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Chemical Bonding and


Organic chemistry is a broad ®eld which intersects with such diverse areas as biology,
medicine and pharmacology, polymer technology, agriculture, and petroleum engineering.
At the heart of organic chemistry are fundamental concepts of molecular structure and
reactivity of carbon-containing compounds. The purpose of this text is to explore this
central core, which is concerned with how the structures of organic compounds are related
to reactivity. Reactivity, in turn, determines the methods that can be used for synthesis.
Understanding of structure, reactivity, and synthesis can be used within organic chemistry
or applied to other ®elds, such as those named above, which require contributions from
organic chemistry. Structure includes the description of bonding in organic molecules and
the methods for determining, analyzing, and predicting molecular structure. Dynamic
aspects of structure, such as conformational equilibria, are also included. Stereochemistry
is also a crucial aspect of structure in organic chemistry. Reactivity pertains to the aspects
of a given structure that determine its chemical transformations. Is the molecule electron-
rich or electron-poor? Is it easily reduced or oxidized? What is the distribution of the most
reactive electrons? Which bonds are weakest and therefore most likely to engage in
reactions? Unlike structure, which is an inherent property of the molecule, reactivity
usually describes an interaction with other molecules. Understanding reactivity includes
describing the mechanisms, that is, the stepwise process by which reactions occur.
Reactivity also encompasses the stereochemical aspects of the transformation. Synthesis
encompasses those activities which are directed toward ®nding methods that convert
existing substances into different compounds. Synthesis involves the control of reactivity
to achieve speci®ed transformations. It involves the choice of reagents, catalysts, and
reaction conditions that will accomplish a given transformation within the required
parameters. In various circumstances, the limiting parameters might include yield,
purity of product, stereochemical control, availability or cost of reagents, or safety and
environmental consequences. Structure, reactivity, and synthesis are all interrelated.
2 Synthesis is built on knowledge of both structure and reactivity, and understanding
reactivity ultimately rests on detailed knowledge about molecular structure. A ®rm
CHEMICAL BONDING grounding in the principles of structure and chemical bonding is therefore an essential
AND STRUCTURE starting point for fuller appreciation of reactivity and synthesis. In this ®rst chapter, we will
discuss the ideas that have proven most useful to organic chemists for describing and
organizing facts, concepts, and theories about the structure of organic molecules.
Structural formulas serve as key devices for communication of chemical information,
and it is important to recognize the symbolic relationship between structural formulas and
molecular structure. The current system of structural formulas arose largely as a result of
research done in the last half of the 19th century. Elemental analyses, interrelation of various
compounds, and systematic investigation of the reactivity of various ``functional groups''
permitted chemists to correctly deduce much information about molecular structure. For
most molecules, it became possible to draw conclusions as to which atoms were directly
connected (constitution). Lines drawn between atoms were used to represent direct
connections or bonds. It was recognized that the various elements formed a characteristic
numbers of bonds. The capacity of an element to form bonds was called valence, and the
number of bonds a given element could form was called its valence number. These
structural deductions predated modern electronic concepts of atomic and molecular
structure and the nature of the forces that bind atoms together in molecules. Nevertheless,
structural formulas proved to be readily adaptable to description of chemical bonding in
terms of electron-pair bonds since the bonds came to symbolize the shared pair of electrons.
The precise description of molecular structure speci®es nuclear positions with respect
to other nuclei in the molecule and the distribution of the electrons associated with the
nuclei. Because chemical properties are primarily determined by the outer shell of valence
electrons, chemists focus attention primarily on these electrons. Spectroscopic methods
and diffraction methods, especially X-ray crystal structure determination, have provided a
large amount of information about atomic positions and bond lengths. Dynamic aspects of
molecular structure involving such issues as alternative molecular shapes arising by bond
rotations (conformations) can also be characterized by spectroscopic methods, especially
nuclear magnetic resonance (NMR) spectroscopy. These experimental methods for
structure determination have been joined by computational methods. Computational
approaches for calculating molecular structures are based on systematic searching for
the most stable arrangement of the atoms having a particular bonding pattern (molecular
connectivity). Computational methods can be based on observed relationships between
energy and structure (molecular mechanics) or on theoretical descriptions of bonding
based on quantum chemistry.
Theories of molecular structure attempt to describe the nature of chemical bonding
both qualitatively and quantitatively. To be useful to chemists, the bonding theories must
provide insight into the properties and reactivity of molecules. The structural theories and
concepts that are most useful in organic chemistry are the subject of this chapter. Our goal
is to be able to relate molecular structure, as depicted by structural formulas and other
types of structural information, such as bond lengths and electronic distributions, to the
chemical reactivity and physical properties of molecules.

1.1. Valence Bond Approach to Chemical Bonding

The idea put forth by G. N. Lewis in 1916 that chemical bonding results from a
sharing of electron pairs between two atoms was a fundamental advance in bonding
theory.1 The concept of valence is related to the number of electrons available to each atom 3
and, for the second-row elements, to the ``octet rule,'' that is, to the stability associated with
four pairs of electrons. Lewis's proposal was put on the sound ground of quantum VALENCE BOND
mechanics by Heitler and London's treatment of the hydrogen molecule in 1927. This APPROACH TO
treatment marked the beginning of what we now know as valence bond theory.2 A central
feature of this theory was the conclusion that most of the binding energy between the two
atoms at the most stable internuclear separation results from sharing of the electrons
between the two nuclei. This conclusion arose in a direct way from the Heitler±London
calculations. If electron 1 were constrained to be associated only with nucleus l, and
electron 2 with nucleus 2, then the calculated binding energy was only a small fraction of
the experimentally determined bond energy. If this constraint was removed so that the
electrons were indistinguishable and permitted to interact equally with both nuclei, the
calculated potential energy curve exhibited a deep minimum at the equilibrium inter-
nuclear distance. The bonding energy associated with this minimum corresponded quite
well with the experimental bond energy. The covalent bond represented by a line in the
simple notation H H then takes on more precise meaning. It symbolizes the presence of
two bonding electrons in the region between the two nuclei. The region of space occupied
by an electron is called an orbital. In the H2 molecule, the bonding arises from the two
electrons in an orbital formed by overlap of the spherically symmetrical 1s atomic orbital
of each hydrogen atom, as shown in Fig. 1.1. Similarly, the bonding orbitals of other
molecules arise from the atomic orbitals of the constituent atoms.
Application of valence bond theory to more complex molecules involves writing as
many plausible Lewis structures as possible that correspond to the correct molecular
connectivity. Valence bond theory assumes that the actual molecule is a hybrid of these
``canonical forms.'' As a simple example, the hydrogen chloride molecule is considered to
be a hybrid of the limiting canonical forms H Cl, H Cl , and H Cl . In mathematical
terms, the molecule can be represented as the weighted combination of the contributing
structures. Unfortunately, the extension of this approach to larger molecules results in a
large number of canonical structures, which makes both conceptual and computational
interpretation dif®cult. For example, more than 175 individual structures, most with charge
separation, can be written for benzene.3 For this reason, qualitative concepts which arise
from the valence bond treatment of simple molecules are applied to larger molecules. The
key ideas that are used to adapt the concepts of valence bond theory to complex molecules
are hybridization and resonance. In this qualitative form, valence bond theory describes
molecules in terms of orbitals that are mainly localized between two atoms. The shapes of
these orbitals are assumed to be similar to those of orbitals described by more quantitative

Fig. 1.1. Representation of s bond of H2 formed by

overlap of 1s orbitals.

1. G. N. Lewis, J. Am. Chem. Soc. 38:762 (1916).

2. W. Heitler and F. London, Z. Phys. 44:455 (1927). For a historical review, see M. Simonetta, in Structural
Chemistry and Molecular Biology, A. Rich and N. Davidson, eds., W. H. Freeman, San Francisco, 1968, pp.
3. C. Amovilli, R. D. Harcourt, and R. McWeeny, Chem. Phys. Lett. 187:494 (1991).
4 treatment of simpler molecules. The properties of complex molecules are regarded as
derived from the combination of the properties of the constituent bonds. This conceptual
CHEMICAL BONDING approach is in accord with a large body of chemical knowledge which indicates that
AND STRUCTURE structure and reactivity of similar bonds and groups are relatively constant in different

1.1.1. Orbital Hybridization

The concepts of directed valence and orbital hybridization were developed by Linus
Pauling soon after the description of the hydrogen molecule by the valence bond theory.
These concepts were applied to an issue of speci®c concern to organic chemistry, the
tetrahedral orientation of the bonds to tetracoordinate carbon.4 Pauling reasoned that
because covalent bonds require mutual overlap of orbitals, stronger bonds would result
from better overlap. Orbitals that possess directional properties, such as p orbitals, should
therefore be more effective than spherically symmetric s orbitals.
The electronic con®guration of a carbon atom in its ground state is 1s2 2s2 2p2 , and is
not consistent with a simple rationalization of the tetrahedral bonding at carbon. Pauling
suggested that four atomic orbitals (2s, 2px , 2py , 2pz ) are replaced by a set of four
equivalent hybrid orbitals, designated sp3 . The approximate shapes of these orbitals are
shown in Fig. 1.2. Notice particularly that the probability distribution is highly directional
for the sp3 orbitals, with the region of greatest probability concentrated to one side of the
Orbital hybridization has two important consequences. First, four bonds, rather than
two, can be formed to carbon. Second, the highly directional sp3 orbitals provide for more
effective overlap and stronger bonds. Thus, although an isolated carbon atom with one
electron in each of four equivalent sp3 -hybridized orbitals would be of higher energy than
the ground state, the energy required in a formal sense to promote two electrons from a 2s
orbital to sp3 orbitals is more than compensated for by the formation of four bonds rather
than two. In addition, each of the bonds is stronger owing to the directional properties of
the hybrid orbitals. Tetrahedral geometry is predicted by the mathematical description of
hybridization. Methane is found experimentally to be a perfect tetrahedron, with each
H C H bond angle equal to 109.5 . The valence bond representation of methane in Fig.
1.3 shows the orbital overlaps that give rise to four equivalent C H bonds. These bonds, in
which the electron density is cylindrically symmetric about the internuclear axis are called
s bonds.
The hybridization concept can also be applied to molecules containing double and
triple bonds. The descriptive valence bond approach to the bonding in ethylene and

Fig. 1.2. Cross section of

angular dependence of orbi-

4. L. Pauling, J. Am. Chem. Soc. 53:1367 (1931).


Fig. 1.3. Valence bond structural representa-

tion of methane resulting from overlap of H
1s orbitals with four equivalent sp3 orbitals
of carbon.

acetylene and their congeners is analogous to that for methane. In ethylene (Fig. 1.4), each
carbon bears three ligands and is sp2 hybridized. Three sp2 orbitals are generated from the
2s and two of the 2p orbitals. The three sp2 orbitals are coplanar and orthogonal to the
remaining 2p orbital. A bond is formed between the two carbon atoms by overlap of an sp2
orbital of each. The four hydrogens are bonded by s bonds involving hydrogen 1s orbitals
and the remaining two sp2 hybrid orbitals. Additional bonding between the two carbon
atoms is portrayed as resulting from overlap of the unhybridized p orbitals on each carbon
atom, each of which contains one electron. This overlap is somewhat less effective than
that of a s bond and corresponds to a p bond. The electron distribution in a p bond is
concentrated above and below the plane of the s framework. The molecule is planar, and
the plane de®ned by the nuclei is a nodal plane for the p system. The hybridization at each
carbon atom of acetylene is sp, and the two carbon atoms are considered as bonded by a s
bond and two p bonds, as shown in Fig. 1.4.
The concept of hybrid orbitals is deeply ingrained in the thinking of organic chemists,
as widely re¯ected in texts and the research literature. However, Pauling and others
recognized that there was a different conceptual starting point in which multiple bonds can
be represented as bent bonds.4

ethylene acetylene

Fig. 1.4. The p bond in ethylene and the p bonds in acetylene.

6 It has been shown that description of bonding based on the bent-bond concept can be just
as successful in describing molecular structure as the hybridization concept.5 We will,
CHEMICAL BONDING however, use the hybridization terminology.
AND STRUCTURE The relation between the number of ligands on carbon (its coordination number),
hybridization, and molelcular geometry is summarized in Table 1.1. Unless all the ligands
on a particular carbon atom are identical, there will be deviations from the perfectly
symmetrical structures implied by the hybridization schemes. For example, whereas
methane and carbon tetrachloride are tetrahedral with bond angles of 109.5 , the
C C C angle in cyclohexane is 111.5 . The H C H angle in formaldehyde is 118
rather than 120 . Benzene, however, is a regular hexagon with 120 bond angles.
Large deviations in bond angles from the normal values are found in cyclopropane,
cyclobutane, and other molecules containing three- and four-membered rings. These
molecules are less stable than molecules with larger rings, and the difference in energy is
referred to as angle strain. Because the three carbon atoms of a cyclopropane ring are
required by symmetry to be at the vertices of an equilateral triangle, the internuclear angles
are 60 . This arrangement represents a serious distortion of the normal tetrahedral bond
angle and engenders unique chemical and physical properties. To develop a valence bond
model of the bonding in cyclopropane, it is assumed than the carbon atoms will adopt the
hybridization that produces the most stable bonding arrangement.6 The orbitals used for
forming the carbon±carbon bonds in cyclopropane can overlap more effectively if they
have more p character than normal sp3 bonds, since additional p character corresponds to a
reduced bond angle. Consequently, the orbitals used for bonding to hydrogen must have
increased s character. This adjustment in hybridization can be described quantitatively by
assignment of numerical values to the ``percent s character'' in the C H bonds. Values of
33% and 17%, respectively, have been suggested for the C H and C C bonds of
cyclopropane, on the basis of NMR measurements.7 The picture of the bonding in
cyclopropane indicates that the region of maximum orbital overlap would not correspond
to the internuclear axis. The C C bonds are described as ``bent bonds'' (Fig. 1.5).
The change in hybridization is associated with a change in electronegativity. The
greater the s character of a particular carbon orbital, the greater is its electronegativity. As a
result, carbon atoms that are part of strained rings are more electronegative than normal
toward hydrogen.8 Figure 1.6 shows some calculated charges for cyclopropane and other

Table 1.1. Dependence of Structure on Hybridization of Carbon

Number of
ligands Hybridization Geometry Examples
4 sp Tetrahedral Methane, cyclohexane, methanol,
carbon tetrachloride
3 sp2 Trigonal Ethylene, formaldehyde, benzene
methyl cation, carbonate ion
2 sp Linear Acetylene, carbon dioxide,
hydrogen cyanide, allene (C-2)

5. P. A. Shultz and R. P. Messmer, J. Am. Chem. Soc. 115:10925, 10938, 10943 (1993).
6. For a review of various descriptions of the bonding in cyclopropane, see A. de Meijer, Angew. Chem. Int. Ed.
Engl. 18:809 (1979); K. B. Wiberg, in The Chemistry of the Cyclopropyl Group, Z. Rappoport, ed., John Wiley
& Sons, New York, Chapter 1, 1987; B. Rozsondai, in The Chemistry of the Cyclopropyl Group, Vol. 2, Z.
Rappoport (ed.), John Wiley & Sons, New York, Chapter 3, 1995.
7. F. J. Weigert and J. D. Roberts, J. Am. Chem. Soc. 89:5962 (1967).
8. K. B. Wiberg, R. F. W. Bader, and C. D. H. Lau, J. Am. Chem. Soc. 109:1001 (1987).

Fig. 1.5. Bent bonds in cyclopropane.

Fig. 1.6. Charge distributions in strained cyclic hydro-

carbons in comparison with cyclohexane. Data are from
Chem. Soc. 109:1001 (1987).

strained hydrocarbons in comparison with the unstrained reference cyclohexane. Notice

that the greater the distortion from the normal tetrahedral angle, the greater is the negative
charge on carbon. This relative electronegativity is re¯ected in both the acidity and the
NMR chemical shifts of hydrogens attached to strained ring systems.
Even more drastic distortions from ideal geometry are found when several small rings
are assembled into bicyclic and tricyclic molecules. The synthesis of such highly strained
molecules is not only a challenge to the imagination and skill of chemists, but also
provides the opportunity to test bonding theories by probing the effects of unusual bonding
geometry on the properties of molecules. One series of such molecules is the propellanes.9
The structures of some speci®c propellanes and the strain energies of the molecules are
shown in Fig. 1.7. Each of the molecules in Fig. 1.7 has been synthesized, and some of
their physical and structural properties have been analyzed. In the propellanes with small
rings, the bridgehead must be severely ¯attened to permit bonding. In order to attain this
geometry, the hybridization at the bridgehead carbons must change as the size of the
bridges decreases. Whereas the hybridization at the bridgehead carbons in [4.4.4]propel-
lane can be approximately the normal sp3 , in [2.2.2]propellane the ¯attening of the
bridgehead must result in a change to approximately sp2 hybridization, with the central
bond between the two bridgehead carbons being a s bond formed by overlap of two p
orbitals. The distortion is still more extreme in [1.1.1]propellane, in which the bridgehead

9. K. B. Wiberg, Acc. Chem. Res. 17:379 (1984); K. B. Wiberg, Chem. Rev. 89:975 (1989).
10. J. E. Jackson and L. C. Allen, J. Am. Chem. Soc. 106:591 (1984); K. B. Wiberg, R. F. W. Bader, and C. D. H.
Lau, J. Am. Chem. Soc. 109:985 (1987); K. B. Wiberg, R. F. W. Bader, and C. D. H. Lau, J. Am. Chem. Soc.
109:1001 (1987).

Fig. 1.7. Strain energies of some propellanes in kcal=mol.

carbon is an ``inverted carbon'' with all four bonds to one side. The resulting bond has
quite special characteristics and is not adequately described as a localized bond.10

[1.1.1]propellane [2.2.2]propellane [4.4.4]propellane

The distortion of the bond angles in propellanes leads both to strain and to unusual
chemical reactivity. [3.2.1]Propellane, for example, is found to have a strain energy of
67 kcal=mol, as compared to 27 kcal=mol for cyclopropane. The molecule is exceptionally
reactive and undergoes a variety of reactions involving the cleavage of the central bond
under mild conditions. For example, it undergoes bromination instantaneously at 50 C.11
The strain should be less in [3.3.3]propellane, in which a smaller distortion at the
bridgehead carbons is required to permit bonding. This is re¯ected by the lower strain
energy of 34 kcal=mol. On the other hand, the smaller bridges lead to increased strain.
[2.2.1]Propellane conforms to the expectation that it would be highly reactive. It can be
observed when isolated in solid argon at 45 K but decomposes at temperatures higher than
this and cannot be isolated as a pure substance.12 [1.1.1]Propellane is a surprisingly stable
substance. Although the strain is comparable to that of [3.1.1]- and [2.2.1]propellane, the
relief of strain on rupture of the center bond is quite small, leading to greater thermal
stability.13 The ``inverted'' center bond is largely p in character, and, as a result, there is a
considerable charge density external to the ring. This permits a variety of radical and
electrophilic addition reactions to occur.14

I2 NO2

(PhS)2 Bu3SnH

SPh SnBu3

11. K. B. Wiberg and G. J. Burgmaier, J. Am. Chem. Soc. 94:7396 (1972).

12. K. B. Wiberg, C. M. Breneman, and T. J. LePage, J. Am. Chem. Soc. 112:61 (1990); A. Gobbi and G. Frenking,
J. Am. Chem. Soc. 116:9275 (1994).
13. K. B. Wiberg and F. H. Walker, J. Am. Chem. Soc. 104:5239 (1982); C. Y. Zhao, Y. Zhang, and X. Z. You, J.
Phys. Chem. 101:3174 (1997).
14. K. B. Wiberg and S. T. Waddell, J. Am. Chem. Soc. 112:2194 (1990); D. S. Toops and M. R. Barbachyn, J. Org.
Chem. 58:6505 (1993).
1.1.2. Resonance 9
A second concept that makes valence bond theory useful for the structural description SECTION 1.1.
of complex molecules is resonance theory. Resonance theory is an extension of valence APPROACH TO
bond theory which recognizes that, for many molecules, more than one Lewis structure CHEMICAL BONDING

can be written. Its usefulness in organic chemistry lies in its being a convenient way of
depicting electron delocalization. Resonance theory is particularly useful in describing
conjugated compounds and reactive intermediates. Arguments based on resonance theory
are usually made in a qualitative way, although a mathematical treatment can be applied.15
The elements of resonance theory that are necessary for qualitative applications can be
summarized as follows:

a. Whenever alternative Lewis structures can be written for a molecule that differ
only in assignment of electrons among the nuclei, with the nuclear positions being
constant for all the structures, then the molecule is not adequately represented by a
single Lewis structure but has weighted properties of all of the alternative Lewis
b. All structures are restricted to the maximum number of valence electrons that is
appropriate for each atom, that is, two for hydrogen and eight for the ®rst-row
c. Some individual Lewis structures are more stable than others. The structures that
approximate the actual molecule most closely are those that incorporate the
following features: maximum number of covalent bonds, minimum separation
of unlike charges, and placement of any negative charges on the most electro-
negative atom (or any positive charge on the most electropositive atom). Stated in
another way, the most favorable (lowest-energy) resonance structure makes the
greatest contribution to the true (hybrid) structure.
d. In most cases, the delocalization of electrons, as represented by the writing of
alternative Lewis structures, is associated with enhanced stability relative to a
single localized structure. This is not always true, however, since molecules and
ions are known in which electron delocalization produces an increase in energy
relative to a localized model.

