Sigma Bond

A sigma bond, written σ bond, is a type of covalent bond in which the bonding electron density lies along the axis joining two atomic nuclei. In the usual localized, two-center description, its defining feature is the absence of a nodal plane containing that axis. Sigma bonds are commonly pictured as arising from head-on orbital overlap. They account for ordinary single bonds and the axial component of conventional double and triple bonds. (goldbook.iupac.org)

Orbital overlap and symmetry

In valence bond theory, a sigma bond forms when appropriately oriented atomic orbitals on neighboring atoms overlap along the internuclear axis. Common combinations include:

• s–s overlap, as in the hydrogen molecule, H₂.
• s–p overlap, used in a simple description of hydrogen chloride, HCl.
• p–p head-on overlap, used in a simple description of chlorine, Cl₂.
• Overlap involving hybrid orbitals, as in carbon–hydrogen and carbon–carbon bonds in many organic compounds.

An ordinary two-center, two-electron bond contains a shared pair of electrons. Head-on overlap places bonding density in the region between the nuclei, rather than on opposite sides of a plane passing through the bond axis. (openstax.org)

The Greek letter σ is fundamentally a symmetry designation, not a label for one particular orbital shape or chemical element. In an idealized diatomic description, a sigma orbital is unchanged by rotation about the internuclear axis. For localized bonds in larger molecules, the absence of a nodal plane containing the bond axis is the more useful distinction. This local classification should not be confused with the symmetry of orbitals extending over an entire molecule. (goldbook.iupac.org)

Sigma and pi components of multiple bonds

A pi bond differs from a sigma bond because its orbital has a nodal plane containing the internuclear axis. In the familiar p-orbital picture, pi bonding results from side-by-side overlap, with electron density on either side of that plane. Sigma bonding instead results from overlap directed along the axis. (openstax.org)

For conventional localized bonds in main-group molecules, the standard decomposition is:

Thus, ethene, C₂H₄, has five sigma bonds—four C–H bonds and one C–C sigma component—and one pi bond. Ethyne, C₂H₂, has three sigma bonds and two pi bonds. A double or triple bond remains one connection between the same two atoms; σ and π describe different components of that connection. (openstax.org)

These components are not normally drawn separately in a Lewis structure. The decomposition supplies an orbital interpretation of the single, double, or triple lines used in that notation. (openstax.org)

Hybridization and molecular geometry

Orbital hybridization provides a localized model for the directions of sigma bonds. Hybrid orbitals are mathematical combinations of atomic orbitals on the same atom; their overlap with orbitals on neighboring atoms describes bonding. Hybridization and sigma bonding are therefore related concepts, but they are not synonyms. Sigma bonds can also form from unhybridized orbitals. (openstax.org)

For carbon, common descriptions are:

• sp³: four approximately tetrahedrally directed hybrid orbitals. In methane, each overlaps with a hydrogen 1s orbital, producing four equivalent C–H sigma bonds.
• sp²: three coplanar hybrid orbitals, with an unhybridized p orbital available for pi bonding. This describes each carbon in ethene.
• sp: two oppositely directed hybrid orbitals, leaving two p orbitals available for the two pi components of the ethyne triple bond.

These models relate the sigma-bond framework to tetrahedral, trigonal-planar, and linear arrangements, respectively. (openstax.org)

Molecular-orbital description

In molecular orbital theory, bonding is described through orbitals that may extend over several atoms. Combining atomic wave functions of suitable symmetry produces both a bonding sigma orbital, σ, and an antibonding sigma orbital, σ*. The bonding combination increases density between the nuclei and lowers the orbital energy relative to the corresponding antibonding combination. The antibonding orbital has an internuclear node that reduces density in the bonding region. (openstax.org)

For H₂, its two electrons occupy the bonding orbital formed mainly from the two hydrogen 1s orbitals. In the elementary molecular-orbital model, bond order is

H₂ therefore has bond order one. Occupying σ* reduces the net bonding contribution. The asterisk means antibonding; it does not change the orbital’s sigma symmetry. In particular, a node separating the nuclei is different from a nodal plane containing the bond axis. (openstax.org)

Rotation about sigma bonds

Rotation about an isolated sigma-bond axis can preserve head-on overlap. Consequently, many carbon–carbon single bonds in open-chain molecules permit internal rotation without bond cleavage. This does not mean that rotation is energetically unrestricted: ethane has a rotational barrier of approximately 12 kJ mol⁻¹, with staggered arrangements more stable than eclipsed arrangements. (openstax.org)

A carbon–carbon double bond behaves differently. Rotation misaligns the p orbitals responsible for its pi component, creating a much larger barrier. This restricted rotation underlies an important form of isomerism in alkenes. Even a sigma-bonded ring may constrain rotation because changing one bond’s orientation also affects the rest of the ring. (openstax.org)

Scope and limitations

The sigma–pi distinction is useful for describing connectivity, geometry, and rotational behavior, but localized bonds and whole-molecule orbitals are different levels of description. A set of locally sigma-bonded orbitals can form combinations with pi symmetry relative to a molecular plane. Consequently, statements about orbital symmetry must specify the relevant axis or plane; the local label alone does not determine how an orbital combination behaves throughout a molecule. (goldbook.iupac.org)

Likewise, a fixed placement of pi bonds can be inadequate when electrons are delocalized. In benzene, for example, the sigma framework connects the atoms, while the pi electrons extend around the carbon ring. Resonance structures represent that delocalization rather than alternative molecules with permanently different bond placements. (openstax.org)

References

1. 1 Valence Bond Theory — Chemistry: Atoms First 2e, OpenStaxopenstax.org
2. 2 Hybrid Atomic Orbitals — Chemistry 2e, OpenStaxopenstax.org
3. 3 Multiple Bonds — Chemistry 2e, OpenStaxopenstax.org
4. 4 Molecular Orbital Theory — Chemistry: Atoms First 2e, OpenStaxopenstax.org
5. 6 Conformations of Ethane — Organic Chemistry, OpenStaxopenstax.org
6. 4 Cis–Trans Isomerism in Alkenes — Organic Chemistry, OpenStaxopenstax.org
7. 2 Cis–Trans Isomerism in Cycloalkanes — Organic Chemistry, OpenStaxopenstax.org