The challenge of the so-called electron configurations of the transition metals.
Quite different meanings are attached by chemists to the words element, atom, orbital, order of orbitals or configurations. This causes conceptual inconsistencies, in particular with respect to the transition-metal elements and their atoms or ions. The different meanings will here be distinguished carefully. They are analyzed on the basis of empirical atomic spectral data and quasi-relativistic density functional calculations. The latter are quite reliable for different average configuration energies of transition-metal atoms. The so-called "configurations of the chemical elements", traditionally displayed in periodic tables, are the dominant configurations of the lowest spin-orbit levels of the free atoms. They are chemically rather irrelevant. In many-electron systems the ns and np AOs are significantly below the more hydrogen-like nd ones. Even (n+1)s is below nd for all light neutral atoms from C onwards, but only up to the first elements of the respective long rows! The most common orbital order in transition-metal atoms is 3p << 3d < 4s etc. The chemically relevant configuration in group g is always d(g) instead of d(g-2) s(2). Conceptually clear reasoning eliminates apparent textbook inconsistencies between simple quantum-chemical models and the empirical facts. The empirically and theoretically well-founded Rydberg (n-deltal) rule is to be preferred instead of the historical Madelung (n+l) rule with its large number of exceptions.