1.11:
MO Theory and Covalent Bonding
Molecular orbital theory describes the distribution of electrons throughout a molecule rather than localizing them to specific bonds between atoms.
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 sigma molecular orbitals. The sigma orbital electron density is centered around the internuclear axis.
Sideways overlap, such as the side-on overlap of two p orbitals, results in pi 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 pi bonding orbitals are typically equal in energy, or degenerate, as are the pi antibonding orbitals.
Molecular orbital theory predicts the stability of covalent bonds from the bond order of the molecule, which is the number of electrons in bonding orbitals minus the number of electrons in antibonding orbitals divided by two.
A bond order of greater than zero indicates that one or more covalent bonds can exist, whereas a bond order of zero means that bonds should not exist.
Molecular orbital theory is also useful for polyatomic molecules like benzene. The Lewis model of benzene cannot accurately represent its delocalized electrons, whereas molecular orbital theory assigns those electrons to three pi bonding molecular orbitals covering the entire carbon ring.
1.11:
MO Theory and Covalent Bonding
The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while out-of-phase waves produce nodes or regions of no electron density.
The in-phase combination of two atomic s orbitals on adjacent atoms produces a lower energy σs bonding molecular orbital in which most of the electron density is directly between the nuclei. The out-of-phase addition produces a higher energy σs* antibonding molecular orbital, in which there is a node between the nuclei.
Similarly, the wave function of p orbitals gives rise to two lobes with opposite phases. When p orbitals overlap end to end, they create σ and σ* orbitals. The side-by-side overlap of two p orbitals generates π bonding and π* antibonding molecular orbitals.
The filled molecular orbital diagram shows the number of electrons in bonding and antibonding molecular orbitals. An electron contributes to a bonding interaction only if it occupies a bonding orbital. The net contribution of the electrons to the bond strength of a molecule is determined from the bond order, which is calculated as follows:
The bond order is a guide to the strength of a covalent bond; a bond between two given atoms becomes stronger as the bond order increases. If the distribution of electrons in the molecular orbitals yields a bond order of zero, a stable bond does not form.
The molecular orbital theory is also useful for polyatomic molecules. The Lewis model of benzene (C6H6), which has a planar hexagonal structure with sp2 hybridized carbon atoms, cannot accurately represent its delocalized electrons. However, the molecular orbital theory assigns those electrons to three π bonding molecular orbitals covering the entire carbon ring. This results in a fully occupied (6 electrons) set of bonding molecular orbitals that endow the benzene ring with additional thermodynamic and chemical stability.
Suggested Reading
This text is adapted from Openstax, Chemistry 2e, Section 8.4 Molecular Orbital Theory.