1.9. What Can We Learn? Coupling and Connectivity

There are four practical pieces of information that can be extracted from a typical ¹H NMR spectrum. The fourth of these is a general idea of the connectivity of each signal’s hydrogen atom(s) (how many hydrogen atoms are connected to atoms adjacent to the signal).

1.9.1. Near Spin Effects and Signal Splitting

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 things, 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. Each electron generates a (very) small magnetic moment which all align antiparallel to the field and affect chemical shift (see Section 1.6.1). Because they all align antiparallel every electron near a nucleus slightly reduces the magnetic field experienced by the nucleus.

This also happens with nuclei of the same element and isotope near the nucleus being probed. Those nuclei are also aligning with the external magnetic field, generating their own magnetic moments, and locally affecting the magnetic field strength. Generally, hydrogen atoms within three bonds of each other are close enough to affect the field strength each of them experiences. However, because they can align parallel or antiparallel this effect is more complex.

Consider a hydrogen atom attached to a carbon atom (H_a, Figure 1.27). This hydrogen has a certain amount of electron density near it that affects its ΔE value and defines its chemical shift value.

Figure 1.27 – A Generic Hydrogen Atom Generates a ¹H NMR Signal with a Generalized Chemical Shift.

However, within three bonds of it there is another chemically distinct hydrogen atom. The nucleus of this atom also aligns with the external magnetic field, parallel or antiparallel, and generates its own magnetic moment. Just as with the electrons this magnetic moment will affect the effective magnetic field experienced by H_a. However, there are now two possible options: alignment parallel slightly increases the effective magnetic field; alignment antiparallel slightly decreases the effective magnetic field (Figure 1.28).

Figure 1.28 – Effects from Nearby Magnetic Moments of Atoms on Effective Field Strength.

Half of the molecules in the sample have the neighbour hydrogen nucleus parallel and slightly increase the chemical shift of H_a. Half of the molecules in the sample have the neighbour hydrogen nucleus antiparallel and slightly decrease the chemical shift of H_a. Both types of molecules are detected by the spectrometer and both “chemical shifts” are recorded. The total signal gets split between the options (Figure 1.29). This also splits the integration between the new peaks (i.e. the blue line and red line combined integrate to 1).

Figure 1.29 – Signal of a Generic Hydrogen Atom is Split via Coupling with One Nearby Hydrogen Atom.

Both “peaks” are now part of the same signal; the signal itself is the combination of the two. The splitting process is referred to as spin coupling. The difference in position between the two peaks is called the coupling constant, represented with an italic uppercase J (Figure 1.30). This value is reported in hertz, not ppm. This is primarily for accuracy (the values are normally very small).

Figure 1.30 – Representation of Coupling Constant.

The exact same effect occurs iteratively for each additional hydrogen atom “felt” by H_a. Consider the same hydrogen but with two nearby hydrogen atoms (Figure 1.31). For simplicity, these two are chemically distinct from H_a but are chemically equivalent to each other. The signal for H_a is effectively split twice (once for each hydrogen nucleus).

Figure 1.31 – Signal of a Generic Hydrogen Atom is Split via Coupling with Two Nearby Equivalent Hydrogen Atoms.

Again, adding more (chemically equivalent) hydrogen atoms nearby just repeats this process (Figure 1.32).

Figure 1.32 – Signal of a Generic Hydrogen Atom is Split via Coupling with Three Nearby Equivalent Hydrogen Atoms.

Spin coupling only occurs if the nearby nuclei are chemically distinct from the nucleus generating the signal. Spin coupling cannot occur between chemically equivalent nuclei (Figure 1.33). For example, the signal for the three chemically equivalent hydrogen atoms in the above example is split once by H_a. It is NOT split again by the “other” hydrogen atoms. All three are chemically equivalent and all give rise to the same signal.

Figure 1.33 – Chemically Equivalent Nuclei Do Not Spin Couple to Each Other.

