculations. 

You now have enough experience with DFT calculations to imagine how calculations could be performed that would be relevant for each of the three examples listed above. For instance, DFT calculations could be used to determine the relative energy of various kinds of lattice defects that could potentially exist in a solid material. Similar calculations could be used to determine the equilibrium positions of reactive molecules on the surfaces of ice crystals that could be thought of as mimics for polar stratospheric clouds. 

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

Figure 15 Potential energy curves for two H atoms over a graphite surface, for the case where the target atom is initially chemisorbed, and the carbon lattice is allowed to relax for each configuration of the H atoms. Cases (a) and (b) correspond to the collinear and quasi-collinear configurations. The potential energy is plotted as a function of the distance of the incident H above the surface, for three positions of the target H 1.49 A (solid line, filled circles), 1.69 A (dashed line, open diamonds), and 1.89 A (dotted line, filled squares). The symbols correspond to the DFT calculations, and the lines correspond to the model PES. Taken from Ref. [90],...

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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