Solid supercell model

We use a periodic supercell model based on the large unit cell (LUC) method [22] which is free from the limitations of different cluster models applicable mainly to ionic solids, e.g., alkali halides. The main computational equations for calculating the total energy of the crystal within the framework of the LUC have been given in Refs. [22-24]. Here, we shall outline some key elements of the method. The basic idea of the LUC is in computing the electronic structure of the unit cell extended in a special manner at k = 0 in the reduced Brillouin zone (BZ), which is equivalent to a band structure calculation at those BZ k points, which transform to the reduced BZ center on extending the unit cell [22]. The total energy of the crystal is... 

The third type of method is the multiconflgurational supercell approach, which is the focus of the present chapter. Within this approach, an infinite site-disordered solid is modeled with a set of... 

We conclude this chapter by discussion of the superceU use for the solid-solution modeling. In this case the supercells of different size allow different percentages of doping in solid solution to be modeled. 

The converged FES at T = I m of a (7 x 7 x 12)-supercell model containing 2352 atoms is shown in Fig. 3.4. The two basins associated with the bulk solid and bulk liquid phases have equal minima, as is expected to occur at Tm- In contrast, the... 

So far, most of the quantum-chemical computations of solid compounds have assumed a free molecular model that is the intermolecular effects are initially not considered. Although these second-order effects are minor in many cases and do not cause much disagreement with solid-state NMR measurements, they might become significant and should not be neglected. Recently a series of publications has addressed this problem, based on a supercell technique.38-41 The appealing feature of this new method is that it can deal not only with free molecules but also with crystals, amorphous materials or materials with defects. 

The theoretical chemistry community developed density functional theory for finite molecular systems which involve molecules and cluster models that describe the catalytic systems. They use the same constructs used in many ab initio wavefunction methods, i.e. Gaussian or Slater basis sets. The solid-state physics community, on the other hand, developed density functional theory to describe bulk solid-state systems and infinite surfaces by using a supercell approach along with periodic basis functions, i.e. plane waves . Nearly all of our discussion has focused on finite molecular systems. In the next section we will describe in more detail infinite periodic systems. 

Periodic DFT codes define a system within a supercell of a particular shape and size that is repeated infinitely in all three dimensions. It is standard practice in simulations of gas solid interfaces to define a layer, or slab, of atoms and a layer of vacuum within the periodically replicated supercell, such that the physical model is of alternating layers of solid and vacuum. By tuning the thickness of the vacuum, the solid slabs can be separated to the point where... 

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