Some fundamental structure±stability relationships can be employed to illustrate the

use of resonance concepts. The allyl cation is known to be a particularly stable
carbocation. This stability can be understood by recognizing that the positive charge is
delocalized between two carbon atoms, as represented by the two equivalent resonance
structures. The delocalization imposes a structural requirement. The p orbitals on the three
contiguous carbon atoms must all be aligned in the same direction to permit electron
delocalization. As a result, there is an energy barrier to rotation about the carbon±carbon

15. For a classical presentation of resonance theory, see G. W. Wheland, Resonance Theory in Organic Chemistry,
John Wiley & Sons, New York, 1955. Models of molecular structure based on mathematical description of
valence bond theory have been developed: F. W. Bodrowicz and W. A. Goddard III, in Modern Theoretical
Chemistry, Methods of Electronic Structure Theory, Vol. 3, H. F. Schaefer III, ed., Plenum Press, New York,
1977, Chapter 4; A. Voter and W. A. Goddard III, Chem. Phys. 57:253 (1981); N. D. Epiotis, Uni®ed Valence
Bond Theory of Electronic Structure, Springer-Verlag, Berlin, 1983; D. J. Klein and N. Trinajstic, eds., Valence
Bond Theory and Chemical Structure, Elsevier, Amsterdam, 1990; D. L. Cooper, J. Gerratt, and M. Raimondi,
Chem. Rev. 91:929 (1991).
10 bonds in the allyl cation. The most stable geometry is planar, and the barrier to rotation is
estimated to be 36±38 kcal=mol.16
H +C C+
resonance interaction
disrupted by rotation

Another important and familiar example of resonance is the stabilization of the

enolate anions formed by deprotonation of carbonyl compounds. This can be illustrated by
considering the relative acidity of 2-methylpropene (isobutene) and 2-propanone (acetone).
The relative acidity is indicated by the pK values, which are 25 and 45, respectively.
The difference of 20 pK units (20 powers of 10) shows that it is much easier for a proton
to be removed from acetone than from isobutene. The main reason for the difference in
acidity is the difference in stability of the two conjugate bases. A resonance-stabilized
anion is generated in each case, but one of the contributing structures for the acetone anion
has a negative charge on oxygen. In both resonance structures for the anion of isobutene,
the negative charge is on carbon. Because oxygen is a more electronegative element than
carbon, application of resonance theory leads to the conclusion that the acetone anion will
be more stable than the isobutene anion and that acetone will therefore be more acidic.
– –

C CH2 C CH2 C O C O–

Another example of the effect of resonance is in the relative acidity of carboxylic

acids as compared to alcohols. Carboxylic acids derived from saturated hydrocarbons have
pKa values near 5, whereas saturated alcohols have pKa values in the range 16±18. This
implies that the carboxylate anion can accept negative charge more readily than an oxygen
on a saturated carbon chain. This can be explained in terms of stabilization of the negative
charge by resonance.17

O O– R
O– O O– O–
Resonance stabilization of Alcoholate anions have negative
carboxylate anion. charge localized on a single oxygen.

One of the structural implications of the delocalization of the negative charge, the identity
of the two C O bond lengths, intermediate between those of single and double bonds, has
been veri®ed by many crystal structure determinations.
Dynamic structural characteristics can also be interpreted in terms of resonance.
There is a substantial barrier to rotation about the C N single bonds in carboxamides. A
frequently observed consequence is the nonidentity of NMR peaks due to the syn and anti

17. F. G. Bordwell and A. V. Satish, J. Am. Chem. Soc. 116:8885 (1994); P. C. Hiberty and C. P. Byrman, J. Am.
Chem. Soc. 117:9875 (1995); J. D. da Motta Neto and M. A. C. Nascimento, J. Phys. Chem. 100:15105 (1996).
substituents on nitrogen. The barrier is in the range of 15±20 kcal=mol.18 A planar 11
structure is imposed by the necessity of p-orbital overlap for delocalization. Other
structural parameters of amides, such as bond lengths and bond force constants, are VALENCE BOND
also consistent with the resonance model.19 APPROACH TO

a b
∆G* = 15–20 kcal
R N R N+ R N b R N a
O O– O O

Resonance concepts are especially important in systems in which two or more double
bonds are in conjugation. Resonance structures permit a description of the interaction
between the bonds. Carbonyl compounds having a carbon±carbon double bond adjacent to
the carbonyl group provide a good example of how structural features can be related to
resonance interactions. While only a single uncharged stucture can be drawn, two
structures with charges can be drawn. The structure with a negative charge on oxygen
is far more important because of the higher electronegativity of oxygen relative to carbon.
The structure with a positive charge on oxygen is unfavorable and would make only a
minor contribution.

H C O H C O– H C O+
+ –
major significant minor
contributor contributor contributor

Some of the structural features of this class of compounds which are in accord with the
resonance picture are as follows:

a. The CO bond is not as strong as in saturated carbonyl compounds. This is

revealed by the infrared stretching frequency, which comes at lower energy
(typically 1690 cm 1 versus 1730 cm 1 for saturated compounds).
b. Carbon-13 NMR spectroscopy also reveals that the b carbon is less shielded (lower
electron density) than is the case for a simple alkene. This results from the
delocalization of p electrons from this carbon to the carbonyl oxygen.
c. The chemical reactivity of the double bond is also affected by the presence of the
conjugated carbonyl group. Simple alkenes are not very reactive toward nucleo-
philes. In contrast, double bonds adjacent to carbonyl groups do react with
nucleophiles. The partial positive charge depicted by the resonance structure
makes the b carbon subject to nucleophilic attack.

18. B. M. Pinto, in Acyclic Organonitrogen Stereodynamics, J. B. Lambert and Y. Takeuchi, eds., VCH Publishers,
New York, 1992, pp. 149±175.
19. The issue of resonance in carboxamides has recently been reexamined. Most of the structural consequences
predicted by resonance are consistent with a stabilizing interaction which results in a net shift of electron
density from nitrogen to carbon and oxygen; A. J. Bennet, V. Somayaji, R. S. Brown, and B. D. Santarsiero, J.
Am. Chem. Soc. 113:7563 (1991); A. Greenberg, T. D. Thomas, C. R. Bevilacqua, M. Coville, D. Ji, J.-C. Tsai,
and G. Wu, J. Org. Chem. 57:7093 (1992).
12 Also, the carbonyl group stabilizes the negative charge that develops at the a carbon as a
result of nucleophilic attack. All of these effects are summed up by saying that the
CHEMICAL BONDING carbonyl group acts as an electron-withdrawing group toward the double bond, as is
AND STRUCTURE depicted in the most important of the charged resonance structures.
There are also substituents that can act as electron-releasing groups through
resonance. Among familiar examples are alkoxy and amino groups in vinyl ethers and
enamines, respectively.

– –
+ +

We might wonder how important such resonance effects are since the resonance structures
have the unfavorable feature of charge separation and place a positive charge on
electronegative atoms. Several approaches have been taken to determining the importance
of these interactions. Most are based on molecular orbital theory (see Sections 1.3 and
1.6). Typically, the results reveal only small ground-state structural changes, but para-
meters which re¯ect reactivity do indicate that these molecules are very much enhanced in
reactivity toward electrophiles.20 Carbon and proton NMR shifts are also up®eld in vinyl
ethers and enamines, as implied by the charged resonance structures. The most detailed
analyses suggest that there is indeed a p polarization of the type indicated, but that it is
compensated by a s polarization in the opposite sense.21


π delocalization σ polarization

The most impressive example of resonance stabilization is benzene, in which the

delocalization is responsible for a stabilization of 30±36 kcal=mol, the resonance energy of

cyclohexatriene benzene

We will return to the aromatic stabilization of benzene in more detail in Chapter 9, but
substituted benzenes provide excellent examples of how proper use of the resonance
concept can be valuable in predicting reactivity. Many substituents can be readily classi®ed

20. A. R. Katritzky and M. Karelson, Tetrahedron Lett. 31:2987 (1990); K. B. Wiberg, R. E. Rosenberg, and P. R.
Rablen, J. Am. Chem. Soc. 113:2890 (1991).
21. K. B. Wiberg and P. R. Rablen, J. Am. Chem. Soc. 115:9234 (1993).
as electron-releasing or electron-withdrawing simply by noting whether the substituent can 13
donate or accept electrons by p-orbital interaction with the ring.
Electron-withdrawing substituents POLARITY, AND
N N– –O

+ +

O N(CH3)2 N(CH3)2 O + O– –O
+ O–

+ +

Electron-releasing substituents
+ + +

– – – –

We will address this issue further in Chapter 10, where the polar effects of the substituents
on both the s and p electrons will be considered. For the case of electrophilic aromatic
substitution, where the energetics of interaction of an approaching electrophile with the p
system determines both the rate of reaction and position of substitution, simple resonance
arguments are extremely useful.

1.2. Bond Energy, Polarity, and Polarizability

1.2.1. Bond Energies

Of the various geometric parameters associated with molecular shape, the one most
nearly constant from molecule to molecule and most nearly independent of substituent
effects is bond length. Bond lengths to carbon depend strongly on the hybridization of the
carbon involved but are little in¯uenced by other factors. Table 1.2 lists the interatomic
distances for some of the most common bonds in organic molecules. The near constancy
of bond lengths from molecule to molecule re¯ects the fact that the properties of individual
bonds are, to a good approximation, independent of the remainder of the molecule.
Table 1.3 gives some bond-energy data. Part A includes bond energies for some
simple diatomic molecules and generalized values for some of the types of bonds found

Ê )a
Table 1.2. Bond Lengths (A

sp3 C H 1.09 sp3 ±sp3 C C 1.54 sp2 ±sp2 C C 1.46 C O 1.42

sp2 C H 1.086 sp3 ±sp2 C C 1.50 sp2 ±sp2 CC 1.34 CO 1.22
sp C H 1.06 sp3 ±sp C C 1.47 sp±sp CC 1.20

a. From experimental values tabulated for simple molecules by M. J. S. Dewar and W. Thiel, J. Am. Chem. Soc. 99:4907 (1977).
14 most often in organic molecules. The assumption that bond energies are independent of the
remainder of the molecule is a rather rough one. Part B of Table 1.3 lists some speci®c
CHEMICAL BONDING C H, C C, and other bond energies. It is apparent that some are substantially different
AND STRUCTURE from the generalized values. For example, the CH2 H bond dissociation energies listed for
propene and toluene are 85 kcal=mol, which is signi®cantly less than for a C H bond in
ethane (98 kcal=mol). The reason for the relative weakness of these particular bonds is that
the allyl and benzyl radicals that are produced by the bond dissociations are stabilized by

CH2• • CH2 CH2 CH2

A similar explanation lies behind the diminished strength of the sp3 ±sp3 carbon±
carbon bond in ethylbenzene. The general trend toward weaker C C bonds with increased
substitution that can be recognized in Table 1.3 re¯ects the increased stability of
substituted radicals relative to primary radicals.
The bond energies in Table 1.3 refer to homolytic bond dissociation to uncharged
radical fragments. Many reactions involve heterolytic bond cleavages. The energy for
heterolytic cleavage of C H or C C bonds in the gas phase is very high, largely because
of the energy required for charge separation. However, in solution, where stabilization of
the ions by solvation becomes possible, heterolytic bond dissociation can become
energetically feasible. Heterolytic bond dissociations are even more sensitive to structural
changes than homolytic ones. Table 1.4 gives a series of comparable ionization energies
for cleavage of H from hydrocarbons and Cl from chlorides in the gas phase. Besides

Table 1.3. Bond Energies (kcal=mol)

A. Some common bond energiesa

H H 103 C H 98 CC 145

C C 81 N H 92 CC 198
O O 34 O H 109 NN 225
Cl Cl 57 Cl H 102 CO 173
Br Br 45 Br H 87 C O 79
I I 36 I H 71 C N 66

B. Some speci®c bond dissociation energiesb

H3 C H 104 H3C CH3 88 H3 C F 108

CH3CH2 H 98 H5C2 CH3 85 H3 C Cl 84
H2CCH H 110c (CH3)2CH CH3 83 H3 C Br 70
HCC H 131 PhCH2 CH3 70 H3 C I 56
H2CCHCH2 H 85 H5C2 C2H5 82 H3 C OH 91
PhCH2 H 85 (CH3)2CH CH(CH3)2 78
H2N H 103 H2CCH2 171c
CH3NH H 92 HCCH 228c
CH3O H 102

a. From Table 1, G. J. Janz, Thermodynamic Properties of Organic Compounds, Academic Press, New York, 1967.
b. Except where noted, from J. A. Kerr, Chem. Rev. 66:465 (1966).
c. K. M. Ervin, S. Gronert, S. E. Barlow, M. K. Gilles, A. G. Harrison, V. M. Bierbaum, C. H. DePuy, W. C. Lineberger, and G.
B. Ellison, J. Am. Chem. Soc. 112:5750 (1990).
Table 1.4. Heterolytic Bond Dissociation Energies for 15
Some C H and C Cl Bondsa
R H ! R  H R Cl ! R  Cl BOND ENERGY,
R (kcal=mol) (kcal=mol)

CH3 312.2 227.1

CH3CH2 272.6 190.3
(CH3)2CH 249.9 171.0
CH2CH 290.2
CH2CHCH2 255.3

a. Data from C. G. Screttas, J. Org. Chem. 45:333 (1980).

noting the higher energies in comparison with the homolytic bond dissociation energies,
one can see that branching decreases the energy requirement for heterolytic bond cleavage
more dramatically than for homolytic cleavage. These bond-energy relationships are
consistent with the familiar order of carbocation stability, tert > sec > pri > methyl. Note
also that the heterolytic bond dissociation energies for allyl and vinyl bonds re¯ect the
stability of allyl cations and the instability of vinyl cations.
Smaller, but nevertheless signi®cant, differences in energies of organic molecules also
result from less obvious differences in structure. Table 1.5 gives the heats of formation of
some hydrocarbons. These energy values represent the heat evolved on formation of the
compound from its constituent elements under standard conditions. The heats of formation
therefore permit precise comparison of the stability of isomeric compounds. The more
negative the heat of formation, the greater is the stability. Direct comparison of compounds
having different elemental composition is not meaningful, because the total number of
bonds formed is then different.
Part A of Table 1.5 shows all the acyclic C4±C6 and some of the C8 hydrocarbons. A
general trend is discernible in the data. Branched-chain hydrocarbons are more stable than
straight-chain hydrocarbons. For example, DHf for n-octane is 49:82 kcal=mol, whereas
the most highly branched isomer possible, 2,2,3,3-tetramethylbutane, is the most stable of
the octanes, with DHf of 53:99 kcal=mol. Similar trends are observed in the other series.
Part B of Table 1.5 gives heats of formation for the C4, C5, and some of the C6
alkenes. A general relationship is also observed for the alkenes. The more highly
substituted the double bond, the more stable is the compound. There are also other factors
that enter into alkene stability. trans-Alkenes are usually more stable than cis-alkenes,
probably largely because of increased nonbonded repulsion in the cis isomer.22

1.2.2. Electronegativity and Polarity

Another fundamental property of chemical bonds is polarity. In general, it is to be

expected that the distribution of the pair of electrons in a covalent bond will favor one of
the two atoms. The tendency of an atom to attract electrons is called electronegativity.
There are a number of different approaches to assigning electronegativity, and most are
numerically scaled to a de®nition originally proposed by Pauling.23 Part A of Table 1.6

22. For a theoretical discussion of this point, see N. D. Epiotis, R. L. Yates, and F. Bernardi, J. Am. Chem. Soc.
97:5961 (1975).
23. For leading references, see G. Simons, M. E. Zandler, and E. R. Talaty, J. Am. Chem. Soc. 98:7869 (1976).
16 Table 1.5. Standard Enthalpies of Formation of Some Hydrocarbons (kcal=mol)a

CHAPTER 1 A. Saturated hydrocarbons

Butane 30.15 Octane 49.82
2-Methylpropane 32.15 2-Methylheptane 51.50
3-Methylheptane 50.82
C5 4-Methylheptane 50.69
Pentane 35.00 2,2,-Dimethylhexane 53.71
2-Methylbutane 36.90 2,3-Dimethylhexane 51.13
2,2-Dimethylpropane 36.97 2,4-Dimethylhexane 52.44
3,3-Dimethylhexane 52.61
C6 2,2,3-Trimethylpentane 52.61
Hexane 39.96 2,2,4-Trimethylpentane 53.57
2-Methylpentane 41.66 2,2,3,3-Tetramethylbutane 53.99
3-Methylpentane 41.02
2,3-Dimethylbutane 42.49
2,2-Dimethylbutane 44.35

B. Alkenes

C4 C6
1-Butene 0.03 1-Hexene 9.96
trans-2-Butene 2.67 trans-2-Hexene 12.56
cis-2-Butene 1.67 cis-2-Hexene 11.56
2-Methylpropene 4.04 trans-3-Hexene 12.56
cis-3-Hexene 11.56
C5 2-Methyl-1-pentene 13.56
1-Pentene 5.00 3-Methyl-pentene 11.02
trans-2-Pentene 7.59 4-Methyl-1-pentene 11.66
cis-2-Pentene 6.71 2-Methyl-2-pentene 14.96
2-Methyl-1-butene 8.68 3- Methyl-2-pentene 14.32
3-Methyl-1- butene 6.92 2,3-Dimethyl-1-butene 14.78
2- Methyl-2-butene 10.17 3,3-Dimethyl-1-butene 14.25
2,3-Dimethyl-2-butene 15.91

a. From F. D. Rossini, K. S. Pitzer, R. L. Arnett, R. M. Braun, and G. C. Pimentel, Selected Values of Physical and
Thermodynamic Properties of Hydrocarbons and Related Compounds, Carnegie Press, Pittsburgh, 1953.

gives the original Pauling values and also a more recent set based on theoretical calculation
of electron distributions. The concept of electronegativity can also be expanded to include
functional groups. Part B of Table 1.6 gives some values which are scaled to be
numerically consistent with elemental electronegativities, as well as a set based on
theoretical electron distribution calculations. These electronegativity values can serve to
convey a qualitative impression of the electron-attracting capacity of these groups.
The unequal distribution of electron density in covalent bonds produces a bond
dipole, the magnitude of which is expressed by the dipole moment, having the units of
charge times distance.24 Bonds with signi®cant bond dipoles are described as being polar.
The bond and group dipole moments of some typical substituents are shown in Table 1.7.

