Source: Chapter 1, Prof. Forrest Michael, University of Washington
Difficulty: Intermediate | Prerequisites: Lewis structures, formal charge, resonance (Lectures 1 and 2 notes), basic atomic orbital shapes from general chemistry.
Molecular orbital (MO) theory moves beyond Lewis structures to explain bonding in terms of how atomic orbitals combine. Where Lewis structures show electrons as dots and lines, MO theory shows them as waves that can add constructively (bonding) or destructively (antibonding). This lecture also covers dipoles: how uneven electron distribution creates partial charges along individual bonds, and how those bond dipoles add up (or cancel) to give the molecule an overall dipole moment. You need hybridisation and electronegativity from general chemistry, and the resonance concepts from Lecture 2 come in when comparing dipole moments in molecules with delocalised electrons.
Atomic orbitals combine to form molecular orbitals: bonding (lower energy, electrons here hold the molecule together) and antibonding (higher energy, electrons here weaken the bond). Sigma bonds form from head-on orbital overlap, pi bonds from side-on overlap. A molecule's dipole moment is the vector sum of all its bond dipoles, and resonance can increase or decrease the overall dipole by redistributing electron density.
LCAO (Linear Combination of Atomic Orbitals)
The assumption that molecular orbitals are formed by adding or subtracting atomic orbitals from the bonding atoms. Think of it as two waves meeting: if they reinforce each other, you get a bonding orbital; if they cancel, you get an antibonding orbital.
Bonding molecular orbital
A molecular orbital lower in energy than the parent atomic orbitals. Electron density is concentrated between the nuclei, holding the atoms together.
Antibonding molecular orbital
A molecular orbital higher in energy than the parent atomic orbitals, marked with an asterisk (*). Electron density is pushed away from the internuclear region. Electrons in these orbitals weaken the bond.
Sigma (σ) bond
A bond formed by head-on overlap of orbitals along the internuclear axis. Every single bond is a sigma bond. In simple terms, the electrons sit directly between the two atoms.
Pi (π) bond
A bond formed by side-on (lateral) overlap of p orbitals, found in double and triple bonds. The electron density sits above and below (or in front of and behind) the internuclear axis, not directly between the atoms.
Bond dipole
The separation of partial positive and negative charges along a single bond, caused by a difference in electronegativity between the two atoms.
Molecular dipole moment
The overall dipole of the entire molecule, found by vector addition of all individual bond dipoles. If the bond dipoles cancel (as in a perfectly symmetric molecule), the molecular dipole is zero.
Hybridisation (sp, sp², sp³)
The mixing of atomic orbitals to form new hybrid orbitals suited for bonding. sp³ gives tetrahedral geometry, sp² gives trigonal planar, and sp gives linear.
Atomic orbitals on adjacent atoms combine to produce molecular orbitals
N atomic orbitals in → N molecular orbitals out (conservation of orbitals)
Constructive combination (in-phase overlap) → bonding MO, lower in energy
Destructive combination (out-of-phase overlap) → antibonding MO, higher in energy
For second-row diatomics, the ordering (from lowest energy upwards) is:
1s (bonding)
2s (bonding)
2p orbitals fill next, with sigma and pi levels depending on the specific molecule
Electrons fill from lowest energy upward, two per orbital (Aufbau principle applies)
Sigma bonds: head-on overlap along the bond axis. All single bonds are sigma bonds. The first bond in a double or triple bond is also sigma.
Pi bonds: side-on overlap of parallel p orbitals. The second bond in a double bond is a pi bond. The second and third bonds in a triple bond are both pi bonds.
A double bond = 1 sigma + 1 pi. A triple bond = 1 sigma + 2 pi.
sp³: four equivalent hybrid orbitals, tetrahedral geometry (109.5°), e.g. CH₄
sp²: three hybrid orbitals in a plane, trigonal planar (120°), with one unhybridised p orbital for pi bonding, e.g. ethene
sp: two hybrid orbitals, linear (180°), with two unhybridised p orbitals, e.g. ethyne
A bond dipole arises whenever two bonded atoms differ in electronegativity
The arrow points from δ+ toward δ- (from the less electronegative atom toward the more electronegative one)
The molecular dipole moment is the vector sum of all bond dipoles
Symmetrical molecules can have polar bonds but zero net dipole (e.g. CO₂, where two equal C=O dipoles point in opposite directions and cancel)
CH₃OCH₃ (dimethyl ether, structure A): the C-O bond dipoles point inward toward oxygen, giving a net dipole
CH₃COCH₃ (acetone, structure B): the C=O bond is more polar than C-O single bonds. Additionally, resonance in the carbonyl group moves electron density onto oxygen, increasing the partial negative charge there
Result: the dipole moment of B (acetone) is greater than A (dimethyl ether)
Resonance in acetone is less influential than in a carboxylate, but it still shifts electron density enough to increase the dipole
Bond order (MO theory):
BO = (bonding electrons - antibonding electrons) / 2
Number of bonds by type:
Single bond = 1 σ
Double bond = 1 σ + 1 π
Triple bond = 1 σ + 2 π
Dipole moment direction:
Points from δ+ to δ- (from less electronegative to more electronegative atom). The net molecular dipole is the vector sum of all bond dipoles.
