CHAPTER III
MOLECULAR ORBITAL THEORY: A Pictorial Description
Molecular Orbital theory is predicated on the idea that atomic orbitals, be they regular or hybridized, can
be combined in a linear manner, by addition or subtraction, to produce a realistic picture of the distribution
of electron density and energy within a molecular entity. Organic chemists find it easiest to deal in pictures
rather than mathematical descriptions and that is what we will attempt to do here. Consequently we will use
word pictures, as well as drawings, to define the molecular orbitals that organic chemists find so useful.
As we did previously, when we were dealing with the electronic description of atoms, we will attempt to
combine AO’s, and especially HAO’s, to create a picture of MO’s. The overriding principle that will be
applied utilizes the LCAO method (Linear Combination of Atomic Orbitals). This method states that a
combination of a specific number of AO’s must always produce the same number of MO’s. [Note: If two
AO’s are combined, for example, then two MO’s must be produced.] The resultant pictorial description can
be applied to a portion of a molecule’s valence electron distribution or the entire molecular array. It does
not matter which because the importance of the method is the information that is conveyed. Consequently
the information conveyed describes how energy and electrons are distributed in a molecular array, or some
part of that molecule, that might be of particular interest.
When combining AO’s and HAO’s (or even MO’s) using the LCAO method there are generally two
types of results that are of interest to the organic chemist. The most basic result is to create what is called
the sigma (σ) framework or σ MO description. In some circumstances a second result will arise out of the σ
MO description and we will call this the pi (π) framework or π MO description. We will describe the basics
of σ MO construction first and then move on to the construction of the more reactive π MO’s second.
A σ MO is produced by combining in a pictorial manner two AO’s head-on along the same axis. (As we
will see shortly the term “combination” will become synonymous with the pictorial idea of overlap of
orbital lobes.) There are numerous ways to accomplish the creation of a single σ MO but no matter how it
is done the result is that two AO’s, when combined along a particular axis leads to two σ MO’s called the
sigma (σ) and sigma star (σ*) MO’s. The σ MO is lower in energy than the σ* MO. The σ MO will be
occupied by the bonding electrons, thus it is called a bonding MO, while the σ* MO will be electronically
unoccupied, and thus it is called an anti-bonding MO. The bonding MO is the important interaction because
of the attraction of the two atoms towards one another which manifests itself as an energy stabilization or a
bonding of the covalent type. Because of the importance of the bonding MO we will consider it to be the
ground state energetically. One must never forget, however, that the anti-bonding MO is always present
even though the interactions of the atoms are repulsive which means it is normally unoccupied by electrons.
The anti-bonding MO, when occupied by electrons, is considered to be the excited state energetically i.e.
higher in energy than its related ground state. [Note: The ground state is defined as being the most stable, or
of lowest energy, state in which the electrons of the bond can reside under normal environmental
conditions. The excited state is less stable or higher in energy and thus it is less likely for electrons to reside
in an excited state for long under normal environmental conditions.]
As a simple example let us create σ and σ* MO’s for a C-H bond from the linear combination of the 1s
atomic orbital of a hydrogen atom combined with a lone sp3 hybridized atomic orbital from a carbon atom
as shown in the diagrams on the next page. The diagram on the top is meant to present a picture of the
LCAO process that occurs when these two atomic orbitals are brought together to create a single C-H bond.
When two orbitals are combined head-on there are two MO’s created in which one achieves overlap while
the other has a node that prevents overlap. When overlap occurs a bond is created. (We will elaborate these
pictures in other settings later.) The diagram on the bottom is called an energy correlation diagram and it
describes the relative energies of the MO’s that are pictured in the top diagram. In an energy correlation
diagram the bonding MO’s move down in energy to a lower or more stable energy relative to the original
atomic orbital energies. The anti-bonding MO’s move up in energy to a higher or less stable energy relative
to the original atomic orbital energies by the same amount as the bonding MO moved down in energy. The
bonding MO is then occupied by one electron from a hydrogen atom and one electron from a carbon atom.
The two bonding electrons are paired and occupy this σ bonding MO to create the single C-H covalent
bond that results. [Note: The relative energy difference between the AO of hydrogen and the HAO of
carbon leads to the look of the bonding and anti-bonding MO's in the LCAO energy process in the bottom
diagram.]