24. For more detailed discussion of dipole moments, see L. E. Sutton, in Determination of Organic Structures by
Physical Methods, Vol. 1, E. A. Braude and F. C. Nachod, eds., Academic Press, New York, 1955, Chapter 9; V.
I. Minkin, O. A. Osipov, and Y. A. Zhdanov, Dipole Moments in Organic Chemistry, Plenum Press, New York,
Table 1.6. Atomic and Group Electronegativities 17
A. Atomic electronegativities SECTION 1.2.
H 2.1 C 2.5; 2.35 N 3.0; 3.16 O 3.5; 3.52 F 4.0; 4.00 POLARITY, AND
Si 1.8; 1.64 P 2.1; 2.11 S 2.5; 2.52 Cl 3.0; 2.84 POLARIZABILITY
As 2.0; 1.99 Se 2.4; 2.40 Br 2.8; 2.52
I 2.5

B. Empirical electronegativities for some organic functional groupsb

CH3 2.3; 2.55 H 2.28; 1.20 F 3.95; 4.00

CH2Cl 2.75; 2.61 NH2 3.35; 3.12 Cl 3.03; 3.05
CHCl2 2.8; 2.66 NH3 3.8; 3.21 Br 2.80; 2.75
CCl3 3.0; 2.70 NO2 3.4; 3.22 I 2.28;
CF3 3.35; 2.71 OH 3.7; 3.55
Ph 3.0; 2.58
CHCH2 3.0; 2.58
CCH 3.3; 2.66
CN 3.3; 2.69

a. From L. Pauling, The Nature of the Chemical Bond, 3rd edition, Cornell University Press, Ithaca,
New York, 1960. Boldface values from G. Simons, M. E. Zandler, and E. R. Talaty, J. Am. Chem.
Soc. 98:7869 (1976).
b. From P. R. Wells, Prog. Phys. Org. Chem. 6:111 (1968). Boldface values from R. J. Boyd and S.
L. Boyd, J. Am. Chem. Soc. 114:1652 (1992).

It is possible to estimate with a fair degree of accuracy the dipole moment of a molecule as
the vector sum of the component bond dipoles. A qualitative judgment of bond polarity
can be made by comparing the electronegativities of the bound atoms or groups. The larger
the difference in electronegativity, the greater will be the bond dipole.
For most purposes, hydrocarbon groups can be considered to be nonpolar. There are,
however, small dipoles associated with C H bonds and bonds between carbons of
different hybridization or substitution pattern. For normal sp3 carbon, the carbon is
found to be slightly negatively charged relative to hydrogen.25 The electronegativity
order for hybridized carbon orbitals is sp > sp2 > sp3 . Scheme 1.1 lists the dipole
moments of some hydrocarbons and some other organic molecules.
Electronegativity is a fundamental characteristic of atoms that is transferred into
functional groups. Electronegativity correlates strongly with position in the periodic table.

Table 1.7. Bond and Group Dipoles for Some

Organic Functional Groupsa

Bond momentsb Bond momentsb Group momentsb

C H 0.4 C N 0.22 MeO 1.3

C F 1.41 C O 0.74 NH2 1.2
C Cl 1.46 CO 2.3 CO2H 1.7
C Br 1.38 CN 3.5 COMe 2.7
C I 1.19 NO2 3.1
CN 4.0

a. From C. P. Smyth, Dielectric Behavior and Structure, McGraw-Hill

Book Company, New York, 1955, pp. 244, 253.
b. In e.s. units  1018.

18 Scheme 1.1. Dipole Moments for Some Organic Compoundsa

0.34 0.800 0.253 0
0.503 0 0.366 0.781

B. Substituted molecules
H H H Cl H Cl
Cl Cl Cl H H Cl O
1.90 0 1.34 1.63
3.92 3.46 1.30 1.70 1.74 2.88 3.96

a. Units are in debye. Data are from Handbook of Chemistry and Physics, 78th edition, CRC Press, Inc., Boca
Raton, Florida, 1997.

Electronegativity increases going to the right in any row of the periodic table and decreases
going down any column. Because electronegativity is such an important property in
relation to chemical reactivity, there has been much effort to relate it to other atomic
properties. Mulliken pointed out that there is a relationship between ionization energy and
electron af®nity and the numerical electronegativity scale.26 The Mulliken electronega-
tivity can be expressed as
I A

where I is ionization potential and A is electron af®nity. Ionization energy measures the
energy required to remove an electron from an atom, whereas electron af®nity is the
energy released upon addition of an electron to an element. Both of these energies re¯ect
the degree of attraction the atomic nucleus has for electrons and correlate with position in
the periodic table. The metallic atoms readily release electrons, whereas the halogen atoms
are avid electron acceptors.
The polarity of covalent bonds between carbon and substituents is the basis of
important structure±reactivity relationships in organic chemistry. The effects of polar
bonds are generally considered to be transmitted in two ways. Successive polarization
through bonds is called the inductive effect. It is expected that such an effect would
diminish as the number of intervening bonds increases.

δ+ δδδ+

26. R. S. Mulliken, J. Chem. Phys. 2:782 (1934); R. S. Mulliken, J. Chem. Phys. 3:573 (1935).
The second component is called a ®eld effect and is attributed to through-space interactions 19
of the electric dipoles resulting from polar bonds.

In Chapter 4, we will discuss the relative importance of inductive effects and ®eld effects
on reactivity. Generally, ®eld effects appear to be the dominant mechanism for the
transmission of electrostatic effects of polar bonds to other parts of a molecule.
One of the most extensively explored series of substituent effects involves the acidity
of carboxylic acids. The pKa values of some derivatives of acetic acid are presented in
Table 1.8. These data illustrate that substitution of hydrogen by a more electronegative
atom or group increases the equilibrium constant for ionization, that is, makes the
derivative a stronger acid. The highly electronegative ¯uorine atom causes a larger
increase in acidity than the somewhat less electronegative chlorine atom. A slight acid-
weakening effect of a methyl substituent is observed when propanoic acid is compared
with acetic acid. The pKa data refer to measurements in solution, and some care must be
taken in interpreting the changes in acidity solely on the basis of electronegativity. In fact,
measurements in the gas phase show that propanoic acid is a slightly stronger acid than
acetic acid.27 In the case of acid dissociation in solution, both the proton and the
carboxylate anion are strongly solvated, and this greatly favors the dissociation process
in solution relative to the gas phase. We can discuss trichloroacetic acid, in which polar
C Cl bonds have replaced C H bonds as an example.

δ– δ–
H O H O Cl O Cl O
δ+ δ+
H C C H C C – Cl C C Cl C C –
δ– δ–
H O H H O Cl O H Cl O
very little dipolar stabilization strong dipolar stabilization
of the anion of the anion

Table 1.8. Acidity of Substituted Acetic Acids

H2O (pKa )a Gas phase (DG)b

(CH3)3CCO2H 5.0 337.6

(CH3)2CHCO2H 4.9 339.0
CH3CH2CO2H 4.9 340.4
CH3CO2H 4.8 341.5
HCO2H 3.8 338.3
FCH2CO2H 331.6
ClCH2CO2H 2.7 329.0
F3CCO2H 317.4
Cl3CCO2H 0.7
O2NCH2CO2H 1.3

a. From Stability Constants and Stability Constants, Supplement

No. 1, Special Publications 17 (1964) and 25 (1971), The
Chemical Society, London.
b. DG for AH ! H  A in kcal=mol at 300 K; from G.
Caldwell, R. Renneboog, and P. Kebarle, Can. J. Chem.
67:611 (1989).

27. R. Yamdagni and P. Kebarle, J. Am. Chem. Soc. 95:4050 (1973).

20 For the acid dissociation equilibrium,

dissociation places a negative charge on the carboxylate residue and increases the electron
density at the carboxyl group carbon and oxygen atoms. For acetic acid, where R  CH3,
this increase occurs adjacent to the carbon on the methyl group, which bears a very small
negative charge. In the case of trichloroacetic acid, R  CCl3, the corresponding carbon is
somewhat positive as a result of the C Cl bond dipoles (inductive effect). The cumulative
effect of the three C Cl bond dipoles establishes a strong dipole (®eld effect) associated
with the CCl3 group. As a result, the development of negative charge is more favorable,
and trichloroacetic acid is a stronger acid than acetic acid.
It is always important to keep in mind the relative nature of substituent effects. Thus,
the effect of the chlorine atoms in the case of trichloroacetic acid is primarily to stabilize
the dissociated anion. The acid is more highly dissociated than in the unsubstituted case
because there is a more favorable energy difference between the parent acid and the anion.
It is the energy differences, not the absolute energies, that determine the equilibrium
constant for ionization. As we will discuss more fully in Chapter 4, there are other
mechanisms by which substituents affect the energy of reactants and products. The
detailed understanding of substituent effects will require that we separate polar effects
from these other factors.
It can be seen from the data in Table 1.8 that alkyl substituents slightly decrease the
acidity of carboxylic acids in solution. This is a general effect and is attributable to two
factors. One is a steric effect. The increasing steric bulk somewhat destabilizes the
carboxylate anion by decreasing the effectiveness of solvation.28 Alkyl groups also have an
inductive=®eld effect that decreases acidity. This results from the weak electron-donating
character of the alkyl substituent which causes acetic acid and other alkanoic acids to be
weaker acids than formic acid both in solution and in the gas phase. The alkyl group
donates charge density to the carbonyl carbon, thereby reducing the acidity of the carboxyl
The second column in Table 1.8 shows the free energy for dissociation of some of the
same acids in the gas phase. The effects of strongly electron-withdrawing groups are still
evident. There is frequently a large difference in the energy of chemical processes in the
gas and solution phases because of the importance of solvation. In the gas phase, alkyl
groups enhance acidity. This is attributed to the greater polarizability of the larger
substituents. In the case of molecules in the gas phase, any stabilization of the negative
charge must be accomplished by internal charge redistribution.30 With larger substituents,
the larger molecular volume and the larger number of atoms that can participate lead to a
greater stabilization.

1.2.3. PolarizabilityÐHardness and Softness

Another property that is closely related to electronegativity and position in the

periodic table is polarizability. Polarizability is related to the size of atoms and ions and the
28. K. Bowden and R. G. Young, Can. J. Chem. 47:2775 (1969).
29. A. D. Headley, M. E. McMurry, and S. D. Starnes, J. Org. Chem. 59:1863 (1994); M. R. F. Siggel and T. D.
Thomas, J. Am. Chem. Soc. 114:5795 (1992).
30. G. Caldwell, R. Renneboog, and P. Kebarle, Can. J. Chem. 67:611 (1989).
ease with which the electron cloud can be distorted. There is a mathematical correlation 21
between polarizability and atomic volume, and polarizability is also related to the LUMO±
HOMO energy gap. (See Section 1.6 if the terms HOMO and LUMO are unfamiliar.) BOND ENERGY,
hard soft
Qualitative relationship between orbital
energies, hardness, and softness

Numerical measures of polarizability analogous to electronegativity have been

de®ned.31 Hardness Z is numerically expressed as

Z  12 I A

where I is the ionization potential and A is the electron af®nity. Softness s is the opposite
of hardness and is numerically expressed as

s  1=Z

These two properties are closely related to the HOMO and LUMO energies of molecules
and ions. The larger the HOMO±LUMO gap, the greater is the hardness. Numerically,
hardness is approximately equal to half the energy gap, as de®ned above for atoms. In
general, chemical reactivity increases as LUMO energies decrease and HOMO energies
increase. The implication is that softer chemical species, those with smaller HOMO±
LUMO gaps, will tend to be more reactive than harder ones. In qualitative terms, this can
be described as the ability of nucleophiles or bases to donate electrons more readily to
electrophiles and acids to begin the process of bond formation. Interactions between harder
chemical entities are more likely to be dominated by electrostatic interactions. Table 1.9
gives some hardness values for atoms and common small molecules and ions.
Figure 1.8 shows the I ±A gap (2Z) for several radicals. Note that there is a correlation
with electronegativity and position in the periodic table. The halogen anions and radicals
become progressively softer from ¯uorine to iodine. Across the second row, softness
decreases from carbon to ¯uorine. Highly electronegative atoms tend to be hard, whereas
less electronegative atoms are softer. Polarizability is also a function of atomic number.
Larger atoms are softer than smaller atoms of similar electronegativity. The charge on an
atom also in¯uences polarizability. Metal cations, for example, become harder as the
oxidation number increases. Values for the hardness of some metal cations that are
frequently of interest in organic chemistry are included in Table 1.9. A useful precept for
understanding Lewis acid±base interactions is that hard acids prefer hard bases, and soft
acids prefer soft bases. The hard±hard interactions are dominated by electrostatic
attraction, whereas soft±soft interactions are dominated by mutual polarization.32

31. R. G. Parr and R. G. Pearson, J. Am. Chem. Soc. 105:7512 (1983).

32. R. G. Pearson, J. Am. Chem. Soc. 85:3533 (1963); T. L. Ho, Hard and Soft Acids and Bases in Organic
Chemistry, Academic Press, New York, 1977; W. B. Jensen, The Lewis Acid±Base Concept, Wiley-
Interscience, New York, 1980, Chapter 8.
22 Table 1.9. Hardness of Some Atoms, Acids,
and Basesa
H 6.4 H 1 H 6.8
Li 2.4 Li 35.1 F 7.0
C 5.0 Mg2 32.5 Cl 4.7
N 7.3 Na 21.1 Br 4.2
O 6.1 Ca2 19.7 I 3.7
F 7.0 Al3 45.8 CH3 4.0
Na 2.3 Cu 6.3 NH2 5.3
Si 3.4 Cu2 8.3 OH 5.6
P 4.9 Fe2 7.3 SH 4.1
S 4.1 Fe3 13.1 CN 5.3
Cl 4.7 Hg2 7.7
Pb2 8.5
Pd2 6.8

a. From R. G. Parr and R. G. Pearson, J. Am. Chem. Soc.

105:7512 (1983).

Another useful generalization is the principle of maximum hardness.33 This states

that molecular arrangements that maximize hardness are preferred. Electronegativity and
hardness determine the extent of electron transfer between two molecular fragments in a
reaction. This can be approximated numerically by the expression

wX wY
DN 
2ZX  ZY 

Fig. 1.8. Ionization energy (I ) and electron af®nity (A) gaps in eV for radicals. [Adapted from R. G.
Pearson, J. Am. Chem. Soc. 110:7684 (1988).]

33. R. G. Pearson, Acc. Chem. Res. 26:250 (1993); R. G. Parr and Z. Zhou, Acc. Chem. Res. 26:256 (1993); R. G.
Pearson, J. Org. Chem. 54:1423 (1989); R. G. Parr and J. L. Gazquez, J. Phys. Chem. 97:3939 (1993).
where w is absolute electronegativity and Z is hardness for the reacting species. For 23
example, one can calculate the values for each of the four halogen atoms reacting with the
methyl radical to form the corresponding methyl halide. MOLECULAR
X  CH3  ! CH3 X


F 10.4 7.0 0.23 9.4

Cl 8.3 4.7 0.17 7.5
Br 7.6 4.2 0.14 5.8
I 6.8 3.7 0.10 4.7

According to this analysis, the C X bond will be successively both more polar and harder
in the order I < Br < Cl < F. This result is in agreement with both the properties and the
reactivities of the methyl halides. When comparable bonds are considered, reacting species
of greater hardness result in a larger net charge transfer, which adds an increment to the
exothermicity of bond formation. That is, bonds formed between two harder reactants will
be stronger than those between two softer reactants.34 This is an example of a general
relationship that recognizes that there is an increment to bond strength resulting from
added ionic character. Indeed, quite accurate estimates of bond strength can be made by
methods that add an increment due to the electronegativity difference between atoms.35
The concepts of electronegativity, hardness, and polarizability are all interrelated. For
the kind of qualitative applications we will make in discussing reactivity, the concept that
initial interactions between reacting molecules can be dominated by either partial electron
transfer by bond formation (soft reactants) or by electrostatic interaction (hard reactants) is
a useful generalization.
The ideas about bond length, bond energies, polarity, and polarizability discussed in
this section are very useful because of the relative constancy of these properties from
molecule to molecule. Thus, data obtained from simple well-characterized molecules can
provide a good guide to the properties of substances whose structures are known but which
have yet to be studied in detail. Organic chemists have usually discussed this transferability
of properties in terms of valence bond theory. Thus, the properties are thought of as
characteristic of the various types of atoms and bonds. The properties of the molecule are
thought of as the sum of the properties of the bonds. This has been a highly fruitful
conceptual approach in organic chemistry. As we shall see in the next section, there is an
alternative description of molecules which is also highly informative and useful.

1.3. Molecular Orbital Theory and Methods

Another broad approach to the description of molecular structure that is of

importance in organic chemistry is molecular orbital theory. Molecular orbital (MO)
theory pictures electrons as being distributed among a set of molecular orbitals of discrete
34. P. K. Chattaraj, A. Cedillo, R. G. Parr, and E. M. Arnett, J. Org. Chem. 60:4707 (1995).
35. R. R. Reddy, T. V. R. Rao, and R. Viswanath, J. Am. Chem. Soc. 111:2914 (1989).
24 energies. In contrast to the orbitals described by valence bond theory, which are usually
concentrated between two speci®c atoms, molecular orbitals can extend over the entire
CHEMICAL BONDING molecule. MO theory is based on the SchroÈdinger equation,
Hc  Ec

in which c is a wave function describing an orbital, H is the Hamiltonian operator, and E

is the energy of an electron in a particular orbital. The wave function describes the
interaction of the electron with the other electrons and nuclei of the molecule. The total
electronic energy is the sum of the individual electron energies:
E  cHc dt when c2 dt  1

In order to make the mathematics tractable, approximations must be made. The

choice of approximations has produced a variety of MO methods, the judicious application
of which can provide valuable insight into questions of bonding, structure, dynamics, and
reactivity. The discussion that follows will not be suf®ciently detailed or complete for the
reader to understand how the calculations are performed or the details of the approxima-
tions. Instead, the nature of the information that is obtained will be described, and the ways
in which organic chemists have applied the results of MO theory will be illustrated.
Several excellent books are available which provide detailed treatment of various aspects
of MO methods.36
There is a trade-off between the accuracy of the calculation and the amount of
computation required. In general, the more severe the approximations, the more limited is
the range of applicability of the particular calculation. An organic chemist who wishes to
make use of the results of MO calclulations must therefore make a judgment about the
suitability of the various methods to the particular problem. The rapid increases that have
occurred in computer speed and power have made the application of sophisticated methods
practical for increasingly larger molecules.
Mathematically, the molecular orbitals are treated as linear combinations of atomic
orbitals, so that the wave function, c, is expressed as a sum of individual atomic orbitals
multiplied by appropriate weighting factors (atomic coef®cients):

c  c1 f1  c2 f2      cn fn

The coef®cients indicate the contribution of each atomic orbital to the molecular orbital.
This method of representing the molecular orbital wave function in terms of combinations
of atomic orbital wave functions is known as the linear combination of atomic orbitals
approximation (LCAO). The combination of atomic orbitals chosen is called the basis set.

