Source: Libre Text Notes, Purdue University Organic Chemistry
Difficulty: Introductory
Prerequisites: Basic understanding of atomic structure, electron configuration, and Lewis dot structures (General Chemistry I or equivalent).
Tags: atomic orbitals, covalent bonding, sigma bond, bond length, bond dissociation energy, bond strength, valence bond theory, hybrid orbitals, sp3 hybridization, tetrahedral geometry, methane, ethane, ammonia, water, orbital overlap, potential energy curve
This chapter sits right at the start of organic chemistry and answers a foundational question: how and why do atoms share electrons to form covalent bonds? If you have covered Lewis structures and electron configurations in general chemistry, this is the next layer of detail. Valence bond theory explains bonding in terms of orbital overlap, and hybridization explains why molecules adopt the geometries they do. Every reaction mechanism you meet later in organic chemistry relies on understanding which orbitals are involved and how they interact, so this material is load-bearing for the entire course.
Covalent bonds form when atomic orbitals overlap. Sigma (σ) bonds are the most common type, with cylindrical symmetry and free rotation. Carbon, nitrogen, and oxygen atoms mix their s and p orbitals into sp³ hybrids to explain observed molecular geometries (tetrahedral for CH₄, trigonal pyramidal for NH₃, bent for H₂O). Lone pairs occupy hybrid orbitals too, and they compress bond angles below the ideal 109.5°.
Valence bond theory
A model of covalent bonding that describes bond formation as the overlap of half-filled (or empty) atomic orbitals on adjacent atoms. Each overlapping pair of orbitals shares two electrons.
Think of it as: the idea that bonds happen because orbitals from two atoms physically meet in the same region of space.
Sigma bond (σ bond)
A covalent bond formed by head-on (end-to-end) overlap of orbitals, with cylindrical symmetry around the bond axis. A cross-section through a sigma bond at any point along the axis produces a circle.
In simple terms, this is the standard single bond you draw in Lewis structures, and it allows free rotation around the bond axis.
Bond length
The optimal internuclear distance at which a covalent bond is most stable (lowest potential energy). Measured in picometres (pm).
Think of it as: the "resting length" of the bond when the attractive and repulsive forces between the two nuclei are perfectly balanced.
Bond strength / bond dissociation energy (BDE)
The energy difference between the lowest-energy bonded state (at the optimal bond length) and the state where the two atoms are completely separated. Usually reported in kJ/mol.
In simple terms, this is how much energy you would need to put in to break the bond entirely.
Orbital overlap
The spatial region where two atomic orbitals from different atoms occupy the same volume. Bonds can only form when atoms are close enough for their orbitals to overlap.
Potential energy curve
A graph of potential energy versus internuclear distance for two bonding atoms. It shows three regimes: no overlap (too far apart, no attraction), optimal overlap (energy minimum, bond forms), and excessive overlap (nuclei too close, repulsion dominates).
Hybrid orbitals
New orbitals formed by mathematically mixing (combining) standard atomic orbitals on the same atom. Hybridization produces orbitals of equal energy and equivalent shape that point in specific directions, explaining observed molecular geometries.
sp³ hybridization
The mixing of one s orbital and three p orbitals on the same atom to produce four equivalent sp³ hybrid orbitals. These four orbitals point towards the corners of a tetrahedron, with ideal bond angles of 109.5°.
Think of it as: the atom reshuffling its orbitals so it can make four identical bonds (or hold lone pairs) arranged as far apart from each other as possible.
Covalent bonds form when half-filled orbitals on two atoms overlap and share a pair of electrons.
The simplest example is H₂: each hydrogen has one electron in a 1s orbital. The two 1s orbitals overlap head-on to form a σ bond containing two electrons.
Bonds can only form when atoms are close enough for orbital overlap. If they are too far apart, there is no attraction and no bond.
As two atoms approach each other from a large distance:
Initially there is no interaction (no overlap, no attraction).
As orbitals begin to overlap, attractive forces lower the potential energy.
At the optimal distance, potential energy reaches its minimum. This distance is the bond length.
If the atoms are pushed closer still, repulsive forces between the nuclei dominate, and the potential energy rises sharply.
The depth of the energy well (the difference between the minimum and zero) equals the bond dissociation energy.
A useful analogy: covalent bonds behave like springs.
They have a defined resting length (the bond length).
They can be compressed, stretched, or bent, but doing so costs energy.
This is why molecules vibrate, and why infrared spectroscopy can detect bond types.
Cylindrical symmetry: a cross-section perpendicular to the bond axis at any point is a circle.
Free rotation: atoms connected by a single σ bond can rotate relative to each other without breaking the bond.
Sigma bonds can form from different orbital combinations:
1s + 1s (e.g. H₂)
1s + 2p (e.g. HF)
2p + 2p (e.g. F₂, where two half-filled 2p orbitals overlap end-on)
Methane (CH₄): Carbon's ground-state electron configuration is 2s² 2p². That gives only two half-filled orbitals, but carbon forms four bonds in methane.
Solution: the one 2s and three 2p orbitals mix to form four equivalent sp³ hybrid orbitals, each with one electron.
The four sp³ orbitals arrange themselves tetrahedrally (bond angle 109.5°), which is the geometry observed in CH₄.
Each sp³ orbital on carbon overlaps with a hydrogen 1s orbital to form a C–H σ bond.
