13.7 1H NMR Spectroscopy and Proton Equivalence

Proton Equivalence and 1H NMR Spectroscopy

Chemical Relationships of Protons

To interpret a 1H NMR spectrum, you need to figure out which protons in a molecule are equivalent (giving the same signal) and which are distinct (giving separate signals). There are four key relationships to know.

Chemically unrelated protons are bonded to different types of atoms or sit in clearly different chemical environments (e.g., a methyl proton vs. a hydroxyl proton). These always appear as separate signals with different chemical shifts.

Homotopic protons occupy identical chemical environments and can be interchanged by a symmetry operation like rotation around a bond. The three methyl protons in ethane are a classic example. Homotopic protons share the same chemical shift and contribute to a single NMR signal.

Enantiotopic protons sit in mirror-image environments and can be interchanged by reflection through a plane of symmetry. The two methylene protons in glycine are enantiotopic. In a standard (achiral) NMR solvent, enantiotopic protons behave just like homotopic protons: same chemical shift, same signal. However, if you replace one enantiotopic proton with a different atom or group, you get a pair of enantiomers (e.g., L-alanine and D-alanine). This substitution test is how you confirm they're enantiotopic rather than homotopic.

Diastereotopic protons are in different chemical environments because of an adjacent stereocenter, and they cannot be interchanged by any symmetry operation. The methylene protons adjacent to the stereocenter in 2-bromobutane ($\ce{CH3CHBrCH2CH3}$) are diastereotopic. These protons have different chemical shifts and appear as separate signals. Replacing one diastereotopic proton with another group produces diastereomers (e.g., L-threonine and L-allo-threonine), which is the substitution test for diastereotopicity.

NMR Signals and Proton Equivalence

Predicting how many signals a molecule will show in its 1H NMR spectrum comes down to correctly grouping equivalent protons.

• Chemically unrelated protons each give a distinct signal.
• Homotopic protons share a single signal. Example: the three methyl protons in ethanol ($\ce{CH3CH2OH}$) are homotopic and produce one signal.
• Enantiotopic protons also share a single signal in achiral solvents. Example: the four methylene protons in 1,2-dibromoethane ($\ce{BrCH2CH2Br}$) are enantiotopic and produce one signal.
• Diastereotopic protons give separate signals. Example: the methylene protons adjacent to the chiral center in 2-bromobutane ($\ce{CH3CHBrCH2CH3}$) are diastereotopic and appear as two distinct signals.

The total number of distinct signals equals the number of sets of chemically nonequivalent protons. Remember that each pair of diastereotopic protons counts as two separate sets, not one.

Proton Equivalence in 1H NMR Analysis

Once you have a spectrum, here's how to work through it systematically:

1. Count the distinct signals. Each signal corresponds to a set of equivalent protons (homotopic or enantiotopic) or to an individual diastereotopic proton. For example, ethyl acetate ($\ce{CH3COOCH2CH3}$) shows 3 distinct signals: the acetyl methyl, the methylene, and the ethyl methyl.

2. Determine relative integration. The area under each signal is proportional to the number of protons producing it. Homotopic and enantiotopic protons all contribute to the same signal, so a methyl group with three homotopic protons gives an integration of 3. Compare the integration ratios across signals to figure out how many protons are in each group.

3. Analyze the splitting pattern. Splitting follows the $n+1$ rule, where $n$ is the number of neighboring nonequivalent protons coupled to the signal. Homotopic and enantiotopic neighbors act as a single set for splitting purposes. Diastereotopic neighbors each couple independently, which can produce more complex splitting. For example, the methylene signal in ethyl acetate is a quartet because the $\ce{CH2}$ protons have three neighboring methyl protons ($n = 3$, so $3 + 1 = 4$ lines).

4. Assign each signal to specific protons. Combine chemical shift, integration, and splitting to match each signal to its corresponding protons. Consider the electronic environment: protons near electronegative atoms are deshielded and appear further downfield. In ethanol ($\ce{CH3CH2OH}$), the methyl signal appears near ~1.2 ppm while the methylene signal appears near ~3.7 ppm because the $\ce{CH2}$ is directly attached to the electronegative oxygen.

Advanced NMR Techniques

• The Free Induction Decay (FID) is the raw time-domain signal detected by the NMR instrument after a radiofrequency pulse excites the nuclei.
• A Fourier transform converts the FID from the time domain into the frequency-domain spectrum you actually read and interpret.
• The Nuclear Overhauser Effect (NOE) reveals spatial proximity between protons that are close in three-dimensional space (typically < 5 Å), even if they're far apart in the bonding network. This is especially useful for determining stereochemistry and conformation.
• Magnetic resonance occurs when the applied radiofrequency matches the Larmor frequency of the nuclei, which is the precession frequency of the nuclear spin in the external magnetic field.