d- and s-orbital populations in the d block: unbound atoms in physical vacuum versus chemical elements in condensed matter. A Dronskowski-population analysis.

The electron configurations of Ca, Zn and the nine transition elements M in between (and their heavier homologs) are reviewed on the basis of density functional theory and experimental facts. The d-s orbital energy and population patterns are systematically diverse. (i) The dominant valence electron configuration of most free neutral atoms M0 of groups g = 2–12 is 3dg−24s2 (textbook rule), or 3dg−14s1. (ii) Formal Mq+ cations in chemical compounds have the dominant configuration 3dg−q4s0 (basic concept of transition metal chemistry). (iii) M0 atoms in metallic phases [M∞] of hcp, ccp(fcc) and bcc structures have intermediate populations near 3dg−14s1 (lower d populations for Ca (ca. ½) and Zn (ca. 10)). Including the 4p valence orbitals, the dominant metallic configuration is 3dg−δ4(sp)δ with δ ≈ 1.4 (±0.2) throughout (except for Zn). (iv) The 3d,4s population of atomic clusters Mm varies for increasing m smoothly from single-atomic 3dg−24s2 toward metallic 3dg−14s1. – The textbook rule for the one-electron energies, i.e., ns < (n−1)d, holds 'in a broader sense' for the s block, but in general not for the d block, and never for the p block. It is more important to teach realistic atomic orbital (AO) populations such as the ones given above. [ABSTRACT FROM AUTHOR]