Crystals gradient corrections

Both HF and DFT calculations can be performed. Supported DFT functionals include LDA, gradient-corrected, and hybrid functionals. Spin-restricted, unrestricted, and restricted open-shell calculations can be performed. The basis functions used by Crystal are Bloch functions formed from GTO atomic basis functions. Both all-electron and core potential basis sets can be used. 

The theoretical basis of CASTEP is the density functional theory (DFT) in the local density approximation (LDA) or gradient-corrected LDA version, as developed by Perdew and Wang (GGA).6-7 The DFT description of electron gas interactions is known to be sufficiently accurate in most cases, and it remains the only practical way of analyzing periodic systems. LDA is known to underestimate bond lengths in molecules and cell parameters in crystals, while GGA is typically more accurate to these optimized geometries. In the present calculations, we selected GGA, which is the default setting in CASTEP. 

DFT-PW calculations [91] were performed on a SiC crystal for different SP meshes to investigate which one corresponds to the best convergence of the results for the total energy per unit cell. The experimental value a = 4.35 A was taken for the fee lattice constant of SiC, the electron-ion interaction was described by ultrasoft, Vandebildt-type pseudopotentials [93], the cutoff energy for the plane-wave basis set was taken to be 1000 eV. The generalized gradient corrections (GGA) DPT method was used (see Chap. 7). 

Fig. 15. (a) Intramolecular hydrogen bonds in urea crystal with displacement ellipsoids at 50% probability, (b) Static deformation density obtained from the multipolar analysis of the experimental data corrected for the thermal diffuse scattering. Theoretical deformation density obtained using (c) the Hartree-Fock method (d) the DFT method by generalized gradient approximation (contours at 0.0675 eA-3) (reproduced with permission from Zavodnik et al. [69]). 

Detailed analysis of the electric field gradient tensors has shown that both sites in both oxides have the principal value directed along the crystal fi axis, correcting several earlier studies on these materials [160]. 

Naturally, the flux to be used depends upon the crystal to be grown. Many times, it is a matter of trial and error to establish the proper flux needed. The two most important parameters are the degree of supercooling and the temperature gradient achieved. If these are not within the correct range, one does not obtain single crystal growth. This method has been used in the past only because of its relative simplicity of apparatus and materials. However, the quality of crystals so-produced has been rather poor. Crystals produced by this method are suitable for structure determinations, but are poor in optical quality and are not suited for electronic applications. 

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