Molecular dipole moments determine a compound's solubility, boiling point, and intermolecular interactions. Polar molecules dissolve well in polar solvents ("like dissolves like"), which is why acetone mixes with water but hexane does not. MO theory underpins the design of organic semiconductors and dyes: engineers tune the energy gap between bonding and antibonding orbitals to control which wavelengths of light a molecule absorbs, which is how OLED screens produce their colours.
Students often confuse bonding MOs with bonds and antibonding MOs with "anti-bonds." Antibonding orbitals are not bonds that repel; they are higher-energy orbitals that, when occupied, reduce the net bonding.
A common error is thinking pi bonds are stronger than sigma bonds. Sigma bonds involve more direct overlap and are generally stronger. Pi bonds are the "extra" bonds in double and triple bonds.
Students sometimes think a molecule with polar bonds must have a net dipole. If the bond dipoles cancel by symmetry (CO₂, CCl₄), the molecule is nonpolar overall.
Confusing the dipole arrow direction: in chemistry, the dipole arrow conventionally points from positive to negative (from low electronegativity to high). Some textbooks use the opposite convention for the "dipole moment vector," so check which convention your course uses.
⚠️ Be ready to fill in an MO energy diagram for a simple diatomic and calculate bond order from it.
⚠️ "How many sigma and pi bonds are in this molecule?" is a bread-and-butter exam question. Count them: every single bond is one sigma; every double bond is one sigma plus one pi; every triple bond is one sigma plus two pi.
⚠️ Expect a question comparing molecular dipole moments. You will need to consider both electronegativity differences and molecular geometry (vector addition of bond dipoles).
⚠️ The acetone vs. dimethyl ether comparison (or similar) tests whether you understand how resonance affects dipole moment. Resonance in the carbonyl group pushes electron density onto oxygen, increasing the dipole.
True or false: Combining two atomic orbitals produces one molecular orbital.
False. Two atomic orbitals produce two molecular orbitals (one bonding, one antibonding).
Fill in the blank: A double bond consists of one ___ bond and one ___ bond.
Sigma; pi.
True or false: CO₂ has a net molecular dipole moment.
False. The two C=O bond dipoles are equal and opposite, so they cancel.
Fill in the blank: sp² hybridisation gives a ___ geometry with bond angles of approximately ___°.
Trigonal planar; 120.
True or false: Electrons in antibonding orbitals strengthen the bond.
False. They weaken it.
Q: How many sigma and pi bonds are in ethyne (C₂H₂, which has a carbon-carbon triple bond)?
A: Three sigma bonds (one C-C and two C-H) and two pi bonds (the second and third bonds of the triple bond). Total: 3σ + 2π.
Q: Using MO theory, what is the bond order of a molecule with 8 electrons in bonding MOs and 4 electrons in antibonding MOs?
A: Bond order = (8 - 4) / 2 = 2. This represents a double bond.
Q: Explain why acetone (CH₃COCH₃) has a larger dipole moment than dimethyl ether (CH₃OCH₃).
A: Acetone has a C=O double bond, which is more polar than the C-O single bonds in dimethyl ether. Additionally, resonance in the carbonyl group of acetone moves electron density onto oxygen, increasing the charge separation and the overall dipole.
Q: What hybridisation is the carbon in a C=O bond, and what geometry does that predict?
A: The carbon is sp² hybridised (three groups attached: two from the methyl groups and one from the double-bonded oxygen). This gives a trigonal planar geometry around that carbon with approximately 120° bond angles.
MO theory provides the foundation for understanding UV-Vis spectroscopy later in the course: electrons absorb light and jump from bonding to antibonding orbitals, and the energy gap determines what wavelength is absorbed. Dipole moments connect to intermolecular forces (Chapter 2 or 3, depending on your syllabus), which determine boiling points, solubility, and physical properties. Hybridisation and geometry are essential for understanding stereochemistry, which begins in the next few chapters.
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