Suggestion Concerning the Role of Wave-Function Symmetry in Transition Metals and Their Alloys

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Abstract
Past attempts to describe the d electrons of the transition metals have been based on one or the other of two extreme views: the one, the conduction‐band model, treats the d electrons as though they belong to the lattice as a whole rather than to particular atoms; the other, the shell model, treats the d electrons as though they are completely localized. The purpose of this paper is to point out that the relative symmetries of d wave functions and the lattice geometry should determine which d electrons may be approximated by a localized, or shell, model, which electrons would be better approximated by bonding molecular orbitals, and which electrons may be treated by the conduction‐band approximation. The b.c.c. metals are particularly discussed since in this lattice geometry, two of the d wave functions are directed toward next‐nearest neighbors and away from the eight nearest neighbors whereas three of the wave functions are strongly perturbed by the nearest neighbors. It is pointed out that electrons which occupy states involving the former wave functions should be localized whereas electrons which occupy states involving the latter wave functions are best described by a molecular orbital: it is further pointed out that a possible description of the molecular orbitals in question is a bonding t2g band. In this model the conduction band is a valence band composed of an s and three p orbitals. From a knowledge of the Hall constants and the magnetic characteristics of chromium and iron, a schematic density‐of‐states curve is constructed.