36. M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGraw-Hill, New York, 1969; W. T.
Borden, Modern Molecular Orbital Theory for Organic Chemists, Prentice-Hall, Englewood Cliffs, New
Jersey, 1975; H. E. Zimmerman, Quantum Mechanics for Organic Chemists, Academic Press, New York,
1975; I. G. Csizmadia, Theory and Practice of MO Calculations on Organic Molecules, Elsevier, Amsterdam,
1976; M. J. S. Dewar and R. C. Dougherty, The PMO Theory of Organic Chemistry, Plenum Press, New York,
1975; T. A. Albright, J. K. Burdett, and M.-H. Whangbo, Orbital Interactions in Chemistry, John Wiley &
Sons, New York, 1985; W. G. Richards and D. L. Cooper, Ab Initio Molecular Orbital Calculations for
Chemists, 2nd ed., Clarendon Press, Oxford, U.K., 1983; W. J. Hehre, L. Radom, P. Schleyer, and J. Pople, Ab
Initio Molecular Orbital Theory, Wiley-Interscience, New York, 1986.
A minimum basis set for molecules containing C, H, O, and N would consist of 2s, 2px , 25
2py , and 2pz orbitals for each C, N, and O and a 1s orbital for each hydrogen. The basis
sets are mathematical expressions describing the properties of the atomic orbitals. MOLECULAR
Two main streams of computational techniques branch out from this point. These are ORBITAL THEORY
referred to as ab initio and semiempirical calculations. In both ab initio and semiempirical
treatments, mathematical formulations of the wave functions which describe hydrogen-like
orbitals are used. Examples of wave functions that are commonly used are Slater-type
orbitals (abbreviated STO) and Gaussian-type orbitals (GTO). There are additional
variations which are designated by additions to the abbreviations. Both ab initio and
semiempirical calculations treat the linear combination of orbitals by iterative computa-
tions that establish a self-consistent electrical ®eld (SCF) and minimize the energy of the
system. The minimum-energy combination is taken to describe the molecule.
The various semiempirical methods differ in the approximations which are made
concerning repulsions between electrons in different orbitals. The approximations are then
corrected for by ``parameterization,'' whereby parameters are included in the protocol to
adjust the results to match more accurate calculations or experimental data. The reliability
and accuracy of the semiempirical methods have evolved, and the increasing power of
computers has permitted wider application of the more accurate methods. The earliest
semiempirical methods to be applied extensively to organic molecules included the
extended HuÈckel theory37 (EHT) and the CNDO (complete neglect of differential overlap)
methods.38 These methods gave correct representations of the shapes and trends in charge
distribution in the various molecular orbitals but were only roughly reliable in describing
molecular geometry. These methods tend to make large errors in calculation of total
energies of molecules. Improved semiempirical calculations give better representations of
charge distributions, molecular geometry, and ground-state total energies. Among these
methods are MINDO-3,39 MNDO,40 AM1,41 and PM3.42 (The acronyms refer to titles of
the methods.) There are differences among the methods in the ranges of compounds for
which the results are satisfactory.
Ab initio calculations are iterative procedures based on self-consistent ®eld (SCF)
methods. Normally, calculations are approached by the Hartree±Fock closed-shell approx-
imation, which treats a single electron at a time interacting with an aggregate of all the
other electrons. Self-consistency is achieved by a procedure in which a set of orbitals is
assumed, and the electron±electron repulsion is calculated; this energy is then used to
calculate a new set of orbitals, which in turn are used to calculate a new repulsive energy.
The process is continued until convergence occurs and self-consistency is achieved.43
The individual ab initio calculations are further identi®ed by abbreviations for the
basis set orbitals that are used. These abbreviations include, for example, STO-3G,44
4-31G,45 and 6-31G.46 In general, the ab initio calculations make fewer assumptions than
semiempirical methods, and therefore the computations are more demanding.
37. R. Hoffmann, J. Chem. Phys. 39:1397 (1963).
38. J. A. Pople and G. A. Segal, J. Chem. Phys. 44:3289 (1966).
39. R. C. Bingham, M. J. S. Dewar, and D. H. Lo, J. Am. Chem. Soc. 97:1285, 1294, 1302 (1975).
41. M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, and J. J. P. Stewart, J. Am. Chem. Soc. 109:3902 (1985).
42. J. J. P. Stewart, J. Comput. Chem. 10:209, 221 (1989).
43. C. C. J. Roothaan, Rev. Mod. Phys. 23:69 (1951); R. Pariser and R. G. Parr, J. Chem. Phys. 21:767 (1953); J. A.
Pople, J. Phys. Chem. 61:6 (1957).
44. W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys. 51:2657 (1971).
45. R. Ditch®eld, W. J. Hehre, and J. A. Pople, J. Chem. Phys. 54:724 (1971).
46. W. J. Hehre, R. Ditch®eld, and J. A. Pople, J. Chem. Phys. 56:2257 (1972).
26 Another distinguishing aspect of MO methods is the extent to which they deal with
electron correlation. The Hartree±Fock approximation does not deal with correlation
CHEMICAL BONDING between individual electrons, and the results are expected to be in error because of this,
AND STRUCTURE giving energies above the exact energy. MO methods that include electron correlation have
been developed. The calculations are usually done using Mùller±Plesset perturbation
theory and are designated MP calculations.47
Among the most widely used ab initio methods are those referred to as G148 and
G2. These methods incorporate large basis sets including d and f orbitals, called 6-
311**. The calculations also have extensive con®guration interaction terms at the Mùller±
Plesset fourth order (MP4) and further terms referred to as quadratic con®guration
interaction (QCISD).50 Finally, there are systematically applied correction terms calibrated
by exact energies from small molecules.
Current MO methods give excellent results on ground-state molecular geometry and
charge distribution. They can also give excellent agreement with experimental data in the
calculation of relative molecular energies. The calculation of these quantities normally
refers to isolated molecules; i.e., the calculated values correspond to those for the molecule
in the gas phase. The energy changes associated with dynamic processes can be studied by
calculation of molecular energy as a function of molecular distortion. Much effort is also
being devoted to the description of reaction processes. This is an especially formidable
task because information about solvent participation and exact separation of reacting
molecules is imprecise. In cases where good assumptions about such variables can be
made, ab initio MO calculations can give good estimates of the energy changes associated
with chemical reactions.
The results of all types of MO calculations include the energy of each MO, the total
electronic energy of the molecule relative to the separated atoms, and the coef®cients of
the atomic orbitals (AOs) contributing to each MO. Such information may be applied
directly to a number of physical and chemical properties. The total electronic energy
obtained by summing the energies of the occupied orbitals gives the calculated molecular
energy. Comparison of isomeric molecules permits conclusions about the relative
stabilities of the compounds. Conclusions about molecular stability can be checked by
comparison with thermodynamic data when they are available. Conformational effects can
be probed by calculating the total energy as a function of molecular geometry. The
minimum energy should correspond to the most favorable conformation. Most calculations
are done on single molecules, not an interacting array of molecules. Thus, the results are
most comparable to the situation in the gas phase, where intermolecular forces are weak.
The types of data which are obtained by MO calculations are illustrated in the following
The coef®cients for the AOs that comprise each MO may be related to the electron
density at each atom by the equation

qr  nj cjr 2

47. C. Mùller and M. S. Plesset, Phys. Rev. 46:618 (1934); J. S. Brinkley and J. A. Pople, Int. J. Quantum Chem.
9S:229 (1975); K. Raghavachari and J. B. Anderson, J. Phys. Chem. 100:12960 (1996).
48. J. A. Pople, M. Head-Gordon, D. J. Fox, K. Raghavachari, and L. A. Curtiss, J. Chem. Phys. 90:5622 (1989);
M. Head-Gordon, J. Phys. Chem. 100:13213 (1996).
49. L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys. 94:7221 (1991); L. A. Curtiss,
K. Raghavachari, and J. A. Pople, J. Chem. Phys. 98:1293 (1993).
50. J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Chem. Phys. 87:5968 (1987).
which gives the electron density at atom r as the sum over all the occupied MOs of the 27
product of the number of electrons in each orbital and the square of the coef®cient at atom
r for each orbital. To illustrate, the coef®cients calculated for the methyl cation by the MOLECULAR
CNDO=2 method are given in Table 1.10. There are seven MOs generated from the three ORBITAL THEORY
orbitals for the six-electron system. The carbon atom is calculated to have 3.565 electrons
(exclusive of the 1s electrons), and each hydrogen atom is calculated to have 0.812
0:435  30:188  1:000 electron. A sample calculation of the hydrogen electron density
from the orbital coef®cients follows:

qH  20:35282  20:09992  20:52102  0:812

Further examination of Table 1.10 reveals that the lowest unoccupied molecular orbital,
orbital. The MO picture is in agreement with the usual qualitative hybridization picture for
the methyl cation.
MO methods can also be used to calculate heats of formation (DHf ) of molecules or
heats of reaction (DH) by comparing the heats of formation of reactants and products. The
total stabilization energy calculated for even a small hydrocarbon, relative to the separated
nuclei and electrons, is very large (typically, 50,000±100,000 kcal=mol for C2 and C4
compounds, respectively). The energy differences that are of principal chemical interest,
such as DH for a reaction, are likely to be in the range of 0±50 kcal=mol. A very small
error, relative to the total energy, in a MO calculation becomes an enormous error in a
calculated DH. Fortunately, the absolute errors for compounds of similar structure are
likely to be comparable so that the errors will cancel in calculation of the energy
differences between related molecules. Calculation of heats of formation and heats of
reaction is frequently done on the basis of isodesmic reactions51 in order to provide for
maximum cancellation of errors in total binding energies. An isodesmic reaction is de®ned
as a process in which the number of formal bonds of each type is kept constant; that is, the
numbers of C H, CC, CO, etc., bonds on each side of the equation are identical.52
Although the reaction may not correspond to any real chemical process, the calculation can

Table 1.10. Coef®cients of Wave Functions Calculated for Methyl Cation by the CNDO=2

Orbital C2s C2px C2py C2pz H H H

c1 0.7915 0.0000 0.0000 0.0000 0.3528 0.3528 0.3528

c2 0.0000 0.1431 0.7466 0.0000 0.0999 0.4012 0.5011
c3 0.0000 0.7466 0.1431 0.0000 0.5210 0.3470 0.1740
c4 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000
c5 0.6111 0.0000 0.0000 0.0000 0.4570 0.4570 0.4570
c6 0.0000 0.5625 0.3251 0.0000 0.5374 0.5377 0.0003
c7 0.0000 0.3251 0.5625 0.0000 0.3106 0.3101 0.6207

a. The orbital energies (eigenvalues) are not given. The lowest-energy orbital is c1 ; the highest-energy orbital, c7 .

51. W. J. Hehre, R. Ditch®eld, L. Radom, and J. A. Pople, J. Am. Chem. Soc. 92:4796 (1970).
52. D. A. Ponomarev and V. V. Takhistov, J. Chem. Educ. 74:201 (1997).
28 Table 1.11. Calculated and Experimental DH Values for Some Isodemic Reactions

CHAPTER 1 Calculated Calculated

CHEMICAL BONDING DH (4-31G)a DH (6-31G)b Experimental
Reaction (kcal=mol) (kcal=mol) DH (kcal=mol)

CH3 CH2 CH3  CH4 ! 2CH3 CH3 1.0 0.8 2.6

3CH4 ! 2CH3 CH3  CH2 CH2 58 50.4 43.9

H2 CCO  CH4 ! CH2 CH2  H2 CO 12.8 13.3 15.0

CH3 CN  CH4 ! CH3 CH3  HCN 12.0 11.7 14.4

b. From W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. Pople, Ab Initio Molecular Orbital Theory, John Wiley & Sons,
New York, 1986, pp. 299±305.

provide a test of the reliability of the computational methods because of the comparability
of DHf data. The ``experimental'' DH for a reaction can be obtained by summation of
tabulated DHf for reactants and products. Table 1.11 gives some DH values calculated at
the 4-31G and 6-31G level of theory for some isodesmic reactions.
The relative merits of various MO methods have been discussed in the literature.53 In
general, the ab initio type of calculations will be more reliable, but the semiempirical
calculations are faster in terms of computer time. The complexity of calculation also
increases rapidly as the number of atoms in the molecule increases. The choice of a
method is normally made on the basis of evidence that the method is adequate for the
problem at hand and the availability of appropriate computer programs and equipment.
Results should be subjected to critical evaluation by comparison with experimental data or
checked by representative calculations using higher-level methods. Table 1.12 lists some
reported deviations from experimental DHf for some small hydrocarbons. The extent of
deviation gives an indication of the accuracy of the various types of MO calculations in
this application.
The use of MO methods to probe the relationship between structure and energy can
be illustrated by a study of CH3  , CH3 , and CH3 . The study employed ab initio
calculations and the 4-31G basis set and was aimed at exploring the optimum geometry
and resistance to deformation in each of these reaction intermediates.54 Figure 1.9 is a plot
of the calculated energy as a function of deformation from planarity for the three species.
Whereas CH3  and CH3  are found to have minimum energy at y  0 , that is, when the
molecule is planar, CH3 is calculated to have a nonplanar equilibrium geometry. This
calculated result is in good agreement with a variety of experimental observations which
will be discussed in later chapters where these intermediates are discussed in more detail.

53. J. A. Pople, J. Am. Chem. Soc. 97:5306 (1975); W. J. Hehre, J. Am. Chem. Soc. 97:5308 (1975); T. A. Halgren,
D. A. Kleier, J. H. Hall, Jr., L. D. Brown, and W. N. Lipscomb, J. Am. Chem. Soc. 100:6595 (1978); M. J. S.
Quantum Chemistry, 3rd ed., Allyn and Bacon, Boston, 1983, pp. 507±512; W. Hehre, L. Radom, P. v. R.
Chapter 6; B. H. Besler, K. M. Merz, Jr., and P. Kollman, J. Comput. Chem. 11:431 (1990); M. Sana and M. T.
Nguyen, Chem. Phys. Lett. 196:390 (1992).
54. E. D. Jemmiss, V. Buss, P. v. R. Schleyer, and L. C. Allen, J. Am. Chem. Soc. 98:6483 (1976).
Table 1.12. Deviations of Calculated DHf Values from Experimental DHf Dataa 29
b c d
Hydrocarbon MNDO AM1 PM3 3-21G 6-31G G2 MP4=QCI SECTION 1.3.
Methane 5.9 9.0 4.9 0.9 0.5 0.7 0.6 ORBITAL THEORY
Ethane 0.3 2.6 2.1 0.2 1.9 0.2 0.7 AND METHODS
Ethene 3.1 4.0 4.2 1.6 2.4 0.3 0.1
Allene 1.6 0.6 1.5 2.6 6.8 0.0e
1,3-Butadiene 2.7 3.6 5.0 4.7 2.9f 0.5g
Cyclopropane 1.5 5.1 3.5 2.4
Cyclobutane 18.7 0.2 10.6
Cyclopentane 12.0 10.5 5.6 6.1f
Cyclohexane 5.3 9.0 1.5 9.1f
Benzene 1.5 2.2 3.6 4.0h

a. Except as noted, energy (kcal/mol) comparisons are from M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, and J. J. P. Stewart, J.
Am. Chem. Soc. 107:3902 (1985).
b. J. J. P. Stewart, J. Comput. Chem. 10:221 (1989).
c. J. A. Pople, M. Head-Gordon, D. J. Fox, K. Raghavachari, and L. A. Curtiss, J. Chem. Phys. 90:5622 (1989); L. A. Curtiss, K.
d. M. Sana and M. T. Nguyen, Chem. Phys. Lett. 196:390 (1992).
e. D. W. Rogers and F. W. McLafferty, J. Phys. Chem. 99:1375 (1993).
f. M. Selmi and J. Tomasi, J. Phys. Chem. 99:5894 (1995).
g. M. N. Glukhovtsev and S. Laiter, Theor. Chim. Acta 92:327 (1995).
h. A. Nicolaides and L. Radom, J. Phys. Chem. 98:3092 (1994).



δ+ δ+
:X C+ C X C

Fig. 1.9. Total energy as a function of distortion from

planarity for methyl cation, methyl radical, and methyl
anion. [Reproduced from J. Am. Chem. Soc. 98:6483
(1976) by permission of the American Chemical Society.]
Table 1.13. Calculated Stabilization Resulting from Substituents on
30 the Methyl Cation
CHEMICAL BONDING Stabilization in kcal=mol
Substituent 4-31Ga 6-31G*b;c MP2=6-31G**c MP3=6-31G*d

F 2.1 14.16 21.5

OH 48.0 53.77 62.7
NH2 93.0 87.33 97.8
CH3 30.0 30.2 41.5 34.1
CHCH2 53.9 66.1
CHO 5.2 0.2
CN 13.0 4.3
NO2 40.7 22.3

a. Y. Apeloig, P. v. R. Schleyer, and J. A. Pople, J. Am. Chem. Soc. 99:1291 (1977).

b. F. Bernardi, A. Bottoni, and A. Venturini, J. Am. Chem. Soc. 108:5395 (1986).
c. X. Creary, Y.-X. Wang, and Z. Jiang, J. Am. Chem. Soc. 117:3044 (1995).
d. Y. Apeloig, in Heteroatom Chemistry, E. Block, ed., VCH Press, Weinheim, 1990, p. 27.

An ab initio study using 4-31G basis set orbitals gave the stabilization energies shown in
Table 1.13.55 The table shows the calculated stabilization, relative to the methyl cation, that
results from electron release by the substituent. The p-donor effects of the ¯uorine,
oxygen, and nitrogen atoms are partially counterbalanced by the inductive electron
withdrawal through the s bond. In the case of the oxygen and nitrogen substitutents,
the p-donor effect is dominant, and these substituents strongly stabilize the carbocation.
For the ¯uorine substituent, the balance is much closer and the overall stabilization is
calculated to be quite small. We will return to the case of the methyl group and its
stabilizing effect on the methyl cation a little later.
In the case of the methyl anion, stabilization will result from electron-accepting
substituents. Table 1.14 gives some stabilization energies calculated for a range of
substituents.56 Those substituents that have a low-lying p orbital capable of accepting
electrons from the carbon 2pz orbital (BH2, CN, NO2, and CHO) are strongly
stabilizing. Electronegative substituents without p-acceptor capacity reveal a smaller
stabilization of the methyl anion. The order is F > OH > NH2, which parallels the ability
of these substituents to act as s-electron acceptors. The strong effect of the tri¯uoromethyl
group is a combination of both s- and p-bond effects.
The substituent stabilization effects calculated for the methyl cation and the methyl
anion refer to the gas phase, where no solvation effects are present, and therefore are
substantially larger, in terms of energy, than would be the case in solution, where solvation
contributes to stabilization and attenuates the substituent effects.
The allyl carbocation is an example of an intermediate whose structure has been
extensively investigated by MO methods. The hybridization=resonance approach discussed
earlier readily rationalizes some of the most prominent features of the allyl carbocation.
The resonance structures suggest a signi®cant stabilization and imply that the molecule
would be planar in order to maximize the overlap of the p system.
+ +

56. A. Pross, D. J. DeFrees, B. A. Levi, S. K. Pollack, L. Radom, and W. J. Hehre, J. Org. Chem. 46:1693 (1981).
Table 1.14. Calculated Stabilization of Methyl 31
Anion by Substituents
Stabilization in kcal=mol
Substituent 4-31Ga 6-31G*b QC150c

BH2 68 61.4 54.0

CH3 2 1.4 3.2
NH2 5 3.3 0.5
F 25 14.6 10.4
CHCH2 38
CHO 72
CN 61
CF3 57
NO2 98


b. G. W. Spitznagel, T. Clark, J. Chandrasekhar, and P. v. R.
Schleyer, J. Comput. Chem. 3:363 (1982).
c. A. M. El-Nahas and P. v. R. Schleyer, J. Comput. Chem.
15:596 (1994).

