Difficulty: Introductory to Intermediate. Prerequisites: electronegativity, Lewis structures, basic understanding of atomic orbitals (s and p).
This is the second half of Lecture 3, covering how electronegativity differences between atoms lead to polar bonds, and how atomic orbitals combine to form molecular bonds. These ideas set the stage for understanding molecular geometry, intermolecular forces, and reaction mechanisms later in the course. If electronegativity is still unclear, review the first set of notes from this lecture before continuing.
When two atoms with different electronegativities share electrons, the electrons spend more time near the greedier atom, creating a polar bond with partial charges. Covalent bonds form when atomic orbitals overlap: a sigma (σ) bond is end-to-end overlap, and the resulting molecular orbital sits lower in energy than the original atomic orbitals. Every bonding orbital has a corresponding antibonding orbital at higher energy.
Bond polarization
The unequal sharing of electrons in a covalent bond, caused by a difference in electronegativity between the two bonded atoms. The more electronegative atom pulls the shared electrons closer to itself.
Think of it as: a tug-of-war for electrons, where the stronger atom wins but does not take them completely.
Polar covalent bond
A covalent bond in which the electron density is unevenly distributed because one atom is more electronegative than the other. The bond has a partial negative charge (δ−) on the more electronegative atom and a partial positive charge (δ+) on the less electronegative atom.
In simple terms, this means the electrons are shared but not equally.
Dipole moment
A vector quantity that measures the degree of polarity of a bond. It points from the positive end (δ+) to the negative end (δ−) and is larger when the electronegativity difference is greater.
Think of it as: an arrow showing which direction the electrons are being pulled.
Covalent bond
A bond formed when two atomic orbitals overlap completely, sharing a pair of electrons between two nuclei.
Sigma bond (σ bond)
A covalent bond formed by the end-to-end (head-on) overlap of two atomic orbitals. It is the strongest type of covalent bond and allows free rotation around the bond axis.
In simple terms, this means the orbitals point straight at each other and overlap along the line connecting the two nuclei.
Antibonding orbital (σ)*
A molecular orbital that results from the destructive (out-of-phase) combination of two atomic orbitals. It is higher in energy than the original atomic orbitals, and electrons in this orbital weaken or cancel a bond.
Think of it as: the opposite of a bond. If the bonding orbital pulls atoms together, the antibonding orbital pushes them apart.
Bond energy
The difference in energy between the bonding molecular orbital and the original atomic orbitals. It represents how much energy is released when the bond forms, or how much energy is needed to break it.
Orbital phase
Atomic orbitals have a wave-like nature, with positive (+) and negative (−) phases, analogous to the peaks and troughs of a transverse wave. Constructive overlap (same phase) creates bonding orbitals. Destructive overlap (opposite phase) creates antibonding orbitals.
In most covalent bonds, the electrons are not shared equally. The more electronegative atom pulls the electron density towards itself.
This creates partial charges: δ− on the electronegative atom, δ+ on the less electronegative one.
The greater the electronegativity difference between the two atoms, the more polarised the bond.
The dipole moment is a vector that points from the positive end to the negative end of a polar bond.
It measures the magnitude of the bond's polarity.
As the electronegativity difference increases, the dipole moment increases.
Methanol (CH₃OH): The C–O bond is polar. Oxygen is more electronegative than carbon, so the shared electrons sit closer to oxygen. Each C–H bond is only very slightly polar (carbon and hydrogen have similar electronegativities).
Hydrogen chloride (HCl): In the gas phase, HCl is a highly polarised covalent bond. In aqueous solution, it dissociates fully into H⁺ and Cl⁻, so there is no covalent bond at all.
Ammonia (NH₃): Nitrogen is slightly more electronegative than hydrogen, but the difference is small. The N–H bonds are only weakly polar, and nitrogen carries a small δ− while each hydrogen carries a small δ+. Nitrogen ends up fairly neutral overall because the partial charges nearly cancel.
A covalent bond forms when two atomic orbitals overlap, sharing a pair of electrons between the two nuclei.
The electrons occupy a new molecular orbital that is lower in energy than the separate atomic orbitals. This energy drop is the bond energy.
A sigma bond is formed by end-to-end (head-on) overlap of two atomic orbitals along the internuclear axis.
Example: Two hydrogen 1s orbitals overlap to form an H–H σ bond.
The bonding electron pair sits in a molecular orbital concentrated between the two nuclei.
When two atomic orbitals combine, they produce two molecular orbitals: one bonding (σ) and one antibonding (σ*).
The bonding orbital is lower in energy than the original atomic orbitals. Electrons here stabilise the molecule.
The antibonding orbital is higher in energy. Electrons here destabilise the molecule.
This process reflects quantum mechanical mixing: the number of molecular orbitals always equals the number of atomic orbitals that combined.
Atomic orbitals behave like waves and have phases (positive and negative regions), analogous to peaks and troughs of a transverse wave.
Same-phase overlap (constructive interference) creates the bonding orbital.
Opposite-phase overlap (destructive interference) creates the antibonding orbital.
A polar bond is drawn with an arrow pointing from δ+ to δ−. The arrow has a small cross at the positive end (+→). The length of the arrow indicates the magnitude of the dipole.
Start with two separate H atoms, each with one electron in a 1s orbital, at the same energy level.
