Chemical Bonding
A complete guide to how and why atoms form bonds, from first principles to molecular structure
Why Bonds Form
Atoms form bonds for one reason: the bonded state is lower in energy than the unbonded state. When two hydrogen atoms approach each other, the nucleus of each atom attracts the electrons of the other. At the right distance, this attraction outweighs the repulsion between the two nuclei, and the system settles into an energy minimum. That minimum is the bond.
The energy released when a bond forms is called the bond dissociation energy - the same amount of energy you would need to put back in to break the bond apart. Stronger bonds release more energy when they form and require more energy to break. For example, it takes 436 kJ/mol to break an H-H bond, and the equilibrium bond length where energy is at its minimum is just 74 pm.
The octet rule and why it works
Atoms tend to bond until they reach eight electrons in their valence shell (or two for hydrogen). This is not a fundamental law - it is a consequence of the fact that filled electron shells are unusually stable. The noble gases already have filled shells, which is why they rarely form bonds. Every other element bonds to get closer to that configuration.
Ionic vs Covalent Bonding
Bonding is not a binary choice between ionic and covalent - it is a spectrum determined by electronegativity difference. When two atoms share electrons equally, the bond is purely covalent. When one atom completely takes electrons from another, the bond is purely ionic. Most real bonds fall somewhere in between.
The bonding spectrum
Covalent bonds
Atoms share electron pairs. Formed between nonmetals with similar electronegativities. The shared electrons are attracted to both nuclei simultaneously, holding the atoms together.
Covalent bonds can be nonpolar (equal sharing, as in H₂ or Cl₂) or polar (unequal sharing, as in H-Cl or O-H), depending on the electronegativity difference.
Ionic bonds
One atom transfers electrons to another, creating oppositely charged ions held together by electrostatic attraction. Formed between metals and nonmetals with large electronegativity differences.
Ionic compounds form crystal lattices, not discrete molecules. NaCl is not a molecule - it is a repeating 3D array of Na⁺ and Cl⁻ ions.
Common electronegativity values (Pauling scale)
Lewis Structures
Lewis structures are the starting point for understanding any molecule. They show which atoms are bonded, how many bonds connect them, and where lone pairs (nonbonding electrons) sit. Getting the Lewis structure right is essential because hybridization, geometry, and polarity all follow from it.
How to draw a Lewis structure
- 1. Count total valence electrons. Add up valence electrons for each atom. For ions, add electrons for negative charges, subtract for positive. Example: CO₂ has 4 + 6 + 6 = 16 valence electrons.
- 2. Draw the skeleton. Place the least electronegative atom in the center (hydrogen is always terminal). Connect atoms with single bonds. Each bond uses 2 electrons.
- 3. Distribute remaining electrons as lone pairs. Fill octets on outer atoms first, then place leftover electrons on the central atom.
- 4. Form multiple bonds if needed. If the central atom lacks an octet, convert lone pairs from adjacent atoms into bonding pairs (double or triple bonds).
- 5. Check formal charges. The best structure minimizes formal charges. If charges exist, negative charge should sit on the more electronegative atom.
Formal charge
Formal charge = (valence electrons) - (lone pair electrons) - (1/2 bonding electrons). It tells you how electron ownership in the Lewis structure compares to the free atom.
Key rule: the sum of all formal charges must equal the overall charge of the molecule or ion. A structure with formal charges of 0 on every atom is preferred over one with separated charges.
Exceptions to the octet rule
Sigma and Pi Bonds
The Lewis structure shows you how many bonds exist. The next question is what kind of orbital overlap creates each bond. This matters because it determines bond strength, rotation, and the molecule's 3D shape.
Sigma (σ) bonds
Formed by head-on overlap of orbitals directly along the bond axis. Electron density is concentrated between the two nuclei.
The first bond between any two atoms is always a sigma bond. Sigma bonds allow free rotation because the electron density is symmetric around the bond axis.
Pi (π) bonds
Formed by side-by-side overlap of p orbitals. Electron density sits above and below the bond axis, not between the nuclei.
Pi bonds prevent rotation because rotating would break the side-by-side overlap. This is why double bonds are rigid and create geometric (cis/trans) isomers.
How to count sigma and pi bonds
The rule is simple: the first bond between any two atoms is always sigma. Every additional bond is pi.