1.9.2. Standard Splitting Patterns

There are four very common splitting patterns (commonly called “multiplets”, Table 1.2). Each has its own abbreviation and characteristic ratio of intensities. Knowing these four makes interpreting many NMR spectra much easier.

Table 1.2 – Standard Splitting Patterns for Spin-Coupled Nuclei.

There are additional splitting patterns as the number of chemically equivalent hydrogen atoms increases (e.g. quintet, sextet, septet etc.). In practice, quintets and septets are uncommon and sextets are very rarely encountered. These patterns do not have abbreviations. The peak intensity ratios for these patterns may be predicted but do not require memorization at an introductory level.

1.9.3. Advanced Coupling – Multiple Couplings

Spin coupling can occur multiple times for each set of chemically distinct nuclei nearby. Functionally, the signal is split for one set of nuclei and then split again (and again, etc.) for each additional set.

Consider the ¹H NMR signals for 1,1-dichloropropane (Figure 1.34). The hydrogen at position 1 (blue) will spin couple to a set of two chemically equivalent hydrogens (red, at position 2). The expected signal will be a triplet. The three chemically equivalent hydrogens at position 3 (green) will spin couple a set of two chemically equivalent hydrogens (red, at position 2). The expected signal will be a triplet. However, the situation is more complex for the hydrogens at position 2.

Figure 1.34 – ¹H NMR Spectrum of 1,1-Dichloropropane.

The hydrogens at position 2 (red) will spin couple to a set of one chemically equivalent hydrogen (blue, at position 1) AND a set of three chemically equivalent hydrogens (green, at position 3). The expected signal will split into a doublet AND the doublet will further split into a quartet. The resulting peak shape is properly called a “doublet of quartets” (dq) and looks much more complicated.

With careful analysis one could theoretically show that the peak shape matches some overlapping pattern of two quartets (Figure 1.35).

Figure 1.35 – Example of a Simple Doublet of Quartets.

In practice this is very challenging. The exact shape and number of peaks will depend on several factors, primarily the ratio between the coupling constants (in this example J_H1-H2 and J_H2-H3). If a third (or more) couplings are added the shape becomes exponentially more complex. At the same time, other complications beyond introductory considerations can alter peak ratios and/or add additional splitting. For example, the height of the far left and far right peaks is not identical due to a phenomenon beyond the scope of an introductory text. When interpreting a spectrum with a complex signal like this it is acceptable to describe the signal as a generic multiplet (abbreviation m) rather than trying to deconvolute the specific coupling patterns making up the shape. The actual expected coupling pattern is described if the structure is known or when predicting the shape of signals for a spectrum. For example: if given only the spectrum of Figure 1.34 the red signal is described as a “multiplet (m)”; if given the spectrum AND the structure the signal is described as a “doublet of quartets (dq)” because the specific coupling pattern is knowable.

1.9.4. How To Predict Multiplicity (Signal Shape)

It is possible to analyze a chemical structure and determine the multiplicity (shape, coupling pattern) of the signals present in the compound’s ¹H NMR spectrum. The molecule is analyzed to determine how many different sets of chemically equivalent hydrogens there are. Then each set is predicted to split based on each set of chemically distinct neighbours are within three bonds’ distance.

Identify in some way which sets of hydrogen atoms are chemically equivalent. See Section 1.6.3. The speed of this step often improves dramatically with practice and may eventually be done internally (in your mind’s eye). This text uses colour-coding but a common alternative would be to use number- or letter-coding for each group of hydrogens.

For each set of chemically equivalent hydrogens check which, if any, other set(s) are within three bonds of connectivity. It is often helpful to work systematically.

Assign multiplicity. Technically, when multiple couplings occur there are specific rules for the order that they should be listed in. These require more information than is typically given. For now, when multiple couplings occur list them in any order as long as it is understandable (e.g. dq or qd).

Summarize (if needed).

Steps 2 and 3 are often combined and done concurrently. As an extension of this task, it is expected that students are able to draw peak shapes with proper intensity ratios for the common coupling patterns (s, d, t, q). Drawings of more complex patterns would not be expected as their exact shapes can vary significantly.