Basis Sets in the Electron-structure Calculations of Crystals

Basis Sets in the Electron-structure Calculations of Crystals... 

Thus, to the best of our knowledge, there is a lack of embedding cluster studies on the yttrium ceramics where with a sufficient precision both aspects of the ECM were taken in account. In the study [44], we attempted to fill such a gap and carried out the electronic structure calculations of the YBa2Cu307 ceramics at the Moller-Plesset level with a self-consistent account of the infinite crystal surrounding to the quantum cluster. The Gaussian basis set employed (6-31IG) was larger than those used in previous cluster calculations [16,20,22,29]. 

The choice of the basis set is of particular importance when treating periodic systems where a large variety of chemical bonding can be found. The following three approaches to the basis-set choice define three types of methods of the electronic-structure calculations in crystals [10] atomic-sphere (AS) methods, plane-wave (PW) methods, localized atomic-like orbitals (LCAO) methods. Each method has its advantages and disadvantages. 

The electronic structures of poiy(fluoroacetylene) and poly(difluoroacetylene) have been investigated previously using the ab initio Hartree-Fock crystal orbital method with a minimum basis set (42). Only the cis and trans isomers with assumed, planar geometries were studied. The trans isomer was calculated to be more stable in both cases, and the trans compounds were predicted to be better intrinsic semiconductors and more conductive upon reductive doping than trans polyacetylene. However, our results show that head-to-tail poly(fluoroacetylene) prefers the cis structure and that the trans structure for poly(difluoroacetylene) will not be stable. Thus the conclusions reached previously need to be re-evaluated based on our new structural information. Furthermore, as noted above, addition of electrons to these polymers may lead to structural deformations that could significantly change the conductive nature of the materials. 

Let us now find out whether these classical enthalpies may be reproduced by electronic-structure calculations (VASP) on Sn/Zn supercells using ultra-soft pseudopotentials, plane-wave basis sets and the GGA. We therefore have to theoretically determine the total energies of all crystal structure types under consideration (a-Sn, j6-Sn, Zn) as a function of the composition SnxZni x by a variation of the available atomic sites in terms of Sn and Zn occupation, just as for the preceding oxynitrides (CoOi- N ). In the present case, supercells with a total of 16 atoms were generated, and nine different compositions per structure were numerically evaluated. Because this amounts to a significant computational task, the use of pseudopotentials is mandatory, and this also allows the rapid calculation of interatomic forces and stresses for structural... 

Based on the same underlying principles as the molecular-based quantum methods, solid state quantum mechanics represents bulk material using periodic boundary conditions. The imposition of these boundary conditions means that it becomes possible to expand the electron density in periodic functions such as plane waves, as an alternative to the atom-based functions used in the molecular case. The efficiency of the calculations is enhanced by the use of pseudo-potentials to represent the core electrons and to make the electron density as smooth as possible near the nucleus, hence reducing the complexity of the plane wave expansion of the electron density. Because of the number of choices available for pseudo potentials, basis sets and whether calculations are done in real or reciprocal space, there are many choices of software for performing solid state quantum mechanical calculations. A few examples which have been used in crystal structure prediction include the Vienna ab initio Simulation Package (VASP), CASTEP and CRYSTAL. " A wider ranging introduction to the area can be found in the references. ... 

The electronic structure for the MgO crystal was calculated in [608] both in the LCAO approximation and in the PW basis. In both cases the calculations were done by the density-functional theory (DFT) method in the local density approximation (LD A). The Monkhorst Pack set of special points of BZ, which allows a convergence to be obtained (relating to extended special-points sets) in the calculations of electronic structure, was used in both cases. For the LCAO calculations the Durand Barthelat pseudopotential [484] was used. In the case of the PW calculations the normconserving pseudopotential and a PW kinetic energy cutoff of 300 eV were used. 

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