How do atomic orbitals combine to form molecular orbitals?

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In molecular orbital theory, atomic orbitals combine to form molecular orbitals (MOs) through a process known as the linear combination of atomic orbitals (LCAO) approximation. In this approach, each molecular orbital is constructed as a superposition of the atomic orbitals belonging to the atoms in a molecule.1

The shape and energy of these resulting molecular orbitals depend on how the individual atomic orbitals interfere with one another:1

  • Constructive interference: When atomic orbitals are summed, their amplitudes reinforce each other in the internuclear region. This creates a bonding orbital, which has an enhanced electron density between the nuclei, resulting in a lower energy state compared to the isolated atomic orbitals.2
  • Destructive interference: When the difference between atomic orbitals is taken, their amplitudes subtract from one another. This creates a nodal plane—a region of zero amplitude—between the nuclei. This results in an antibonding orbital, which excludes electrons from the internuclear region and possesses a higher energy state.2

Generally, for every n atomic orbitals that combine, n molecular orbitals are formed, which are then filled by valence electrons according to the building-up principle and the Pauli exclusion principle.2