Theory
Atomic nuclei in a magnetic field
Important NMR-active nuclei
Parameters from an NMR spectrum
Chemical shifts
As mentioned earlier, not all nuclei of a given isotope resonate at exactly the same frequency. This is because a given nucleus is surrounded by electrons which are also magnetic and, in the presence of the magnetic field, these provide a fluctuating magnetic field that opposes the main field of the NMR magnet. As a consequence, the nuclei are shielded from the main magnetic field and require a higher field to bring them to resonance and thus they can be considered to have higher Larmor frequencies. The degree of shielding depends on the electron distribution around the nucleus and hence on the chemical environment. Thus, interpretation of chemical shift values allows identification of molecular structural fragments. Chemical shifts are measured relative to that of a reference substance placed into the sample. For 1H and 13C shifts in organic solvents, this is tetramethylsilane (TMS). The chemical shift is then defined as δ(H) = (difference in the resonance frequency in Hz between the analyte and TMS) × 106/(operating frequency of the spectrometer). Chemical shifts are thus quoted in ppm and are independent of the operating frequency of the spectrometer, which allows comparisons irrespective of magnetic field strength. For aqueous samples, an alternative reference compound is used, of which trimethylsilyl [2,2,3,3–2H4]-propionic acid sodium salt (TSP) is the most common example. The chemical shifts for TMS and TSP are set arbitrarily to zero. Typical 1H and 13C NMR chemical shifts of a variety of important molecular fragments are shown in Tables 2 and 3, respectively.
Fragmenta,b |
δ(13C) | Multiplicityc |
---|---|---|
CH3.C; CH3,C=C | 0–30 | q |
CH3.S | 7–20 | q |
C.CH2.C | 10–70 | t |
CH.(C)3 | 18–68 | d |
CH3.COX | 18–30 | q |
Acetylenic C | 20–100 | d, s |
CH3.N | 25–50 | q |
C.CH2.COX | 25–60 | t |
C.(C)4 | 30–80 | s |
(C)2.CH.COX | 35–75 | d |
C.CH2.N | 35–75 | t |
(C)2.CH.N | 40–90 | d |
(C)3.C.COX | 45–100 | s |
CH3O | 50–62 | q |
(C)3.C.N | 50–100 | s |
C.CH2O | 57–90 | t |
(C)2.CH.O | 65–100 | d |
(C)3.C.OC | 70–110 | s |
CH2=C | 80–135 | t |
Aromatic CH | 80–140 | d |
C=C | 80–160 | d, s |
OCO | 85–110 | t, d, s |
Aromatic C (not CH) | 90–160 | s |
Nitrile | 115–125 | s |
C.COX | 165–180 | s |
C.COOH | 175–185 | s |
C.CHO | 195–205 | d |
C.CO.C | 205–220 | s |
C.CS.C | 220–240 | s |
Indirect ( J ) spin–spin coupling
The resonance lines of individual nuclei can show further splitting because of indirect spin–spin coupling. This is given the symbol J, is measured in hertz and is independent of the observation frequency. Such spin coupling arises from a magnetic interaction between NMR-active nuclei and is transmitted via the intervening electrons, hence the term ‘indirect’. Coupling is only observed within a molecule. Thus for two spin-½ nuclei, such as protons, the resonance line for each proton is split into a doublet, the two lines corresponding to the two possible orientations of the adjacent proton relative to the magnetic field. For extended coupling chains, each component of a doublet can be split further into doublets of doublets and so on. If a given proton is adjacent to two equivalent other protons (as in a CH2 group) then, of the four possible orientations of the two protons, two of them are identical (up/down is the same as down/up) and a 1:2:1 triplet results. For such ‘first–order’ systems, the multiplicity can be deduced on the basis of Pascal’s triangle according to the number of equivalent coupled nuclei. In situations where the chemical shift difference between the protons is large compared to the J-coupling, this simple rule applies. For situations where the chemical shift between coupled partners is not large compared to the magnitude of the coupling constant (δ/J<10), or in symmetrical molecules, more complex rules have to be applied and sometimes the only way to interpret a spectrum is via a computer simulation. For 1H–1H interactions, the coupling does not normally extend beyond three bonds, with four–bond couplings being quite small, if resolvable. Three–bond 1H–1H couplings provide valuable information on the dihedral angles between C–H vectors through an empirical equation known as the Karplus equation. Typically, for CH–CH fragments, if the CH vectors have a dihedral angle of 180°, the coupling is of the order of 10 Hz; for 90° it is close to zero, and for 0° it is about 6 Hz. In olefinic systems, the three–bond coupling across a C=C double bond is about 6 to 10 Hz for a cis arrangement and 12 to 16 Hz for a trans arrangement. All of these values are modified by the presence of substituents with varying electronegativities. Hence the J-coupling is a valuable parameter for distinguishing between isomers and for measuring molecular conformations. Compilations of coupling constants have been made and empirical models for calculating them in various conformations have been proposed (Pretsch et al. 1989).Peak areas
