Point 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 groups Gd of a supercell model with one point defect for a superceU are sym-morphic, they belong to the crystal class Fd = Sd with all the types of crystal lattices possible for this crystal class. The point sjonmetry of the cycUc-cluster coincides for the host crystal - with the point-symmetry group F, for the defective crystal - with the point-symmetry group Sd-... 

Nevertheless, the calculation [683] demonstrates (1) the efficiency of the more detailed symmetry analysis for the supercell choice when the periodic defect calculations are made in the complicated crystaUine structures with the symmetry of a nonsym-morphic space group and noncubic lattice (2) the reality of the supercell model for the nonempirical LCAO calculations of the point defects in such a complicated crystalline structure as a rutile structure 3) higher efficiency of LCAO basis compared with LAPW basis in the snpercecell calculations of defective crystals. Moreover, the supercell model allows the dependence of the electronic properties of doped crys-... 

The Green-function method appeared to be very useful for displaying the chemical trends in defect energy levels [727,728]. However, the calculation of other defective-crystal properties (defect-formation energy, lattice relaxation, local-states localization) requires approaches based on molecular cluster or supercell models. Only recently have these models been used in the first-principles calculations to study point defects in SrTiOs. 

Section 4.5 Surface relaxations were examined using asymmetric slab models of five, six, seven, or eight layers with the atoms in the two bottom layers fixed at bulk positions and all remaining atoms allowed to relax. For Cu(100), the supercell had c(2 x 2) surface symmetry, containing 2 atoms per layer. For Cu(l 11), (y/3 X /3)R30 surface unit cell with 3 atoms per layer was used. All slab models included a minimum of 23 A of vacuum along the direction of the surface normal. A 6x6x1 /c-point mesh was used for all calculations. 

The 3D-RISM-MCSCF approach has been applied to carbon monoxide (CO) solute in ambient water [33]. Since it is known that the Hartree-Fock method predicts the electronic structure of CO in wrong character [167], the CASSCF method (2 core, 8 active orbitals, 10 electrons) in the basis sets of double zeta plus polarization (9s5pld/4s2pld) augmented with diffuse functions (s- and p-orbitals) was used. Water was described by the SPC/F model [127] and the site-centered local pseudopotential elaborated by Price and Halley for CP simulation [40]. The 3D-RISM/KH integral equations for the water distributions specified on a grid of 64 points in a cubic supercell of size 20 A were solved at each step of the SCF loop by using the method of modified direct inversion in the iterative subspace (MDIIS) [27, 29] (see Appendix). 

The model. Many different models can be proposed for the simulation of a single physical or chemical phenomenon. For example, a point defect in a crystalline system can be simulated either with a finite cluster with a defect at the center of the cluster and by assuming that the cluster is big enough and border effects are small, or with a periodic supercell approach, with the defects repeated periodically in such a way that the defect-defect interaction is small, if the supercell is big enough. 

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