Pseudopotential, soft

Vanderbilt D 1990 Soft self-consistent pseudopotentials in a generalized eigenvalue formalism Phys. Rev. B 41 7892-5... 

Ultrasoft pseudopotentials have now been constructed for all elements for all elements from H to Bi [10]. It has been shown that without any loss of accuracy even for first-row and transition-elements small PW basis-sets comparable in size to those necessai y for soft normconserving pseudopotentials for A1 or Si can be used. For any further details, see [9,. 37]. 

In a second approach of the reactivity, one fragment A is represented by its electronic density and the other, B, by some reactivity probe of A. In the usual approach, which permits to define chemical hardness, softness, Fukui functions, etc., the probe is simply a change in the total number of electrons of A. [5,6,8] More realistic probes are an electrostatic potential cf>, a pseudopotential (as in Equation 24.102), or an electric field E. For instance, let us consider a homogeneous electric field E applied to a fragment A. How does this field modify the intermolecular forces in A Again, the Hellman-Feynman theorem [22,23] tells us that for an instantaneous nuclear configuration, the force on each atom changes by... 

The interaction between ions and valence electrons is described in a standard manner by pseudopotentials. Sodium clusters allow to use local pseudopotentials. We employ here a soft shape in terms of error functions... 

A theoretical analysis based on ab-initio molecular dynamics has been reported [10], The study employed a plane wave basis, and soft core, norm conserving pseudopotentials were used to describe the ions. The supercells consisted of 10 - 12 layers of AIN with 4-16 atoms in each layer. For most calculations, a 12 A vacuum region separated the surfaces. One side of each slab was terminated by hydrogen atoms to reduce charge transfer caused by the finite width of the slab. The electron affinities of different surface configurations of AIN are listed in TABLE 1, where prior results for the diamond (111) surface are also listed. 

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-... 

For ice X and the (fee) antifluorite structure the quantification of various aspects of their structural and chemical character and their dependence with pressure was found using AIM in a novel approach. Metallic character was found to be present in the antifluorite structure, but did not persist with increased pressure since the BCPs then fell within the pseudopotential core radii. In future studies on the antifluorite structure it will be necessary to replace the core with the true all electron distribution. In addition we present a hypothesis for the physical meaning of the O—O bonding interactions, namely that they indicate the onset of, soft phonon modes that are known to accompany structural changes. The fact that there are no O—O interactions in the antifluorite structure is consistent with this hypothesis, since to date there aren t any higher pressure phases of ice than antifluorite ice and so no pressure induced phase change can occur in this structure. Thus our hypothesis would explain why there are no O—O interactions in the antifluorite structure. 

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. 

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