Adding the atomic orbitals.

The sum of the wave functions produces an orbital with increased  hence increased 2,  hence increased electron density between the nuclei.

This prevents the positively charged nuclei from repelling each other while both nuclei are held together by their attraction to the electron density between them.

This MO is called a bonding molecular orbital (BMO) because electrons in this orbital hold the two nuclei together. The BMO is of lower energy (i.e. more stable) than the two isolated atomic orbitals.

Subtracting the atomic oprbitals

Anti-bonding orbital. Less electron density between the atoms, nuclei repel, no bonding.The ABMO is of higher energy (i.e. less stable) than the two isolated atomic orbitals.

MO energy diagram for the H2 molecule:

Electronic Configuration of H2 :(1s)2

Bond Order (BO) is a measure of the degree of bonding between two atoms. Bond order of one signifies a single bond, bond order of two a double bond and bond order of three a triple bond.

Bond Order (BO) is calculated by the relationship:

BO of H2 = (2 – 0) / 2 = 1, single bond

Consider a possible He2 molecule:

He2 (1s)2 (*1s)2

BOof He2 = = 0 i.e. there is no bond, the molecule cannot exist

Combination of:

two s AO’s

or end-on combination of one s AO + one p AO

or

end-on combination of two p AOs

generates one  (sigma) and one * (sigma star) MO.

Sigma () MOs are bonding MOs. Sigma star (*) MOs are anti-bonding MOs.

In  bonds the electron density is concentrated along the bond axis, that is along the imaginary line joining the two atomic nuclei.

Sideways-on combination of two p AOs produces a  (pi, bonding) and a * (pi star, anti-bonding) MO.

Unlike  bonds, in  bonds the electron density is concentrated above and below the bond axis, that is above and below the imaginary line joining the two atomic nuclei.

Double bonds involve one  and one  bonding MO. Triple bonds involve one  and two bonding Mos.

In molecules electrons occupy MOs in order of increasing energy (Aufbau Principle). The Pauli Principle (an MO can contain a maximum of 2 electrons with opposite spins) and Hund’s Rule (orbitals of equal energy fill singly before filling in pairs) also apply.

MULTIPLE BONDS – NITROGEN MOLECULE

The valence shell of N is 2s2 2px1, 2py1, 2pz1. In the nitrogen molecule, NN, the two nitrogen atoms are held together by three electron pairs, i.e. a triple bond.

A triple bond consists of a sigma (σ) bond and two pi (π) bonds.

In a simplified picture we can regard the triple bond as being built up from interactions of the three p orbitals on the two nitrogen atoms:

When two nitrogen atoms come together, as illustrated above, the 2px orbitals will overlap in a head-on fashion to give a σ bonding orbital, while the 2py and 2pz orbitals overlap sideways-on to form two π bonding orbitals.

Note that each interaction of two orbitals also generates a corresponding antibonding orbital which is not shown here.