Combine them to produce two molecular orbitals:
σ (bonding): lower in energy, occupied by both electrons (paired, opposite spins).
σ* (antibonding): higher in energy, empty.
The energy gap between the 1s atomic orbital and the σ bonding orbital is the bond energy.
The antibonding orbital is raised by roughly the same amount above the atomic orbital level.
Bond polarity is why water dissolves salt but oil does not: the polar O–H bonds in water can stabilise ions through electrostatic interactions, while the nearly nonpolar C–H bonds in oil cannot. Understanding which bonds are polar is the first step to predicting solubility, boiling points, and how molecules interact with biological receptors.
Sigma bonds and molecular orbital theory underpin everything from drug design (how tightly a drug binds to a protein) to materials science (why diamond is hard and graphite is soft).
Students often think a polar bond means the molecule itself is polar. A molecule can have polar bonds that cancel out due to symmetry (e.g. CO₂ has two polar C=O bonds, but the molecule is linear and nonpolar overall).
Students confuse "polar covalent" with "ionic." A polar covalent bond is still a shared-electron bond; an ionic bond involves a complete transfer of electrons. HCl in the gas phase is polar covalent; HCl in water dissociates into ions.
Students sometimes assume the antibonding orbital is always occupied. In H₂, it is empty. Antibonding orbitals matter when they are populated (e.g. in He₂, which does not form a stable bond because both σ and σ* are filled).
Students forget that combining N atomic orbitals always produces exactly N molecular orbitals. You cannot create or destroy orbitals; you can only redistribute them.
⚠️ You will very likely be asked to identify which atom in a bond carries δ+ and which carries δ−, based on electronegativity. Practise this with common bonds: C–O, C–N, O–H, N–H, C–Cl.
⚠️ Drawing and interpreting molecular orbital energy diagrams (especially for H₂) is a staple exam question. Know which orbital is bonding, which is antibonding, and where the electrons go.
⚠️ "What type of bond is formed by end-to-end overlap of two atomic orbitals?" The answer is a sigma (σ) bond. This is the kind of straightforward definition question that appears frequently.
⚠️ Expect conceptual questions about what happens when HCl moves from gas phase to aqueous solution (goes from polar covalent to fully ionic/dissociated).
True or False: In a polar covalent bond, electrons are transferred completely from one atom to another.
Answer: False. The electrons are shared unequally, not transferred.
Fill in the blank: A sigma bond is formed by ______ overlap of two atomic orbitals.
Answer: End-to-end (head-on).
True or False: The antibonding orbital in H₂ is occupied by two electrons.
Answer: False. In H₂, only the bonding orbital is occupied.
Fill in the blank: As the electronegativity difference between two bonded atoms increases, the ______ of the bond increases.
Answer: Polarity (or dipole moment).
True or False: HCl is a polar covalent bond in both the gas phase and in aqueous solution.
Answer: False. In aqueous solution, HCl dissociates completely into H⁺ and Cl⁻.
Q: Explain why the C–O bond in methanol is polar, and indicate which atom carries the partial negative charge.
A: Oxygen is more electronegative than carbon, so it pulls the shared electrons closer to itself. Oxygen carries δ− and carbon carries δ+.
Q: Describe what happens to the bonding in HCl when it moves from the gas phase into aqueous solution.
A: In the gas phase, HCl has a highly polarised covalent bond. In aqueous solution, the bond breaks entirely: H⁺ and Cl⁻ ions form, and no covalent bond remains.
Q: What is a sigma (σ) bond? How does it differ from the atomic orbitals that form it?
A: A sigma bond is a molecular orbital formed by end-to-end overlap of two atomic orbitals. It is lower in energy than the original atomic orbitals and concentrates electron density along the internuclear axis.
Q: When two 1s orbitals on separate hydrogen atoms combine, how many molecular orbitals are produced, and what are they called?
A: Two molecular orbitals are produced: one bonding orbital (σ) at lower energy and one antibonding orbital (σ*) at higher energy.
Q: Why is nitrogen described as "fairly neutral" in ammonia (NH₃), even though it is more electronegative than hydrogen?
A: The electronegativity difference between nitrogen and hydrogen is small, so the N–H bonds are only weakly polar. The partial charges on nitrogen are modest, and the overall electron distribution leaves nitrogen close to neutral.
Bond polarity leads directly into molecular polarity and intermolecular forces (dipole-dipole interactions, hydrogen bonding), which determine physical properties such as boiling point, solubility, and viscosity.
Sigma bonds connect to hybridisation (sp³, sp², sp) in the next lectures, and to pi (π) bonds, which form by side-to-side overlap rather than end-to-end. Together, sigma and pi bonds explain double and triple bonds. Molecular orbital theory also underpins conjugation and aromaticity later in the course.
Bond polarization, polar covalent bond, nonpolar covalent bond, ionic bond, dipole moment, dipole vector, partial charge, delta plus, delta minus, δ+ δ−, sigma bond, σ bond, antibonding orbital, σ*, molecular orbital, MO diagram, MO theory, bond energy, orbital overlap, orbital phase, constructive interference, destructive interference, covalent bond formation, HCl polarity, methanol polarity, ammonia polarity, organic chemistry, Purdue organic chemistry, OChem lecture 3