Page 268 - Academic Press Encyclopedia of Physical Science and Technology 3rd Organic Chemistry

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Encyclopedia of Physical Science and Technology EN012G-576 July 28, 2001 12:44

214 Physical Organic Chemistry

There are three rules to be obeyed in dealing with reso-
nance: (1) In each contributing resonance form every atom
must satisfy the octet rule (as modified by the exceptions
above) and resonance forms with a nonoctet atom can
usually be ignored; (2) resonance expresses the delocal-
ization of electrons, but the resonance hybrid has a single
geometry, with fixed nuclei; and (3) resonance provides C. Atomic Orbitals
stabilization, such that the resonance hybrid is of lower
Lewis structures do not describe the geometry of
energy than would be expected for any of its contributing
molecules. The set of bonds in a molecule describes only
resonance forms. This stabilization is called resonance the connectivity—which atom is bonded to which other
energy. atom or atoms. Indeed, most of the structures 2–20 are
Electron pushing, symbolized with curved arrows, pro- not drawn with any attempt at correct geometry. To de-
vides a convenient method for generating additional res- scribethegeometry,anotherapproachisnecessary.Orbital
onance forms. The rule is to delocalize a lone pair (or a theory provides a complementary approach to molecular
pair of electrons in a multiple bond, or, more rarely, in a structure.
single bond) toward an adjacent atom so as to form a mul- Orbital theory takes account of the wave nature of elec-
tiple bond, while also removing an electron pair from that trons. The uncertainty principle of quantum mechanics
adjacent atom to avoid a violation of the octet rule. For prohibits locating an electron exactly. Instead only prob-
example, delocalizing an electron pair from O right of bi- abilities can be specified, as described by a wave func-
carbonate ion (12) generates another resonance form (19), tion ψ. For a single electron that wave function is called
and delocalizing an electron pair from O left generates yet an orbital, and its square is the probability of finding the
another (20). Benzene (21) is an example of delocaliz-
electron “at” the point x, y, z in three-dimensional space:
ing electrons in multiple bonds. The second resonance
2
form is not just the first one rotated by 60 ; the nuclei P(x, y, z) = [ψ(x, y, z)] . (3)
◦
remain fixed, and the electrons of the double bonds are
delocalized. It is possible to express ψ as a mathematical formula
with a value at every point in space but it is often more
convenient just to sketch surfaces of constant ψ.For
some orbitals, called s orbitals, the surface is a sphere.
For some other orbitals, called p orbitals, the surface re-
sembles a pair of flattened spheres separated by a plane
where ψ(x, y, z) = 0. Such a plane is called a nodal plane
and it divides the region of space where ψ(x, y, z) > 0
from the region where ψ(x, y, z) < 0. There is no further
significance to positive or negative ψ(x, y, z) since only
the probability in Eq. (3) is measurable. There are also d
orbitals, with two nodal planes.
It takes a little imagination to reconstruct a three-
dimensional surface of constant ψ from its illustration on
a two-dimensional page. The sphere of an s orbital can be
illustrated as a circle, as shown in Fig. 1. The near-spheres
It is tedious to draw all resonance forms, and a short- of a p orbital are rarely illustrated accurately. Instead
hand notation is often used. Bonds that are present in some stylized (very approximate) versions are often used, as
resonance forms but not in all are shown as dotted, formal also shown in Fig. 1.
charges that are present in some resonance forms but not
all are shown as δ+ or δ− (same symbolism as before,
different context), and lone pairs are not shown. Thus dia-
zomethane (13, 18), bicarbonate ion (12, 19, 20), and ben-
zene (21) become 22, 23, and 24, respectively. For this last
a further abbreviation, often applied to cyclic compounds,
is to omit hydrogens attached to carbons and to symbolize
each carbon as a vertex. Moreover, the six dotted lines are

often simplified to a circle, as in 24 . FIGURE 1 Atomic orbitals.