Descriptions of Spin Systems

DESCRIPTIONS OF SPIN SYSTEMS

It is often helpful to categorize spin systems in terms of the chemical and magnetic equivalence of coupled protons. Protons are chemically equivalent if they have the same chemical environment and thus the same chemical shift. Chemical equivalence can result from either identical environments or rapid rotations which yield an “average” environment for a group of protons. Considering toluene, it is seen that the two meta protons are found in the plane of the ring between the ortho and para protons.

They have the same chemical environment and thus absorb at the same frequency. The methyl group is a singlet indicating that the three methyl protons absorb at the same frequency and thus are chemically equivalent, yet in the conformation shown it is clear that the environment of each proton is not the same. One is found in the plane of the ring while a second is above and the third is below the plane of the ring. However, due to rapid rotation of the methyl group, these hydrogens rapidly exchange positions and thus all absorb at an “average” frequency and all are chemically equivalent by rotation.

Protons are magnetically equivalent if they have the same chemical shift and are coupled equally to other equivalent nuclei in the molecule. This is simi-lar to chemical equivalence but is a more rigorous definition of equivalence. For example, the methyl protons of isobutane are chemically and magnetically equivalent since they absorb at the same frequency and are all coupled equally to the methine proton (which should be split into a 10-line multiplet!). Likewise the two methyl groups of p-xylene are chemically and magnetically equivalent because they are coupled equally (J = 0) to the aromatic protons both ortho and meta to them.

On the other hand, the ortho protons of o-dibromobenzene are chemically equivalent because they have the same environment, but they are magnetically nonequivalent since a given ortho proton is not coupled equally to the two meta protons (there is a 1,2 interaction with one and a 1,3 interaction with the other and J_1,2 = J_1,3). By the same arguments the methylene groups of 1,4-dibromo-cis-2-butane are chemically equivalent but magnetically nonequivalent because each methylene group is not coupled equally to the chemically equivalent vinyl hydro-gens (again J_1,2 = J_1,3). Of course this also means that the vinyl hydrogens are magnetically nonequivalent since a given vinyl hydrogen is not equally coupled to the two methylene groups.

We would expect that the spectrum of the latter compound would consist of two signals: a two-proton triplet in the vinyl region and a four-proton doublet in the allylic region. This is because the coupling constant J_1,3 is zero. It if were not zero, then a more complicated spectrum would result. Thus magnetic nonequivalence can lead to much more complicated spectra.

Using chemical and magnetic equivalence, it is possible to designate the num-ber and type of different protons in a spin system. This is done by choosing letters of the alphabet to indicate protons of similar chemical shift: ABC or MNO or XYZ. For only two types of protons, letters from the first part and last past of the alphabet are chosen (A, X). If three types are present, then letters from the middle group are also used (e.g., A, M, X). A subscript is used to indicate how many of each type of protons is present in the spin system. Several spin systems are shown below with their designations. All are examples of groups of chem-ically and magnetically equivalent protons. A molecule can contain more than one spin system if they are isolated from each other.

Protons that are chemically equivalent but magnetically nonequivalent are indi-cated by, for example, AA . The examples of such systems given below illustrate the method. This system for designating spin systems is merely a labeling device. The appearance of actual spectra will depend on the magnitude of the various J values. Nevertheless this is a convenient and common way of categorizing coupled proton systems.

Another structural factor which can lead to nonequivalence of aliphatic protons is the symmetry properties of protons:

1. Aliphatic protons which are interconvertible by a rotational axis are termed homotopic and are chemically and magnetically equivalent. For example, the methylene protons of diphenylmethane are homotopic, as are the methy-lene protons and the methyl protons of propane.

2. Methylene protons which are not interconvertible by rotation but are inter-convertible by reflection through a plane of symmetry are enantiotopic and are chemically and magnetically equivalent in an achiral environment. Alternatively protons are enantiotopic if sequential replacement by a dif-ferent group gives a pair of enantiomers. The methylene protons of methyl propionate are enantiotopic because they are interchangeable by reflection but not rotation. (The protons of both methyl groups are interchangeable by rotation and are thus homotopic.) Replacement of H_a and H_b by another group such as hydroxy gives R- and S-methyl lactate, respectively. The benzylic protons of benzyl alcohol are enantiotopic by the same criteria.

3. Methylene protons which are not interconvertible by either reflection or rotation are diastereotopic and are chemically and magnetically nonequivalent. 

The presence of one or more chiral centers in a molecule leads to diastereotopic methylene groups since the replacement of each proton by another group gives a pair of diastereomers. Since diastereotopic protons are not related by symmetry, they have unique environments and thus unique chemical shifts and coupling constants.

The C-2 methylene protons H_a and H_b in ethyl-3-azido-4-oxopentanoate are diastereotopic because of the chiral center at C-3 (Figure 11.22). The protons H_a and H_b have slightly different chemical shifts and split each other, and they are not coupled equally to the C-3 methine proton H_c . Thus H_a and H_b split each other into an AB quartet, which is further split into doublets by H_c . Note that the splitting for each proton of the AB quartet has a different coupling constant with H_c . Although H_c is slightly obscured by the CH₂ protons of the ethyl group, it can be seen that the signal for this proton is not a triplet but rather looks like a doublet of doublets, as expected from the fact that J_ac ≠ J_bc .