Formation of a Carbon to Hydrogen Sigma MO Bond
node
LCAO Process Pictorially
antibond
sp3-HAO
1s-AO
+
Hydrogen
overlap (no-node)
Carbon
LCAO Orbital Energy Process
bond
Sigma Star
Anti-bonding Orbital
Carbon HAO
Hydrogen AO
Sigma
Bonding Orbital
Another simple example is to create a carbon to carbon single bond by combining a lone sp3 HAO
from one carbon atom with a lone sp3 HAO from another carbon atom as is shown below. The plus sign
that is appended to the picture of an AO or HAO is meant to represent the coefficients of the mathematical
wave functions that describe electron density distributions in the lobes of orbitals. [The dark lobe will have
the minus sign coefficient in our pictorial description.] When the like sign lobes come together as a linear
combination an overlap situation will be created and thus represent an attractive bonding condition which is
beneficial and lower in energy. Bonding overlap is more stable than the anti-bonding situation where an
unlike sign linear combination represents a repulsive interaction having a higher energy. Thus bringing the
plus lobe of one carbon’s sp3 HAO up to the plus lobe of another carbon’s sp3 HAO, along the same axis,
will result in a stable bonding situation for the two available electrons. Conversely bringing the plus lobe of
one carbon atom up to the minus lobe of another carbon atom, both sp3 hybridized and along the same axis,
will result in the repulsive interaction of an anti-bond which is very unstable. Thus the covalent bonding
electrons will normally occupy the more stable MO. [Note as a reminder: With HAO’s of the sp1, sp2, or sp3
type there are two lobes for each hybridized atomic orbital. One lobe of an HAO is much larger than the
other lobe and the larger lobe is assigned a plus coefficient by convention while the smaller lobe is assigned
the minus coefficient (or in our case is dark). These two lobes of an HAO actually result from the LCAO
process of combining portions of two different types of AO’s, namely s and p, to create the resultant HAO
of interest. Also note the symmetric look of the MO's created for C-C bonding compared to C-H bonding
above.]
Carbon to Carbon Sigma MO Bond Formation Using sp3 HAO's
Antibond Formation by Head-to-Tail Addition
node
+
Bonding Molecular Orbital Produced from Head-to-Head Addition
overlap
+
Bonding MO of σ -Type
Electron Distribution in MO's Created
σ *-Antibond
C-sp3
C-sp3
σ -Bond MO
Now let’s see how an actual molecule is described in terms of the σ MO description. Ethane is a simple
organic molecule having a condensed molecular formula of CH3CH3. [Note: A molecular formula specifies
the type and number of atoms in a particular molecule. A condensed molecular formula not only specifies
the type and number of atoms in a molecule but it also groups the atoms into molecular fragments that
somewhat describe the structural relationship of the fragments. Consequently ethane is two methyl radicals
that are bonded together. (A radical is an odd electron molecular entity.) We will use condensed molecular
formalism, along with other ways of describing structure, extensively.] Ethane contains six C-H σ bonds
that are covalent and one C-C σ bond that holds the two carbon atoms together using a covalent bond. Each
carbon atom is thus part of a molecular fragment that can be described as a methyl-group (CH3-group). The
carbon atom of a methyl-group is sp3 hybridized and three of these four sp3 lobes of the carbon HAO’s are
covalently bonded via the 1s AO’s of the three attached hydrogen atoms. The methyl-group can therefore
be pictured as a methyl radical or a CH3 entity with a single electron in the unbonded sp3 hybridized carbon
orbital of this fragment. Each C-H bond can be described in terms of a bonding MO like that above in the
C-H bond example. Bringing two methyl radicals together along the axis of the singly occupied sp3
hybridized carbon orbitals creates the σ MO of the C-C bonding type when the lobes having a + coefficient
are involved. If plus and minus lobes of two methyl radicals come together then a σ* MO of the C-C antibonding type is created. These are the two possible linear combinations for the bringing of two methyl
radicals together along the same axis. This result provides a picture of ethane having its six C-H bonds and
a single C-C bond arrayed in a tetrahedral manner. This picture gives a good accounting of the distribution
of mass in the ethane molecule. The MO energy correlation diagram adds to this picture by providing a
more detailed description of the distribution of electron energy in the ethane molecule. [Note: The ground
state of an organic molecule is assumed to contain all the bonding electrons of the molecular array of
interest in the most stable molecular orbitals.]
