suggests that one popular basis, the LANL2DZ (Los Alamos National Laboratory),
parameterized for H to Pu, may be particularly useful.
8.3.4 Transition Metals.................................................
The bonding in and structures of transition metal compounds constitute a subject
with rules somewhatsui generisto one primarily versed in organic and main group
chemistry. The relative complexity of bonding in these compounds arises from the
presence in their compounds ofpartiallyfilled d- or (for the lanthanides and
actinides) f-level atomic orbitals, when the compound is viewed as consisting of
ions surrounded by ligands. This viewpoint is possible not only for simple ionic
compounds Mn+Xn", but also for covalent compounds and “complexes”, since the
metal can be assigned an at least formal oxidation state. The classification of a
particular element as a transition metal, a lanthanide or an actinide is not always
unambiguous and universally adhered to. For example, the scandium atom has one
d electron, but in any compound in which it has an oxidation number above two, it
will have no d electrons. Zinc has ten d electrons, but its compounds, formed by loss
of two s electrons, also have this fully filled d shell. Were compounds of scandium
(I) or (II) and Zn(III) recognized, with one and nine d electrons, respectively, these
elements would be classified as transition metals. Below are generally accepted
classifications for TM-type elements, with the hedge that the electronic structures
are idealized in that subtle shifts in occupancy are possible. For example, a Cu(I)
compound may not have the expected 3d^9 4s^1 , but rather the 3d^10 4s^0 arrangement.
Transition metals, first row, Ti (Z¼22, 3d^2 4s^2 ) – Cu (Z¼29, 3d^9 4s^2 )
Transition metals, second row, Zr(Z¼40, 4d^2 5s^2 ) – Ag (Z¼47, 4d^9 5s^2 )
Transition metals, third row, Hf (Z¼72, 5d^2 6s^2 ) – Au (Z¼70, 5d^9 6s^2 )
Lanthanides, Ce (Z¼58, 4f^1 5d^1 6s^2 ) – Yb (Z¼70, 4f^14 6s^2 )
Actinides, Th (Z¼90, 6d^2 7s^2 ) – Es (Z¼99, 5f^11 7s^2 ) (stopping at what appears
to be the last element available in at least milligram amounts [ 98 ]).
The electronic structures of compounds of these elements is complicated by
ambiguities in filling the d or f shells, which can give rise to low-spin and high-spin
compounds with the same number of formal metal electrons (i.e. with the metal in
the same oxidation state) but with different ligands, depending on the gap between
the so-called (for d-shell atoms)t2gandegsets of orbitals. An accessible and
reasonably compact introduction to the structure of TM compounds and the role
therein of d orbitals is given by Cotton et al. [ 99 ]. Hoffmann, in his Nobel Lecture,
presents an interesting and original set of rules, the isolobal analogy, for interpret-
ing the structures of such species and drawing analogies, which “[allows] us to see
the simple essence of seemingly complex structures” [ 100 ]. The detailed properties
of individual elements are discussed in standard textbooks, e.g. [ 101 , 102 ].
I outline the main salient points relevant to computations on TM compounds.
First, as indicated above, one needs an understanding of the rules behind the
550 8 Some “Special” Topics