We
present here a general conceptualization of the nature of metal–metal
(M–M) bonding in transition-metal (TM) complexes across the
periods of TM elements, by use of ab initio valence-bond theory. The
calculations reveal a dual-trend: For M–M bonds in groups 7
and 9, the 3d-series forms charge-shift bonds (CSB), while upon moving
down to the 5d-series, the bonds become gradually covalent. In contrast,
M–M bonds of metals having filled d-orbitals (groups 11 and
12) behave oppositely; initially the M-M bond is covalent, but upon
moving down the Periodic Table, the CSB character increases. These
trends originate in the radial-distribution-functions of the atomic
orbitals, which determine the compactness of the valence-orbitals
vis-à-vis the filled semicore orbitals. Key factors that gauge
this compactness are the presence/absence of a radial-node in the
valence-orbital and relativistic contraction/expansion of the valence/semicore
orbitals. Whenever these orbital-types are spatially coincident, the
covalent bond-pairing is weakened by Pauli-repulsion with the semicore
electrons, and CSB takes over. Thus, for groups 3–10, which
possess (n – 1)s2(n – 1)p6 semicores, this spatial-coincidence is
maximal at the 3d-transition-metals which consequently form charge-shift
M–M bonds. However, in groups 11 and 12, the relativistic effects
maximize spatial-coincidence in the third series, wherein the 5d10 core approaches the valence 6s orbital, and the respective
Pauli repulsion generates M–M bonds with CSB character. These
considerations create a generalized paradigm for M–M bonding
in the transition-elements periods, and Pauli repulsion emerges as
the factor that unifies CSB over the periods of main-group and transition
elements.