1.6. What Can We Learn? Number of H Types
There are four practical pieces of information that can be extracted from a typical 1H NMR spectrum. The first of these is the number of different “types” of hydrogens in the sample (the number of different chemical environments for hydrogens in the sample).
1.6.1. Chemical Shift and Electron Density Basics
The chemical shift for an NMR signal is determined by the ΔE value for the nuclei that generated it (see Section 1.4). This value is dependent on several factors, primarily the strength of the external magnetic field as experienced by those nuclei.
As charged particles spin they generate very small electric fields (magnetic moments) around themselves. This is true for the nuclei, but it is also true for the electrons around those nuclei. The electrons each generate their own (very) small magnetic moment (Figure 1.12).
Figure 1.12 – Representation of Magnetic Moments Generated by Electrons Orbiting a Nucleus.
These magnetic moments also have directionality. However, they all align antiparallel to the external field. Although each electron’s magnetic moment is very small, when added together they have enough strength to affect the overall external field strength experienced by the nucleus they surround (Figure 1.13). Every electron near a nucleus slightly reduces the magnetic field experienced by the nucleus.
Figure 1.13 – Applied vs. Effective Magnetic Field Strength.
The amount of electron density around a nucleus affects the magnetic field experienced by it. This affects the ΔE value for that nucleus. The result is a change in the chemical shift for that nucleus’ signal. The amount of electron density around a nucleus directly affects its chemical shift.
Because each hydrogen in a molecule will be in a slightly different chemical environment (closer to or further from areas of high and low electron density) they will each produce their own signal in a 1H NMR spectrum. However, it is possible for more than one hydrogen in a molecule to experience exactly the same chemical environment and thus produce exactly the same signal. When this happens the atoms are considered to be “chemically equivalent” and will not produce different signals from each other.
1.6.2.1. Equivalency By Symmetry
Different hydrogen atoms in a molecule can be chemically equivalent by symmetry. The most common way for this to occur is for there to be an internal mirror plane that relates them (Figure 1.14).
Figure 1.14 – Examples of Internal Mirror Planes Making Hydrogen Atoms Chemically Equivalent.
To understand why pairs of hydrogen atoms related this way are chemically equivalent consider the distances between each of those atoms and the other atoms of the molecule (Figure 1.15). Each is exactly the same distance away from an equivalent atom with its equivalent amount of electron density. As a result, they have exactly the same amount of electron density around them and are chemically equivalent.
Figure 1.15 – Example of Highlighted Interatomic Distances for Equivalent Electron Densities.
1.6.2.2. Equivalency By Rotation
Symmetry alone can identify sets of equivalent atoms, but will miss another important relationship. Consider the two orange hydrogen atoms of butanol above (Figure 1.14). By symmetry, these are equivalent to each other. It appears that they are different from the black hydrogen atom connected to the same carbon. In actuality, these three are all chemically equivalent.
Different hydrogen atoms in a molecule can be chemically equivalent by rotation around sigma (σ) bonds. Recall that, typically, there is free rotation around most sigma bonds. As the bond is rotated different conformations are generated (Figure 1.16).
Figure 1.16 – Example of Sigma Bond Rotation Making Hydrogen Atoms Chemically Equivalent.
Because each of these conformations is energetically equivalent they are equally populated; in the sample there will be an equal number of molecules in conformation A as conformation B and conformation C. At the same time, they are rapidly interconverting. The net result is that on a time-averaged scale each of these hydrogen atoms experiences the same amount of electron density (i.e. an average of the electron density it experiences in each of conformations A, B, and C). As a result, they are chemically equivalent to each other and will give rise to the same signal in 1H NMR spectroscopy.
Technically this is not always true. Systems where this does not apply tend to result in significantly more complex spectra. Examples with this phenomenon will not feature in this text but may be encountered in other sources. This is mentioned only to remind students that NMR spectroscopy can generate challenging and intricate results even in cases that otherwise appear simple.
Finally, it is important to remember that chemical equivalence by both symmetry and rotation can occur (Figure 1.17).
Figure 1.17 – Example of Both an Internal Mirror Plane and Sigma Bond Rotation Making Hydrogen Atoms Chemically Equivalent.
1.6.2.3. Substitution Test Basics
It can be challenging to determine if two hydrogen atoms in a molecule are chemically equivalent. In these cases performing a so-called “substitution test” can be helpful. Substitution tests are usually performed to help with other complications (see Section 1.9.1) but may be used simply to determine chemical equivalence.
To determine if two atoms are chemically equivalent replace each atom with a hypothetical group and compare the resulting structures (Figure 1.18). Many sources use “Z” as it does not correspond to any element or functional group. If the resulting two structures are chemically identical (the same compound) then the two atoms that were replaced were chemically equivalent. If they are different compounds they are not chemically equivalent. For now, if the result is a pair of compounds that are related through stereochemistry (enantiomers or diastereomers) the system requires more analysis (see Section 1.10.1 and subsections therein). Remember that rotations and conformation changes are allowed when determining the relationship between structures.
Figure 1.18 – Examples of Simple Substitution Tests to Determine Chemical Equivalency.
1.6.3. How To Determine the Number of H Types
It is possible to analyze a chemical structure and determine how many different signals should be present in the compound’s 1H NMR spectrum. The molecule is analyzed to determine how many different sets of chemically equivalent hydrogens there are. This is directly equal to how many signals are expected.
Redraw the molecule showing all hydrogen atoms. Indicating geometry is often helpful. This step may be omitted after sufficient practice but is especially helpful when starting out.
Check for obvious chemical equivalency by symmetry and/or rotation. In some molecules checking for symmetry first will work better, while in others rotation will be easier. It is often helpful to work systematically. This text uses colour-coding but a common alternative would be to use number- or letter-coding for each group of hydrogens.
Check for equivalence between all potentially unique groups of hydrogens. A substitution test works best but may be time consuming. It is often helpful to work systematically, such as by going from left-to-right one-by-one. Only one substitution is required for each group of equivalent atoms. The speed of this step often improves dramatically with practice and may eventually be done internally (in your mind’s eye).
Count the number of unique groups. This is the number of expected signals.
Note that in Step 2 “obvious” is subjective. For example, it may not have been obvious that an internal mirror plane makes the red hydrogen atoms equivalent, or that a second rotation makes all nine green atoms equivalent. If these are missed in Step 2 they are typically caught during the substitution tests of Step 3. Do not worry if not all equivalencies are obvious, the answer can still be reached relatively quickly using additional substitution tests. For example, the three groups of equivalent hydrogens found in Step 2 are found to be chemically equivalent when doing simple substitution tests.
