Molecular Orbital Theory I

Molecular orbital theory describes the distribution of electrons throughout a molecule rather than localizing them to specific bonds between atoms. 

Like atomic orbitals, molecular orbitals are wave functions describing where electrons are likely to be. These functions are estimated by a mathematical process called the linear combination of atomic orbitals. 

Waves can interact either constructively or destructively. 

Constructive interference between in-phase atomic orbitals corresponds to greater electron density between the positively charged nuclei, making the molecule more stable. This bonding molecular orbital is lower in energy than either of the original atomic orbitals.

Destructive interference between out-of-phase atomic orbitals corresponds to lower electron density in a nodal plane between the nuclei, making the molecule less stable. This antibonding molecular orbital is higher in energy than the atomic orbitals and is marked with a star or asterisk.

Molecular orbitals are classified by the way the atomic orbitals overlap. Head-on combination of atomic orbitals along the internuclear axis, such as the overlap between two s orbitals or two end-to-end p orbitals, results in σ molecular orbitals. The σ orbital electron density is centered about the internuclear axis. 

Sideways overlap, such as the side-on overlap of two p orbitals, results in π molecular orbitals. Here, the electron density is concentrated on opposite sides of the internuclear axis.

The orientation of the three different p orbitals means that typically, one pair overlaps end-to-end and the other two pairs overlap sideways. The π bonding orbitals are typically equal in energy, or degenerate, as are the π antibonding orbitals.

Orbitals can overlap if their energies are similar and their symmetries match. So, two 2s orbitals can overlap, but a 2s orbital generally has negligible overlap with a 1s or 2p orbital.