the great majority of cases) topzorbitals (taking the framework plane, i.e. the
molecular plane, to be thexyplane).
2.Orbital interaction energies are limited toa,band 0. The Fock matrix orbital
interactions are limited toa,band 0, depending on whether theHijinteraction is,
respectivelyi,i, adjacent, or further-removed. The value ofbdoes not vary
smoothly with the separation of the orbitals, although logically it should
decrease continuously to zero as the separation increases.
3.Fock matrix elements are not actually calculated. The Fock matrix elements are
not any definite physical quantities, but rather energy levels relative toain units
of |b|, making them 0 or"1. One can try to estimateaandb, but the SHM does
not define them quantitatively.
4.Overlap integrals are limited to 1 or 0. We pretend that the overlap matrixSis a
unit matrix, by settingSij¼dij. This enables us to simplifyHC¼SC«(Eq.4.54)
to the standard eigenvalue formHC¼C«(Eq.4.59) and soH¼C«C"^1 , which
is the same as saying that the SHM Fock matrix is directly diagonalized to give
thec’s ande’s.
Now compare these four points with the corresponding features of the EHM:
4.4.1.2 Extended Huckel Method€
1.All valence s and p orbitals are used in the basis set. As in the SHM each
element of the Fock matrix is an integral representing an interaction between
two orbitals; however, in the EHM the basis set is not just a set of 2pzorbitals but
rather the set of valence-shell orbitals of each atom in the molecule (the deriva-
tion of the secular equations says nothing about what kinds of orbitals we are
considering). Thus each hydrogen atom contributes a 1sorbital to the basis set
and each carbon atom a 2sand three 2porbitals. Lithium and beryllium,
although they have no 2pelectrons, are assigned a 2sand three 2porbitals
(experience shows that this works better than omitting these basis functions) so
the atoms from lithium to fluorine each contribute a 2sand three 2porbitals. A
basis set like this, which uses the normal valence orbitals of atoms, is called a
minimal valence basis set.
2.Orbital interaction energies are calculated and vary smoothly with geometry.
The EHM Fock matrix orbital interactionsHijare calculated in a way that
depends on the distance apart of the orbitals, so their values vary smoothly
with orbital separation.
3.Fock matrix elements are actually calculated. The EHM Fock matrix elements
are calculated from well-defined physical quantities (ionization energies) with
the aid of well-defined mathematical functions (overlap integrals), and so are
closely related to ionization energies and have definite quantitative values.
4.Overlap integrals are actually calculated. We do not in effect ignore the overlap
matrix, i.e. we do not set it equal to a unit matrix. Instead, the elements of the
overlap matrix are calculated, eachSijdepending on the distance apart of the
4.4 The Extended H€uckel Method 153