Two atoms share electrons. That is a covalent bond. But how their orbitals overlap turns out to matter enormously — it decides whether the two atoms can rotate freely, whether the bond is strong or weak, and whether the electrons in it are locked in place or available to attack something. Sorting bonds into sigma and pi is the distinction that makes the rest of the course work.
Sigma bonds
A sigma (σ) bond forms from head-on orbital overlap directly along the axis joining the two nuclei. Every connection between two atoms contains exactly one sigma bond — no more, no fewer. A single bond is that sigma and nothing else; a double or triple bond is that same sigma with one or two pi bonds stacked on top of it.
Because head-on overlap is symmetric all the way around the internuclear axis, spinning one atom relative to the other changes nothing about the overlap. This is why rotation around a single bond is free — the basis of conformational analysis in Module 4, where the question is not whether a molecule can rotate but which of its freely accessible rotational arrangements it prefers.
Head-on overlap is also efficient overlap: the orbitals meet where the electron density is highest on both. Sigma bonds are therefore strong, and their electrons are held tightly between the nuclei, buried in the space the two atoms share. Another molecule approaching from outside cannot easily reach them. So under ordinary conditions a sigma bond keeps its electrons to itself: it is the scaffolding a molecule is built from, not the part that reacts.
Pi bonds
A pi (π) bond is built from the unhybridized p orbitals left over after hybridization — one leftover p on an sp² atom, two on an sp atom. These p orbitals stand perpendicular to the plane of the sigma framework, and two neighboring ones overlap sideways, above and below the internuclear axis.
Two consequences follow immediately, and both are load-bearing.
Pi bonds block rotation. Sideways overlap only works while the two p orbitals stay parallel. Twisting one atom rotates its p orbital out of alignment and destroys the overlap, which costs roughly 65 kcal/mol for a C=C — far more than thermal energy at room temperature can supply. So the two ends of a double bond are locked relative to each other.
Pi electrons are exposed. Sideways overlap is less efficient than head-on overlap, so the electrons sit further from the nuclei, in clouds above and below the molecular plane rather than buried between the atoms. They are more loosely held and, unlike sigma electrons, they are out where something else can reach them. That is the whole reason a double or triple bond is the part of a molecule that reacts: any molecule short of electrons and looking for some will find them here first, sticking out of the surface, rather than buried in the sigma framework holding everything together.
Three C–H bonds: 3 σ. One C–C bond: 1 σ. The C≡N triple bond: 1 σ + 2 π.
Total: 5 σ and 2 π. The methyl carbon is sp³ (4 groups); the nitrile carbon is sp (2 groups — the methyl and the nitrogen); the nitrogen is sp (1 group to carbon plus 1 lone pair). The C–C≡N unit is therefore linear, and nitrogen's lone pair sits in an sp orbital pointing away along that axis, which is why nitriles coordinate metals end-on.
Bond length and strength
More bonds between the same two atoms pull them closer together and hold them more firmly.
| Bond | Length | Strength | Made of |
|---|---|---|---|
| C–C | ~154 pm | ~83 kcal/mol | 1σ |
| C=C | ~134 pm | ~147 kcal/mol | 1σ + 1π |
| C≡C | ~120 pm | ~200 kcal/mol | 1σ + 2π |
Read the increments rather than the totals. Going from one bond to two adds about 64 kcal/mol — that is the strength of the first pi bond. Going from two to three adds only about 53 — the second pi bond is weaker still, because by the time the atoms are that close the geometry is crowded and the overlap less favorable. Throughout, each pi bond is worth substantially less than the sigma bond it accompanies, which is exactly what you would expect from sideways versus head-on overlap.
Energies here are quoted in kcal/mol, as the rest of this course does; you will also see kJ/mol in other sources, where 1 kcal = 4.184 kJ.
Bond strength is not the same as reactivity
A triple bond is the strongest carbon–carbon bond in the table, and alkynes are among the more reactive functional groups in the course — a functional group being any of the small, recurring arrangements of atoms (C=C, C≡C, O–H, C=O and a few dozen more) that behave the same way wherever they turn up, and so give a molecule its chemistry. That is not a contradiction. Total bond strength measures what it would cost to pull the two atoms entirely apart; reactivity is about what it costs to break the weakest accessible component and what you get in return. Breaking one pi bond of an alkyne costs relatively little and gains a new sigma bond, which is a good trade. Keep the two ideas separate and a lot of apparent paradoxes in Modules 7 and 13 dissolve.
What carries forward
Three habits start here. Count sigma and pi correctly, because hybridization depends on the sigma-plus-lone-pair count and not the total. Remember that pi electrons are the accessible ones — every mechanism in Modules 7, 9 and 13 begins with a pi bond attacking something or being attacked. And remember that pi bonds lock geometry, which is the door into stereochemistry.