In chemistry, sigma (σ) most commonly refers to a sigma bond, the simplest and strongest type of covalent bond between two atoms. It forms when atomic orbitals overlap end-to-end, concentrating electron density directly between the two nuclei. Every single bond in a molecule is a sigma bond, and sigma bonds also form the backbone of every double and triple bond.
How Sigma Bonds Form
A sigma bond forms when two atomic orbitals point toward each other and overlap head-on. Picture two balloons being pushed together tip-to-tip: the shared space between them is where the bonding electrons spend most of their time. This end-to-end overlap creates a region of high electron density sitting right along the line connecting the two atomic nuclei, which is what holds the atoms together.
Several combinations of orbitals can form sigma bonds. Two s orbitals can overlap (as in a hydrogen molecule), an s orbital can overlap with a p orbital (as in a C-H bond), or two hybrid orbitals can overlap with each other (as in a C-C bond). What matters isn’t which specific orbitals are involved, but that they meet head-on along the axis between the nuclei.
What Makes Sigma Bonds Different From Pi Bonds
Sigma bonds have cylindrical symmetry around the bond axis. If you could look straight down the bond like peering through a telescope, the electron density would appear evenly distributed in a circle. This symmetry is what gives sigma bonds one of their most important physical properties: free rotation.
Pi (π) bonds, by contrast, form from the sideways overlap of p orbitals that sit perpendicular to the bond axis. Their electron density is concentrated above and below the line between the nuclei rather than along it. This sideways overlap locks the atoms in place, preventing rotation. A double bond consists of one sigma bond plus one pi bond. A triple bond has one sigma bond plus two pi bonds. The sigma bond always comes first, forming the core connection, with pi bonds layered on top.
Because sigma bonds overlap more directly between the nuclei, they are generally stronger than pi bonds. In ethane, for instance, the carbon-carbon single bond (a pure sigma bond) has a dissociation energy of about 368 kJ/mol. The pi component of a double bond adds less energy than the sigma component contributes on its own.
Free Rotation Around Sigma Bonds
Because of their cylindrical symmetry, sigma bonds allow the groups on either end to rotate relative to each other, almost like a swivel joint. In ethane, the two methyl groups can spin freely around the central C-C bond. There is a small energy barrier of about 12 kJ/mol that slightly favors the staggered arrangement (where the hydrogen atoms are offset) over the eclipsed arrangement (where they line up), but this barrier is tiny compared to the 350 kJ/mol it takes to break the bond entirely. At room temperature, molecules easily flip between arrangements.
Double bonds, with their added pi bond, form a rigid planar structure. This is why molecules like fats can be “cis” or “trans”: the locked double bond prevents the groups from rotating into a different arrangement. Some single bonds can also have restricted rotation when neighboring groups are physically bulky enough to get in each other’s way, a situation called steric hindrance. In biphenyl, for example, the hydrogen atoms on two connected rings crowd each other, settling into a preferred angle of about 39° between the rings.
Sigma Bonds and Hybridization
The number of sigma bonds an atom forms is directly tied to its hybridization state, which describes how its orbitals blend together before bonding. In organic chemistry, you can determine an atom’s hybridization by counting its sigma bonds and lone pairs (together called the steric number).
- Four sigma bonds (steric number 4): sp3 hybridization, producing a tetrahedral shape. Carbon in methane is the classic example.
- Three sigma bonds (steric number 3): sp2 hybridization, producing a flat triangular shape. Carbon in ethylene (with one double bond) fits here.
- Two sigma bonds (steric number 2): sp hybridization, producing a linear shape. Carbon in acetylene (with a triple bond) is the textbook case, forming one sigma bond to hydrogen and one sigma bond to the other carbon, with two pi bonds layered on top of that second sigma bond.
Atoms hybridize specifically to form more stable sigma bonds. The hybrid orbitals are shaped to overlap more effectively head-on, producing stronger bonds than unhybridized orbitals would.
Bonding and Antibonding Sigma Orbitals
When two atomic orbitals combine to form a sigma bond, molecular orbital theory says they actually produce two new orbitals: a bonding sigma orbital (σ) and an antibonding sigma-star orbital (σ*). Only the bonding orbital is typically occupied by electrons in a stable molecule, but the antibonding orbital exists as an empty, higher-energy possibility.
In the bonding orbital, electron density builds up between the two nuclei, pulling them together. The orbital looks like an egg shape encompassing both atoms, with the highest concentration of electrons right in the middle. In the antibonding orbital, the opposite happens: there’s a node (a region of zero electron density) between the nuclei, with electrons pushed out toward the far sides of each atom. Placing electrons in this orbital weakens or destabilizes the bond. These antibonding orbitals become important in spectroscopy and chemical reactions, where electrons can be excited or transferred into them.
Other Uses of Sigma in Chemistry
Beyond sigma bonds, the term “sigma” appears in a few other chemical contexts. A sigma complex (or σ-complex) is an intermediate that forms during certain reactions involving aromatic rings. In electrophilic aromatic substitution, for instance, an incoming group temporarily bonds to the ring, disrupting its flat, delocalized electron system and creating a short-lived species called a Wheland intermediate. In nucleophilic aromatic substitution, a similar intermediate called a Meisenheimer adduct (or σ-adduct) forms when a nucleophile attacks the ring.
In organometallic chemistry, sigma complexes describe a different situation: a metal atom interacting with the electrons of an existing sigma bond in another molecule. The first example, reported by Kubas in 1984, involved a transition metal interacting with an H-H bond. These complexes feature a three-center, two-electron bonding arrangement where the sigma bond donates its electron density to the metal without fully breaking apart.
Sigma is also used as a label in molecular orbital diagrams to identify orbitals with the right symmetry properties, and it appears in Hammett sigma constants, which quantify how strongly a chemical group on a benzene ring pulls or pushes electron density. But for most chemistry students encountering the term for the first time, sigma means one thing: the strong, head-on, freely rotating bond at the core of every covalent connection.