Molecular Orbital Theory Review
Dr. Michaelis
Chem 351, Winter 2017
Sections 1–8
1. Atomic orbitals
You learned in Chem 105 and 106 that electrons have both wave- and particle-like properties. Because of this
wave-particle duality, knowing the exact location and velocity of an electron is impossible. This means that you must
abandon your cherished mental images of electrons as tiny spheres revolving in circular orbits around the atomic nucleus
in favor of the more accurate, but less intuitive model provided to us by quantum mechanics.
Quantum mechanics tells us that the behavior of a negatively-charged electron near a positively-charged nucleus
is best described by the Schrödinger equation, which takes into account the wave- and particle-like properties of
electrons. The solutions to the Schrödinger equation are called wave functions (ψ), which you can think of as standing
electron waves. Standing electron waves can only exist at certain energy levels, and electrons at different energy levels
are described by different wave functions. The square of the wave function (ψ2) for an electron at a given energy level is
proportional to electron density, i.e., the probability that an electron at that energy level will be in a certain location. For
historical reasons, we will frequently call these wave functions orbitals.
Wave functions (or orbitals) have many of the familiar properties of standing waves: ψ can be positive or negative,
or can equal zero, depending on where you look. To avoid confusion with positive and negative electrostatic charges, we
will sometime refer to the sign of a wave functions as its “phase” and will generally use color or shading to indicate areas
of a given wave function that have opposite sign. Locations where ψ = 0 are called nodes. Nodes always separate areas
where ψ is positive from areas where ψ is negative. At a node, electron density is zero, because ψ2 = 0. We will see that
higher energy wave functions (i.e., orbitals) have more nodes than lower energy wave functions.
In organic chemistry we will deal primarily with atoms from the first and second rows of the periodic table. For first
row atoms (principle quantum number = 1), there is only one kind of wave function or orbital available: the 1s orbital
(Figure 1). Recall that the 1s orbital has a spherical shape, with the nucleus at the center of the sphere, and has no
nodes.
For second row atoms (principle quantum number = 2), there are four atomic orbitals available: one 2s orbital and
three 2p orbitals (Figure 1). The 2s orbital has a spherical shape like the 1s orbital, but unlike the 1s orbital, the 2s orbital
has a spherical nodal surface ~ 1 Å from the nucleus. The three 2p orbitals (2px, 2py, and 2pz, aligned along the x, y, and
z axes respectively, each separated from the other by a 90°
angle) have a two-lobed dumbbell shape with a nodal plane at
the nucleus that is orthogonal (or perpendicular) to the orbital
axis (e.g., for the 2px orbital, the nodal plane is the yz plane)
The outer surface of and the inner sphere of the 2s orbital have
opposite phase. For the 2p orbitals, one of the dumbbell lobes
has positive phase, and the other has negative phase. The 2s
orbital is higher in energy than the 1s orbital. The the 2px, 2py,
and 2pz are equal in energy to each other, but are higher in
energy than the 2s orbital.
Figure 1. Atomic orbitals available to first row elements
2. Orbital Hybridization
In Chem 351, we will use a concept called orbital hybridization to explain the structure, bonding, and threedimensional geometry of many organic molecules. You should be aware that orbital hybridization is an oversimplification
of what is actually going on in organic molecules, and does not adequately explain some important observations that are
best understood using molecular orbital theory and a lot of math. However, when combined with an understanding of the
other “answers to why” concepts, orbital hybridization helps us make useful predictions, so we will continue to use it. If
you want to know more, take Chem 552 with Dr. Savage!
We will use orbital hybridization to explain the threedimensional geometry of carbon atoms in organic molecules.
Carbon atoms each have four orbitals: 2s, 2px, 2py, and 2pz.
In an sp3-hybridized carbon atom, we mix all four of these
orbitals together to generate four new hybrid orbitals, called sp3
orbitals (Figure 2A). The four sp3 orbitals are equal in energy
to each other, and have a distorted dumbbell shape, with one
lobe much larger than the other lobe and a node at the
nucleus. Ideally, each of the four sp3 orbitals is separated from Figure 2. (A) Combination of one 2s orbital and three 2p
all the others by a 109.5° angle, so that an sp3-hybridized orbitals to generate four sp3 orbitals. (B) Ideally, each sp3
carbon atom in an organic molecule has a tetrahedral geometry orbital is separated from the others by 109.5°.
