Antibonding Orbitals

ANTIBONDING ORBITALS

The overlap of AOs to give a new MO in which an electron pair is shared by the interacting atoms was illustrated in Figure 1.2. The new MO, which contains the shared electron pair, is of lower energy than the AOs from which it was produced by overlap. This energy change (ΔE) is illustrated in Figure 1.3 (N represents the nucleus of some element in the bond formation process). The ΔE is related closely to the bond energy of the bond produced. The same model holds irrespective of the type of AOs which overlap (simple AOs or hybrid AOs) or the type of bond formed (σ or π ).

While this model is easy to visualize and understand, it is actually only half of the story. When AOs interact, the number of new MOs which are produced from that interaction must equal the number of AOs which initially interact. 

Furthermore, for each MO produced which is lower in energy than the energy of the interacting AOs, there will be one produced which will be higher in energy by the same amount (Figure 1.4). So when two half-filled AOs interact, there will be two MOs produced, one of lower energy which will contain the electron pair and is termed the bonding MO. The second molecular orbital is of higher energy, is unfilled, and is termed the antibonding MO.

For each bond in a molecule which is described by the overlap of AOs, there will be a bonding MO which is of lower energy and when filled with an electron pair gives rise to a stable bond between elements. There will also be an antibonding MO which is of higher energy and thus unfilled. Antibonding orbitals correspond to the situation where nuclei are moved to within the bonding distance of one another but there is no electron sharing; in fact the electrons and nuclei actually repel one another. This electronic and nuclear repulsion is what increases the energy of the antibonding level. Because the bonding MO is filled and the antibonding MO is unfilled, the system is at a lower net energy than the individual AOs and bond formation takes place. This occurs for both σ and π bonds as shown in Figure 1.5 (the antibonding orbitals are indicated by the asterisk). Overlap of an sp³ AO on a carbon with a 1s AO on a hydrogen gives a σ -bonding MO that is filled with two electrons and an unfilled, higher energy, antibonding MO termed a σ ^∗ MO. Likewise, overlap of two 2p AOs on carbon gives a π MO which contains a shared pair of e⁻ and a π ^∗ MO which is of higher energy and is unfilled.

Thus far it would appear that antibonding orbitals are real orbitals, but they seem to be merely mathematical artifacts since they are unfilled and thus do not enter into bonding or energy considerations. For ground-state molecules this is actually true — all of the electrons are found in bonding orbitals. Why, then, should we even concern ourselves with their existence?

The answer lies in the realization that antibonding orbitals are still, in fact, orbitals. They are regions of space where one could have electrons. In ground-state molecules, electrons fill the lower energy bonding orbitals. Suppose, how-ever, you wished to take an electron out of a bonding orbital and move it to a higher level. Where would it go? Or suppose you wished to add electrons to a molecule which already had its bonding orbitals filled. Where would the electrons go? Suppose an electron-rich reagent were to donate electrons to a molecule. Where would the electrons go?

In these examples the electrons could go into a higher energy, unfilled MO which could be a nonbonding orbital (when one is present) or an antibonding orbital (which is always present). Thus it is most common to have the elec-trons go into an antibonding MO. Although they are of high energy, antibonding orbitals are usually unfilled and can accept electrons from several sources if sufficient energy is available to promote electrons into the antibonding energy level. Absorption of light energy can cause an electron to be promoted from the highest occupied molecular orbital (HOMO), which is usually a bonding MO, to the lowest unoccupied molecular orbital (LUMO), which is most often an antibonding MO. For example, if an olefin which contains a carbon – carbon π bond is exposed to ultraviolet light of the correct frequency (and hence energy), the molecule can absorb the energy of the light by promoting a π electron from the bonding MO into the antibonding MO. This new electronic state is termed an excited state and is higher in energy than the initial electron-paired state called the ground state. (The electron spins can be paired in the singlet excited state or unpaired in the triplet excited state.) Excited states of molecules are high-energy states which are much more reactive than ground states and can be described in terms of the population of antibonding orbitals. Consequently, almost all photochemical reactions which occur by the reactions of excited-state species are intimately dependent on the existence of and population of antibond-ing orbitals.

The reduction of organic molecules by the addition of electrons can take place by chemical reagents or at the surface of electrodes. In either case electrons are added to the organic compound, thus reducing it. Now electrons cannot just go anywhere; they must go into an unfilled orbital. Thus, during a reduction, electrons are injected into the LUMO of the molecule, which is often an anti-bonding orbital. Population of the antibonding orbital raises the total energy of the molecule and subsequent reactions follow. The electrochemical reduction of alkyl bromides illustrates the process well. An electron is added into the σ ^∗ orbital of the carbon – bromine bond, which is the LUMO of a saturated alkyl bromide. Population of the antibonding orbital raises the energy of the molecule and weakens the carbon – bromine bond, which then dissociates to give bromide ion and a carbon-centered free radical which has an unpaired electron in a hybrid AO (nonbonded energy level).

Almost all dissolving metal and electrochemical reductions follow this same general sequence. An electron is donated into an unfilled orbital which is usu-ally an antibonding MO, the energy of the molecule is raised, and chemical change ensues.

When a nucleophile attacks an electrophile, it donates a pair of electrons to the electrophile. Electron donation must take place by an overlap interaction between a filled orbital on the nucleophile which contains the electron pair to be donated and an unfilled orbital (LUMO) on the electrophile, which is usually an antibonding orbital. Population of the LUMO by electron donation raises the energy of the system leading to bonding change and new bond formation. Addition of an alkoxide to a ketone is a typical example of the process. The electron pair to be donated is in a hybrid AO and therefore is at a nonbonding energy level (n). Overlap with the π ^∗ orbital of the carbonyl group starts to populate the π ^∗ orbital. This weakens the π bond, and the carbon – oxygen π bond of the carbonyl group is broken and a new lower energy σ bond is formed between the oxygen of the alkoxide and the carbonyl carbon. The electrons of the π bond end up in a nonbonding AO on oxygen in the product. This process is shown schematically.

Nucleophilic additions and substitutions are the most widespread of all organic reactions, and all have the same general orbital requirements. An orbital containing an electron pair of the nucleophile overlaps with an antibonding orbital of the electrophile, which leads to population of the antibonding level (in most cases). This raises the energy of the system and bond and electron reorganization follows to give products. The electron pair must be able to be donated (i.e., not tightly bound or of higher energy) and the antibonding orbital be of sufficiently low energy to ensure effective overlap.

Thus it is seen that, although antibonding orbitals are not a major factor in describing the bonding of ground-state molecules, they can play a pivotal role in the reactions of molecules. Therefore it is important to keep in mind the existence of antibonding orbitals and their ability to accept electrons and control the reactivity of molecules.