HOMO AND LUMO

HOMO-LUMO ("filled-empty") Orbital Interactions

A fundamental principle: all steps of all heterolytic reaction mechanisms are either Bronsted or Lewis acid-base reactions

• They involve either proton transfer (Bronsted), or unshared pair/empty orbital interactions (Lewis).
• When the interacting atomic orbitals are considered, the Bronsted reactions can be seen as simply a special case of the Lewis, in which the empty orbital is the antibonding orbital of the H-X bond.

In short, all heterolytic reactions are just examples of interactions between filled atomic or molecular orbitals and empty atomic or molecular orbitals - that is, Lewis acid-base reactions. Here is a diagram to explain this point:

The interaction of any two atomic or molecular orbitals, as you learned in general chemistry, produces two new orbitals.

• One of the new orbitals is higher in energy than the original ones (the antibonding orbital), and one is lower (the bonding orbital).
• When one of the initial orbitals is filled with a pair of electrons (a Lewis base), and the other is empty (a Lewis acid), we can place the two electrons into the lower energy of the two new orbitals.
• The "filled-empty" interaction therefore is stabilizing.

When we are dealing with interacting molecular orbitals, the two that interact are generally

• The highest energy occupied molecular orbital (HOMO) of one molecule,
• The lowest energy unoccupied molecular orbital (LUMO) of the other molecule.
• These orbitals are the pair that lie closest in energy of any pair of orbitals in the two molecules, which allows them to interact most strongly.
• These orbitals are sometimes called the frontier orbitals, because they lie at the outermost boundaries of the electrons of the molecules.

Here is the filled-empty interaction redrawn as a HOMO-LUMO interaction.

Let's look at some examples. First, a reaction that you would have categorized as a Lewis acid-base reaction when you were studying general chemistry:

NH₃ has an unshared pair on nitrogen, occupying the HOMO (it is generally true that unshared pairs occupy HOMOs). BH₃ has an empty valence orbital on B, since B is a Group II element. This is the LUMO.

Here are pictures of the two orbitals from AM1 semi-empirical molecular orbital calculations:

NH3 HOMO	BH3 LUMO

The HOMO-LUMO energy diagram above describes the formation of a bond between N and B.

Now let's try a slightly more complex case. Here's a typical Bronsted acid-base reaction:

The curly arrows track which bonds are made, and which are broken, but they do not indicate what orbitals are involved.

• Water is both a Bronsted base (capable of accepting a proton) and a Lewis base, with one of its unshared pairs (the HOMO).
• H-Cl is a Bronsted acid, capable of donating a proton, but it also is a Lewis acid, using the s* orbital of the H-Cl bond (the LUMO).
• Here are pictures of the relevant HOMO and LUMO, again from AM1 semi-empirical molecular orbital calculations:

H2O HOMO	HCl LUMO

• The interaction stabilizes the unshared pair of the oxygen, while simultaneously breaking the H-Cl bond because the interaction is with the antibonding orbital.

Another example is the S_N2 reaction, which involves the HOMO of the nucleophile and the s* orbital of the R-X bond:

Here are the relevant orbitals:

OH- HOMO	CH3-Cl LUMO

The interaction stabilizes the unshared pair of the oxygen, while simultaneously breaking the CH₃-Cl bond because the interaction is with the antibonding orbital.

Other examples include the reaction of alkenes with H-X, where the HOMO is the p MO of the alkene and the LUMO is the H-X s* orbital:

and the capture of the carobcation in an SN1 reaction by nucleophile:

You should need no reminder that the carbocation is stabilized by a filled-empty interaction between the empty p orbital of the positive carbon and the s orbital of an adjacent C-H or C-C bond

In short, all heterolytic reactions proceed because the energy of a pair of electrons is lowered by the interaction of a filled atomic or molecular orbital with an empty one.

The same reasoning can be appllied to bimolecular pericyclic reactions like the Diels-Alder cycloaddition.

Diastereomers

Diastereomers (sometimes called diastereoisomers) are stereoisomers that are not enantiomers. Diastereomerism occurs when two or more stereoisomers of a compound have different configurations at one or more (but not all) of the equivalent (related) stereocenters and are not mirror images of each other. When two diastereoisomers differ from each other at only one stereocenter they are epimers. Each stereocenter gives rise to two different configurations and thus to two different stereoisomers.

Diastereomers differ from enantiomers in that the latter are pairs of stereoisomers which differ in all stereocenters and are therefore mirror images of one another. Enantiomers of a compound with more than one stereocenter are also diastereomers of the other stereoisomers of that compound that are not their mirror image. Diastereomers have different physical properties and different reactivity, unlike enantiomers.

Cis-trans isomerism and conformational isomerism are also forms of diastereomerism.

Diastereoselectivity is the preference for the formation of one or more than one diastereomer over the other in an organic reaction.

L-Threonine (2S,3R) and D-Threonine (2R,3S)

Enantiomers

Enantiopure compounds refer to samples having, within the limits of detection, molecules of only one chirality.
Enantiomers have, when present in a symmetric environment, identical chemical and physical properties except for their ability to rotate plane-polarized light (+/−) by equal amounts but in opposite directions (although the polarized light can be considered an asymmetric medium). A mixture of equal parts of an optically active isomer and its enantiomer is termed racemic and has zero net rotation of plane-polarized light.
Enantiomers of each other often show different chemical reactions with other substances that are also enantiomers. Since many molecules in the body of living beings are enantiomers themselves, there is often a marked difference in the effects of two enantiomers on living beings. In drugs, for example, the working substance is often one of two enantiomers, while the other one is responsible for adverse effects.
Enantioselective preparations
There are two main strategies for the preparation of enantiopure compounds. The first is known as chiral resolution. This method involves preparing the compound in racemic form, and separating it into its isomers. In his pioneering work, Louis Pasteur was able to isolate the isomers of tartaric acid because they crystallize from solution as crystals each with a different symmetry. A less common method is by enantiomer self-disproportionation.
The second strategy is asymmetric synthesis: the use of various techniques to prepare the desired compound in high enantiomeric excess. Techniques encompassed include the use of chiral starting materials (chiral pool synthesis), the use of chiral auxiliaries and chiral catalysts, and the application of asymmetric induction. The use of enzymes (biocatalysis) may also produce the desired compound.
Enantioconvergent synthesis is the synthesis of one enantiomer from a racemic precursor molecule utilizing both enantiomers. Thus, the two enantiomers of the reactant produce a single enantiomer of product.

Enantiopure medications
Advances in industrial chemical processes have made it economical for pharmaceutical manufacturers to take drugs that were originally marketed as a racemic mixture and market the individual enantiomers. In some cases, the enantiomers have genuinely different effects. In other cases, there may be no clinical benefit to the patient. In some jurisdictions, single-enantiomer drugs are separately patentable from the racemic mixture. It is possible that both enantiomers are active. Or, it may be that only one is active, in which case separating the mixture has no objective benefits, but extends the drug’s patentability.