heavy-metal-containing molecules [ 64 ] that might not be very amenable to ab initio
or to other semiempirical approaches (see Chapter 8, Section 8.3.4).
4.4.4 Strengths and Weaknesses of the Extended Huckel Method€
4.4.4.1 Strengths
One big advantage of the EHM over ab initio methods (Chapter 5), more elaborate
semiempirical methods (Chapter 6), and density functional theory (DFT) methods
(Chapter 7), is that the EHM can be applied to very large systems, and can treat
almost any element since the only element-specific parameter needed is an ioniza-
tion energy, which is usually available. In contrast, more elaborate semiempirical
methods have not been parameterized for as many elements (although recent para-
meterizations of PM3 and MNDO for transition metals make these much more
generally useful than hitherto – Section 6.2.6.7). For ab initio and DFT methods,
basis sets may not be available for elements of interest, and besides, ab initio and
even DFT methods are hundreds of times slower than the EHM and thus limited to
much smaller systems. The applicability of the EHM to large systems and a wide
variety of elements is one reason why it has been extensively applied to polymeric
and solid-state structures. The EHM is faster than more elaborate semiempirical
methods because calculation of the Fock matrix elements is so simple and because
this matrix needs to be diagonalized only once to yield the eigenvalues and
eigenvectors; in contrast, semiempirical methods like AM1 and PM3 (Chapter 6),
as well as ab initio calculations, require repeated matrix diagonalization because the
Fock matrix must be iteratively refined in the SCF procedure (e.g. Section 5.2.3.6.5).
The spartan reliance of the EHM on empirical parameters helps to make it
relatively easy (in the right hands) to interpret its results, which depend, in the
last analysis, only on geometry (which affects overlap integrals) and ionization
energies. With a strong dose of chemical intuition this has enabled the method to
yield powerful insights, such as counterintuitive orbital mixing [ 65 ], and the very
powerful Woodward–Hoffmann rules [ 38 ].
The applicability to large systems, including polymers and solids, containing
almost any kind of atom, and the relative transparency of the physical basis of the
results, are the main advantages of the EHM.
Surprisingly for such a conceptually simple method, the EHM has a theoreti-
cally-based advantage over otherwise more elaborate semiempirical methods like
AM1 and PM3, in that it treats orbital overlap properly: those other methods use the
“neglect of differential overlap” or NDO approximation (Section 6.2), meaning that
they takeSij¼dij, as in the simple H€uckel method. This can lead to superior results
from the EHM [ 66 ].
The EHM is a very valuable teaching tool because it follows straightforwardly
from the simple H€uckel method yet uses overlap integrals and matrix orthogonali-
zation in the same fashion as the mathematically more elaborate ab initio method.
164 4 Introduction to Quantum Mechanics in Computational Chemistry