that semiempirical methods like AM1 and PM3 treat only the valence electrons
explicitly and in effect collapse the inner electrons into the nuclei. The valence
electrons then move in the electrostatic potential field of a set of “pseudonuclei”,
each with a charge equal to the algebraic sum of an atomic number and the charge
of the inner electrons.
Pseudopotentials for molecules come from parameterization for atoms using
Dirac–Fock calculations. Since the pseudopotentials are parameterized for atoms,
we are assuming that the inner electrons are little affected on going from atoms to
molecules. The results justify this assumption. Actually, some pseudopotentials
handle all but the outermost electron shell (all but, say,n¼5), and some all but the
two outermost (all but, say,n¼5 and 4); these are called, respectively, larger-core
or full core, and small core pseudopotentials. Since these calculations do not
directlyuse the Dirac–Fock equation, they are sometimes calledquasirelativistic
calculations. Pseudopotentials are invoked by specifying a basis set that has been
specially designed for them, and a pseudopotential basis set (ECP basis set) is often
simply called a pseudopotential or ECP. They can be used in Hartree–Fock, MP2,
CI, and DFT calculations, and are the standard method of treating molecular
relativistic effects, and of reducing the computational strain incurred by the pres-
ence of large numbers of electrons even when relativity is not significant. Another
problem sometimes met with in heavy atoms is caused by spin-orbit coupling. This
and electron correlation effects are addressed with pseudopotentials in a recent
paper [ 90 ].
8.3.3 Some Heavy Atom Calculations.................................
The efficacy of a technique is sometimes best highlighted by studying trends. A
comprehensive review of compounds of the carbon homologue series Si, Ge, Sn
and Pb has been published by Karni et al. [ 91 ]. The rotational barriers in ethane and
its various Si, Ge, Sn and Pb homologs were computed by Schleyer et al. [ 92 ], using
pseudopotentials; relativistic effects were important only for Pb (Z¼82). Pseudo-
potential calculations have been extended to the sixth element in this series, with
studies of (114)X 2 and (114)X 4 ,X¼H, F, Cl [ 93 ]. Relativity can be neglected for
certain properties for iodine (Z¼53), krypton (Z¼36) and even Xenon (Z¼54):
MP2 studies on the geometry and thermochemistry of iodine oxides with extended
Pople-type basis sets and comparison with earlier work showed that “relativistic
effects are either small or cancel” [ 94 ], and DFT calculations on fluorides of
krypton and xenon (and some work on radon) with and without relativistic effects
showed that for bond lengths, dissociation energies, force constants, and charges
“relativistic effects...are negligible” [ 95 ]. An extensive list of basis functions,
which enables those available for a desired atom to be identified and downloaded
for computation, is available online [ 96 ]. A brief presentation of popular pseudo-
potentials is given by Cramer [ 97 ]. The literature and some experimentation
8.3 A Note on Heavy Atoms and Transition Metals 549