Molecular orbital theory explains chemical bonding in terms of electrons distributed around a molecule. Atomic orbitals combine to form molecular orbitals, which can be bonding or antibonding. Bonding order is calculated to determine the nature of the bond. MO theory better explains molecules with bond orders between single and double bonds and magnetic properties, but calculations are more complicated.
Molecular orbital theory, or MO theory, is a method of explaining the bonding between atoms in terms of electrons distributed around a molecule rather than localized around atoms, in contrast to valence bond theory or VB theory. The electrons in atoms are arranged in orbitals within subshells within shells. As a general rule, it is the electrons in the orbitals within the outermost shell that are involved in chemical bonding, although there are exceptions to this. An orbital can hold a maximum of two electrons, which must have opposite spins. In molecular orbital theory, when two atoms form a chemical bond, the atomic orbitals of the bonding electrons combine to produce molecular orbitals with similar rules regarding the number and spin of the electrons.
Electrons, like all subatomic particles, can behave like waves. Instead of occupying a precise point in space at any given moment, an electron is distributed over all its possible positions around the atomic nucleus and its position can only be expressed in terms of probabilities. An equation developed by physicist Erwin Schrodinger can be used to determine the “wave function” of an atomic orbital, giving the probability of finding an electron at different locations around the nucleus in terms of electron density distribution. Molecular orbital theory explains atomic bonding by adding the wave functions of the atomic orbitals involved in bonding to give the wave functions for the molecular orbitals enclosing the entire molecule.
Since the wave function equation gives both positive and negative values, known as phases, two molecular orbitals are produced. In the first, atomic orbitals are added in phase: from positive to positive and from negative to negative. The second type is where they are out of phase: negative to positive and positive to negative.
In-phase addition gives a molecular orbital with the electron density concentrated in the space between the nuclei, bringing them closer together and resulting in a configuration at a lower energy than the original two atomic orbitals combined. This is known as the bonding orbital. Out-of-phase addition causes the electron density to be concentrated away from the space between the nuclei, further driving them apart and producing a configuration with a higher energy level than atomic orbitals. This is known as an antibonding orbital. The electrons of the atomic orbitals involved in the bonding will prefer to fill the lower energy bonding molecular orbitals.
To determine the nature of the bond between two atoms, the “bonding order” is calculated as: (bonding electrons – antibonding electrons)/2. A bond order of zero indicates that no bond will take place. In comparison, a bond order of 1 indicates a single bond, with 2 and 3 indicating double and triple bonds, respectively.
As a very simple example, the bonding of two hydrogen atoms can be described in terms of molecular orbital theory. Each atom has only one electron, usually in the lowest energy orbital. The wave functions of these orbitals are added, giving a bonding and an antibonding orbital. The two electrons will fill the lower energy bonding orbital, with no electrons in the antibonding orbital. The order of the bond is then (2 – 0)/2 = 1, giving a single bond. This is in agreement with VB theory and observation.
The interaction of two atoms of the next element in the periodic table, helium, gives a different result since there are two electrons in one orbital in each helium atom. When wavefunctions are added, one bonding orbital and one antibonding orbital are produced, as with hydrogen. This time, however, four electrons are involved. Two electrons will fill the bonding orbital and the other two will have to fill the higher energy antibonding orbital. The order of the bonds this time is (2 – 2)/2 = 0, so no bond will take place. Again, this agrees with the VB theory and the observation: helium does not form molecules.
Molecular orbital theory also correctly predicts double and triple bonds for oxygen and nitrogen molecules, respectively. In most cases, MO theory and valence bond theory agree; however, the former better explains molecules where the bond order lies between a single and double bond and the magnetic properties of the molecules. The major disadvantage of molecular orbital theory is that, except for very simple cases like the ones above, the calculations are much more complicated.
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