The pictorial description of the structure of ethane is represented in the upper diagram while the energy
description of the MO’s for ethane are represented in the lower diagram on the next page. The covalent C-C
bond is formed by bringing the positive coefficient lobes of the methyl radicals together along the same
axis. The plus lobes overlap and the resultant σ bond is attractive, lower energy and capable of being
occupied by two electrons having paired spins. The energy correlation diagram shows these two electrons
as occupying the more stable σ MO of the C-C bond. The bonding electrons that hold the carbon and
hydrogen atoms together are represented by straight lines. One straight line between atoms will always
represent a two electron covalent bond. [Reminder: A solid straight line represents a single bond in the
plane of the page. Wedges and hatched wedges represent single bonds that are either in front of the page or
behind the page holding the view.] The stabilization energy for a C-C or a C-H sigma bond is roughly
equivalent to the other and ranges from 90 Kcal/mole/bond to 105 Kcal/mole/bond. Therefore, when
electrons can pair up in σ MO’s during molecule formation a great deal of stability is created.
Consequently the resultant distribution of mass and energy within a molecular array can be described fairly
completely in terms of atomic structure and electron distribution within molecular orbitals. [Note: The
symbol ~ means there is an approximation for the values that follow it in the figure below and elsewhere in
organicese.]
The example given below, namely the development of C-H and C-C bonding and anti-bonding
molecular orbital schemes for ethane, can be mimicked for C-O, C-N, N-H and O-H single bonds and
molecules that contain these molecular fragments. We have chosen to exemplify the C-H and C-C single
bond MO schemes because they are so important to organicese. We will not go through each of these other
single bond heteroatom examples (C-O, C-N, N-H and O-H) here. We will however point out that in the
development of MO bonding schemes for heteroatoms, single bond examples use HAO’s almost
exclusively. When MO schemes are created for molecules that have a variety of single bond molecular
fragments HAO’s are usually involved in molecule building. The lone atomic exception is hydrogen (H)
which can only share electrons through its 1s orbital. Additionally we must say that C, N and O can be
hybridized, prior to bonding, in all possible ways e.g. sp, sp2 and sp3. However, the utilization of specific sp
and sp2 hybridization examples in the bonding of these atoms in molecules will necessitate the introduction
of the second type of molecular orbital we have mentioned previously, namely π type MO’s. Before
describing that second type of result we must add that molecularly bonded N and O atoms have nonbonding electrons that always occupy HAO-like orbitals. In fact, heteroatoms are often times
distinguishable by these non-bonding electrons. In MO schemes containing heteroatoms, the relative
energy of the non-bonding electrons does not change significantly during the LCAO process. Consequently
non-bonding electrons, which remain in an HAO, are normally carried through the energy correlation
process relatively unchanged and will be located in an energy correlation diagram at its center between the
bonding and anti-bonding MO’s. Electrons that occupy non-bonding MO’s are thus assumed to have zero
relative energy with respect to electrons that occupy the more stable bonding MO’s or electrons that might
occupy a less stable anti-bonding MO.
Molecular Structure of Ethane
H
H
H
C
H
+
H
C
H
H
H
H
H
H
Distrubution of Mass: Line Drawing of C-H Bonds
The C-C covalent bond is shown using sp3 HAO's
Distribution of Electron Energies in σ -MO's
σ * MO's
Antibond MO's
Energy
Increases
C-C Bond
C-H Bonds
σ MO's
Energy Difference between Bonding and Antibonding Orbitals ~
90 to 105 Kcal/mole/bond while the difference in energy between
a C-C bond and a C-H bond ~ 0 to 15 Kcal/mole/bond.
H
The second type of result we must consider, the π bond, is created when p-AO’s can potentially overlap
in an MO bonding scheme. All organic molecules are held together by a basic structure that results from the
overlap of AO’s and/or HAO’s along a common axis. The creation of σ MO’s, as illustrated in the previous
descriptions above, is a basic phenomenon that occurs with all organic molecular entities. These σ MO’s
are then occupied by valence electrons to cement the bonding of the atoms together. When sp and sp2
hybridized atoms interact along a common axis another possible type of orbital overlap is created between
the p-AO’s that are perpendicular to that covalent bonding axis. The side-on or parallel interaction created
by the overlap of these p-AO’s leads to the possibility of adding a second bond between the atoms of
interest. This second bonding possibility results from this parallel overlap. A π MO is then created with the
formation of this second bond and thus the sum of a σ bond and a π bond is what is called a double bond. If
two p-AO’s interact simulaneously in this parallel manner, side-on between the two atoms of interest and
perpendicular to each other, then a triple bond is created from the lone σ MO plus these two p-AO’s. Let us
examine these so-called multiple bonds in more detail. We will confine this examination to the C=C double
bond of ethene (CH2=CH2) first, the C=O double bond of formaldehyde (H2C=O) second and finally below
the CN triple bond of acetonitrile (CH3CN).
