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Physical Organic Chemistry 217

unusually stable. Benzene (21 or 24; Fig. 7), with six show the bonds at the rear atom as partially hidden by the
pi electrons in the three pi bonds, is an example. The sigma bond, depicted as a circle. All of these methods are
conclusion is very general, and other examples include used below.
cyclopentadienyl anion (25;4n + 2 = 6), pyrrole (26;
4n + 2 = 6, including the lone pair), cyclopropenyl cation A. Bond Distances and Bond Angles
(27;4n + 2 = 2),andnaphthalene(28;4n + 2 = 10 around
Bond distances are governed by the interplay between the
periphery). In contrast, cyclic systems containing 4n
accumulation of the electrons in the overlap region and
(n = 1, 2,...) pi electrons, such as cyclobutadiene (29;
the repulsions of the electrons for each other and of the
4n = 4) are unusually unstable. The unusual stability of
nuclei for each other. For each bond there is an optimum
cyclic systems containing 4n + 2 pi electrons is called aro-
distance that minimizes the total energy. That distance
maticity, and the instability of cyclic systems containing
shortens with the number of electrons bonding the two
4n pi electrons is called antiaromaticity. This is a dis-
atoms together. For example, the C C distances in ethane
tinction not accessible from considerations of resonance
(CH 3 CH 3 ), ethene (CH 2 CH 2 ), and ethyne (HC CH)
hybrids. ˚
are 1.54, 1.34, and 1.20 A , respectively.
The optimum values for bond angles are governed
largely by the mutual repulsion of electron pairs. For
an octet atom it might be expected that its four electron
Owing to the power of modern computers, it is now pos- pairs would be as far apart from each other as possible.
sible to calculate electronic structures, geometries, ther- The optimum arrangement then is to direct them toward
modynamic properties, and dynamic behavior of large the vertices of a regular tetrahedron. Methane (CH 4 ; 30)
molecules with a reliability of ±1 kcal/mole. The meth- is exactly such a molecule. The HCH angle is tetrahe-
ods are quantum mechanical, of greater generality than dral, 109.5 . Likewise, sp -hybridized carbons in other
3
◦
Eq. (8). Software programs are widely available for per- molecules have angles that are tetrahedral or nearly so.
forming such computations and for visualizing the results. Angles at nitrogen and oxygen, as in NH 3 (6), H 2 O(7),
and related molecules, are also close to tetrahedral, to min-
imize the repulsions of the four electron pairs, regardless
II. MOLECULAR STRUCTURE: of whether they are in bonds or lone pairs. The deviations
STEREOCHEMISTRY
from the idealized 109.5 are due to a greater s character
◦
for lone pairs, which are held closer to the nucleus, or a
Stereochemistry is that aspect of molecular structure that
greater p character for electrons that are unequally shared
deals with the geometry of molecules in three dimensions.
with a more electronegative atom.
Isomers are different molecules with the same atomic
composition (same number of each kind of atom). For
example, both CH 3 OCH 3 and CH 3 CH 2 OH have two car-
bons, six hydrogens, and an oxygen but they are assembled
differently. Likewise, CH 3 CH 2 CH 2 CH 3 and (CH 3 ) 3 CH
have the same atoms but different connectivity. Isomers Since every octet atom has four electron pairs, it might
that differ in connectivity are often called constitutional bethoughtthateverysuchatomistetrahedral.However,an
isomers. They have different Lewis structures. In contrast, unhybridized p orbital must be used for each pi bond and
stereoisomers have the same connectivity and the same the remaining electron pairs then minimize their mutual
2
Lewis structures but they are still different molecules. repulsions. For an sp -hybridized atom, with three such
◦
Even the simplest aspects of stereochemistry often re- pairs, the angle between them is 120 , and with two, on
◦
quire a method for displaying the three-dimensional struc- an sp-hybridized atom, it is 180 . Thus the HCH angle
ture of molecules on a two-dimensional page. One such in ethene (CH 2 CH 2 ) and the CNC angle in CH 2 NCH 3
◦
method is to use ordinary lines for bonds that are in the (31) are both close to 120 and the HCC angle in ethyne
◦
plane of the page, a wedge for a bond that comes forward, (HC CH) is 180 .
and a dotted line for a bond that goes behind the page.
Another possibility is to draw a perspective view of the
B. Conformations about Single Bonds
molecule, with thicker lines for bonds at the front (rather
than shortening distant bonds, as in true perspective), or Conformations are different molecular structures related
with bonds in front “concealing” bonds behind. Still an- by rotation about single bonds. Since a sigma bond is
other possibility is to sight along a single bond, show the cylindrically symmetric, there is little restriction to ro-
bonds at the front atom as emanating from that atom, and tating around it. The restriction does not come from the