Bond Order
Bond order is the number of bonding electron pairs shared between two atoms. A single bond has order 1, a double bond has order 2, a triple bond has order 3. Bond order connects directly to two measurable properties: higher bond order means shorter bond length and greater bond strength.
In molecules with resonance (like benzene), bond order can be fractional. Benzene's C-C bonds have an order of 1.5 - halfway between a single and double bond. This is reflected in their bond length (140 pm), which falls between a typical C-C single bond (154 pm) and C=C double bond (134 pm).
| Bond | Order | Length (pm) | Energy (kJ/mol) |
|---|---|---|---|
| C-C | 1 | 154 | 346 |
| C=C | 2 | 134 | 614 |
| C≡C | 3 | 120 | 839 |
| C-O | 1 | 143 | 358 |
| C=O | 2 | 123 | 799 |
| C-N | 1 | 147 | 305 |
| C=N | 2 | 129 | 615 |
| C≡N | 3 | 116 | 891 |
| N≡N | 3 | 110 | 945 |
Why double bonds are not twice as strong
A C=C double bond (614 kJ/mol) is less than twice a C-C single bond (346 kJ/mol). This is because the pi bond is weaker than the sigma bond - side-by-side overlap is less effective than head-on overlap. The pi bond adds about 268 kJ/mol on top of the sigma bond. This is why pi bonds are more reactive - they are easier to break.
Bond Energy and Bond Length Trends
Two factors determine bond strength and length beyond bond order:
Atomic size
Larger atoms have longer bonds because their valence orbitals are farther from the nucleus. Longer bonds mean less orbital overlap and weaker bonds. This is why H-F (570 kJ/mol) is much stronger than H-I (297 kJ/mol) even though both are single bonds - fluorine is a much smaller atom than iodine.
Electronegativity
Bonds between atoms with a large electronegativity difference tend to be stronger because the electrostatic attraction between partial charges adds to the covalent bond strength. This ionic character strengthens the bond beyond what pure covalent sharing would predict.
Hydrogen halide bonds - atomic size effect
| Bond | Length (pm) | Energy (kJ/mol) | Trend |
|---|---|---|---|
| H-F | 92 | 570 | Shortest, strongest |
| H-Cl | 127 | 432 | |
| H-Br | 141 | 366 | |
| H-I | 161 | 297 | Longest, weakest |
Using bond energies to estimate reaction enthalpy
You can estimate the enthalpy change of a reaction by summing the energies of bonds broken (positive, costs energy) and bonds formed (negative, releases energy): ΔH ≈ Σ(bonds broken) - Σ(bonds formed). If more energy is released forming new bonds than is consumed breaking old ones, the reaction is exothermic.
Resonance
Sometimes a single Lewis structure cannot accurately represent a molecule. When electrons can be delocalized across multiple positions, we draw resonance structures - two or more Lewis structures that differ only in the placement of electrons (never atoms). The real molecule is a weighted average of all resonance structures, called the resonance hybrid.
Resonance in the carbonate ion (CO₃²⁻)
Resonance is not "flipping" between structures. The molecule does not switch back and forth. The resonance hybrid is the only real structure - individual resonance structures are just our limited way of drawing it.
Rules for drawing resonance structures
Why resonance matters
Resonance stabilizes molecules. Delocalized electrons are spread over a larger volume, which lowers the overall energy. This is why carboxylate ions (two equivalent resonance structures) are much more stable than alkoxide ions (no resonance), and why carboxylic acids are more acidic than alcohols.
Putting It Together
Chemical bonding is the foundation for everything else in molecular chemistry. Here is how the concepts in this guide connect to the topics you will study next:
Bonding leads to hybridization
The number of sigma bonds and lone pairs around an atom determines its hybridization (sp, sp², or sp³), which in turn determines the orbital shapes and angles.
Hybridization determines geometry
VSEPR theory uses the electron arrangement from the Lewis structure to predict 3D molecular shape. Four electron regions give tetrahedral, three give trigonal planar, two give linear.
Geometry determines polarity
A molecule with polar bonds can still be nonpolar if the geometry causes the bond dipoles to cancel (like CO₂). The 3D arrangement of bonds decides the net molecular dipole.
Resonance explains reactivity
Whether electrons are localized or delocalized affects acidity, basicity, and reaction rates. Resonance stabilization of conjugate bases is the reason carboxylic acids are acidic while alcohols are not.
See bonding in action
Explore real molecules in 3D - toggle orbitals, bond types, and lone pairs to see how bonding shapes molecular structure.