Just as the valence electrons of atoms occupy atomic orbitals (AO), the shared electron pairs of covalently bonded atoms may be thought of as occupying molecular orbitals (MO). It is convenient to approximate molecular orbitals by combining or mixing two or more atomic orbitals. In general, this mixing of n atomic orbitals always generates n molecular orbitals. The hydrogen molecule provides a simple example of MO formation. In the following diagram, two 1s atomic orbitals combine to give a sigma (σ) bonding (low energy) molecular orbital and a second higher energy MO referred to as an antibonding orbital. The bonding MO is occupied by two electrons of opposite spin, the result being a covalent bond.
The notation used for molecular orbitals parallels that used for atomic orbitals. Thus, s-orbitals have a spherical symmetry surrounding a single nucleus, whereas σ-orbitals have a cylindrical symmetry and encompass two (or more) nuclei. In the case of bonds between second period elements, p-orbitals or hybrid atomic orbitals having p-orbital character are used to form molecular orbitals. For example, the sigma molecular orbital that serves to bond two fluorine atoms together is generated by the overlap of p-orbitals (part A below), and two sp3 hybrid orbitals of carbon may combine to give a similar sigma orbital. When these bonding orbitals are occupied by a pair of electrons, a covalent bond, the sigma bond results. Although we have ignored the remaining p-orbitals, their inclusion in a molecular orbital treatment does not lead to any additional bonding, as may be shown by activating the fluorine correlation diagram below.
Another type of MO (the π orbital) may be formed from two p-orbitals by a lateral overlap, as shown in part A of the following diagram. Since bonds consisting of occupied π-orbitals (pi-bonds) are weaker than sigma bonds, pi-bonding between two atoms occurs only when a sigma bond has already been established. Thus, pi-bonding is generally found only as a component of double and triple covalent bonds. Since carbon atoms involved in double bonds have only three bonding partners, they require only three hybrid orbitals to contribute to three sigma bonds. A mixing of the 2s-orbital with two of the 2p orbitals gives three sp2 hybrid orbitals, leaving one of the p-orbitals unused. Two sp2 hybridized carbon atoms are then joined together by sigma and pi-bonds (a double bond), as shown in part B.
The manner in which atomic orbitals overlap to form molecular orbitals is actually more complex than the localized examples given above. These are useful models for explaining the structure and reactivity of many organic compounds, but modern molecular orbital theory involves the creation of an orbital correlation diagram. Two examples of such diagrams for the simple diatomic elements F2 and N2 will be drawn above when the appropriate button is clicked. The 1s and 2s atomic orbitals do not provide any overall bonding, since orbital overlap is minimal, and the resulting sigma bonding and antibonding components would cancel. In both these cases three 2p atomic orbitals combine to form a sigma and two pi-molecular orbitals, each as a bonding and antibonding pair. The overall bonding order depends on the number of antibonding orbitals that are occupied. The subtle change in the energy of the σ2p bonding orbital, relative to the two degenerate π-bonding orbitals, is due to s-p hybridization that is unimportant to the present discussion.
One example of the advantage offered by the molecular orbital approach to bonding is the oxygen molecule. Here, the correlation diagram correctly accounts for the paramagnetic character of this simple diatomic compound. Likewise, the orbital correlation diagram for methane provides another example of the difference in electron density predicted by molecular orbital calculations from that of the localized bond model. Click on the compound names for these displays.
A cartoon of the p and π orbitals of a double bond may be examined by .
A model of the π orbitals of ethene may be examined by .
The p-orbitals in these model are represented by red and blue colored spheres or ellipses, which represent different phases, defined by the mathematical wave equations for such orbitals.
Finally, in the case of carbon atoms with only two bonding partners only two hybrid orbitals are needed for the sigma bonds, and these sp hybrid orbitals are directed 180º from each other. Two p-orbitals remain unused on each sp hybridized atom, and these overlap to give two pi-bonds following the formation of a sigma bond (a triple bond), as shown below.
The various hybridization states of carbon may be examined by .