These structural effects are also found by MO calculations. Calculations at the MP4=6-
311G** level have been performed on the allyl cation and indicate a rotation barrier of
36±38 kcal=mol.57

1.4. HuÈckel Molecular Orbital Theory

Before computers enabled elaborate MO calculations to be performed routinely, it

was essential that greatly simplifying approximations be applied to the molecules of
interest to organic chemists. The most useful of these approximations were those
incorporated in HuÈckel molecular orbital (HMO) theory for treatment of conjugated
systems. HMO theory is based on the assumption that the p system can be treated
independently of the s framework in conjugated planar molecules and that it is the p
system that is of paramount importance in determining the chemical and spectroscopic
properties of conjugated polyenes and aromatic compounds. The basis for treating the s
and p systems as independent of each other is their orthogonality. The s skeleton of a
planar conjugated system lies in the nodal plane of the p system and does not interact with
it. Because of its simplicity, HMO theory has been extremely valuable in the application of
MO concepts to organic chemistry. It provides a good qualitative description of the p
molecular orbitals in both cyclic and acyclic conjugated systems. In favorable cases such
as aromatic ring systems, it provides a quite thorough analysis of the relative stability of
related structures.
In the HMO approximation, the p-electron wave function is expressed as a linear
combination of the pz atomic orbitals (for the case in which the plane of the molecule
coincides with the x±y plane). Minimizing the total p-electron energy with respect to the
coef®cients leads to a series of equations from which the atomic coef®cients can be
extracted. Although the mathematical operations involved in solving the equation are not
32 dif®cult, we will not describe them in detail but will instead concentrate on the
interpretation of the results of the calculations. For many systems, the HuÈckel MO
CHEMICAL BONDING energies and atomic coef®cients have been tabulated.58
AND STRUCTURE The most easily obtained information from such calculations is the relative orderings
of the energy levels and the atomic coef®cients. Solutions are readily available for a
number of frequently encountered delocalized systems, which we will illustrate by
referring to some typical examples. Consider, ®rst, linear polyenes of formula Cn Hn2
such as 1,3-butadiene, 1,3,5-hexatriene, and so forth. The energy levels for such
compounds are given by the expression

E  a  mj b


mj  2 cos for j  1; 2; . . . ; n

and n is the number of carbon atoms in the conjugated chain. This calculation generates a
series of MOs with energies expressed in terms of the quantities a and b, which symbolize
the Coulomb integral and resonance integral, respectively. The Coulomb integral, a, is
related to the binding of an electron in a 2p orbital, and this is taken to be a constant for all
carbon atoms but will vary for heteroatoms as a result of the difference in electronegativity.
The resonance integral, b, is related to the energy of an electron in the ®eld of two or more
nuclei. In the HuÈckel method, b is assumed to be zero when nuclei are separated by
distances greater than the normal bonding distance. The approximation essentially
assumes that the electron is affected only by nearest-neighbor nuclei. Both a and b are
negative numbers and represent unspeci®ed units of energy.
The coef®cient corresponding to the contribution of the 2p AO of atom r to the jth
MO is given by
 1=2  
2 rjp
crj  sin
n1 n1

Carrying out the numerical operations for 1,3,5-hexatriene gives the results shown in Table
1.15. Because the molecule is a six-p-electron system, c1 , c2 , and c3 are all doubly

Table 1.15. Energy Levels and Coef®cients for HMOs of 1,3,5-Hexatriene

cj mj c1 c2 c3 c4 c5 c6

c1 1.802 0.2319 0.4179 0.5211 0.5211 0.4179 0.2319

c2 1.247 0.4179 0.5211 0.2319 0.2319 0.5211 0.4179
c3 0.445 0.5211 0.2319 0.4179 0.4179 0.2319 0.5211
c4 0.445 0.5211 0.2319 0.4179 0.4179 0.2319 0.5211
c5 1.247 0.4179 0.5211 0.2319 0.2319 0.5211 0.4179
c6 1.802 0.2319 0.4179 0.5211 0.5211 0.4179 0.2319

58. C. A. Coulson and A. Streitwieser, Jr., Dictionary of p-Electron Calculations, W. H. Freeman, San Francisco,
1965; E. Heilbronner and P. A. Straub, HuÈckel Molecular Orbitals, Springer-Verlag, Berlin, 1966.
occupied, giving a total p-electron energy of 6a  6:988b. The general solution for this 33
system is based on the assumption that the electrons are delocalized. If this assumption
were not made and the molecule were considered to be composed of alternating single and È CKEL
double bonds, the total p-electron energy would have been 6a  6b, identical to that for MOLECULAR
three ethylene units. The differences between the electron energy calculated for a system of
delocalized electrons and that calculated for alternating single and double bonds is referred
to as the delocalization energy and is a measure of the extra stability afforded a molecule
containing delocalized electrons compared to a molecule containing localized bonds. The
calculated delocalization energy (DE) for 1,3,5-hexatriene is 0:988b. The value of b (as
expressed in conventional energy units) is not precisely de®ned. One of the frequently used
values is 18 kcal=mol, which is based on the value of 36 kcal=mol for the resonance energy
of benzene, for which the calculated DE is 2b.
Inspection of the coef®cients and a familiarity with the way they translate into
symmetry properties of orbitals can be used in an extremely powerful way to aid in
understanding a number of aspects of the properties of conjugated unsaturated compounds.
Such considerations apply particularly well to the class of reactions classi®ed as concerted,
which will be described in detail in Chapter 11. It can be seen in Table 1.15 that the
coef®cients are all of like sign in the lowest-energy orbital, c1 , and that the number of
times that a sign change occurs in the wave function increases with the energy of the
orbital. A change in sign of the coef®cients of the AOs on adjacent atoms corresponds to
an antibonding interaction between the two atoms, and a node exists between them. Thus,
c1 has no nodes, c2 has one, c3 has two, and so on up to c6 , which has ®ve nodes and no
bonding interactions in its combination of AOs. A diagrammatic view of the bonding and
antibonding interactions among the AOs of 1,3,5-hexatriene is presented in Fig. 1.10.
Notice that for the bonding orbitals c1 , c2 , and c3, there are more bonding interactions
than antibonding interactions, whereas the opposite is true of the antibonding orbitals.
The success of simple HMO theory in dealing with the relative stabilities of cyclic
conjugated polyenes is impressive. Simple resonance arguments do not explain the unique
stability of benzene as compared with the elusive and unstable nature of cyclobutadiene.
(Two apparently analogous resonance structures can be drawn in each case.) This contrast
in stability is readily explained by HuÈckel's rule, which states that a species will be strongly
stabilized (aromatic) if it is composed of a planar monocyclic array of atoms, each of
which contributes a p orbital to the p system, when the number of electrons in the p system
is 4n  2, where n is an integer. By this criterion, benzene, with six p electrons, is
aromatic, whereas cyclobutadiene, with four, is not. An understanding of the theoretical
basis for HuÈckel's rule can be gained by examining the results of HMO calculations. For
cyclic polyenes, the general solution for the energy levels is

E  a  mj b

2jp n 1=2 for n odd
mj  2 cos for j  0; 1; 2; . . . ;
n n=2 for n even

and n is the number of carbon atoms in the ring. This solution gives the energy level
diagrams for cyclobutadiene and benzene shown in Fig. 1.11.
The total p-electron energy of benzene is 6a  8b, corresponding to a DE of 2b.
Cyclobutadiene is predicted to have a triplet ground state (for a square geometry) and zero
34 DE, since the p-electron energy is 4a  4b, the same as that for two independent double
bonds. Thus, at this level of approximation, HMO theory predicts no stabilization for
CHEMICAL BONDING cyclobutadiene from delocalization and furthermore predicts that the molecule will have
AND STRUCTURE unpaired electrons, which would lead to very high reactivity. In addition, cyclobutadiene
would suffer angle strain, which is not present in benzene. The extreme instability of
cyclobutadiene is then understandable. Higher-level MO calculations modify this picture
somewhat and predict that cyclobutadiene will be a rectangular molecule, as will be
discussed in Chapter 9. These calculations, nevertheless, agree with simple HMO theory in

Fig. 1.10. Graphic representation of p-molecular orbitals of 1,3,5-hexatriene as combinations of 2p

AOs. The sizes of the orbitals are roughly proportional to the coef®cients of the HuÈckel wave

Fig. 1.11. Energy level diagrams for cyclobutadiene and benzene.

concluding that there will be no stabilization of butadiene resulting from delocalization of

the p electrons of the conjugated double bonds.
A useful mnemonic device for quickly setting down the HMOs for cyclic systems is
Frost's circle.59 If a regular polygon of n sides is inscribed in a circle of diameter 4b with
one corner at the lowest point, the points at which the corners of the polygon touch the
circle de®ne the energy levels. The energy levels obtained for benzene and cyclobutadiene
with Frost's circle are shown in Fig. 1.12.
The energy level diagrams for charged C3H3 and C5H5 systems are readily
constructed and are presented in Fig. 1.13. Cyclopropenyl cation has a total of two p
electrons, which occupy the bonding HMO, and a total p-electron energy of 2a  4b. This
gives a DE of 2b and is indicative of a stabilized species. Addition of two more p electrons
to the system to give cyclopropenide anion requires population of higher-energy anti-
bonding orbitals and results in a net destabilization of the molecule. The opposite is true
for the C5H5 case, where the anionic species is stabilized more than the cation and the
cation is predicted to have unpaired electrons.

Fig. 1.12. Energy level diagrams for cyclobutadiene and benzene,

illustrating the application of Frost's circle.

59. A. A. Frost and B. Musulin, J. Chem. Phys. 21:572 (1953).


Fig. 1.13. Energy level diagrams for C3H3 and C5H5 systems.

Monocyclic conjugated polyenes are referred to as annulenes, and there exists ample
experimental evidence to support the conclusions based on application of HMO theory to
neutral and charged annulenes. The relationship between stability and structure in cyclic
conjugated systems will be explored more fully in Chapter 9.
While HuÈckel's 4n  2 rule applies only to monocyclic systems, HMO theory is
applicable to many other systems. HMO calculations of fused-ring systems are carried out
in much the same way as for monocyclic species and provide energy levels and atomic
coef®cients for the systems. The incorporation of heteroatoms is also possible. Because of
the underlying assumption of orthogonality of the s and p systems of electrons, HMO
theory is restricted to planar molecules.
Although the HuÈckel method has now been supplanted by more complete treatments
for theoretical analysis of organic reactions, the pictures of the p orbitals of both linear and
cyclic conjugated polyene systems that it provides are correct as to symmetry and the
relative energy of the orbitals. In many reactions where the p system is the primary site of
reactivity, these orbitals correctly describe the behavior of the systems. For that reason, the
reader should develop a familiarity with the qualitative description of the p orbitals of
typical linear polyenes and conjugated cyclic hydrocarbons. These orbitals will be the
basis for further discussion in Chapters 9 and 11.

1.5. Qualitative Application of Molecular Orbital Theory

As with valence bond theory, the full mathematical treatment of MO theory is too
elaborate to apply to many situations. It is important to be able to develop qualitative
approaches based on the fundamental concepts of MO theory that can be applied without
the need for detailed calculations. A key tool for this type of analysis is a molecular orbital
energy diagram. The construction of an approximate energy level diagram can be
accomplished without recourse to detailed calculations by keeping some basic principles
in mind. These principles can be illustrated by referring to some simple examples.
Consider, ®rst, diatomic species formed from atoms in which only the 1s orbitals are
involved in the bonding scheme. The two 1s orbitals can combine in either a bonding or an
antibonding manner to give two molecular orbitals, as indicated in Fig. 1.14.
The number of molecular orbitals (bonding  nonbonding  antibonding) is equal
to the sum of the atomic orbitals in the basis set from which they are generated. The
bonding combination is characterized by a positive overlap in which the coef®cients are of
like sign, while the antibonding combination is characterized by a negative overlap with
coef®cients of opposite sign.

Fig. 1.14. Graphic description of combination of two 1s orbitals to give two molecular orbitals for
H2 (A) and HHe (B).

Orbitals are occupied by a maximum of two electrons, beginning with the orbital of
lowest energy (the Aufbau principle). The number of electrons is determined by the
number of electrons present on the interacting atoms. The orbitals in Fig. 1.14A could be
applied to systems such as H2  (one electron), H2 (two electrons), He2  (three electrons),
or He2 (four electrons). A reasonable conclusion would be that H2 would be the most
stable of these diatomic species because it has the largest net number of electrons in the
bonding orbital (two). The He2 molecule has no net bonding because the antibonding
orbital contains two electrons and cancels the bonding contribution of the occupied
bonding orbital. Both H2  and He2  have one more electron in bonding orbitals than in
antibonding orbitals. These species have been determined to have bond energies of 61 and
60 kcal=mol, respectively. The bond energy of H2, for comparison, is 103 kcal=mol.
A slight adjustment in the energy level diagram allows it to be applied to hetero-
nuclear diatomic species such as HHe . The diagram that results from this slight
modi®cation is shown in Fig. 1.14B. Rather than being a symmetrical diagram, this
diagram shows the He 1s level to be lower than the H 1s level, owing to the increased
nuclear charge on helium. Calculations for the HHe ion indicate a bond energy of
43 kcal=mol.60
The second-row elements, including carbon, oxygen, and nitrogen, involve p atomic
orbitals as well as 2s orbitals. An example of a heteronuclear diatomic molecule involving
these elements is carbon monoxide, CO. The carbon monoxide molecule has 14 electrons,
and the orbitals for each atom are 1s, 2s, 2px , 2py , and 2pz . For most chemical purposes,
the carbon 1s and oxygen 1s electrons are ignored. This simpli®cation is valid because the
energy gap between the 1s and 2s levels is large and the effect of the 1s levels on the
valence electrons is very small. The 10 valence electrons are distributed among eight MOs
generated by combining the four valence AOs from carbon with the four from oxygen, as
illustrated in Fig. 1.15.
Figure 1.16 illustrates in a qualitative way the interactions between the AOs that give
rise to the MOs. Each pair of AOs leads to a bonding and an antibonding combination. The
2s orbitals give the s and s* orbitals. The 2px and 2py combinations form MOs that are p
in character. The 2pz combination gives a s-type orbital labeled s0 as well as the
corresponding antibonding orbital. The lower ®ve orbitals are each doubly occupied,
accounting for the 10 valence-shell electrons in the molecule. Of these ®ve occupied
orbitals, one is antibonding; thus, the net number of bonding electrons is six, consistent
with the triple bond found in the Lewis structure for carbon monoxide. The shapes of the

60. H. H. Michels, J. Chem. Phys. 44:3834 (1966).


Fig. 1.15. Energy levels in the carbon monoxide molecule. (Adapted

from H. B. Gray and G. P. Haight, Basic Principles of Chemistry, W.
A. Benjamin, New York, 1967, p. 289.)

molecular orbitals can also be depicted as in Fig. 1.17. Here the nodes in the MOs are
represented by a change from solid to dashed lines, and the sizes of the lobes are scaled to
represent the distribution of the orbital. One gains from these pictures an impression of the
distortion of the bonding orbital toward oxygen as a result of the greater electronegativity
of the oxygen atom.

Fig. 1.16. Interaction of atomic orbitals of carbon and oxygen leading to molecular orbitals of
carbon monoxide.

Fig. 1.17. Representation of the molecular orbitals of carbon monoxide.

Energies are given in atomic units (1 a.u. 27.21 eV). (From W. L. Jorgensen
and L. Salem, The Organic Chemist's Book of Orbitals, Academic Press, New
York, 1973. Reproduced with permission.)
40 Just as we were able to state some guiding rules for application of resonance theory, it
is possible to state some conditions by which to test the correctness of an MO energy level
CHEMICAL BONDING diagram derived by qualitative considerations.
a. The total number of MOs must equal the number of AOs from which they were
b. The symmetry of the MOs must conform to the symmetry of the molecule. That is,
if a molecule possesses a plane of symmetry, for example, all the MOs must be
either symmetric (unchanged) or antisymmetric (unchanged except for sign) with
respect to that plane.
c. AOs that are orthogonal to one another do not interact. Thus, two different carbon
2p orbitals will not contribute to the same MO.
d. The energies of similar AOs (s or p) are lower for elements of higher electro-
negativity. MOs will re¯ect these differences in energy.
e. The relative energy of MOs in a molecule increases with the number of nodes in
the orbital.

By applying these rules and recognizing the elements of symmetry present in the molecule,
it is possible to construct MO diagrams for more complex molecules. In the succeeding
paragraphs, the MO diagrams of methane and ethylene are constructed on the basis of
these kinds of considerations.
To provide a basis for comparison, Fig. 1.18 gives the results of an ab initio
calculation on the methane molecule.61 This particular calculation used as a basis set
the 1s, 2s, and three 2p orbitals of carbon and the 1s orbitals of the four hydrogens. The
lowest MO is principally 1s in character. A signi®cant feature of this and other MO
calculations of methane is that, unlike a picture involving localized bonds derived from sp3
hybrid carbon orbitals, there are not four equivalent orbitals. We can obtain an under-
standing of this feature of the MO picture by a qualitative analysis of the origin of the
methane MOs. We will consider the orbitals to be derived from the carbon 2s, 2px , 2py , and
2pz orbitals and ignore the carbon 1s orbital. The most convenient frame of reference for
the tetrahedral methane molecule is a cube with hydrogen atoms at alternate corners and
the carbon atom centered in the cube, as shown in Fig. 1.19. This orientation of the
molecule reveals that methane possesses three twofold symmetry axes, one each along the
x, y, and z axes. Because of this molecular symmetry, the proper MOs of methane must
possess symmetry with respect to these same axes. There are two possibilities: the orbital
may be unchanged by 180 rotation about the axis (symmetric), or it may be transformed
into an orbital of identical shape but opposite sign by the symmetry operation (antisym-

Fig. 1.18. Molecular orbital

energy diagram for methane.
Energies are in atomic units.

