When atomic orbitals interact, the resulting molecular orbital can be of three types: bonding, antibonding, or nonbonding. (Molecular orbital (MO)).
Bonding MOs:
* Bonding interactions between atomic orbitals are constructive (in-phase) interactions.
* Bonding MOs are lower in energy than the atomic orbitals that combine to produce them.
Antibonding MOs:
* Antibonding interactions between atomic orbitals are destructive (out-of-phase) interactions.
* Antibonding MOs are higher in energy than the atomic orbitals that combine to produce them.
Nonbonding MOs:
* Nonbonding MOs are the result of no interaction between atomic orbitals because of lack of compatible symmetries.
* Nonbonding MOs will have the same energy as the atomic orbitals of one of the atoms in the molecule.
As a simple MO example consider the hydrogen molecule, H2 (see molecular orbital diagram), with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:
1s' - 1s" Antisymmetric combination: negated by reflection, unchanged by other operations
1s' + 1s" Symmetric combination: unchanged by all symmetry operations
The symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. Because the H2 molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy (and, hence, more stable) than two free hydrogen atoms. This is called a covalent bond. The bond order is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example, there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms.
The bond order, or number of bonds, of a molecule can be determined by combining the number of electrons in bonding and antibonding molecular orbitals as follows:
Bond order = 0.5*[(number of electrons in bonding orbitals) - (number of electrons in antibonding orbitals)]
The smallest molecule, hydrogen gas exists as dihydrogen (H-H) with a single covalent bond between two hydrogen atoms. As each hydrogen atom has a single 1s atomic orbital for its electron, the bond forms by overlap of these two atomic orbitals. In figure 1 the two atomic orbitals are depicted on the left and on the right. The vertical axis always represents the orbital energies. Each atomic orbital is singly occupied with an up or down arrow representing an electron.
Application of MO theory for dihydrogen results in having both electrons in the bonding MO with electron configuration 1σg2. The bond order for dihydrogen is (2-0)/2 = 1. The photoelectron spectrum of dihydrogen shows a single set of multiplets between 16 and 18 eV (electron volts).[9]
The dihydrogen MO diagram helps explain how a bond breaks. When applying energy to dihydrogen, a molecular electronic transition takes place when one electron in the bonding MO is promoted to the antibonding MO. The result is that there is no longer a net gain in energy.
MO treatment of dioxygen is different from that of the previous diatomic molecules because the pσ MO is now lower in energy than the 2π orbitals. This is attributed to interaction between the 2s MO and the 2pz MO.[11] Distributing 8 electrons over 6 molecular orbitals leaves the final two electrons as a degenerate pair in the 2pπ* antibonding orbitals resulting in a bond order of 2. When these unpaired electrons have the same spin, this type of dioxygen called triplet oxygen is a paramagnetic diradical. When both HOMO electrons pair up with opposite spins in one orbital, the other oxygen type is called singlet oxygen.
Water (H2O) is a bent molecule (105°) with C2v molecular symmetry. The oxygen atomic orbitals are labeled according to their symmetry as a1 for the 2s2 orbital and b2, a1 and b2 for 4 electrons in the 2p orbital. The two hydrogen 1s orbitals are premixed to form a A1 (bonding) and B2 (antibonding) MO.
C2v | E | C2 | σv(xz) | σv'(yz) | |
-----------------------------------------------------------------
A1 | 1 | 1 | 1 | 1 | z | x2, y2, z2
-----------------------------------------------------------------
A2 | 1 | 1 | −1 | −1 | Rz | xy
-----------------------------------------------------------------
B1 | 1 | −1 | 1 | −1 | x, Ry | xz
-----------------------------------------------------------------
B2 | 1 | −1 | −1 |1 | y, Rx | yz
-----------------------------------------------------------------
Mixing takes place between same-symmetry orbitals of comparable energy resulting a new set of MO's for water. The lowest-energy MO, 1a1 resembles the oxygen 2s AO with some mixing with the hydrogen A1 AO. Next is the 1b1 MO resulting from mixing of the oxygen b1 AO and the hydrogen B1 AO followed by the 2a1 MO created by mixing the a1 orbitals. Both MO's form the oxygen to hydrogen sigma bonds. The oxygen b2 AO (the p-orbital perpendicular to the molecular plane) alone forms the 1b2 MO is it is unable to mix. This MO is nonbonding. In agreement with this description the photoelectron spectrum for water shows two broad peaks for the 1b2 MO (18.5 eV) and the 2a1 MO (14.5 eV) and a sharp peak for the nonbonding 1b1 MO at 12.5 eV. This MO treatment of water differs from the orbital hybridisation picture because now the oxygen atom has just one lone pair instead of two. In this sense, water does not have two equivalent lone electron pairs resembling rabbit ears.
