Electronic Structure of Transition Metals. I. Quantum Defects and Model Potential

Abstract

Recent applications of the concept of quantum defects in setting up model pseudopotentials for simple or transition-metal ions presuppose that the atomic-spectroscopy data of such metals can be expressed in terms of certain quantum defects. Experience indicates, however, that the old quantum-defect idea applies only to group I and II metals at best, but not to metals of higher chemical valence (z & 3, z being the nominal valence given by the group number, IA or B, IIA or B, etc. in the Periodic Table). In this paper, a generalized quantum-defect law applicable to elements having z & 2 is deduced empirically from an extensive study of the spectroscopic data of the first six rows of the Periodic Table. The empirical law states that the energy levels F. "I of a single electron in the field of the positive ions of elements having the same inert-gas core, e.g. , the elements of the isoelectric sequence, Li+, Be'+,~" , F'+, which are given (in the Heine-Abarenkov model-potential method) by the spectroscopic term value of the ion plus one electron, i.e. , by the term values of Li, Be+,~~~,F +, by the term values of Li, Be', ', F ', obey the relation E", =-z /(n -5", ) +6", , z -2, for the same quantum defects (5 "6, ). The old quantum defect (5,) and the new quantum defect (6,, equivalent to an "atomic core shift") thus represent the deviation of the atomic potential of a given inert-gas configuration from a Coulombic potential due to a nuclear charge z[e~. On the basis of this empirical law, the parameters of a transition-metal model potential of the Heine-Abarenkov type, adjusted to the energies'", : -E", -0"" have been calculated for all 30 group-B (excepting rare-earth) metals of the Periodic Table; and it has been found that the 1 = 2 model potential parameter A reflects the Ziman-Heine-Hubbard resonance model of s-d hybridization through its strong energy dependence of the form ($-b ") ' for the 3d series, and similarly for the 4d and 5d series. The application of the new model potential to the calculation of the various aspects of the electronic structure of solids will be presented in the next and subsequent papers of this series.

Modeling of the atomic ordering processes in Fe3Al intermetallics by the monte carlo simulation method combined with electronic theory of alloys

“…The problem is attributed to the fact that the form factor of the pseudopotential for transition metals must contain terms responsible for the d-resonance effect. Nevertheless, there is only one model pseudopotential for transition metals proposed by Animalu, [54,55] in which the d-resonance effect is partly taken into account and form factors have been found for a large number of elements. However, calculation of partial ordering energies involves only nondiagonal matrix elements, and it was also shown by Animalu that for such calculations the contribution of the d-resonance effect is relatively small.…”

“…[8,[39][40][41]50,51] Although, Eqs. [2] and [3] can be used without any problem for simple metal alloys, the effects of d-resonance, [54,55,[59][60][61][62][63] self-consistency, [64][65][66][67][68][69] covalency, [68,69] higher-order terms of the perturbation theory, [70,71] and structural relaxations due to the atomic size differences [72,73,74] should be considered for quantitative calculations in the case of transition metal alloys. The importance and the contributions of these effects to the quantitative calculations of ordering energy and its related physical properties have been pointed out in our previous studies on the ordering characteristics of various intermetallics.…”

Effect of three-body forces on the lattice dynamics of noble metals

“…Mishra et al [18] have proposed a generalized Morse potential which simulates, in empirical manner, the three-body forces. Okoye and Pal [19] have studied the phonon dispersion in noble metals by incorporating a short range 3-body interaction potential coupled with Animalu's transition metal non local model potential [20]. Guong [21] has obtained a force constant tensor for Au, using a plane wave based linear response method.…”

Simulation Techniques for Atomic Systems

“…The following model pseudopotentials were applied for calculations: the Ashcroft pseudopotential of empty ionic skeleton [8], HejneÀAbarenkovÀAnimalu nonlocal pseudopotential [9], two-parameter pseudopotential of Gursky and Krasko [10], and LeriboÀAnzhel pseudopotential, which was applied for calculations of properties of light metals with the strong exchange interaction [11].…”