6.1: Formation of Molecular Orbitals from Atomic Orbitals
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Molecular orbital theory extends from quantum theory and the atomic orbital wavefunctions (\(\psi\)) described by the Schrödinger equation. While the Schrödinger equation defines a \(\Psi\) for electrons in individual atoms, we can approximate the molecular wavefunction (what \(\Psi\) would look like if we combined the \(\psi\) of individual atoms). The addition or subtraction of wavefunctions is termed linear combination of atomic orbitals (LCAO). Molecular orbital theory is applied to LCAO to describe bonding.
The LCAO for the wavefunction of two atoms (\(\psi_a\) and \(\psi_b\)) is represented by the general expression below. The coefficients \(c_a\) and \(c_b\) quantify the contribution of each atomic \(\psi\) to the molecular \(\Psi\).
\[\Psi=c_{a} \psi_{a}+c_{b} \psi_{b} \nonumber \]
For two atomic \(\psi\)s to form a bond, three conditions must be satisfied:
Atomic orbitals combine to form molecular orbitals when these three conditions are met. The result is a set of bonding molecular orbitals that are lower in energy than the original atomic orbital energies.