electron spin is taken into account. The time-independent equation is the one most
widely-used in computational chemistry, but the more generaltime-dependent
Schrodinger equation€ , which we shall not examine, is important in certain applica-
tions, like some treatments of the interaction of a molecule with light, since light
(radiation) is composed of time-varying electric and magnetic fields. The time-
dependent density functional theory method of calculating UV spectra (Chapter 7)
is based on the time-dependent Schr€odinger equation.
4.3 The Application of the Schr€odinger Equation
to Chemistry by H€uckel
4.3.1 Introduction
The quantum mechanical methods described in this book are all molecular orbital
(MO) methods, or oriented toward the molecular orbital approach: ab initio and
semiempirical methods use the MO method, and density functional methods are
oriented toward the MO approach. There is another approach to applying the
Schr€odinger equation to chemistry, namely the valence bond method. Basically
the MO method allows atomic orbitals to interact to create the molecular orbitals of
a molecule, and does not focus on individual bonds as shown in conventional
structural formulas. The VB method, on the other hand, takes the molecule,
mathematically, as a sum (linear combination) of structures each of which corre-
sponds to a structural formula with a certain pairing of electrons [ 16 ]. The MO
method explains in a relatively simple way phenomena that can be understood only
with difficulty using the VB method, like the triplet nature of dioxygen or the fact
that benzene is aromatic but cyclobutadiene is not [ 17 ]. With the application of
computers to quantum chemistry the MO method almost eclipsed the VB approach,
but the latter has in recent years made a limited comeback [ 18 ].
The first application of quantitative quantum theory to chemical species signifi-
cantly more complex than the hydrogen atom was the work of H€uckel^20 on unsatu-
rated organic compounds, in 1930–1937 [ 19 ]. This approach, in its simplest form,
focuses on thepelectrons of double bonds, aromatic rings and heteroatoms.
Although H€uckel did not initially explicitly consider orbital hybridization (the
concept is usually credited to Pauling,^21 1931 [ 20 ]), the method as it became widely
applied [ 21 ] confines itself to planar arrays ofsp^2 -hybridized atoms, usually carbon
atoms, and evaluates the consequences of the interactions among thepelectrons
(Fig.4.4). Actually, the simple H€uckel method has been occasionally applied to
(^20) Erich H€uckel, born Berlin, 1896. Ph.D. G€ottingen. Professor, Marburg. Died Marburg, 1980.
(^21) Linus Pauling, born Portland, Oregon, 1901. Ph.D. Caltech. Professor, Caltech. Known for work
in quantum chemistry and biochemistry, campaign for nuclear disarmament, and controversial
views on vitamin C. Nobel Prize for chemistry 1954, for peace 1963. Died near Big Sur,
California, 1994.
102 4 Introduction to Quantum Mechanics in Computational Chemistry