Formation of Molecular Orbitals — Core Principles

Core Principles

Molecular orbitals (MOs) are formed when atomic orbitals (AOs) of combining atoms overlap. This process is described by the Linear Combination of Atomic Orbitals (LCAO) approximation, where AO wave functions either add (constructive interference) to form lower-energy bonding MOs or subtract (destructive interference) to form higher-energy antibonding MOs.

For effective combination, AOs must have comparable energies, proper symmetry, and significant overlap. MOs are classified as sigma ($sigma$) from head-on overlap or pi ($pi$) from sideways overlap. Electrons fill MOs according to the Aufbau principle, Pauli exclusion principle, and Hund's rule.

The resulting MO electronic configuration determines key molecular properties like bond order (stability), and magnetic behavior (paramagnetic for unpaired electrons, diamagnetic for all paired). The energy order of MOs varies for lighter (up to N2) and heavier (O2 onwards) diatomic molecules due to s-p mixing effects.

Important Differences

vs Atomic Orbitals (AOs)

Aspect	This Topic	Atomic Orbitals (AOs)
Belong to	Individual atoms	Entire molecule
Electron localization	Electrons localized around a single nucleus	Electrons delocalized over all nuclei in the molecule
Formation	Solutions to Schrödinger equation for isolated atoms	Formed by linear combination (overlap) of atomic orbitals
Number of orbitals	Fixed number for each atom (e.g., one 1s, three 2p)	Number of MOs formed equals the number of combining AOs
Energy levels	Characteristic energy for each orbital in an atom	Bonding MOs are lower energy, antibonding MOs are higher energy than parent AOs
Description of	Electronic structure of isolated atoms	Electronic structure and bonding in molecules

Atomic orbitals describe the probability distribution of electrons around a single atomic nucleus, defining the electronic structure of an isolated atom. In contrast, molecular orbitals describe the probability distribution of electrons across an entire molecule, formed by the combination of atomic orbitals. MOs are delocalized over all nuclei, while AOs are localized to one. The formation of MOs leads to new energy levels (bonding and antibonding) that dictate molecular stability and properties, a concept not applicable to isolated atoms.