Sigma and pi bonds Knowledge-Based Study

Study notes

1. Covalent bonds form when valence atomic or hybrid orbitals of adjacent atoms overlap, allowing a pair of electrons with opposite spins to be shared. The fundamental type of covalent bond formed through this mechanism is the sigma ($\sigma$) bond.

   Characteristics of Sigma Bonds

   • Axial (Head-on) Overlap: A sigma bond forms when orbitals overlap end-to-end along the internuclear axis (the imaginary line connecting the two bonded nuclei).
   • Types of Overlapping Orbitals: Sigma bonds can arise from the overlap of two $s$ orbitals (such as in $H_2$), an $s$ orbital and a $p$ orbital (such as in $HF$), two $p$ orbitals aligned end-to-end, or between hybrid orbitals (such as $sp^3$, $sp^2$, or $sp$).
   • Electron Density Distribution: The shared electron density is concentrated symmetrically along the internuclear axis, exhibiting cylindrical symmetry around the bond axis.
   • Free Rotation: Because the orbital overlap is concentrated along the line connecting the nuclei, atoms joined by a single sigma bond can rotate freely about the bond axis without disrupting orbital overlap.

   Every single covalent bond in a stable molecule is fundamentally a sigma bond.

   When atoms form multiple bonds (double or triple bonds), the additional bonds are formed through parallel, lateral overlap rather than end-to-end overlap. These secondary bonds are called pi ($\pi$) bonds.

   Characteristics of Pi Bonds

   • Lateral (Sideways) Overlap: A pi bond forms from the sideways overlap of two parallel, unhybridized $p$ orbitals on adjacent atoms.
   • Electron Density Distribution: Unlike a sigma bond, the electron density of a pi bond is located in two distinct lobes: one above and one below the internuclear axis. The internuclear axis lies in a nodal plane, where electron density from the pi bond is zero.
   • Restricted Rotation: Rotating the bonded atoms around the internuclear axis would twist the $p$ orbitals out of alignment, breaking the sideways overlap. Therefore, double and triple bonds exhibit restricted rotation, creating rigid planar or linear structural units.
   • Relative Strength: Because sideways overlap is less extensive than direct axial overlap, a pi bond is generally weaker and more chemically reactive than a sigma bond formed between the same two atoms.

   Multiple covalent bonds consist of a combination of sigma and pi bonds:

   • Single Bond: Composed of exactly $1$ $\sigma$ bond.
   • Double Bond: Composed of $1$ $\sigma$ bond and $1$ $\pi$ bond.
   • Triple Bond: Composed of $1$ $\sigma$ bond and $2$ mutually perpendicular $\pi$ bonds.

   Impact on Molecular Geometry and Hybridization

   When determining the steric number and hybridization of a central atom, only sigma bonds and lone pairs of electrons are counted. Pi bonds result from unhybridized orbitals and do not dictate the primary bond angles or molecular framework.

   Representative Examples

   • Ethene ($C_2H_4$): Each carbon atom is $sp^2$ hybridized (trigonal planar). The molecule possesses five $\sigma$ bonds (four $C-H$ and one $C-C$) and one $\pi$ bond (between unhybridized $2p_z$ orbitals on the carbon atoms).
   • Ethyne ($C_2H_2$): Each carbon atom is $sp$ hybridized (linear). The molecule contains three $\sigma$ bonds (two $C-H$ and one $C-C$) and two $\pi$ bonds oriented at right angles to each other.
   • Carbon Dioxide ($CO_2$): The central carbon atom is $sp$ hybridized, forming two $\sigma$ bonds and two $\pi$ bonds with the flanking oxygen atoms, resulting in a linear geometry.