61. W. E. Palke and W. N. Lipscomb, J. Am. Chem. Soc. 88:2384 (1966).


Fig. 1.19. Atomic orbitals of carbon relative to methane in a cubic frame of reference.

metric). The carbon 2s orbital is symmetric with respect to each axis, but the three 2p
orbitals are each antisymmetric with respect to two of the axes and symmetric with respect
to one. The combinations that give rise to MOs that meet these symmetry requirements are
shown in Fig. 1.20.
The bonding combination of the carbon 2s orbital with the four 1s hydrogen orbitals
leads to an MO that encompasses the entire molecule and has no nodes. Each of the MOs
derived from a carbon 2p orbital has a node at carbon. The three combinations are
equivalent, but higher in energy than the MO with no nodes. The four antibonding orbitals
arise from similar combinations, but with the carbon and hydrogen orbitals having
opposite signs in the region of overlap. Thus, the MO diagram arising from these
considerations shows one bonding MO with no nodes and three degenerate (having the
same energy) MOs with one node. The diagram is given in Fig. 1.21. Note that except for

Fig. 1.20. Atomic orbital combinations giving rise to bonding molecular orbitals for

Fig. 1.21. Qualitative molecular orbital diagram for

42 inclusion of the 1s orbital, this qualitative picture corresponds to the calculated orbital
diagram in Fig. 1.18.
CHEMICAL BONDING A qualitative approach cannot assign energies to the orbitals. In many cases, it is,
AND STRUCTURE however, possible to assign an ordering of energies. The relationship between relative
energy and number of nodes has already been mentioned. In general, s-type orbitals are
lower in energy than p-type orbitals because of this factor. Conversely, antibonding s*
orbitals are higher in energy than antibonding p* orbitals. Orbitals derived from more
electronegative atoms are lower in energy than those derived from less electronegative
The process of constructing the MOs of ethylene is similar to that used for carbon
monoxide, but the total number of AOs is greater, 12 instead of 8, because of the additional
AOs from hydrogen. We must ®rst de®ne the symmetry of ethylene. Ethylene is known
from experiment to be a planar molecule.

H H H H z
C C C C x

This geometry possesses three important elements of symmetry, the molecular plane and
two planes that bisect the molecule. All MOs must be either symmetric or antisymmetric
with respect to each of these symmetry planes. With the axes de®ned as in the diagram
above, the orbitals arising from carbon 2pz have a node in the molecular plane. These are
the familiar p and p* orbitals.


C 2pz C 2pz

The p orbital is symmetric with respect to both the x±z plane and the y±z plane. It is
antisymmetric with respect to the molecular (x±y) plane. On the other hand, p* is
antisymmetric with respect to the y±z plane.
The remaining AOs are the four H 1s, two C 1s, and four C 2p orbitals. All lie in the
molecular plane. Only two combinations of the C 2s and H 1s orbitals meet the molecular
symmetry requirements. One of these, s, is bonding between all atoms, whereas s* is
antibonding between all nearest-neighbor atoms. No other combination corresponds to the
symmetry of the ethylene molecule.

σ σ*
Let us next consider the interaction of 2py with the four hydrogen 1s orbitals. There 43
are four possibilities that conform to the molecular symmetry:


Orbital A is bonding between all nearest-neighbor atoms, whereas B is bonding within the
CH2 units but antibonding with respect to the two carbons. The orbital labeled C is C C
bonding but antibonding with respect to the hydrogens. Finally, orbital D is antibonding
with respect to all nearest-neighbor atoms. Similarly, when the 2px orbitals are considered,
four possible combinations arise. Notice that the nature of the overlap of the 2px orbitals is
different from that in the 2py case, so that the two sets of MOs should have different


The ®nal problem in construction of a qualitative MO diagram for ethylene is the

relative placement of the orbitals. There are some guidelines which are useful. First,
because p-type interactions are normally weaker than s-type, we expect the separation
between s and s* to be greater than that between p and p*. Within the sets ABCD and
EFGH, the orbitals can be placed in the order A < B < C < D and E < F < G < H on the
basis that C H bonding interactions will outweigh C C antibonding interactions arising
from relatively weak p±p overlaps. The placement of the set ABCD in relation to EFGH is
not qualitatively obvious. Calculations give the results shown in Fig. 1.22.62 Pictorial
representations of the orbitals are given in Fig. 1.23.
The kind of qualitative considerations that have been used to construct the ethylene
MO diagram do not give an indication of how much each AO contributes to the individual

Fig. 1.22. Ethylene

molecular orbital
energy levels. Ener-
gies are given in
atomic units.

62. W. L. Jorgensen and L. Salem, The Organic Chemists's Book of Orbitals, Academic Press, New York, 1973.
44 MOs. This information is obtained from the coef®cients provided by an MO calculation.
Without these coef®cients, we cannot specify the shapes of the MOs very precisely.
CHEMICAL BONDING However, the qualitative ideas do permit conclusions about the symmetry of the orbitals.
AND STRUCTURE As will be seen in Chapter 11, just knowing the symmetry of the MOs provides very useful
insight into many chemical reactions.

Fig. 1.23. Representation of the molecular orbitals of ethylene. (From W. L. Jorgensen

and L. Salem, The Organic Chemist's Book of Orbitals, Academic Press, New York,
1973. Reproduced with permission.)

Fig. 1.23. (continued )

46 1.6. Application of Molecular Orbital Theory to Reactivity
CHEMICAL BONDING The construction of MO diagrams under the guidance of the general principles and
symmetry restrictions which have been outlined can lead to useful insights into molecular
structure. Now we need to consider how these structural concepts can be related to
reactivity. In valence bond terminology, structure is related to reactivity in terms of
substituent effects. The impact of polar and resonance effects on the electron distribution
and stability of reactants, transition states, and intermediates is assessed. In MO theory,
reactivity is related to the relative energies and shapes of the orbitals that are involved as
the reactants are transformed to products. Reactions which can take place through
relatively stable transition states and intermediates are more favorable and faster than
reactions which proceed through less stable ones. The symmetry of the MOs is a
particularly important feature of many analyses of reactivity based on MO theory. The
shapes of orbitals also affect the energy of reaction processes. Orbital shapes are quanti®ed
by the atomic coef®cients. The strongest interaction (bonding when the overlapping
orbitals have the same sign) occurs when the orbitals on two reaction centers have high
coef®cients on the atoms which undergo bond formation.
The qualitative description of reactivity in MO terms must begin with a basic
understanding of the MOs of the reacting systems. At this point, we have developed a
familiarity with the MOs of ethylene and conjugated unsaturated systems from the
discussion of HuÈckel MO theory and the construction of the ethylene MOs from AOs.
To apply these ideas to new systems, we need to be able to understand how a change in
structure will affect the MOs. One approach to this problem is called perturbation
molecular orbital theory or PMO for short.63 In this approach, a system under analysis
is compared to another related system for which the MO pattern is known, and the MO
characteristics of the new system are deduced by analyzing how the change in structure
affects the MO pattern. The types of changes that can be handled in a qualitative way are
substitution of atoms by other elements, with the resulting change in electronegativity and
changes in connectivity that revise the pattern of direct orbital overlap. The fundamental
thesis of PMO theory is that the resulting changes in the MO energies are relatively small
and can be treated as adjustments on the original MO system.
Another aspect of qualitative application of MO theory is the analysis of interactions
of the orbitals in reacting molecules. As molecules approach one another and reaction
proceeds, there is a mutual perturbation of the orbitals. This process continues until the
reaction is complete and the new product (or intermediate in a multistep reaction) is
formed. PMO theory incorporates the concept of frontier orbital control. This concept
proposes that the most important interactions will be between a particular pair of orbitals.64
These orbitals are the highest ®lled orbital of one reactant (the HOMO, highest occupied
molecular orbital) and the lowest un®lled (LUMO, lowest unoccupied molecular orbital)
orbital of the other reactant. The basis for concentrating attention on these two orbitals is
that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO

63. C. A. Coulson and H. C. Longuet-Higgins, Proc. R. Soc. London, Ser. A 192:16 (1947); L. Salem, J. Am.
Chem. Soc. 90:543 (1968); M. J. S. Dewar and R. C. Dougherty, The PMO Theory of Organic Chemistry,
Plenum Press, New York, 1975; G. Klopman, Chemical Reactivity and Reaction Paths, Wiley-Interscience,
New York, 1974, Chapter 4.
64. K. Fukui, Acc. Chem. Res. 4:57 (1971); I. Fleming, Frontier Orbital and Organic Chemical Reactions, John
Wiley & Sons, New York, 1976; L. Salem, Electrons in Chemical Reactions, John Wiley & Sons, New York,
1982, Chapter 6.
theory is that interactions are strongest between orbitals that are close in energy. Frontier 47
orbital theory proposes that these strong initial interactions will guide the course of the
reaction as it proceeds to completion. A further general feature of MO theory is that only APPLICATION OF
MOs of matching symmetry can interact so as to lead to bond formation. Thus, analysis of MOLECULAR
a prospective reaction path will direct attention to the relative energy and symmetry of the REACTIVITY
interacting orbitals.
These ideas can be illustrated here by considering some very simple cases. Let us
consider the fact that the double bonds of ethylene and formaldehyde have very different
chemical reactivities. Formaldehyde reacts readily with nucleophiles whereas ethylene
does not. The p bond in ethylene is more reactive toward electrophiles than the
formaldehyde CO p bond. We have already described the ethylene MOs in Figs. 1.22
and 1.23. How will those of formaldehyde differ? In the ®rst place, the higher atomic
number of oxygen provides two additional electrons so that in place of the CH2 group of
ethylene, the oxygen of formaldehyde has two pairs of nonbonding electrons. The key
change, however, has to do with the frontier orbitals, the p (HOMO) and p* (LUMO)
orbitals. These are illustrated in Fig. 1.24. One signi®cant difference between the two
molecules is the lower energy of the p and p* orbitals in formaldehyde. These are lower in
energy than the corresponding ethylene orbitals because they are derived in part from the
lower-lying (more electronegative) 2pz orbital of oxygen. Because of its lower energy, the
p* orbital is a better acceptor of electrons from the HOMO of any attacking nucleophile
than is the LUMO of ethylene. On the other hand, we also can see why ethylene is more
reactive toward electrophiles than formaldehyde. In electrophilic attack, it is the HOMO
that is involved as an electron donor to the approaching electrophile. In this case, the fact
that the HOMO of ethylene lies higher in energy than the HOMO of formaldehyde will
mean that electrons can be more easily attracted by the approaching electrophile. The
unequal electronegativities of the oxygen and carbon atoms also distort the p-MOs.
Whereas the p-MO has a symmetrical distribution in ethylene, the formaldehyde p-MO
has a higher atomic coef®cient at oxygen. This results in a net positive charge in the
vicinity of the carbon atom, which is a favorable circumstance for approach by a
nucleophilic reactant.
One principle of PMO theory is that the degree of perturbation is a function of the
degree of overlap of the orbitals. Thus, in the qualitative application of MO theory, it is
important to consider the shapes of the orbitals (as indicated quantitatively by their atomic
coef®cients) and the proximity that can be achieved within the limits of the geometry of
the reacting molecules. Secondly, the strength of the interaction between orbitals depends on
their relative energy. The closer the orbitals are in energy, the greater will be their mutual
interaction. This principle, if used in conjunction with reliable estimates of relative orbital
energies, can be of value in predicting the relative importance of various possible interactions.

Fig. 1.24. Relative energy of the p and p* orbitals in

ethylene and formaldehyde.
48 Let us illustrate these ideas by returning to the comparisons of the reactivity of
ethylene and formaldehyde toward a nucleophilic species and an electrophilic species. The
CHEMICAL BONDING perturbations which arise as both a nucleophile and an electrophile approach are sketched
AND STRUCTURE in Fig. 1.25. The electrophilic species E must have a low-lying empty orbital. The
strongest interaction will be with the ethylene p orbital, and this leads to a stabilizing effect
on the complex because the electrons are located in an orbital that is stabilized. The same
electrophilic species would lie further from the p orbital of formaldehyde because the
formaldehyde orbitals are shifted to lower energy. As a result, the mutual interaction with
the formaldehyde HOMO will be weaker than in the case of ethylene. The conclusion is
that such an electrophile will undergo a greater stabilizing attraction on approaching within
bonding distance of ethylene than on approaching within bonding distance of formalde-
hyde. In the case of Nu , a strong bonding interaction with p* of formaldehyde is possible
(Fig. 1.25D). In the case of ethylene, there may be a stronger interaction with the HOMO,
but this is a destabilizing interaction because both orbitals are ®lled and the lowering of
one orbital is canceled by the raising of the other. Thus, we conclude that a nucleophile
with a high-lying HOMO will interact more favorably with formaldehyde than with
The ideas of MO theory can be used in a slightly different way to describe substituent
effects. Let us consider, for example, the effect of a p-donor substituent or a p-acceptor
substituent on the MO levels of ethylene and upon the reactivity of substituted ethylenes.
We can take the amino group as an example of a p-donor substituent. The nitrogen atom
provides an additional 2pz orbital and two electrons to the p system. The p orbitals of
aminoethylene are very similar to those of an allyl anion but with some distortion because
the system is no longer symmetrical. The highest charge density is on the terminal atoms,
that is, the nitrogen atom and the b carbon, since the HOMO has a node at the center
carbon. Furthermore, the HOMO is considerably higher in energy than the HOMO in
ethylene. The HOMO in aminoethylene resembles c2 of the allyl anion. It is not quite so
high in energy as the allyl c2 because of the greater electronegativity of the nitrogen atom,
but is substantially higher than the HOMO of ethylene. Thus, we expect aminoethylene,
with its high-lying HOMO, to be more reactive toward electrophiles than ethylene.
Furthermore, the HOMO has the highest coef®cients on the terminal atoms, so we
expect an electrophile to become bonded to the b carbon or nitrogen, but not to the a
carbon. On the other hand, the LUMO will now correspond to the higher-energy c3 of the

Fig. 1.25. PMO description of interaction of ethylene

and formaldehyde with an electrophile (E ) and a
nucleophile (Nu ).
allyl anion, so we expect aminoethylene to be even less reactive toward nucleophiles than 49
is ethylene.
HOMO π ψ1

π MO energy levels for ethylene with a π-donor substituent.

An example of a p-acceptor group is the formyl group as in acrolein.


In this case, the p-MOs resemble those of butadiene. Relative to the butadiene orbitals,
however, the acrolein orbitals lie somewhat lower in energy because of the effect of the
more electronegative oxygen atom. This factor also increases the electron density at
oxygen relative to carbon.




π MO energy levels for ethylene with a π-acceptor substituent.

The LUMO, which is the frontier orbital in reactions with nucleophiles, has a larger
coef®cient on the b-carbon atom, whereas the two occupied orbitals are distorted in such a
way as to have larger coef®cients on oxygen. The overall effect is that the LUMO is
relatively low-lying and has a high coef®cient on the b-carbon atom. The frontier orbital
theory therefore predicts that nucleophiles will react preferentially at the b-carbon atom.
MO calculations at the 6-31G** level have been done on both acrolein and
aminoethylene. The resulting MOs were used to calculate charge distributions. Figure
1.26 gives the p-electron densities calculated for butadiene, acrolein, and aminoethylene.65
Inclusion of the hydrogen and s orbitals leads to overall charges as shown. These charge
distributions result from s polarization which is counter to the p polarization.
Notice that the MO picture gives the same qualitative picture of the substituent effects
as described by resonance structures. The amino group is pictured by resonance as an
electron donor which causes a buildup of electron density at the b carbon, whereas the
formyl group is an electron acceptor which diminishes electron density at the b carbon.

2 CH CH O–

65. K. B. Wiberg, R. E. Rosenberg, and P. R. Rablen, J. Am. Chem. Soc. 113:2890 (1991).
50 0.342 0.604 0.797
0.604 0.342 0.026 0.830 0.176

0.608 0.353 1.324 0.903 0.588

0.353 0.608 0.165 0.412
0.434 0.056
ψ1 O N

total π 0.957 0.952 0.952 0.957 0.456 0.962 0.886 1.594 0.875 1.079 1.092

+0.009 H H H H
+0.210 +1.251 +0.064 +0.492
H H O –1.321 H H
–0.007 H +0.047
N –0.555
total π and σ charges

Fig. 1.26. Charge distribution in butadiene, acrolein, and aminoethy-

lene. Data are from K. B. Wiberg, R. E. Rothenberg, and P. R. Rablen,

The chemical reactivity of these two substituted ethylenes is in agreement with the ideas
encompassed by both the MO and resonance descriptions. Enamines, as amino-substituted
alkenes are called, are very reactive toward electrophilic species, and it is the b carbon that
is the site of attack. For example, enamines are protonated on the b carbon. Acrolein is an
electrophilic alkene, as predicted, and the nucleophile attacks the b carbon.
Both MO theory and experimental measurements provide a basis for evaluation of the
energetic effects of conjugation between a double bond and adjacent substituents. Table
1.16 gives some representative values. The theoretical values DE are for the isodesmic

CH2 CH X + CH4 → CH3 X + CH2 CH2

and are calculated at the ab initio 4-31G level of theory. These values refer to the gas
phase. The DH values are based on the experimentally determined thermodynamic DHf of
the compounds. Notice that both electron-withdrawing and electron-accepting substituents
result in a net stabilization of the conjugated system. This stabilization results from the
lowering in energy of the lowest-lying MO in each case. The effect on the HOMO is

Table 1.16. Stabilization Resulting from Conjugation of Ethylene with


Substituent (kcal=mol) (kcal=mol) Substituent (kcal=mol) (kcal=mol)

H 0 0 NH2 13.3 13.3

F 6.4 6.7 (3.4) CN 3.3 4.8
CH3 4.3 5.4 COCH3 4.0 10.5 (3.8)
OCH3 10.9 12.3 (4.9) CO2CH3 8.0 11.9 (3.4)

a. From A. Greenberg and T. A. Stevenson, J. Am. Chem. Soc. 107:3488 (1985). Values in parentheses are
from J. Hine and M. J. Skoglund, J. Org. Chem. 47:4766 (1982) and are based on experimental
equilibrium measurement values. These measurements are in solution, and the difference between the
two sets of values may re¯ect the effect of solvent.
different for electron-withdrawing as compared with electron-accepting substituents. For 51
donor substituents, the HOMO is raised in energy, relative to the HOMO in ethylene. For
electron-accepting substituents, it is lowered relative to the HOMO in ethylene. APPLICATION OF
Frontier orbital theory also provides the basic framework for analysis of the effect that MOLECULAR
the symmetry of orbitals has upon reactivity. One of the basic tenets of MO theory is that REACTIVITY
the symmetries of two orbitals must match to permit a strong interaction between them.
This symmetry requirement, when used in the context of frontier orbital theory, can be a
very powerful tool for predicting reactivity. As an example, let us examine the approach of
an allyl cation and an ethylene molecule and ask whether the following reaction is likely to

? +
H2C + CH2

The positively charged allyl cation would be expected to be the electron acceptor in any
initial interaction with ethylene. Therefore, to consider this reaction in terms of frontier
orbital theory, the question we need to answer is, ``do the ethylene HOMO and allyl cation
LUMO interact favorably as the reactants approach one another?'' The orbitals that are
involved are shown in Fig. 1.27. If we analyze a symmetrical approach, which would be
necessary for the simultaneous formation of the two new bonds, we see that the
symmetries of the two orbitals do not match. Any bonding interaction developing at
one end would be canceled by an antibonding interaction at the other end. The conclusion
that is drawn from this analysis is that this particular reaction process is not favorable. We
would need to consider other modes of approach to analyze the problem more thoroughly,
but this analysis indicates that simultaneous (concerted) bond formation between ethylene
and an allyl cation to form a cyclopentyl cation is not possible.


bonding interaction anti-bonding interaction


Fig. 1.27. MOs for ethylene and allyl cation.

52 Let us now consider another reaction, this time between the allyl cation and
butadiene. Again, the assumption will be made that it is the frontier p orbitals that will
CHEMICAL BONDING govern the course of the reaction. We will also be slightly more formal about the issue of
AND STRUCTURE symmetry. This can be done by recognizing the elements of symmetry that would be
maintained as the reaction proceeds. If the reaction is to proceed in a single step, the
geometry must permit simultaneous overlap of the orbitals on the carbons where new
bonds are being formed. A geometry of approach that permits such a simultaneous overlap
is shown below.

