CASSCF(4,4)/6-31G* calculations using the C¼Cpandsbonding and anti-
bonding orbitals led to the conclusion that the molecule can rearrange to a carbene
with a barrier of about 200 kJ mol"^1 [ 73 ].
Procedures for more involved CASSCF calculations, including calculations on
exited states, are given by Foresman and Frisch, with caveats for assessing the
reliability of the results, and they reassure the reader “not [to be] discouraged by
difficulties that you may encounter” [ 74 ]. Although CAS and GVB calculations are
the standard ways of handling singlet diradicals, attempts have been and are being
made to extend the reach of DFT here, perhaps bringing these species one day into
the compass of model chemistry methods. Examples are the work of Kazaryan and
Filatov [ 75 ], and Cremer and coworkers [ 76 ]. Open shell molecules in general can
present problems for model chemistries; these, and ways of dealing with them, have
been reviewed by Bally and Borden [ 77 ].
8.3 A Note on Heavy Atoms and Transition Metals........................
All things are Atoms: Earth and Water, Air
And Fire, all,Democritus foretold.
Saw Sulphur, Salt, and Mercury unfold
Amid Millenial hopes of faking Gold.TheMetals,lustrous Monarchs of the Cave,
Are ductile and conductive and opaque
Because each Atom generously gave
Its own Electrons to a mutual Stake,–John Updike, Midpoint, III. The dance of the solids. Composed ca. 1967.8.3.1 Perspective.......................................................
All chemical things are composed of atoms, so one might wonder why heavy atoms
and transition metals should be singled out for special treatment. Part of the justi-
fication is that most of the elements are metals, and most of these are transition-type
metals; I include in this class the lanthanides and actinides (IUPAC recommends
the terms lanthanoids and actinoids, as -ide implies an anion). The high atomic
numbers of most elements, compared to carbon and its neighbors, and the quirky
electronic structures of transition metals, pose problems not encountered routinely
in computations on organic compounds. Beyond about the second (beyond Ar,
Z¼18), certainly beyond the third (beyond Kr,Z¼36), full row of the periodic
table, the pull of the nuclear protons forces the inner electrons to move at a
significant fraction of the speed of light. This makes relativistic corrections often
8.3 A Note on Heavy Atoms and Transition Metals 547