Bonding Models: Sigma/Pi & Band Theory
- Distinguish σ from π bonds and count each in single, double, and triple bonds
- Relate the σ-bond framework and π bonds of a molecule to its hybridization
- Use the electron-sea/band model and solid-type classification to explain conductivity, hardness, and melting point
Sigma and pi: two kinds of overlap
A sigma (σ) bond comes from head-on overlap of orbitals directly along the axis joining two nuclei; its electron density is concentrated on that line, and it can freely rotate. A pi (π) bond comes from side-by-side overlap of unhybridized p orbitals, placing density in lobes above and below the bond axis; it locks the two atoms against rotation. Crucially, the first bond between any two atoms is always the σ bond — π bonds are only ever added on top of an existing σ.
Hybridization builds the σ framework; leftover p orbitals make π
An atom hybridizes exactly enough orbitals to hold its electron domains: sp (2 domains), sp² (3), sp³ (4). Those hybrid orbitals form the σ bonds and hold the lone pairs — the molecule's skeleton. Any p orbitals left unhybridized are what form π bonds. So sp³ (no leftover p) makes only σ bonds; sp² leaves one p orbital for one π bond; sp leaves two p orbitals for two π bonds. Hybridization and the π count are two views of the same electron-domain number.
Count the total σ and π bonds in acrylonitrile, H₂C=CH–C≡N, and give the hybridization of each carbon.
- 1.List every bonded connection: two C–H on the first carbon, one C–H on the second carbon, the C=C double bond, the C–C single bond to the third carbon, and the C≡N triple bond.
- 2.σ count = one per connection: 2 (C–H) + 1 (C–H) + 1 (C=C) + 1 (C–C) + 1 (C≡N) = 6 σ bonds.
- 3.π count = the extra bonds: the C=C double contributes 1 π and the C≡N triple contributes 2 π → 3 π bonds.
- 4.Hybridizations from domain counts: the =CH₂ carbon has 3 domains → sp²; the middle =CH– carbon has 3 domains → sp²; the ≡C carbon has 2 domains → sp.
Counting shortcut: every line you draw between two atoms is one σ bond, so σ bonds = total number of bonded pairs. Then just add the "extra" lines: each double bond adds one π, each triple bond adds two π. You never have to picture the orbitals to get the count right.
From the electron sea to the band model
Metallic bonding pools valence electrons into a delocalized sea around fixed positive cores. Band theory sharpens this: when a huge number of atomic orbitals combine, their energy levels merge into nearly continuous bands. Electrons fill the valence band; just above may sit an empty conduction band. A metal has a partially filled band (or an overlapping empty band), so electrons move into vacant levels with almost no energy — excellent conduction. A large band gap blocks that motion: a big gap gives an insulator, a small gap a semiconductor whose conduction grows with temperature.
Four solid types, four property profiles
Metallic solids (Cu, Fe): a mobile electron sea → conduct as solids, malleable, variable melting points. Ionic solids (NaCl): a lattice of ions → hard, brittle, high-melting, conduct only when molten or dissolved (mobile ions). Molecular solids (CO₂(s), I₂): discrete molecules held by weak intermolecular forces → soft, low-melting, nonconducting. Network covalent solids (diamond, SiC, SiO₂): one continuous web of strong covalent bonds → extremely hard, extremely high-melting, generally nonconducting. Recognize the type and the properties follow.
Do not confuse "strong bonds" with "high melting point" for molecular solids. The covalent bonds inside CO₂ are strong, but melting only pulls whole molecules apart — it overcomes the weak forces between them, not the bonds within them. That is why molecular solids melt low despite strong internal bonds.
How many σ and π bonds are present in ethene, H₂C=CH₂?
Using band theory, why is copper an excellent electrical conductor?
Diamond and silicon carbide are network covalent solids melting above 2000 °C. What must be overcome to melt them?
Which substance is expected to conduct electricity in the solid state?
Two exam reflexes: (1) σ bonds equal the number of bonded pairs, so σ + π together must equal the total bond count you drew — use that to self-check. (2) When asked to explain a solid's property, name the model explicitly — "delocalized electron sea/band" for metals, "continuous covalent network" for diamond, "mobile ions only when molten" for ionic — and connect it directly to the observed property.
Answer the 4 checkpoints as you read.
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