necessary for accurate work. Further, transition metals (TMs) tend to fill their outer
shells in a manner less than straightforward, and to exhibit a more baroque style of
bonding than seen in typical organic compounds. The purpose of this short section
is merely to make readers aware of these problems so that should they seek to carry
out computations on inorganic species they will know that further delving into the
relevant literature may be advisable.
8.3.2 Heavy Atoms and Relativistic Corrections......................
The gain in mass [ 78 ] of the inner electrons in heavier atoms causes their orbitals to
contract and screen the outer electrons better than they otherwise would, causing
outer, valence d and f orbitals to expand, becoming of higher energy and more
reactive (a semipopular account of relativistic effects and computations is given by
Jacoby [ 79 ]). This has striking physical consequences, like the color of gold and the
fact that mercury is liquid, and significantly affects spectra by altering spin-orbit
coupling, while the chemical effects permeate structures and energetics; this is
discussed in Pyykk€o’s comprehensive review of the effects of and computations
dealing with relativity in chemistry [ 80 ]. Other reviews relevant to relativistic
computations discuss pseudopotentials and TM compounds [ 81 , 82 ], transactinide
elements [ 83 ] and the theory of relativistic quantum chemistry [ 84 ]. A thorough
account of relativistic effects in chemistry, a very technical subject, is given in the
two-volume work by Balasubramanian [ 85 ], and the review of Volume B by Wilson
is itself worth reading for a perspective on the subject [ 86 ]. Relativistic effects in
molecules are computed by the Dirac–Fock equation or, more frequently, pseudo-
potential or effective core potential methods. Perturbation methods have also been
applied to atomic and molecular relativistic effects [ 80 ]. The termpseudopotential
is favored by physicists, whileeffective core potentialor ECP tends to be used often
by chemists. The Dirac–Fock method ([ 80 , 87 ] and references therein) is based on
the extension to multielectron systems of the famous one-electron relativistic Dirac
version of the Schr€odinger equation [ 88 ]. It is “The most satisfying way to carry out
relativistic molecular calculations” [ 80 ], but is apparently not very practical for
many-electron molecules (but see a recent calculation on PbH 4 [ 89 ]). Less demand-
ing and much more popular are computations using relativistic pseudopotentials
(relativistic ECPs). A relativistic pseudopotential is a one-electron operator, some-
what analogous to theJ^andK^operators in standard Hartree-Fock theory (Eqs. 5.29
and 5.30), which is incorporated into the Fock operator (Eq. 5.36, and equations
(20)–(21) in [ 80 ]) and modifies it by treating the inner, non-valence electrons in an
average way, and taking relativity into account; the valence electrons are treated
conventionally. This average treatment greatly reduces the number of electrons that
must be directly addressed and the number of basis functions needed. Nonrelativis-
tic or relativistic pseudopotentials can be used even when relativity is not a
problem, to reduce the computational effort arising from many inner-shell elec-
trons. We encountered the concept in a very crude form inChapter 6, where we saw
548 8 Some “Special” Topics