Finally, the EHM, albeit more elaborately parameterized than in its original
incarnation, has been claimed to offer some promise as a serious competitor to
the very useful and popular semiempirical AM1 method (Section 6.2.5.5) for
calculating molecular geometries [ 67 ].
4.4.4.2 Weaknesses
The weaknesses of the standard EHM probably arise at least in part from the fact
that it does not (contrast the ab initio method,Chapter 5) take into account electron
spin or electron–electron repulsion, ignores the fact that molecular geometry is
partly determined by internuclear repulsion, and makes no attempt to overcome
these defects by parameterization (unlike the variation which, with the aid of
careful parameterization, has been claimed to give good geometries [ 67 ]).
The standard EHM gives, by and large, poor geometries and energies. Although
it predicts a C–H bond length of ca. 1.0 A ̊, it yields C/C bond lengths of 1.92, 1.47
and 0.85 A ̊for ethane, ethene and ethyne, respectively, cf. the actual values of 1.53,
1.33 and 1.21 A ̊, and although the favored conformation of an alkane is usually
correctly identified, the energy barriers and differences are generally at best in only
modest agreement with experiment. Because of this inability to reliably calculate
geometries, EHM calculations are usually not used for geometry optimizations,
but rather utilize experimental geometries.
4.5 Summary................................................................
This chapter introduces the application of quantum mechanics (QM) to computa-
tional chemistry by outlining the development of QM up to the Schr€odinger
equation and then showing how this equation led to the simple H€uckel method,
from which the extended H€uckel method followed.
QM teaches, basically, that energy isquantized: absorbed and emitted in discrete
packets (quanta) of magnitudehn, wherehis Planck’s constant andn(Greeknu)
is the frequency associated with the energy. QM grew out of studies of blackbody
radiation and of the photoelectric effect. Besides QM, radioactivity and relativity
contributed to the transition from classical to modern physics. The classical
Rutherford nuclear atom suffered from the deficiency that Maxwell’s electro-
magnetic theory demanded that its orbiting electrons radiate away energy and
swiftly fall into the nucleus. This problem was countered by Bohr’s quantum
atom, in which an electron could orbit stably if its angular momentum was an
integral multiple ofh/2p. However, the Bohr model contained several ad hoc fixes
and worked only for the hydrogen atom. The deficiencies of the Bohr atom were
surmounted by Schr€odinger’s wave mechanical atom; this was based on a combi-
nation of classical wave theory and the de Broglie postulate that any particle is
4.5 Summary 165