Soft pseudopotentials

Each pseudopotential is defined within a cut-off radius from the atom center. At the cut-off, the potential and wavefunctions of the core region must join smoothly to the all-electron-like valence states. Early functional forms for pseudopotentials also enforced the norm-conserving condition so that the integral of the charge density below the cut-off equals that of the aU-electron calculation [42, 43]. However, smoother, and so computationally cheaper, functions can be defined if this condition is relaxed. This idea leads to the so called soft and ultra-soft pseudopotentials defined by Vanderbilt [44] and others. The Unk between the pseudo and real potentials was formaUzed more clearly by Blochl [45] and the resulting... 

Much effort has been put to improve the pseudopotentials. [71,72] The most successful pseudopotential model is the so called ultra-soft pseudopotentials, proposed by Vanderbilt. [73] The model allows one to work with optimally smooth pseudopotentials. Thus the number of plane waves needed to express the pseudo-wavefunctions can be greatly reduced. In the model, pseudo-wavefunctions ipiif match the true orbitals outside a given core radius re, within Tc, are al-... 

The relatively few QM studies of these materials reflect both the structural complexity (including low symmetry) and also the strong scattering associated with the oxygen potential, which makes the generation of reliable and efficient pseudopotentials for PW-LDA calculations difficult. There has been a concerted effort to solve this problem over the last few years which has yielded a new family of ultra-soft pseudopotentials with which oxygen has been described with plane wave cut-offs as low as 500 eV (Vanderbilt, 1990). In the all electron LCAO-HF method the major approximation is associated with the choice of basis set. This has been studied in some detail and reliable basis sets developed (Nada et al., 1990). In the absence of analytic forces, the use of this method to optimize fully the geometry of such complex structures is rare. 

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... 

There are extensive pseudopotential libraries available for download with the simulation packages CPMD (Parrinello et al. 2008), CP2K (Hutter et al. 2009) or online (Vanderbilt Ultra-Soft Pseudopotential Site 2006). However, before applying any pseudopotentials, they should always be tested against all-electron calculations. Pseudopotentials used in conjimction with a particular density functional should have been generated using the same functional. 

In many cases, the required pseudopotential will not be available in any accessible hbrary in this case it may be generated using freely downloadable programs (Vanderbilt Ultra-Soft Pseudopotential Site 2006). 

Vanderbilt Ultra-Soft Pseudopotential Site. (2006). http //www.physics.rutgers.edu/ dhv/uspp/. Accessed 02 July 2011. 

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