Valence Bond Theory

Valence bond theory (VBT), developed principally by Heitler and London and extended by Pauling and Slater, offers a physical, orbital-based picture of how a covalent bond actually forms, going beyond the simple electron-dot bookkeeping of Lewis structures.

The theory pictures each atom bringing to the bond one atomic orbital, singly occupied by one electron. As two such atoms approach each other closely enough, their atomic orbitals overlap in the region between the nuclei. Provided the two electrons involved have opposite spins (as required by the Pauli exclusion principle for them to occupy the same spatial region), this overlap allows the electron pair to be shared between both nuclei, and the resulting concentration of electron density between the nuclei is what constitutes the covalent bond and holds the atoms together. This is exactly how VBT explains the formation of the simplest possible covalent molecule, $\text{H}_2$, from two hydrogen atoms each contributing its single $1s$ electron.

The bond formed depends on the geometry of overlap:

• A sigma ($\sigma$) bond forms from head-on, axial overlap directly along the internuclear axis — this includes $s$–$s$ overlap (as in $\text{H}_2$), $s$–$p$ overlap, and $p$–$p$ overlap along the bond axis. A sigma bond has cylindrical symmetry about the internuclear axis and is, atom-for-atom, the strongest type of covalent bond because the overlap is maximised.
• A pi ($\pi$) bond forms from sideways, lateral overlap of two parallel $p$ orbitals, with electron density concentrated above and below the internuclear axis rather than directly along it. Because this sideways overlap is inherently less extensive than head-on overlap, a pi bond is weaker than a sigma bond and is always found in addition to, never instead of, a sigma bond between the same two atoms.

A single covalent bond is always a pure sigma bond; a double bond is one sigma bond plus one pi bond; a triple bond is one sigma bond plus two mutually perpendicular pi bonds — precisely the picture used later in this chapter to describe the sigma and pi framework of ethyne, $\text{C}_2\text{H}_2$. …