The carbon-to-carbon double bond: Two carbon atoms that are both sp2 hybridized can interact along
the same axis to create σ and σ* MO’s when one of the sp2 orbitals on one carbon overlaps with the sp2
orbital on the other carbon. The carbon atoms are held together by the sharing of two electrons in the
created σ MO because that is the lowest bonding orbital. When this σ bonding occurs the pz AO’s of the
two involved carbons can also come into overlap in a parallel manner. It is this latter interaction or overlap
from the combination of these two pz AO’s that can lead to the second type of MO scheme that is possible;
namely the creation of π and π* MO’s that result from the side-on or parallel overlap of two p-AO’s. Since
the pz AO’s hold one electron each when they bond these electrons will pair and occupy the more stable π
MO leaving the π* MO empty and unoccupied. We can illustrate this process pictorially below. (The other
two σ MO’s that are associated with each carbon atom and singly bonded to hydrogens in ethene are not
shown in this pictorial description.)
There are several interesting consequences that arise when p-AO’s are architecturally forced to interact
and overlap in a parallel manner to create π bonding and π* anti-bonding MO’s of different energies. (1)
The π MO will always accompany a σ MO when a C=C double bond is created. A π MO can not be created
in the absence of a σ MO. (2) The π MO is always of higher energy than the σ MO which it accompanies.
Conversely, the π* MO is always of lower energy than the σ* MO which it accompanies. (3) The π bond is
a weaker bond than a σ bond because the π bonding electrons occupy a larger volume of space than the
underlying σ bonding electrons, the parallel overlap interaction is not nearly as significant as with a σ MO
and the energy difference between the bonding and anti-bonding π -orbitals is less than that of a σ-bond. (4)
Carbon-to-carbon double bonds are usually shorter in length in comparison to a carbon-to-carbon single
bond. This is attributed to the extra overlap associated with the π bond that pulls the two carbon atoms
closer together in addition to the σ bonding that is also present. (5) The electron density of a π MO
occupies space above and below the space occupied by the electrons of the underlying σ MO. The
relevance of all this is that the electrons of a π MO of a double bond are always more accessible to the
environment than the underlying electrons of its associated σ MO which are in fact more stable in energy.
It is also apparent that the electrons of a π bonding MO are separated theoretically from the electrons of its
associated σ bonding MO by a node. Pictorially this means that the atoms of a double bond are restricted to
a rather rigid planar arrangement by the σ bonding MO’s while the electrons of the π MO are more loosely
distributed above and below the plane containing all the atomic mass of this double bond.
C
+
C
C
C
π * MO
C
C
π MO
p
π MO
sp2
σ MO
The carbon-to-oxygen double bond: Overlap of a sp2 hybridized carbon atom along the same axis with a
sp hybridized oxygen atom will create the potential for forming a double bond between these two atoms.
Overlap along the common axis of a sp2 orbital on carbon with a sp2 orbital on oxygen leads to σ and σ*
MO’s of the C-O single bond type. Two of the bonding electrons shared between the carbon and oxygen
atoms of the C-O bond are located in a σ bonding MO. The two pz AO’s can then overlap side-on to create
π and π* MO’s just like the result that was described above for the carbon-to-carbon double bond. The two
electrons from these two pz AO’s are then shared in the more stable π bonding MO. Let’s utilize
formaldehyde (H2C=O) to illustrate pictorially what is occurring at the molecular orbital and energy
correlation diagram levels. (The C-H MO’s are not shown on the energy correlation diagram below.)