The allyl cation could approach from the the top (or bottom) of the s-cis conformation of
butadiene, and the new bonds would be formed from the p orbitals. This arrangement
would maintain a plane of summetry during the course of the reaction. The plane bisects
butadiene between C-2 and C-3 and the allyl cation at C-2. The orbitals can be classi®ed as
symmetric (S) or antisymmetric (A) with respect to this plane. This gives rise to the MO
diagram shown in Fig. 1.28. Because strong interactions will occur only between orbitals
of the same symmetry, the mutual perturbation of the approaching reactants will affect the
orbital energy levels as shown in the diagram. As in all such perturbations, one orbital of
the interacting pair will be stabilized and the other will move to higher energy. The

Fig. 1.28. MO diagram showing mutual perturbation of MOs of butadiene and

allyl cation.
perturbed orbitals at some point on the way to the transition state are shown in the diagram. 53
Eventually, when the reaction has proceeded to completion, a new set of orbitals belonging
to the product will have been formed. These are shown in the center of the diagram, but we APPLICATION OF
will be considering only the initial perturbed set. The lowest-lying p orbitals of both MOLECULAR
butadiene and the allyl cation are ®lled. These will interact, with one moving down in REACTIVITY
energy and the other up. These two changes in energy are partially compensating, with the
total energy change being a net increase in the energy of the system. Both the HOMO and
LUMO are antisymmetric and will interact strongly, but in this case, because only two
electrons are involved, only the energy of the stabilized orbital will affect the total energy
since the destabilized orbital is empty. This HOMO±LUMO interaction then contributes a
net bonding contribution as the transition state is approached. From this analysis, we
conclude that there is the possibility of a favorable bonding interaction between the two
reactant species. Notice that the reaction is only permitted and that nothing can be said
about its actual rate or position of equilibrium on the basis of the analysis given. Such
matters as steric hindrance to approach of the reactants and the geometric requirements for
satisfactory overlap of the orbitals could still cause the reaction to proceed with dif®culty.
The analysis does establish, however, that there is a pathway by which the orbitals of the
reactants can interact in a way that is favorable for reaction.
A more complete analysis of interacting molecules would examine all of the involved
MOs in a similar way. A correlation diagram would be constructed to determine which
reactant orbital is transformed into which product orbital. Reactions which permit smooth
transformation of the reactant orbitals to product orbitals without intervention of high-
energy transition states or intermediates can be identi®ed in this way. If no such
transformation is possible, a much higher activation energy is likely since the absence
of a smooth transformation implies that bonds must be broken before they can be re-
formed. This treatment is more complete than the frontier orbital treatment because it
focuses attention not only on the reactants but also on the products. We will describe this
method of analysis in more detail in Chapter 11. The qualitative approach that has been
described here is a useful and simple way to apply MO theory to reactivity problems, and
we will employ it in subsequent chapters to problems in reactivity that are best described in
MO terms.
It is worth noting that in the case of the reactions of ethylene and butadiene with the
allyl cation, the MO description has provided a prediction that would not have been
recognized by a pictorial application of valence bond terminology. Thus, we can write an
apparently satisfactory description of both reactions.


H2C CH2 H2C + CH2
H2C CH2 H2C + CH2

It is only on considering the symmetry of the interacting orbitals that we ®nd reason to
suspect that only the second of the two reactions is possible.
54 1.7. Interactions between s and p SystemsÐHyperconjugation
CHEMICAL BONDING One of the key assumptions of the HuÈckel approximation is the noninteracton of the
p-orbital system with the s-molecular framework. This is a good approximation for planar
p molecules in which the s framework is in the nodal plane of the p system. For other
molecules, as for example when an sp3 carbon is added as a substituent group, this
approximation is no longer entirely valid. Qualitative application of MO theory can be
enlightening in describing interactions between the p system and substituent groups. In
valence bond theory, a special type of resonance called hyperconjugation is used to
describe such interactions. For example, much chemical and structural evidence indicates
that alkyl substituents on a carbon±carbon double bond act as electron donors to the p
system. In valence bond language, ``no bond'' resonance structures are introduced to
indicate this electronic interaction.

H C +H C
H C C H C C:–

The MO picture of such interactions ¯ows from the idea that individual orbitals encompass
the entire molecule. Thus, while the MO description of ethylene involved no interaction
between the C 2pz orbitals and the H 1s orbitals (see p. 43 to recall this discussion), this
strict separation would not exist in propene because the hydrogens of the methyl group are
not in the nodal plane of the p bond. The origin of interactions of these hydrogens with the
p orbital can be indicated as in Fig. 1.29, which shows propene in a geometry in which two
of the hydrogen 1s AOs are in a position to interact with the 2pz orbital of carbon 2. An ab
initio calculation using a STO-3G basis set was carried out on propene in two distinct
geometries, eclipsed and staggered.

eclipsed staggered

The calculations of the optimum geometry show a slight lenghthening of the C H bonds
because of the electron release to the p system. These calculations also reveal a barrier to
rotation of the methyl group of about 1.5±2.0 kcal=mol. Interaction between the hydrogens
and the p system favors the eclipsed conformation to this extent.66 Let us examine the

Fig. 1.29. Interactions between two hydrogen 1s orbitals and carbon 2pz orbitals stabilize the
eclipsed conformation of propene.
66. W. J. Hehre, J. A. Pople, and A. J. P. Devaquet, J. Am. Chem. Soc. 98:664 (1976); A. Pross, L. Radom, and N. V.
Riggs, J. Am. Chem. Soc. 102:2253 (1980); K. B. Wiberg and E. Martin, J. Am. Chem. Soc. 107:5035 (1985);
A. E. Dorigo, D. W. Pratt, and K. N. Houk, J. Am. Chem. Soc. 109:6589 (1987).
reason for the preference for the eclipsed conformation. This issue can be approached by 55
analyzing the interactions between the carbon 2pz orbitals and the CH3 fragment in a little
more detail. The bonding and antibonding combinations that arise from interaction of the INTERACTIONS
appropriate CH3-p and CH3-p* orbitals with the 2pz orbitals are shown in Fig. 1.30. The BETWEEN s AND p
strongest interaction is a repulsive one between the ®lled CH3-p and CC-p orbitals. It is HYPERCONJUGATION
this interaction which is primarily responsible for the favored eclipsed conformation. The
eclipsed structure minimizes the repulsion by maximizing the separation between the
hydrogens and the p bond. The second interaction is the stabilizing hyperconjugative one
between CH3-p and CC-p*. This is a bonding interaction because p* is an empty orbital
and can accept electron density from CH3-p. It is this bonding interaction which transfers
electron density from the methyl group to the terminal carbon of the double bond. Notice
that there is a correspondence between the MO picture and the valence bond resonance
structure in that both specify a net transfer of electron density from C H bonds to the p
system with a net strengthening of the bond between C-2 and C-3 but a weakening of the
C(1) C(2) p bond.

H +H

hyperconjugation repulsive interaction attractive interaction
between CH3-π and π between CH3-π and π*

One of the fundamental structural facets of organic chemistry, which has been
explained most satisfactorily in MO terms, is the existence of a small barrier to rotation
about single bonds. In ethane, for example, it is known that the staggered conformation is
about 3 kcal=mol more stable than the eclipsed conformation so that the eclipsed
conformation represents a transition state for transformation of one staggered conforma-
tion into another by rotation.

staggered eclipsed

Valence bond theory offers no immediate qualitative explanation since the s bond that is
involved is cylindrically symmetrical. A steric argument based on repulsions between
hydrogens also fails because on detailed examination of this hypothesis, it is found that the

Fig. 1.30. Interactions between CH3-p and CH3-p*

orbitals and carbon 2pz orbitals.
56 hydrogens are too small and too distant from one another to account for the observed
energy. MO ideas, however, succeed in correctly predicting and calculating the magnitude
CHEMICAL BONDING of the ethane rotational barrier.67 The origin of the barrier is a repulsive interaction
AND STRUCTURE between the ®lled C H orbitals which is maximal in the eclipsed geometry.
The interaction can be further examined by consideration of the ethane MOs.68
Because ethane contains two carbon atoms and six hydrogens, the MOs are constructed
from six H 1s, two C 2s, and six C 2p orbitals. Figure 1.31 depicts the seven bonding MOs,
assuming the staggered geometry. The s, s0 , and sx orbitals are not affected much by the
rotation of the two CH3 groups with respect to one another because the H 1s orbitals all
have the same sign within each CH3 group. The other MOs, however, are of a p type,
having a nodal plane derived from the nodal plane of the C 2pz orbitals. The extent of the
overlap in these orbitals clearly changes as the two CH3 groups are rotated with respect to
one another. Analysis of the relative magnitudes of the bonding and antibonding
interactions that take place as rotation occurs indicates that the change in energy of
these two pairs of MOs is the source of the ethane rotational barrier.
The interaction of the lone-pair electrons on an amine nitrogen with adjacent C H
bonds is another example of a hyperconjugative effect that can be described in MO
language. The lone-pair electrons, when properly aligned with the C H bond, lead to a

π′2 π′y


πz πy



Fig. 1.31. Molecular orbitals of ethane reveal-

ing p character of pz , py , p0z , and p0y orbitals.
Only the ®lled orbitals are shown.

67. R. M. Pitzer, Acc. Chem. Res. 16:207 (1983); R. Hoffmann, J. Chem. Phys. 39:1397 (1963); R. M. Pitzer and
W. N. Lipscomb, J. Chem. Phys. 39:1995 (1963); J. A. Pople and G. A. Segal, J. Chem. Phys. 43:5136 (1956).
68. J. P. Lowe, Prog. Phys. Org. Chem. 6:1 (1968); J. P. Lowe, J. Am. Chem. Soc. 92:3799 (1970); J. P. Lowe,
Science 179:527 (1973).
donation of electron density from the lone-pair orbital to the antibonding C H orbital. The 57
overall effect is to weaken the C H bond.
R R + C
: representation
by hyperconjugation
Electron donation from N n orbital to C–H σ* orbital.

In acyclic structures, such effects are averaged by rotation, but in cyclic structures
differences in C H bond strengths based on the different alignments can be recognized.69
The C H bonds that are in an anti orientation to the lone pair are weaker than the C H
bonds in other orientations.
The examples that have been presented in this section illustrate the approach that is
used to describe structure and reactivity effects within the framework of MO description of
structure. In the chapters that follow, both valence bond theory and MO theory will be used
in the discussion of structure and reactivity. Qualitative valence bond terminology is
normally most straightforward for saturated systems. MO theory provides useful insights
into conjugated systems and into effects that depend upon the symmetry of the molecules
under discussion.

1.8. Other Quantitative Descriptions of Molecular Structure

One of the dif®culties of MO computations is that the concept of the electron-pair

bond disappears. The bonding between individual atoms appears as a contribution from
several MOs. Thus, while MO theory is valuable in describing overall molecular
characteristics such as structure, total energy, and charge distribution, it is less useful
for focusing attention on individual parts of a molecule. Although the frontier orbital
concept is a useful guide to reactivity, MO theory provides no unambiguous method to
relate the MOs to properties of a particular atom or functional group. For this reason, many
chemists have pursued theoretical descriptions of molecules that would lend themselves
more readily to the concepts of transferable structural units and functional groups which
arise from qualitative valence bond theory. Although we do not have space here to fully
develop these approaches, we can describe some of the key ideas and illustrate speci®c

1.8.1. Atoms in Molecules

MO calculations can provide the minimum-energy structure, total energy, and overall
electron density of a given molecule. However, this information is in the form of the sum
of the individual MOs and cannot be easily dissected into contributions by speci®c atoms
or groups. How can the properties described by the MOs be related to our concept of
molecules as a collection of atoms or functional groups held together by chemical bonds?
69. A. Pross, L. Radom, and N. V. Riggs, J. Am. Chem. Soc. 102:2253 (1980); T. Laube and T.-K. Ha, J. Am. Chem.
Soc. 110:5511 (1988).
58 One approach is to de®ne critical bond points and surfaces that subdivide molecules into
the constituent atoms. R. F. W. Bader has developed such an approach.70 The total electron
CHEMICAL BONDING density obtained from MO or other computational methods is partitioned among atoms.
AND STRUCTURE The quantitative results can be depicted qualitatively in the form of molecular graphs. The
atoms are connected by atomic interaction lines that de®ne maximum charge density
between neighboring atoms. The atomic interaction lines correspond to chemical bonds by
revealing accumulation of electron density between nuclei. The network of lines consti-
tutes a molecular graph. In addition, the graphs locate critical points where electron
density is either at a maximum or a minimum with respect to dislocation in any of the
directions of three- dimensional space. The similarity to a classical structural formula is
clear, but the molecular graphs are based on quantum-chemical theory rather than the
qualitative concepts of valence bonds and hybridized orbitals. Figure 1.32 gives some
representative molecular graphs and shows the bond critical points in these structures.
The subunits which can be de®ned can include atoms or collections of atoms
corresponding to functional groups. The subunits can be represented as regions of space
de®ned by electon density. These representations correspond well with the qualitative
concepts that arise from valence bond structures. The mathematical evaluation can assign
shape and charge density to atoms. Table 1.17 gives the C and H charge densities in some

Fig. 1.32. (a) Molecular graphs and electron density contours for pentane and hexane. Dots on bond
paths represent critical points. (b) Comparison of molecular graphs for bicycloalkanes and
corresponding propellanes. (Reproduced from Chem. Rev. 91:893 (1991) with permission of the
American Chemical Society.)

70. R. F. W. Bader, Atoms in MoleculesÐA Quantum Theory, Oxford University Press, Oxford, U.K., 1990; R. F.
W. Bader, Chem. Rev. 91:893 (1991).
Table 1.17. Atomic Charges in Organic Structuresa 59
q(C) q(H) SECTION 1.8.
CH4  0.175 0.044 QUANTITATIVE
C2H6  0.184 0.061 DESCRIPTIONS OF
C2H4  0.035 0.017 STRUCTURE
C6H6  0.020 0.020
C2H2 0.136  0.136
3  0.179  0.274
CH3  0.035  0.012
CH3 0.422 0.193

a. From R. F. W. Bader, P. L. A. Popelier, and T. A. Keith, Angew. Chem.

Int. Ed. Engl. 33:620 (1994).

fundamental organic molecules and intermediates.71 Figure 1.33 shows the carbon and
hydrogen atoms dissected from ethane, ethylene, ethyne, and benzene. Especially
noteworthy is the decreasing size of hydrogen as the carbon electronegativity changes
with hybridization in the order sp > sp2 > sp3. Figure 1.34 shows the shape of carbon in
CH3  , CH3 , and CH3 .
Figure 1.35 shows the second-row elements Li through F in their compounds with
hydrogen. Note the transformation of hydrogen from ``hydride'' in LiH to a much smaller,
protonlike entity in HF as the electronegativity of the heavier atom increases.
The lesson in these ®gures is that the qualitative concepts of chemical structures can
be given a pictorial representation based on the quantitative application of the principles of
quantum chemistry. Various, indeed all, molecular properties can, in principle, be
calculated from the electronic distribution these pictures represent.

1.8.2. Electron Density Functionals

Another approach to calculating molecular geometry and energy is based on density

functional theory (DFT).72 DFT focuses on the electron cloud corresponding to a
molecule. The energy of a molecule is uniquely speci®ed by the electron density
functional.73 The calculation involves the construction of an expression for the electron
density. The energy of the system is then expressed as
E  T  ven  Jee  vxc
where T is the kinetic energy, ven and Jee are Coulombic electron±nuclear and electron±
electron interactions, respectively, and vxc are correlation and exchange effects. As in the
Hartree±Fock MO approach, the minimization of energy should provide the most accurate
description of the electronic ®eld. The mathematical problem is to de®ne each of the terms,
with vxc being the most challenging. The formulation cannot be done exactly, but various
approaches have been developed and calibrated by comparison with experimental data.
The methods used most frequently by chemists were developed by A. D. Becke.74 This
approach is often called the B3LYP method. The computations can be done with

71. R. F. W. Bader, P. L. A. Popelier, and T. A. Keith, Angew. Chem. Int. Ed. Engl. 33:620 (1994).
72. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, Oxford,
U.K., 1989.
73. P. Hohenberg and W. Kohn, Phys. Rev. A 136:864 (1964); M. Levy, Proc. Natl. Acad. Sci. U.S.A. 76:6062
74. A. D. Becke, Phys. Rev. A 38:3098 (1988); A. D. Becke, J. Chem. Phys. 96:2155 (1992); A. D. Becke, J. Chem.
Phys. 97:9173 (1992); A. D. Becke, J. Chem. Phys. 98:5648 (1993).

Fig. 1.33. The C and H atoms in ethane (a), ethene (b),

ethyne (c), and benzene (d), respectively. Note that the
H atom is largest in ethane and smallest in ethyne.
(Reproduced from Angew. Chem. Int. Ed. Engl. 33:620
(1994) by permission of Wiley-VCH.)

considerably less computer time than required by the most advanced (G2) ab initio MO
methods (see Section 1.3), and there has been considerable interest in comparing B3LYP
results to MO calculations.
Table 1.18 gives total bonding energies in kilocalories per mole for some simple
molecules. The B3LYP results are comparable in accuracy to G1 and G2 results. Another
comparison was done with a series of cyclic hydrocarbons as the test case. The calculations
were done using an isodesmic reaction scheme. The results are given in Table 1.19. Density
functional calculations have also been successfully extended to functionalized molecules.75

75. A. St. Amant, W. D. Cornell, P. A. Kollmar, and T. A. Halgren, J. Comput. Chem. 16:1483 (1995).

Fig. 1.34. The carbon atoms in the methyl cation (a), radical (b), and anion
(c), respectively. (Reproduced from Angew. Chem. Int. Ed. Engl. 33:620
(1994) by permission of Wiley-VCH.)

DFT turns out to be well suited to quantitative expression of some of the qualitative
concepts introduced in Section 1.2, such as electronegativity, hardness, and softness.76 The
principle of maximum hardness77 (p. 22) can be derived as a consequence of DFT, as can
the concepts of hardness and softness.78
A very simple de®nition of electronegativity also ®nds a foundation in DFT. The
de®nition is

V  n=r

which relates electronegativity to the number of valence-shell electrons and the effective
atomic radius.79 This measure of electronegativity is both empirically correlated and
theoretically related to the Mulliken electronegativity w, de®ned as w  I  A=2.80 The
values assigned for some of the atoms of most interest in organic chemistry are given in
Table 1.20.
Concepts such as relative acidity and carbocation stability can be fundamentally
related to hardness and electronegativity as de®ned by DFT.

–H– –H+

R+ R• R–

The energy difference between R and R can be expressed as

DG  23:06Ered R  Ered R

where the Ered are the reduction potentials of R and R. This energy is approximately the
same as 2w, since it represents the HOMO±LUMO gap for R.81
76. P. W. Chattaraj and R. G. Parr, Struct. Bonding 80:11 (1993); G.-H. Liu and R. G. Parr, J. Am. Chem. Soc.
117:3179 (1995).
77. R. G. Parr and P. K. Chattaraj, J. Am. Chem. Soc. 113:1854 (1991); T. K. Ghanty and S. K. Ghosh, J. Phys.
Chem. 100:12295 (1996).
78. P. K. Chattaraj, H. Lee, and R. G. Parr, J. Am. Chem. Soc. 113:1855 (1991).
79. Y.-R. Luo and S. W. Benson, J. Phys. Chem. 92:5255 (1988); Y.R. Luo and S. W. Benson, J. Am. Chem. Soc.
111:2480 (1989); Y.R. Luo and S. W. Benson, J. Phys. Chem. 94:914 (1990); Y.R. Luo and S. W. Benson, Acc.
Chem. Res. 25:375 (1992).
80. Y.-R. Luo and P. D. Pacey, J. Am. Chem. Soc. 113:1465 (1991).