Ethane (CH₃CH₃): Both carbons are sp³ hybridised. All bonds in ethane are σ bonds.
The C–C bond is formed by sp³ + sp³ overlap.
The C–H bonds are formed by sp³ + 1s overlap.
All σ bonds in ethane have cylindrical symmetry and are free to rotate.
Ammonia (NH₃): Nitrogen has the configuration 2s² 2p³. After sp³ hybridization, four sp³ orbitals form.
Three sp³ orbitals each have one electron and overlap with hydrogen 1s orbitals to form three N–H σ bonds.
The fourth sp³ orbital holds a lone pair.
The molecular shape is trigonal pyramidal (not tetrahedral) because the lone pair is "invisible" to geometry naming.
The lone pair compresses the H–N–H bond angle from the ideal 109.5° down to approximately 107.3°.
Water (H₂O): Oxygen has the configuration 2s² 2p⁴. After sp³ hybridization:
Two sp³ orbitals each have one electron and form O–H σ bonds.
Two sp³ orbitals hold lone pairs.
The molecular shape is bent.
Two lone pairs compress the H–O–H bond angle further, to approximately 104.5°.
Ideal sp³ bond angle: 109.5°
NH₃ bond angle: ~107.3° (one lone pair compresses it)
H₂O bond angle: ~104.5° (two lone pairs compress it further)
C–C single bond length (ethane): 154 pm
The spring-like behaviour of covalent bonds is exactly what infrared (IR) spectroscopy measures. Different bond types vibrate at characteristic frequencies, which is how chemists identify functional groups in unknown compounds. The tetrahedral geometry of sp³ carbon also explains why diamond is so hard: every carbon atom is sp³ hybridised and bonded to four others in a rigid three-dimensional lattice.
"Carbon can only form two bonds because it has two unpaired electrons." This ignores hybridization. The 2s and 2p orbitals mix to give four sp³ hybrids, each singly occupied, allowing four bonds.
"Lone pairs don't affect molecular geometry." Lone pairs occupy space and repel bonding pairs. They compress bond angles: 109.5° in CH₄ drops to 107.3° in NH₃ and 104.5° in H₂O.
"Tetrahedral" and "trigonal pyramidal" are the same thing. Tetrahedral describes the arrangement of all four electron groups. When one of those groups is a lone pair, the visible shape (the atoms only) is trigonal pyramidal, not tetrahedral.
"Bonds form because atoms want full octets." Bonds form because orbital overlap lowers the system's potential energy. The octet rule is a useful shortcut, not a driving force.
⚠️ You will almost certainly be asked to identify the hybridization of a given atom and predict the molecular geometry. Practise working from electron configuration through hybridization to shape.
⚠️ Know the trend: more lone pairs on the central atom means smaller bond angles. Be able to rank CH₄ > NH₃ > H₂O by bond angle and explain why.
⚠️ Be able to sketch the potential energy curve for two bonding atoms and label bond length, bond dissociation energy, the repulsive region, and the no-overlap region.
⚠️ Sigma bonds allow free rotation. This becomes critical when you study conformational analysis (Newman projections) in the next chapter.
True or false: A sigma bond has cylindrical symmetry and allows free rotation. ___
Fill in the blank: The ideal bond angle for sp³ hybridization is ___.
True or false: Water has a tetrahedral molecular shape. ___
Fill in the blank: Bond dissociation energy is the energy difference between the bonded state at optimal distance and the state where atoms are completely ___.
True or false: In ammonia, the lone pair on nitrogen occupies an sp³ hybrid orbital. ___
Answers: 1. True. 2. 109.5°. 3. False (bent). 4. Separated. 5. True.
Q: What type of orbital overlap forms the sigma bond in H₂?
A: Head-on overlap of two 1s orbitals, one from each hydrogen atom.
Q: Explain why methane has a tetrahedral geometry even though carbon's ground-state configuration (2s² 2p²) has only two unpaired electrons.
A: Carbon undergoes sp³ hybridization: the 2s and three 2p orbitals mix to form four equivalent sp³ hybrid orbitals, each containing one unpaired electron. These four orbitals point to the corners of a tetrahedron, giving CH₄ its tetrahedral shape with 109.5° bond angles.
Q: Why is the bond angle in water (~104.5°) smaller than in ammonia (~107.3°)?
A: Water has two lone pairs on the central oxygen (compared to one lone pair on nitrogen in ammonia). Lone pairs occupy more angular space than bonding pairs, so more lone pairs compress the bond angle further.
Q: How does the potential energy curve explain bond length?
A: Bond length corresponds to the internuclear distance at the minimum of the potential energy curve. At this point, attractive forces from orbital overlap and repulsive forces between nuclei are balanced, giving the most stable (lowest energy) arrangement.
Q: In ethane (CH₃CH₃), what type of orbital overlap forms the carbon-carbon bond?
A: sp³ + sp³ overlap, forming a sigma (σ) bond.
This material connects directly to conformational analysis (Chapter 3 in most textbooks), where free rotation around σ bonds produces different conformers visualised with Newman projections. The concept of hybridization also sets up sp² and sp hybridization, which explain the geometry and restricted rotation in alkenes and alkynes. Understanding bond dissociation energies will return in thermodynamics and when predicting reaction feasibility using enthalpy changes.
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