Non-Linear Core Correction

TABLE 1 Some details of first principles calculations of impurities in Ill-nitrides. Columns list the treatment of the 3d shell if specified (nice = non-linear core correction), size and symmetry (c = cubic, w = wurtzite) of the super cell and the points considered in the irreducible wedge of the Brillouin zone (BZ). 

What remedies do we have The brute-force device tried in pioneer days, of incorporating core- and core-valence correlation effects into pseudopotentials just by fitting to experimental reference data containing these effects, does not work since the one-electron/one-center PP ansatz is insufficient for this purpose, cf. below. Certainly more reliable is a DFT description of core contributions to correlation effects which is possible with (and actually implied in) the non-linear core corrections discussed in Section 1.4. Another device, which has shown excellent performance in the context of quantum-chemical ab initio calculations180 and has later been adapted to PP work cf. e.g. refs. 139, 181-184), is that of core-polarization potentials (CPP)... 

Indeed this has been recognized for quite some time. For example, Izquierdo et al. point out that Fe dimer is not properly described if the pseudopotential is constructed from the atomic ground state configuration, 3d 4s Instead they use the more appropriate 3d 4s It is also well known that non-linear core corrections [Louie SG, Froyen S, Cohen ML (1982) Phys Rev B 26 1738] are instrumental to recover the right magnetic momentum even in many bulk systems... 

We have constructed the non-local pseudopotential of iron from the atomic configuration [Ar]3d 4s and of silver from [Kr]4d °5s In both cases we have used the GGA approximation and non linear core corrections. Two different sets of basis have been used single-Z-simple polarized (SZSP) and double-Z-simple-polarized (DZSP), with a single polarizing p-orbital in both cases. The cutoff radii for the pseudoorbitals have been fitted to assure the minimization in energy for the bcc Fe bulk and for the fee Ag bulk. 

However, the Df — 2 random walk fails in one important respect to produce a correct model of the coil formed by a linear polymer soaking in a good solvent (see Chap. 7 on polymers) there is nothing to stop the walker from coming back through a previously visited site. In a non-crosslinked molecule whose constituent monomers repel each other by hard core interactions, this would clearly be impossible. The structure of such a molecule could only be correctly described by a self-avoiding random walk, rather than the simple... 

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