(Figure 2B). The sp3 orbitals can interact with orbitals on other
atoms to form σ bonds---see Answer #3 below.
In an sp2-hybridized carbon atom, we mix the 2s orbital
with the 2px and 2py orbitals to generate three new hybrid
orbitals, called sp2 orbitals (Figure 3A). Note that the 2pz
orbital remains unchanged. The three sp2 orbitals are equal in
energy to each other, but are lower in energy than the 2pz
orbital. Sp2 orbitals have a similar shape as the sp3 orbitals,
though they have more “s-character” than the sp3 orbitals.
Ideally, each of the three sp2 orbitals is separated from the
others by a 120° angle, and from the 2pz orbital by a 90° angle,
so that an sp2-hybridized carbon atom in an organic molecule
has planar geometry (Figure 3B). The sp2 orbitals can interact
with orbitals on other atoms to form σ bonds, whereas the 2pz
orbital can interact with orbitals on other atoms to form π
bonds---see Answer #3 below.
Figure 3. (A) Combination of one 2s orbital and two 2p
orbitals to generate three sp2 orbitals. (B) Ideally, each sp2
orbital is separated from the others by 120° and from the
remaining 2p orbital by 90°.
In an sp-hybridized carbon atom, we mix the 2s orbital
with the 2px orbital to generate two new hybrid orbitals, called
sp orbitals (Figure 4a). Note that the 2py and 2pz orbitals
remain unchanged. The two sp orbitals are equal in energy to
each other, but lower in energy than the 2py and 2pz orbitals.
Sp orbitals have a similar shape as the sp3 and sp2 orbitals,
though they have more “s”-character than the sp3 and sp2
orbitals. Ideally the two sp orbitals are separated from each Figure 4. (A) Combination of one 2s orbital and one 2p
other by a 180° angle and from the 2py and 2pz orbtials by a orbital to generate two sp orbitals. (B) Ideally, each sp
90° angle, so that an sp-hybridized carbon atom in an organic orbital is separated from the others by 180° and from the
molecule has a linear geometry (Figure 4B). The sp orbitals remaining two 2p orbitals by 90°.
can interact with orbitals on other atoms to form σ bonds,
whereas the 2py and 2pz orbitals can interact with orbitals on other atoms to form π bonds---see Answer #3 below.
3. Molecular Orbitals and Bonding
Some general principles:
• Atomic orbitals on nearby atoms can combine to form new molecular orbitals that are shared between the atoms.
• The number of atomic orbitals you mix together equals the number of molecular orbitals formed.
• Two atomic orbitals mix together “in-phase” to form a bonding orbital that is lower in energy than the original atomic
orbital and “out-of-phase” to form an anti-bonding orbital that is higher in energy than the original atomic orbital.
• When considering bonding between two atoms, first construct the relevant molecular orbitals, then fill them with the
available electrons, starting with the lowest energy molecular orbital.
• Each orbital can accommodate a maximum of two electrons, but the electrons must have opposite spin. We will
typically use two vertical arrows, one up and one down arrow to represent paired electrons with opposite spin.
• A “covalent bond” consists of a bonding orbital filled with two electrons
• Orbitals exist, whether or not they are filled with electrons. Empty orbitals are essential in explaining many organic
reactions.
In general, s, sp3, sp2, or sp orbitals on two adjacent atoms can combine to form a σ bonding orbital and a σ* antibonding orbital (Figure 5). The σ orbital is radially symmetric about the interatomic axis, and is concentrated between the
nuclei of the two atoms. The negatively-charged electrons in a filled σ orbital orbital are mostly between the two positivelycharged nuclei, which helps hold the nuclei together, and is one of the reasons that the σ orbital is a bonding orbital. The
σ* orbital is also radially symmetric about the interatomic axis but has a nodal plane between the two nuclei, perpendicular
to the interatomic axis. The σ* orbital is mostly concetrated away from the space between the two nuclei, so that most of
the electron density in a filled σ* orbital is oriented away from the interatomic axis and tends to pull the nuclei apart. The
σ orbital is typically much lower in energy than the two original atomic orbitals, whereas the σ* orbital is typically much
higher in energy than the two original atomic orbitals.