Fig. 1.35. Representations of the atoms in the second-row hydrides AHn . In the hydridic members
LiH, BeH2, and BH3, the A atom consists primarily of a core of decreasing radius, dressed with some
residual valence density. The form and properties of the atoms undergo a marked change at methane,
a nonpolar molecule: no core is visible on the C atom, and the H atoms, considerably reduced in size
and population, now lie on the convex side of the interatomic surface. The increasing polarity of the
remaining members is re¯ected in the decreasing size of the H atom and the increasing convexity of
its interatomic surface. (Reproduced from Angew. Chem. Int. Ed. Engl. 33:620 (1994) by permission
of Wiley-VCH.)
Table 1.18. Comparison of Ab Initio and DFT Calculations 63
of Atomization Energies in kcal=mol.
H2 O 219.3 218.4 219.3 217.0 220.7 DESCRIPTIONS OF
NH3 276.7 275.4 276.6 276.8 279.7 STRUCTURE
CH4 392.5 393.1 393.3 393.5 393.0
C2H6 666.3 667.6 666.6 668.7 667.5
C2H4 531.9 533.5 531.4 534.3 532.1
C2H2 388.9 391.2 386.6 389.0 391.0
CH3OH 480.8 482.6 481.9 480.8 481.3
CH2O 357.2 362.2 358.7 357.9 356.7


Chem. Phys. 90:5622 (1989).
b. L. A. Curtiss, J. E. Carpenter, K. Raghavachari, and J. A. Pople, J. Chem. Phys.
96:9030 (1992).
d. C. W. Bauschlicher, Jr., and H. Partridge, Chem. Phys. Lett. 240:533 (1995).

Table 1.19. Comparison of Ab Initio and DFT

Enthalpies with Experimental Values in
kcal=mol for the Isodemic Reaction:a
Cn Hm  3n mCH4 ! 2n m=2C2 H6

Structure DHf (exp) Ab Initiob DFT

6.99 5.79 5.12

11.51 11.87 9.94

13.12 5.39 5.14

10.43 12.37 8.99

14.21 3.16 1.47

21.73 6.41 3.00

7.66 12.23 9.11

a. A. Fortunelli and M. Selmi, Chem. Phys. Lett. 223:390

b. Gaussian 92.

81. E. M. Arnett and R. T. Ludwig, J. Am. Chem. Soc. 117:6627 (1995).

64 Table 1.20. Electronegativity of Some Atoms by
the De®nition n=ra
CHEMICAL BONDING Atom Single bond Double bond Triple bond
C 5.18 6.00 6.63
N 6.67 8.1
O 8.11 9.7
F 9.92
Cl 7.04
Br 6.13
I 5.25

a. Based on covalent radii given by W. Gordy and R. L. Cook, in

Microwave Molecular Spectroscopy, John Wiley & Sons, New
York, 1984.

The same concept can be applied to carbon radicals bound to atoms other than

R+ + X– +e• R– + X+
+e• –e•
R• + X–

The energy for the electron transfer

2R ! R  R

is given by

DE  I A  2Z  HOMO LUMO gap

These relationships also underlie observed correlations between acidity, hydride af®nity, or
heterolytic bond energies and oxidation potentials. Table 1.21 gives some hardness values
for simple compounds of hydrogen, carbon, and the halogens. Note particularly the trend
towards greater softness in the hydrogen halides and methyl halides as the halogen
becomes larger.

Table 1.21. Hardness for Some Small Moleculesa

H2 8.7 HF 11.0 F2 CH4 10.3 CH3F 9.4

H2O 9.5 Cl 8.0 Cl2 4.6 CH2CH2 6.2 CH3Cl 7.5
NH3 8.2 HBr Br2 4.0 HCCH 7.0 CH3Br 5.8
H2S 6.2 HI 5.3 I2 3.4 C6H6 5.3 CH3I 4.7

a. R. G. Pearson, J. Org. Chem. 54:1423 (1989).

83. D. J. Klein and N. Trinajstic, eds., Valence Bond Theory and Chemical Structure, Elsevier, Amsterdam, 1990.
84. D. L. Cooper, J. Gerratt, and M. Raimondi, Chem. Rev. 91:929 (1991).
85. R. McWeeny, Methods of Molecular Quantum Mechanics, 2nd ed., Academic Press, New York, 1992; R.
McWeeny, NATO ASI Ser., Ser. B 293:325 (1992).
86. J. H. van Lenthe and G. G. Balint-Kurti, J. Chem. Phys. 78:5699 (1983); J. Verbeek and J. H. van Lenthe,
THEOCHEM 229:115 (1991).
87. F. W. Bobrowicz and W. A. Goddard III, in Methods in Electronic Structure, H. F. Shaefer, ed., Plenum Press,
New York, 1977.
1.8.3. Modern Valence Bond Approaches 65
Several methods of quantitative description of molecular structure based on the PROBLEMS

concepts of valence bond theory have been developed.83±87 These methods employ orbitals
similar to localized valence bond orbitals, but permitting modest delocalization. These
orbitals allow many fewer structures to be considered and remove the need for incorporat-
ing many ionic structures, in agreement with chemical intuition. To date, these methods
have not been as widely applied in organic chemistry as MO calculations. They have,
however, been successfully applied to fundamental structural issues. For example,
successful quantitative treatments of the structure and energy of benzene and its hetero-
cyclic analogs have been developed.88 It remains to be seen whether computations based
on DFT and modern valence bond theory will come to rival the widely used MO programs
in analysis and interpretation of structure and reactivity.

General References

York, 1985.
R. F. W. Bader, Atoms in Molecules; A Quantum Theory, Clarendon Press, Oxford, U.K., 1990.
W. T. Borden, Modern Molecular Orbital Theory for Organic Chemists, Prentice-Hall, Englewood Cliffs, New
Jersey, 1975.
I. Fleming, Frontier Orbitals and Organic Chemical Reactions, John Wiley & Sons, New York, 1976.
New York, 1986.
R. F. Hout, W. J. Pietro, and W. J. Hehre, A Pictorial Approach to Molecular Structure and Reactivity, John Wiley
& Sons, New York, 1984.
C. K. Ingold, Structure and Mechanism in Organic Chemistry, 2nd ed., Cornell University Press, Ithaca, New
York, 1969.
R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, Oxford,
U.K., 1989.
L. Salem, Electrons in Chemical Reactions, John Wiley & Sons, New York, 1982.
P. v. R. Schleyer, ed., Encyclopedia of Computational Chemistry, John Wiley & Sons, New York, 1998.
R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry, Verlag Chemie, Weinheim, 1970.
H. E. Zimmerman, Quantum Mechanics for Organic Chemists, Academic Press, New York, 1975.


(References for these problems will be found on page 791.)

1. Use thermochemical relationships to obtain the required information.

(a) The heats of formation of cyclohexane, cyclohexene, and benzene are, respec-
tively, 29:5, 1:1, and 18:9 kcal=mol. Estimate the resonance energy of
benzene using these data.
88. D. L. Cooper, S. C. Wright, J. Gerratt, and M. Raimondi, J. Chem. Soc., Perkin Trans. 2 1989:255; D. L.
Cooper, S. C. Wright, J. Gerratt, P. A. Hyams, and M. Raimondi, J. Chem. Soc., Perkin Trans. 2 1989:719; C.
Amovilli, R. D. Harcourt, and R. McWeeny, Chem. Phys. Lett. 187:494 (1991); J. Gerratt, D. L. Cooper, P. B.
Karadakov, and M. Raimondi, Chem. Soc. Rev. 26:87 (1997).
66 (b) Calculate DH for the air oxidation of benzaldehyde to benzoic acid given that the
heats of formation of benzaldehyde and benzoic acid are 8:8 and
CHEMICAL BONDING 70:1 kcal=mol, respectively.
AND STRUCTURE (c) Using the appropriate heats of formation in Table 1.5, calculate the heat of
hydrogenation of 2-methyl-1-pentene.

2. Suggest an explanation for the following observations:

(a) The dipole moment of the hydrocarbon calicene has been estimated to be as large
as 5.6 D.


(b) The measured dipole moment of p-nitroaniline (6.2 D) is larger than the value
calculated using empirical group moments (5.2 D).
(c) The dipole moment of furan is smaller than and in the opposite direction from that
of pyrrole.

0.71 D 1.80 D

3. Predict the energetically preferred site of protonation for each of the following
molecules and explain the basis of your prediction.
(a) (c)

(b) O (d)

4. What physical properties, such as absorption spectra, bond length, dipole moment,
etc., could be examined to obtain evidence of resonance interactions in the following
molecules? What deviations from ``normal'' physical properties would you expect to
(a) (b) C6H5 C6H5 (c) O

C6H5 O

5. Certain C H bonds have signi®cantly lower bond dissociation energies than do the
``normal'' C H bonds in saturated hydrocarbons. Offer a structural rationalization of
the lowered bond energy in each of the following compounds, relative to the saturated
hydrocarbon C H bond taken as a reference. (The bond dissociation energies are 67
given in kcal=mol.)
CH2 H (85) versus CH3 H (103)

(b) HOCH2 H (92) versus CH3 H (103)

(c) CH3C H (88) versus CH3CH2 H (98)


6. (a) Carboxamides have substantial rotational barriers on the order of 20 kcal=mol for
the process
N CH3* N CH3
CH3 CH3*

Develop a structural explanation for the existence of this barrier in both resonance
and molecular orbital terminology.
(b) In the gas phase the rotational barrier of N ,N -dimethylformamide is about
19.4 kcal=mol, which is about 1.5 kcal=mol less than in solution. Is this change
consistent with the ideas you presented in (a)? Explain.
(c) Explain the relative rates of alkaline hydrolysis of the following pairs of
PhC N 105> PhCNH2 103> Ph N
7. Construct a qualitative MO diagram showing how the p-molecular orbitals in the
following molecules are modi®ed by the addition of the substituent:
(a) vinyl ¯uoride, compared to ethylene
(b) acrolein, compared to ethylene
(c) acrylonitrile, compared to ethylene
(d) benzyl cation, compared to benzene
(e) propene, compared to ethylene
(f) ¯uorobenzene, compared to benzene

8. The data below give the stabilization calculated in kcal=mol by MO methods for the
CH3 X + CH2 CH2 CH4 + CH2 CH X


F 7 6.4
OCH3 7 10.9
NH2 7 13.3
68 (a) Demonstrate that this indicates that there is a stabilizing interaction between the
substituent and a carbon±carbon double bond.
CHEMICAL BONDING (b) Draw resonance structures showing the nature of the interaction.
AND STRUCTURE (c) Construct a qualitative MO diagram which rationalizes the existence of a
stabilizing interaction.
(d) Both in resonance and molecular orbital terminology, explain the order of the
stabilization N > O > F.

9. Construct a qualitative MO diagram for the H-bridged ethyl cation by analyzing the
interaction of the ethylene MOs given in Fig. 1.23 with a proton approaching the
center of the ethylene molecule from a direction perpendicular to the molecular plane.
Indicate which ethylene orbitals will be lowered by this interaction and which will be
raised or left relatively unchanged. Assume that the hydrogens of ethylene are slightly
displaced away from the direction of approach of the proton.

10. In the HuÈckel treatment, atomic orbitals on nonadjacent atoms are assumed to have no
interaction. They are neither bonding nor antibonding. The concept of homoconjuga-
tion suggests that such orbitals may interact, especially in rigid structures which direct
orbitals toward one another. Consider, for example, bicyclo[2.2.1]hepta-2,5-diene:

5 3

6 1

(a) Construct the MO diagram according to simple HuÈckel theory and assign energies
to the orbitals.
(b) Extend the MO description by allowing a signi®cant interaction between the C-2
and C-6 and between the C-3 and C-5 orbitals. Construct a qualitative MO
diagram by treating the interaction as a perturbation on the orbitals shown for (a).

11. (a) Sketch the nodal properties of the highest occupied molecular orbital of
pentadienyl cation (CH2CHCHCHCH2  ).
(b) Two of the p-MOs of pentadienyl are given below. Specify which one is of lower
energy, and classify each as to whether it is bonding, nonbonding, or antibonding.
Explain your reasoning.

1 2 3 4 5
o o o o o

cx  0:50f1  0:50f2 0:50f4 0:50f5

cy  0:58f1 0:58f3  0:58f5

12. The diagrams below give STO-3G calculated charge densities for the benzyl cation
and its a-formyl and a-cyano derivatives. Analyze the effect of these substituents on
the charge density. 69
H –.044
.154 .149 –.084 +.149 N
H .054 H H .097 C O H .110 C
–.020 –.022 –.002
H H .127 H H .119 H H .133
.037 .035 .037
–.062 –.064 –.062
H .071 H .123 H .063 H .121 H .037 H .127
.141 .138 .144

13. Calculate the energy levels and coef®cients for 1,3-butadiene using HuÈckel MO

14. (a) Estimate from HMO theory the delocalization energy, expressed in units of b, of
cyclobutadienyl dication (C4H4 2 ).
(b) Estimate, in units of b, the energy associated with the long-wavelength UV-VIS
absorption of 1,3,5,7-octatetraene. Does it appear at longer or shorter wavelengths
than the corresponding absorption for 1,3,5-hexatriene?

15. Addition of methylmagnesium bromide to 2-methylcyclohexanone followed by

iodine-catalyzed dehydration of the resulting alcohol gave three alkenes in the ratio
A : B : C  3 : 31 : 66. Each isomer gave a mixture of cis- and trans-1,2-dimethylcy-
clohexane on catalytic hydrogenation. When the alkene mixture is heated with a small
amount of sulfuric acid, the ratio A : B : C is changed to 0.0 : 15 : 85. Assign structures
to A, B, and C.

16. The propellanes are highly reactive substances which readily undergo reactions
involving rupture of the central bond. It has been suggested that the polymerization
of propellanes occurs by a dissociation of the central bond:

(CH2)n (CH2)n

(CH2)n • (CH2)n
(CH2)n C (CH2)n C

Somewhat surprisingly perhaps, it has been found that [1.1.1]propellane is consider-

ably less reactive than [2.2.1]propellane. Use the theoretically calculated enthalpy data
below to estimate the bond dissociation energy of the central bond in each of the three
propellanes shown. How might this explain the relative reactivity of the [1.1.1]- and
Enthalpy for addition of hydrogen to give the corresponding bicycloalkane

2:2:1propellane  H2 ! bicyclo2:2:1heptane; DH  99 kcal=mol

2:1:1propellane  H2 ! bicyclo2:1:1hexane; DH  73 kcal=mol
1:1:1propellane  H2 ! bicyclo1:1:1pentane; DH  39 kcal=mol
70 Assume that the bond dissociation energy of the bridgehead hydrogens in each
bicycloalkane is 104 kcal=mol. Indicate and discuss any other assumptions you have

17. Examine the following thermochemical data pertaining to hydrogenation of unsatu-

rated eight-membered ring hydrocarbons to give cyclooctane:

Unsaturated ring hydrocarbon (kcal=mol)

cis,cis,cis,cis-1,3,5,7-Cyclooctatetraene 97.96
cis,cis,cis-1,3,5-Cyclooctatriene 76.39
cis,cis,cis-1,3,6-Cyclooctatriene 79.91
cis,cis-1,5-Cyclooctadiene 53.68
cis,cis-1,4-Cyclooctadiene 52.09
cis,cis-1,3-Cyclooctadiene 48.96
trans-Cyclooctene 32.24
cis-Cyclooctene 22.98

(a) Discuss the differences observed in each isomeric series of compounds, and offer
an explanation for these differences.
(b) Comment on whether the conjugation present in cyclooctatetraene has a stabiliz-
ing or destabilizing effect on the CC bonds.

18. Cyclic amines such as piperidine and its derivatives show substantial differences in the
properties of the axial C-2 and C-6 versus the equatorial C-2 and C-6 C H bonds.


The axial C H bonds are weaker than the equatorial C H bonds as can be
demonstrated by a strongly shifted C H stretching frequency in the IR spectrum.
Axial C-2 and C-6 methyl groups lower the ionization potential of the lone-pair
electrons on nitrogen substantially more than do equatorial C-2 or C-6 methyl groups.
Discuss the relationship between these observations and provide a rationalization in
terms of qualitative MO theory.

19. (a) The strain energy of spiropentane (62.5 kcal=mol) is considerably greater than
twice that of cyclopropane (27.5 kcal=mol). Suggest an explanation.


(b) The fractional s character in bonds to carbon in organic molecules may be

estimated by its relation to 13C 13C coupling constants, as determined by NMR.
Estimate the fractional s character of C-1 in its bond to C-3 of spiropentane, given
the following information: 71

J13 C 13 C
s13 
Ks31

where K is a constant equal to 550 Hz, the 13C 13C coupling constant J between C-1
and C-3 is observed to be 20.2 Hz, and s31 is the s character at C-3 in its bond to C-1.

20. Predict which direction will be favored in the thermodynamic sense for each of the
following reactions:

(a) CH4 + CH3– +

(b) CH4 + N CCH2+ CH3+ + CH3C N

(c) CHF3 + CH3– CF3– + CH4

21. Predict which compound would give the faster (k) or more complete (K) reaction.
Explain the basis for your prediction.
I + Ag+

I + Ag+

(b) K
Ph3CH + –NH2 Ph3C– + NH3
Ph Ph
Ph K _
+ –NH2 Ph + NH3
Ph Ph

(c) K
OH + H+ + + H2O

+ H+ + H2O

22. Computational comparison of structures of the benzyl cation (A) and singlet
phenylcarbene (B) indicates a much greater double-bond character for the exocyclic
72 bond in A than in B.



Can you provide a rationalization of this difference in terms of both valence bond-
resonance and PMO considerations? Explain.

23. The ionization potentials of some substituted norbornadienes have been measured by
photoelectron spectroscopy. The values which pertain to the p orbitals are shown:

IP (eV)

X 1 2

X H 8.69 9.55
CH3O 8.05 9.27
CN 9.26 10.12

Use PMO theory to describe the effect of the substituents on the ionization potential.
Use an MO diagram to explain the interaction of the substituents with the p bonds.
Explicitly take into account the fact that the two orbitals interact and therefore cannot
be treated as separate entities (see Problem 10).

24. Ab initio MO calculations using 4-31G orbitals indicate that the eclipsed conformation
of acetaldehyde is more stable than the staggered conformation.

E = –152.685 au E = –152.683 au
H/C = O eclipsed H/C = O staggered

Provide a rationalization of this structural effect in terms of MO theory. Construct a

qualitative MO diagram for each conformation, and point out the signi®cant
differences that can account for the preference for the eclipsed conformation.

25. Interesting stabilization and structural trends have been noted using MP2=6-31G*
calculations on the effect of substituents on imines. The data below give DE for the
isodesmic reaction and show that stabilization tends to increase with wBE , the group
electronegativity of the substituent. The X NCH2 bond angle decreases with wBE .
Account for these trends. 73

Discuss these trends in relation to the interaction of the nitrogen unshared pair and the
CN electrons with the substituent.

Substituent wBE DE (kcal=mol)  XNCH2  

H 2.20  4.1 110

CH3 2.55 0.0 116
CHO 2.66  3.6 114
CN 2.69 7 4.8 117
CF3 2.71  4.7 118
NO2 3.22 7 10.0 111
OH 3.55 7 20.5 110
F 4.00 7 29.0 108
SiH3 1.90  13.2 120