Again note several consequences that arise as a result of the construction of the formaldehyde molecule
using MO theory as a guide. (1) Two pairs of non-bonding electrons on oxygen remain after the process of
MO building has been completed. These non-bonding electrons occupy HAO’s on oxygen and these
orbitals will be referred to as n-type MO’s. These n-type MO’s have survived the MO building process
without changing their energy situation or hybrid atomic orbital character but yet they are indeed part of the
MO scheme albeit non-bonding contributors. (2) The carbon-based sp2 HAO’s that do not contribute to the
double bond must bond to other atoms usually via a single bond. The MO’s that form by this type bonding
are completely analogous to what has already been presented. Single bonds, like those to hydrogen in this
pictorial description, contribute additional σ and σ* MO’s to the molecular array. (3) Atoms associated
with double bonds are trigonal planar in structure with the π-bonding electrons occupying the space above
and below the double bond plane. These π-bonding electrons are more accessible to the environment than
σ-bonding electrons and thus they are considered to be less stable energetically. (4) The hybridization
scheme exhibited by oxygen when bonded to carbon is limited to sp3 and sp2 types usually. In either
situation oxygen exhibits two pairs of non-bonding electrons that remain hybrid atomic-like after the MO
scheme has been applied. The relevance of all of this is that the electrons of any π MO of a double bond are
2
less stable than the underlying electrons of its associated σ MO and slightly more accessible to the
environment. In the case of a C=O however the non-bonding electrons located in an n-type MO are of
higher energy than the π -bond electrons and thus of greatest accessibility to the environment.
The electrons of the π bonding MO of a C=O can thus be distinguished theoretically from the electrons
of its associated σ bonding MO by having a node that separates them. Pictorially this means that the atoms
of this double bond are restricted to a planar arrangement by the σ bonding MO’s while the electrons of the
π MO are distributed above and below the plane containing all the atomic mass that is associated with this
double bond. Consequently the non-bonding electrons, which are located in the n-type MO’s are also
apparently part of this C=O planar system but these non-bonding electrons are subsequently much more
accessible to the environment than any of the other electrons that are part of this type MO scheme.
Non-bonding
H
H
+
H
H
sp2 CH2
sp2 O
MO's for H2CO
p
p
sp2
2
sp
n-type MO's
sp2 AO's that
become n-type MO's
σ & π MO's
Carbon
Oxygen
Nitrogen can display sp3, sp2 or sp types of hybridization before it bonds to carbon. In all three cases
nitrogen will exhibit a lone pair of non-bonding electrons as part of the MO scheme. The sp type situation
is unique because a triple bond is possible. Triple bonds have very similar characteristics to double bonds
but there are two sets of π and π* MO’s that can be created. This means that the linear array of atoms is
completely surrounded by a cylinder of π-electrons. This picture becomes much clearer when we examine
an example of a triple bond from a MO perspective.
The carbon-to-nitrogen triple bond: Overlap of a sp hybridized carbon along the same axis with a sp
hybridized nitrogen will create σ and σ* MO’s which leads to a bonding of those two atoms. The created σ
bond then has the potential to develop two sets of π and π* MO’s perpendicular to this C-N single bond.
Let’s utilize acetonitrile (CH3CN) to illustrate pictorially what is occurring at the molecular orbital and
energy correlation diagram level in this triple bond example. Let’s assume that the carbon atom of the CN
triple bond is sp hybridized and bonded via a single bond to a methyl group (CH3 = a methyl group). We
can thus construct an MO description for acetonitrile using some of the same pictorial descriptions that we
have applied to the above double bonds.
Again note several consequences that arise as a result of this type of MO construction. (1) The CN triple
bond is linear and extremely short in comparison to other types of carbon-to-nitrogen bonds. In general
triple bonds are shorter than double bonds and double bonds have already been shown to be shorter than
single bonds. Of course the absolute length of a bond depends upon the size of the atoms that make up the
bond in question. Carbon, nitrogen and oxygen are all about the same size so we can safely compare the
lengths of different types of bonds between the important atoms of organicese. Hydrogen is much smaller
and thus its bonds to C, N and O will differ in length considerably. (2) The non-bonding pair of electrons
on nitrogen is probably also linear with the entire CN array. (3) The π bonding MO’s completely surround
the linear axis of the carbon-to-nitrogen bond as if the associated electrons occupy a cylinder in the space
around the σ bond. (4) The CH3-methyl group is attached linearly to the carbon of the CN triple bond and
this entire group is free to rotate around the linear axis. The two atoms of a multiple bond are assumed not
to be able to freely rotate individually about the linear axis of the molecular array because of the π bonds
that are involved. [Note: Of course the entire fragment can freely rotate about the linear axis of the triple
bond.] (5) The hydrogen atoms of the methyl-group are attached by single bonds to the tetrahedral carbon
atom of that group. The methyl-group can freely rotate about the axis of the molecule. There are three σ
MO’s associated with the three C-H bonds of the methyl-group which are not shown in the energy
correlation diagram but are shown pictorially as part of the CH3-fragment.