Figure 5. σ bonding and σ* anti-bonding molecular orbitals formed by (A) two 1s orbitals; (B) an sp3 orbital and a 1s orbital;
and (C) two sp3 orbitals
In general, p orbitals on two adjacent atoms interact by lining up
parallel to each other to form a π bonding orbital and a π* antibonding orbital
(Figure 6). The π orbital is shaped like a hot dog bun, where the two halves of
the bun are on opposite sides of the interatomic axis, with a nodal plane in
between (parallel to the interatomic axis and perpendicular to the two original p
orbitals). Electron density in a filled π orbital is mostly between the two nuclei,
but not along the interatomic axis. Electrons in a filled π orbital hold the two
nuclei together, but not as strongly as do electrons in a filled σ orbital. A filled π
orbital makes the second bond in a double bond (the first bond is a filled σ
orbital; in a triple bond, both the second and third bonds both come from filled π
orbitals). The π orbital is stabilized relative to the two original p orbitals, but not
by as much as is the σ orbital. This means that a π-bond is not as strong as a
σ-bond, and that forming a σ-bond releases more energy than forming a πbond.
The π* orbital essentially looks like two p orbitals lined up out-of-phase.
It has two nodal planes: the first is parallel to the interatomic axis and
perpendicular to the two original p orbitals (this nodal plane is also present in
the π orbital); the second is between the two nuclei, perpendicular to the
interatomic axis. Most of the electron density in a filled π* orbtial is oriented
away from the interatomic axis and tends to pull the nuclei apart, but not as
strongly as do electrons in a filled σ* orbital. The π* orbital is higher in energy Figure 6. π bonding and π* anti-bonding
molecular orbitals from two 2p orbitals
than the two original p orbitals, but not by as much as is the σ* orbital.
Understanding the relative energies of σ, σ*, π, and π* orbitals in organic molecules will help you predict how
organic molecules will react with themselves or with each other. Organic reactions usually happen as the Highest
Occupied Molecular Orbital (HOMO) on one molecule overlaps with the Lowest Unoccupied Molecular Orbital (LUMO) on
another molecule. The HOMO will usually be a bonding orbital (usually π) or a non-bonding orbital (“n”, these are usually
orbitals that hold lone pair electrons), whereas the LUMO will usually be an anti-bonding orbital (σ* or π*).
4. Good vs. Bad orbital overlap
•
Orbitals in a molecule overlap and interact best when they are parallel to each other. Orbitals cannot overlap and
interact when they are orthogonal (perpendicular) to each other.
•
Orbitals interact best when they have the same principal quantum number (i.e., they are on atoms that come from
the same row of the periodic table).
•
Orbitals interact better the closer they are in energy to each other.
5. Resonance (conjugation)
Resonance or conjugation occurs when p orbitals on three or more adjacent atoms align to create a set of π
orbitals (which we will sometimes call the “π-system”) that extend across the participating atoms. The electrons that fill
these π orbtials are delocalized across the entire π-system, and are therefore lower in energy than they would have been
in the original isolated p orbitals.
If you can rearrange the electrons (but not the nuclei) in the Lewis structure of
a molecule to create an equally valid new structure (that also satisfies the octet rule),
it’s a pretty good bet that resonance is occuring in that molecule (Figure 7). Such
equally valid structures are called “resonance structures”, and we use a single line
with an arrowhead at each end to indicate this relationship. It is tempting to think of
Figure 7. Resonance structures of
resonance as a molecule switching back and forth rapidly from one resonance
the acetate anion.
structrure to another, but this is incorrect! You can think of the actual structure of the
molecule as a hybrid of the resonance structures, but you should also remember that resonance comes from an extended
π orbital, in which electrons are delocalized across several adjacent atoms at the same time (this only makes sense when
you think of electrons as standing waves). We will also see that resonance can be used to delocalize charge (positive or
negative) in a way that stabilizes molecules.
