Molecular Orbital Theory I

Molecular orbital theory describes electron distribution throughout a molecule rather than localizing electrons to specific bonds. Like atomic orbitals, molecular orbitals are wave functions showing where electrons are likely to be found. This approach uses quantum mechanics to explain bonding by treating electrons as delocalized across the entire molecular structure.

The linear combination of atomic orbitals is a mathematical process that combines atomic orbital wave functions to generate molecular orbitals. When atomic orbital waves interact, they can combine constructively or destructively. In-phase combinations produce bonding orbitals with higher electron density between nuclei, while out-of-phase combinations create antibonding orbitals with nodal planes and lower stability.

Bonding molecular orbitals form from constructive interference of in-phase atomic orbitals, creating greater electron density between nuclei and lower energy. Antibonding molecular orbitals result from destructive interference of out-of-phase orbitals, producing nodes and higher energy. Electrons preferentially fill bonding orbitals first because they stabilize the molecule, while antibonding orbitals destabilize it.

Sigma (σ) molecular orbitals form from head-on overlap of atomic orbitals along the internuclear axis, such as two s orbitals or end-to-end p orbitals, with electron density centered on the axis. Pi (π) molecular orbitals result from sideways overlap of p orbitals, concentrating electron density on opposite sides of the internuclear axis. Both types can be bonding or antibonding depending on orbital phase alignment.

Pi bonding orbitals are degenerate, meaning they have equal energy, because two p orbitals can overlap sideways in two equivalent orientations perpendicular to the internuclear axis. Similarly, the two pi antibonding orbitals have equal energy. This degeneracy arises from the symmetrical geometry of p orbital lobes and their identical spatial relationships to the internuclear axis.

Atomic orbitals can overlap to form molecular orbitals only if their energies are similar and their symmetries match. For example, two 2s orbitals can overlap effectively, but a 2s orbital has negligible overlap with a 1s or 2p orbital due to energy and symmetry mismatches. This selectivity ensures that only compatible orbitals combine to create stable molecular orbital interactions.

Constructive interference between in-phase atomic orbitals increases electron density between positively charged nuclei, creating attractive forces that stabilize the molecule and lower orbital energy. Destructive interference between out-of-phase orbitals produces nodal planes with reduced electron density, weakening nuclear attraction and destabilizing the molecule. This interference pattern directly determines whether a molecular orbital promotes or inhibits bonding.