The electrons of the π bonding MO of a CN triple bond can again be distinguished theoretically from the
electrons of its associated σ bonding MO by having nodes that separate them. Pictorially this means that the
atoms of this triple bond are restricted to a linear arrangement by the σ bonding MO’s while the electrons
of the π MO’s are distributed cylindrically so that they completely surround the main axis of the molecule
and contain all the atomic mass that is associated with this triple bond. Additionally the non-bonding
electrons, which are located in the n-type MO, are also apparently part of this CN linear system. These nonbonding electrons are, however, much more accessible to the environment than any of the other bonding
electrons that are part of this MO scheme because they are of higher relative energy. Accessibility to the
environment will usually mean that those electrons are the most likely electrons to become involved first in
chemical reactivity. This latter concept of accessibility is what makes molecular orbital theory so extremely
useful when applying organicese to the empirical observations and subsequent hypotheses of organic
chemistry.
Formation of Acetonitrile from a Methyl-group and a CN Triple Bond Fragment
Acetonitrile = CH3CN
H
H
+
H
C
H
C
N
H
H
MO Electron Energy Correlation Diagram for CN Triple Bond Only
Anti-bonding
MO's of σ ∗ &
π ∗ type
n-type MO
π MO's
σ MO's
Note: The AO's & HAO's of C and N are not shown in this correlation
for clarity and neither are the MO's of the methyl-group.
Resonance as an Extension of MO Theory
We have discussed in some detail the theoretical results that arise upon creation of MO’s, using AO’s
and HAO’s to overlap the atoms that bond to one another, for the purpose of constructing molecular
fragments. It is also possible to bond molecular fragments together using additional MO constructs to
create extended MO descriptions of actual molecules. In fact, this is how organic chemists visualize the
construction of organic molecular arrays in organicese. Ethene (C2H4), formaldehyde and acetonitrile are
simple examples of this type of construction. (In the C=C illustration above ethene can be created by
adding four hydrogen atoms, via four σ MO’s of lowest energy, to the C=C double bond fragment.) In the
three examples above the σ MO’s hold the molecular architecture of the atoms together while the π MO’s
are localized to the space surrounding the two atoms that contribute the p AO’s of interest. Connection of
molecular fragments having π MO architectural qualities within overlap distance of one another via one σ
bond leads to the possibility where π electrons can be delocalized or spread out over more than two atoms.
Let’s examine the molecule named acrylonitrile, having the molecular formula C3H3N, as an example of
connecting molecular fragments together where delocalization of π electron density can occur over more
than two atoms. [Note: The capacity to delocalize π electron density over an extended molecular σ MO
system, having more than two atoms, is called resonance in organicese.]
Acrylonitrile (C3H3N) – This molecular array is a familiar feed stock chemical for preparing a host of
different types of plastic materials (acrylics). The distribution of mass and the architecture of acrylonitrile
can be described as the joining together of an ethenyl radical (CH2=CH.) with the cyanidyl radical (.C=N)
using a single two electron covalent bond. In condensed formulation acrylonitrile can be written as
CH2=CH-C=N: where there is a σ MO, containing two electrons, that bonds the fragment radicals (ethenyl
and cyanidyl) together. The σ MO electron description of each fragment is unchanged from previous
descriptions when this bonding of fragments occurs but the π MO description changes in a very unique
way. The electron energy correlation diagram shown below traces the overlap interactions of the fragment
σ & π MO’s that lead to resonance for the relevant MO’s of acrylonitrile, providing a partial explanation
for the concept of π conjugation or delocalization. (Note: Many of the σ & π MO’s of the fragments that
make-up acrylonitrile are not shown below in this particular pictorial description.) [Note The ethenyl
radical comes from ethene by the loss of a hydrogen atom while cyanidyl comes from cyanide anion by the
loss of the single electron of the negatively charged and triply bonded CN entity.]
Only the important MO’s that are produced from the bonding of the ethenyl and cyanidyl radical
fragments are shown in the center of the correlation diagram. The unfilled anti-bonding orbitals are at
highest energy. The two filled orbitals having the same energy as in the cyanidyl fragment correspond
respectively to a non-bonding and a π-bonding MO carried over into the acrylonitrile MO description. The
MO labeled π MO is the most interesting because it is the bonding orbital that has a different energy
correlation as a result of conjugation. The filled MO labeled σ MO is the result of the overlap of the sp2
HAO’s from the ethenyl and cyanidyl radicals that have been brought together to construct the acrylonitrile
σ-architecture.
