Equivalent Ligands

Like ligands in an organic molecule, the hydrogen atoms for example, can be classified into two classes based on their behavior in a given reaction:

1. Chemically equivalent, or, simply, equivalent, ligands: In an organic molecule like ligands that have identical chemical properties are said to be equivalent. They behave exactly the same manner in a given reaction.

2. Chemically non-equivalent, or, simply, non-equivalent, ligands: In an organic molecule like ligands that have different chemical properties are said to be non-equivalent. They behave differently in a given reaction.

Some like ligands in an organic molecule have identical chemical properties under all conditions, meaning both achiral and chiral conditions. They are equivalent under all conditions and are said to be homotopic. Other like ligands in an organic molecule have identical chemical properties under achiral conditions but different chemical properties under chiral conditions. They are equivalent under achiral conditions but non-equivalent under chiral conditions and are said to be enantiotopic. Still other like ligands in an organic molecule have different chemical properties under all conditions. They are non-equivalent under all conditions and can be further classified into two classes, diastereotopic ligands and constitutionally heterotopic ligands; the difference between them is illustrated in examples 3 and 4 below. To determine whether a given pair of like ligands in an organic molecule is homotopic, enantiotopic, diastereotopic, or constitutionally heterotopic, a test known as the replacement test is used.

eg. 1:

To find whether the two hydrogen atoms in 1 are homotopic, enantiotopic, diastereotopic, or constitutionally heterotopic, apply the replacement test to them as follows.

Step 1:  Label the two hydrogen atoms in 1 for identification purposes.

one

 

Step 2:  Replace H(a) in 1 with a hypothetical atom (X).

two

Step 3:
Replace H(b) in  1 with the same hypothetical atom, X.

three

Step 4:  Compare molecules 2 and 3. They are superimposable on each other, so they are identical. Identical molecules have identical chemical properties under all conditions. Since the replacement of H(a) and of H(b) in 1 with the same atom leads to molecules that have identical chemical properties under all conditions, H(a) and H(b) have identical chemical properties under all conditions. Thus, H(a) and H(b) are homotopic.

eg. 2:

four

To find whether the two methyl groups in 4 are homotopic, enantiotopic, diastereotopic, or constitutionally heterotopic, apply the replacement test to them.

five

Molecules 5 and 6 are not superimposable, so they are not identical.  5 and 6 are stereoisomers that are mirror images of each other, meaning that they are enantiomers.  Enantiomers have identical chemical properties under achiral conditions but different chemical properties under chiral conditions.  Since the replacement of CH3(a) and of CH3(b) in 4 with the same atom leads to molecules that have identical chemical properties under achiral conditions but different chemical properties under chiral conditions, CH3(a) and CH3(b) have identical chemical properties under achiral conditions but different chemical properties under chiral conditions.  Thus, CH3(a) and CH3(b) are enantiotopic.

eg. 3:

six

To find whether the two bromine atoms in 7 are homotopic, enantiotopic, diastereotopic, or constitutionally heterotopic, apply the replacement test to them.

seven

 

Molecules 8 and 9 are not superimposable, so they are not identical. 8 and 9 are stereoisomers that are not mirror images of each other, meaning that they are diastereomers.   Diastereomers have different chemical properties under all conditions.  Since the replacement of Br(a) and of Br(b) in 7 with the same atom leads to molecules that have different chemical properties under all conditions, Br(a) and Br(b) have different chemical properties under all conditions. Since application of the replacement test to Br(a) and Br(b) results in diastereomers, Br(a) and Br(b) are said to be diastereotopic.

eg. 4:

eight

To find whether the two methyl groups in 10 are homotopic, enantiotopic, diastereotopic, or constitutionally heterotopic, apply the replacement test to them.

nine

Molecules 11 and 12 are not superimposable, so they are not identical. 11 and 12 have different structural formulas, meaning that they are constitutional isomers. Constitutional isomers have different chemical properties under all conditions.  Since the replacement of CH3(a) and of CH3(b) in 10 with the same atom leads to molecules that have different chemical properties under all conditions, CH3(a) and CH3(b) have different chemical properties under all conditions. Since application of the replacement test to CH3(a) and CH3(b) results in constitutional isomers, CH3(a) and CH3(b) are said to be constitutionally heterotopic.  Notice that the distinction between diastereotopic ligands and constitutionally heterotopic ligands, both of which have different chemical properties under all conditions and are collectively known as heterotopic ligands, originates from their response to the replacement test.

The classification of like ligands in an organic molecule with respect to their behavior in a reaction is summarized schematically below.
ten

To determine whether two like ligands, say L1 and L2, in an organic molecule, say A, are homotopic, enantiotopic, diastereotopic, or constitutionally heterotopic, use the following flowchart.

eleven

The replacement test is not difficult to understand or apply but could be a time consuming exercise. Symmetry elements in molecules, to those who are familiar with them, provide a faster method to find whether two like ligands in an organic molecule are homotopic, enantiotopic, or diastereotopic/constitutionally heterotopic:

1. If two like ligands in a molecule are interchangeable by an axis of symmetry (Cn), they are homotopic.

eg: Consider CH3(a) and CH3(b) in 13.

twelve

The C2 axis in 13 converts 13 into 14, and 13 and 14 are indistinguishable. Thus, CH3(a) and CH3(b) are homotopic.

2. If two like ligands in a molecule are not interchangeable by an axis of symmetry but are by a plane of symmetry (σ), by a point of symmetry (i), or by an improper axis (Sn; σ = S1, i = S2), they are enantiotopic.

eg. 1: Consider CH3(a) and CH3(b) in 15.

thirteen

The plane of symmetry in 15 converts 15 into 16, and 15 and 16 are indistinguishable. Thus, CH3(a) and CH3(b) in 15 are enantiotopic.

eg. 2: Consider the Ph(a) and Ph(b) in 17.

fourteen

The center of symmetry in 17 converts 17 into 18, and 17 and 18 are indistinguishable. Thus, Ph(a) and Ph(b) in 17 are enantiotopic.

eg. 3: Consider Br(a) – Br(d) in 19.

fifteen

The S4 axis in 19, perpendicular to the plane of the ring and passing through its center, converts 19 into 20, and 19 and 20 are indistinguishable. Thus, Br(a) – Br(d) in 19 are enantiotopic.

3. If two or more like ligands in a molecule are not interchangeable by an axis of symmetry nor by a plane of symmetry nor by a point of symmetry nor by an improper axis, they are either diastereotopic or constitutionally heterotopic. Note that symmetry elements cannot be used to distinguish between diastereotopic ligands and constitutionally heterotopic ligands. To distinguish between diastereotopic ligands and constitutionally heterotopic ligands without resorting to the replacement test, use the observation that diastereotopic ligands are always on atoms with the same connectivity while constitutionally heterotopic ligands are always on atoms with different connectivities. The corollary is that constitutionally heterotopic ligands can never reside on the same atom whereas diastereotopic ligands may.

eg. 1:

sixteen

In 21, H(a) and H(b) are neither homotopic nor enantiotopic. H(a) is on a carbon atom bonded to three carbon atoms and H(b) on a carbon atom bonded to two carbon atoms and one hydrogen atom. Thus, H(a) and H(b) are on carbon atoms with different connectivities, meaning that they are constitutionally heterotopic. In contrast, H(b) and H(c), which are neither homotopic nor enantiotopic, reside on the same carbon atom, meaning that they are diastereotopic.

eg. 2:

seventeen

In 22, H(a) and H(b), which are neither homotopic nor enantiotopic, are on different carbon atoms that have the same connectivity. Therefore, they are diastereotopic.

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