6. Hyperconjugation
Hyperconjugation is the stabilizing interaction of a filled orbital
(usually σ or n) with an empty orbital (2p, σ* or π*) on an adjacent
atom in the same molecule. It cannot occur if these orbitals are
orthogonal to each other, and it happens best when the orbitals are
parallel. In hyperconjugation, a filled orbital on atom 1 donates electron
density into an empty orbital on adjacent atom 2 (Figure 8A). This is a
stabilizing interaction because it allows the electrons from the filled
orbital to move to a lower energy level (Figure 8B), and because it
allows the empty orbital to spread out across both atoms 1 and 2. We
will use hyperconjugation to explain conformational preferences of
organic molecules and to rationalize the relative stabilities of
carbocations, radicals, and carbanions, among other things. We will
use specific terminology to talk about hyperconjugation. For example,
the phrase “σ š p hyperconjugation” describes hyperconjugation Figure 8. (A) σ à p hyperconjugation in the tertbetween a filled σ bonding orbital on one atom with an empty p orbital butyl cation. (B) Molecular orbital diagram of σ à
p hyperconjugation.
on an adjacent atom (Figure 8).
7. Electronegativity
Electronegativity is the tendency of an atom to pull electron density toward itself. You can think of
electronegativity as how much an atom “wants” electrons, or alternatively, how happy it would be with extra electrons.
Recall that electronegativity increases as you move across the periodic table (C < N < O < F, etc.) and decreases as you
move down the periodic table (F > Cl > Br > I, etc.). Another useful trend to remember is that the electronegativity of an
atom can change depending on its orbital hybridization. S orbitals are more electronegative than p orbitals, because s
orbitals are held more closely to the nucleus. Therefore, an sp hybridized carbon is more electronegative than an sp2
hybridized carbon because it has more “s-character”. We will use electronegativity to explain some acidity trends and to
predict the extent to which electron density in a particular bond is unevenly distributed or polarized between the two
nuclei.
Consider for example, a σ bond between carbon and oxygen. Because oxygen is more electronegative than
carbon, we would predict that the electron density in the σ-bond would be distributed more densely about the oxygen
atom than about the carbon atom. This would result in a dipole, with a partial positive charge on the carbon, and a partial
negative charge on the oxygen. Another way of saying this is (1) that the filled σ orbital is unevenly distributed between
carbon and oxygen, with more of the σ near the oxygen than the carbon, and (2) that the empty σ* orbital is unevenly
distributed between carbon and oxygen, with more of the σ* near the carbon than the oxygen.
8. Atomic Size
As you move down a column in the periodic table, atomic size (i.e., atomic radius) increases. This increase in
size has some interesting effects: (1) the valence electrons of larger atoms are farther away from the nucleus, and are
therefore held more loosely by the nucleus than are the valence electrons of smaller atoms; (2) in large ions with a single
negative charge, the negative charge is spread out over a larger amount of space than in small ions with a single negative
charge. Thus, Br- and I- are more stable than Cl- and F-, even though Cl- and F- are more electronegative. We can
therefore use atomic size as an explanation for why H-I and H-Br are stronger acids than H-Cl and H-F. We will also use
atomic size to explain why I- and Br- are better nucleophiles (i.e., more reactive in certain organic reactions) in protic
solvent than are Cl- and F-.
9. Steric Repulsion
Steric repulsion or hindrance describes what happens when atoms bump into each other. Even though atoms are
mostly empty space, two atoms cannot occupy the same space at the same time, because of electron-electron repulsion
and the Pauli exclusion principle, which states that only two electrons (with opposite spin) may occupy the same space at
the same time. The bulky size of some functional groups in sterically hindered organic molecules can prevent certain
reactions from happening, or can redirect a reaction down a different pathway that would be expected for a less sterically
hindered organic molecule.
References:
Jones, M. Organic Chemistry, 2nd Edition, W.W. Norton & Company, Inc., New York, 2000.
Smith, J.G. Organic Chemistry, 3rd Edition, McGraw Hill, New York, 2011.