For acrylonitrile the conjugation or delocalization of the two electrons in the π MO result when the πbonding MO of the ethenyl radical interacts with a parallel π-bonding MO of the cyanidyl radical to create
a new Super MO. [Note: Conjugation is defined as the delocalization of π electrons over more that two
covalently bonded atoms via a Super MO.] Super MO’s allow electron density to be spread over more than
two atoms. (In this case the two electrons of the bonding super π MO are delocalized over four atoms.) In
this example the filled π-bonding MO having an unchanged energy becomes a non-bonding-like MO that
has a perpendicular orientation with respect to the bonding Super MO of acrylonitrile. Each bonding MO is
occupied by two electrons but the π conjugated electrons are spread out over more than two atoms in a
linear Super MO while the remaining filled MO’s are localized on two atoms. Linear delocalization of
electron density is thus called conjugation. Conjugation is a modest stabilizing force that usually amounts
to (approximately) ~3 Kcal/mole of stabilization energy per π fragment that is added to the linear molecular
array. [Note: When constructing conjugated MO descriptions, like that of the Super MO of acrylonitrile,
the ordering of the relative energies of the delocalized orbitals corresponds to the number of nodes present.
In this example the bonding Super MO has zero nodes and is thus moved to a more stable energy position
than its untouched and thus non-bonding π-MO partner which has 1 node.] Conjugation can thus result
when two π MO’s are directly bonded together using a bonding σ MO.
Although conjugation is described as “a modest stabilizing force” we will see later that π conjugated
systems play a significant role in organicese because the representation of π delocalization, or conjugation,
of electrons can be interpreted in terms of the concept of resonance. The concept of resonance specifies that
conjugated systems can be represented by more than one valence bond structure. [Note: Valence bond
structures will incorporate line drawings, instead of pictures of orbitals, as a simplification.] When this
criterion is met it usually means that some stabilization force is acting on the π MO system to create a more
stable energy description. Acrylonitrile can thus be represented as valence bond structures, or so-called
canonical forms, that are connected pictorially to one another by a double-headed arrow.
Origins of Resonance
H
Acrylonitrile = C3H3N
C
C
H
N
C
H
Molecular Orbitals Formed by Connecting the Ethenyl & Cyanidyl Radicals
n
n-type MO
Two π MO's
π MO
sp2
sp2
π MO
π Resonance Electrons
σ MO
CH2
CH
C3H3N
N
Super Molecular Orbitals of Conjugation for Acrylonitrile
H
C
C
H
C
Unfilled Anti-Bonding π * MO
H
H
C
C
H
C
Filled Bonding π MO
H
Two Resonance Strucutres Representing the Canonical Forms of Acrylonitrile
H
C
H
C
C
H
N
H
C
H
C
C
N
H
The double-headed arrow in the above drawing is meant to signify that all canonical forms represent
only one molecular entity. The distribution of electron density may differ from atom to atom within the
Super π MO formed, as it does in the acrylonitrile example upon which we focus, or the distribution of
electron density may be equivalent from atom to atom. Consequently curved arrows are used to represent
the flow of electron density within the valence bond (VB) structures of the molecular array of interest. For
acrylonitrile, the canonical form on the left shows the distribution of atomic mass and electron density
distribution in a neutral acrylonitrile structure. [Note: Non-bonding electrons are shown in these VB
examples for completeness but this may not be the usual situation.] The canonical form on the right
represents the charge separated VB structure for acrylonitrile which may have a slightly higher electronic
energy than its neutral counterpart on the left depending upon the environment. [Note: Each canonical form
associated with resonance may exemplify an extreme description of the electron density distribution in the
particular molecule of interest.] The positive charge in the structure on the right means the trivalent carbon
atom at that position is deficient by one electron. The negative charge means the divalent nitrogen atom at
that position has one extra electron. The electrons tend to flow towards the nitrogen atom because it is the
most electronegative atom in the molecule. Consequently, in this extreme charge separated VB structure
there is a formal +1 charge on the trivalent carbon and a formal -1 charge on the nitrogen atom.
