Pseudopotentials atomic, generation

Table 2 shows that in the case of ratile the GGA overestimation of lattice constants is less important in the present calculation than in Ref. 3. Most likely explanation is that the GGA functional is used here only for solid state calculations and not for the pseudopotential generation from the free atom. This procedure has been shown to give more accurate structural results than with the GGA applied both in the potential generation and solid state... 

All calculations presented here are based on density-functional theory [37] (DFT) within the LDA and LSD approximations. The Kohn-Sham orbitals [38] are expanded in a plane wave (PW) basis set, with a kinetic energy cutoff of 70 Ry. The Ceperley-Alder expression for correlation and gradient corrections of the Becke-Perdew type are used [39]. We employ ah initio pseudopotentials, generated by use of the Troullier-Martins scheme [40], The coreradii used, in au, were 1.23 for the s, p atomic orbitals of carbon, 1.12 for s, p of N, 0.5 for the s of H, and 1.9, 2.0, 1.5, 1.97,... 

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... 

Several simple schemes have been formulated to extract ab initio ionic pseudopotentials from atomic calculations. The basic procedure is to generate a potential by inversion of the Kohn-Sham equation. Angular-momentum-dependent screened atomic pseudopotentials, V, are first constructed with the constraints that (1) the valence eigenvalues from the all-electron calculation... 

The crystal orbitals were calculated by the DFT method in the plane-wave basis set with the CASTEP code [377] in the GGA density functional. A set of special points k in the Brillouin zone for all the crystals was generated by the snperceU method (see Chap. 3) with a 5 x 5 x 5 diagonal symmetric extension, which corresponds to 125 points. In all cases, the pseudopotentials were represented by the normconserving optimized atomic pseudopotentials [621], which were also used to calculate the atomic potentials of free atoms. In the framework of both techniques (A, B), the population analysis was performed in the minimal atomic basis set i.e. the basis set involved only occupied or partially occupied atomic orbitals of free atoms. It is well known that the inclusion of diffuse vacant atomic orbitals in the basis set can substantially change the results of the population analysis. For example, if the Mg 2p vacant atomic orbitals are included in the basis set, the charge calculated by technique A for the Mg... 

Copper atoms are modeled using argon core Troullier-Martins pseudopotentials generated using the utility provided by FHI Berlin [46]. 

A further simplication often used in density-functional calculations is the use of pseudopotentials. Most properties of molecules and solids are indeed determined by the valence electrons, i.e., those electrons in outer shells that take part in the bonding between atoms. The core electrons can be removed from the problem by representing the ionic core (i.e., nucleus plus inner shells of electrons) by a pseudopotential. State-of-the-art calculations employ nonlocal, norm-conserving pseudopotentials that are generated from atomic calculations and do not contain any fitting to experiment (Hamann et al., 1979). Such calculations can therefore be called ab initio, or first-principles. ... 

In the present calculation, we used two ab initio methods to investigate structural stability and the potential for carrier generation of X B6 and X Bi2 clusters in c-Si. Here X is from H to Br in the periodic table. The following two methodsused were (i) plane wave ultrasoft pseudopotential method for the optimization of atomic structures and (ii) discrete variational-Xa (DV-Xa) molecular orbital method for the analysis of the fine electronic structures and activation energies of the clusters. 

The concept of atomic or ionic size is one that has been debated for many years. The structure map of Figure 1 used the crystal radii of Shannon and Prewitt and these are generally used today in place of Pauling s radii. Shannon and Prewitt s values come from examination of a large database of interatomic distances, assuming that intemuclear separations are given simply by the sum of anion and cation radii. Whereas this is reasonably frue for oxides and fluorides, it is much more difficult to generate a self-consistent set of radii for sulfides, for example. A set of radii independent of experimental input would be better. The pseudopotential radius is one such estimate of atomic or orbital size. 

Within the density functional theory (DFT), several schemes for generation of pseudopotentials were developed. Some of them construct pseudopotentials for pseudoorbitals derived from atomic calculations [29] - [31], while the others make use [32] - [36] of parameterized analytical pseudopotentials. In a specific implementation of the numerical integration for solving the DFT one-electron equations, named Discrete-Variational Method (DVM) [37]- [41], one does not need to fit pseudoorbitals or pseudopotentials by any analytical functions, because the matrix elements of an effective Hamiltonian can be computed directly with either analytical or numerical basis set (or a mixed one). 

Tests for non-hydrogenic systems are needed to find the performance of the method on a broader spectrum of applications. The use of pseudopotentials within QMC to treat atoms with inner core is well tested [6]. What is not clear is how much time will be needed to generate trial functions, and to reduce the noise level to acceptable limits. Clearly, further work is needed to allow this next step in the development of microscopic simulation algorithms. 

The way i>f p is generated from the atomic calculation is not unique. Common pseudopotentials are generated following the prescription of, e.g., Bachelet, Hamann and Schlriter [82], Kleinman and Bylander [83], Vanderbilt [84] or Troullier and Martins [85]. Useful reviews are Refs. [86, 87, 88]. The pseudopotential approach is very convenient because it reduces the number of electrons treated explicitly, making it possible to perform density-functional calculations on systems with tens of thousands of electrons. Moreover, the pseudopotentials upp are much smoother than the bare nuclear potentials vext. The remaining valence electrons are thus well described by plane-wave basis sets. 

A remark should be made here with respect to the generation and adjustment of the widely used effective core potentials (ECP, or pseudopotentials) [85] in standard non-relativistic quantum chemical calculations for atoms and molecules. The ECP, which is an effective one-electron operator, allows one to avoid the explicit treatment of the atomic cores (valence-only calculations) and, more important in the present context, to include easily the major scalar relativistic effects in a formally non-relativistic approach. In general, the parameters entering the expression for the ECP are adjusted to data obtained from numerical atomic reference calculations. For heavy and superheavy elements, these reference calculations should be performed not with the PNC, but with a finite nucleus model instead [86]. The reader is referred to e.g. [87-89], where the two-parameter Fermi-type model was used in the adjustment of energy-conserving pseudopotentials. 

The results of this procedure for alkaline and alkaline-earth systems were quite good [186,187], at least for atoms, and pseudopotentials of this type were generated [188] and applied [189] for most of the main group elements. However, due to the limited validity of the frozen-core approximation when going from a medium or highly charged one-valence electron ion to a neutral atom or nearly neutral ion, the approach is bound to fail for most other elements. This is especially the case for transition metals, lanthanides and actinides, where small cores are indispensable for accurate pseudopotentials. More recent calibration studies of alkaline and alkaline earth elements exhibited however, that for accu-... 

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