Representing a molecular array using more than one canonical form is considered to be an energy
stabilization process. Consequently, resonance is also considered to be a stabilizing force. Oftentimes the
easiest way to visualize resonance is to represent conjugation or delocalization through the aegis of the
flow of electron density via the canonical forms of VB structure descriptions. The VB canonical structures
of resonance do not always accurately reflect the inert gas rule that we have presented previously but these
extreme forms can be of great assistance in implicating what molecular orbitals will be of greatest interest
and thus most accessible for reactivity in a defined environmental setting. {For example: The carbon atom,
having a +1 formal charge, and the nitrogen atom, having a -1 formal charge, are likely to be the center of
attention for reactivity depending upon the particular environmental setting in acrylonitrile.}
Some other examples where resonance can be examined, in a similar fashion to acrylonitrile, are shown
below with the relevant valence bond structures that contribute to the whole molecule and its molecular
array of electron density. [Non-bonding electrons are usually not shown when resonance structures, and
their canonical forms, are represented pictorially.]
1,3-Butadiene - Typical Conjugated Hydrocarbon
H
H
C
H
C
C
H
C
H
H2C
H
C
H
C
H
CH2
Acetate Anion - Conjugate Bronsted Base of Acetic Acid
O
CH3
Identical Canonical Structures
O
CH3
C
C
O
O
Not shown: The Ionically Bonded Countercation
Urea - Final Excretion Product from Metabolism
H2N
O
O
C
C
NH2
H2N
NH2
Not shown: Other Identical
Canonical Structure
Stabilization by resonance can involve charged ions, charge separated resonance in neutral structures,
more than two resonance structures, or even cyclically delocalized structures. Many different permutations
are possible. Most permutations lead to the same result: More stable systems. In some circumstances the
canonical structure forms are not of equal energy like that in acrylonitrile, 1,3-butadiene and urea where the
charge separated resonance form is of higher energy than its neutral counterpart and thus more polar. In
other circumstances, like the acetate anion, the resonance structures are of equal energy and only differ in
the placement of the electrons or charge within the identical canonical forms. In reality all the structural
canonical forms represent a single molecular entity. As we become more familiar with organicese we will
learn that resonance, conveniently pictured through the VB canonical forms of the structure, represent a
stabilization force of which we will have to be aware.
The examples of resonance and conjugation we have discussed thus far all involve linear delocalization
of electron density. If delocalization of electron density involves conjugation in a cyclic manner then a
particularly stable resonance situation is encountered that will become very familiar when organicese is
utilized to describe the concept of aromaticity. We will not define this term precisely here but we will give
two pertinent examples that may solidify the concept in your mind. [Note: A bend in a line represents a
carbon atom in a particular structure with an appropriate number of hydrogen atoms attached to complete
an octet of electrons about that carbon atom. See the identical benzene canonical forms below. Although
the structure on the left appears to differ from that on the right they are actually identical.]
Benzene - Extremely Stable Aromatic Hydrocarbon
H
C
HC
CH
HC
CH
C
H
Identical Resonance Structures
Carbonate Dianion - A Stable Y-aromatic Example
O
O
O
O
C
C
C
O
O
O
O
O
Not shown: Two Ionically Bonded Countercations
The concept described as MO theory can be of great utility to many different types of scientists. The
reason that MO theory is so useful has to do with the descriptions it provides of the energy distributions of
electron density in molecular arrays. Additionally it can be combined with valence bond theory to provide a
picture of the spatial distribution of mass and electrons in these same molecular arrays. As stated earlier,
earth bound matter is composed exclusively of mass-energy in which most of the mass is found at the
points where the atomic nuclei are located. Most of the chemically accessible energy is contained within
the distribution of electron density among the derived orbitals. Operationally MO’s are valuable predictive
tools that chemists, as well as other scientists, can utilize because of the quantum qualities that are inherent
in theory. As we will learn through practice and use, quantum theories allow chemists to assume that mass
is pretty well localized at particular positions in a molecule. We will also learn that energy is pretty well
confined to discrete orbitals and energy levels within any molecular array. Chemical reactivity thus
involves the movement of mass-energy from the environment to the molecular structure of interest and vice
versa. Consequently, the manipulation of structural mass utilizing the transference of the energy held by
electrons is of prime importance for understanding how matter undergoes the transformations that occur
naturally or unnaturally. In most circumstances valence bond structures will suffice to represent the
movement of mass-energy that occurs during a chemical process. However, it will always be understood
that MO theory supports the VB descriptions that are utilized when applying organicese to real problems
involving chemical and/or biochemical reactivity.