If the NMR data are acquired under conditions in which each scan is acquired on a spin system at equilibrium, the areas under the NMR peaks are directly proportional to the number of nuclei contributing to that peak and to the concentration of the molecule in the sample. If an internal standard of known concentration is added to the sample, absolute concentrations can be determined.Relaxation times
Two times define how fast a nuclear spin interacts with the rest of the sample as a whole (known as the lattice) and how nuclear spins interact with each other in a pair–wise fashion. These are designated T1 and T2. T1 is known as the spin–lattice or longitudinal relaxation time, and is the characteristic time for the exponential process of nuclear spins that reach equilibrium populations in the spin states. For small molecules in mobile solutions, 1H T1 values are usually in the range of 1 to 10 s. The other relaxation time is known as T2, the spin–spin or transverse relaxation time, and is related to the rate of spin dephasing caused by spin–spin flips. For small molecules in free solution T1 = T2. However, macromolecules and exchanging species have short T2 times, typically in the range 10 to 100 ms, even though T1 may be much longer. The difference in values of T2 between small molecules and macromolecules can be used to edit NMR spectra.Diffusion coefficients
The molecular self–diffusion coefficient is a whole molecule property that does not normally appear in NMR spectra. However, it is a valuable measure of molecular mobility and in free solution is related directly to molecular size. It is possible to measure diffusion coefficients using a specially designed NMR experiment, which includes the application of magnetic field gradients.Direct (dipolar) spin–spin coupling
Another important interaction in NMR spectroscopy is called the dipolar coupling. This is a direct magnetic interaction between nuclei through space, not through bonds, as for J-coupling; it is proportional to the inverse cube of the internuclear distance. This dipolar coupling can be several orders of magnitude larger than J couplings. However, it is averaged to zero in isotropic liquids, but in solids is largely responsible for the observed very broad resonance bands. In semi–solids, such as tissues, the dipolar couplings between nuclei are partially averaged out by the considerable molecular freedom and the residual couplings, and hence the line broadening can be removed by the technique of magic–angle–spinning (MAS). However, for molecules tumbling in solution, the fluctuating dipolar interaction is an important relaxation mechanism and, because of the distance dependence involved in its definition, it can be used to interpret nuclear Overhauser enhancements (NOEs) in terms of internuclear distances, and hence provide molecular structural information.Instrumentation
Practical aspects of 1H NMR spectroscopy
Sample preparation
Acquisition of NMR data
Data processing
System tests
Two–dimensional NMR spectroscopy
Experiment | F2 | F1 | NMR interaction | Information | Time/quantitya | Comments |
---|---|---|---|---|---|---|
COSY | δH | δH | 2JHH and 3JHH | H–H coupling connectivity | 0.25/1 | Easy |
DQF-COSY | δH | δH | 2JHH and 3JHH | H–H coupling connectivity | 0.25/1 | Easy |
TOCSY | δH | δH | 2JHH and 3JHH | All H in a spin system | 0.25/1 | Easy |
NOESY | δH | δH | H–H dipolar | rHH, conformation | 5/5 | 10–100 times weaker than COSY |
ROESY | δH | δH | H–H dipolar | rHH, conformation | 5/5 | 10–100 times weaker than COSY |
HETCOR | δC | δH | 1JCH | C–H | 5/10 | 13C detected |
HMQC | δH | δC | 1JCH | C–H | 1/5 | 1H detected |
HSQC | δH | δC | 1JCH | C–H | 1/5 | 1H detected |
HMBC | δH | δC | 2JCH and 3JCH | C–C–H and C–C–C–H | 3/5 | 1H detected |
JRES (homo) | δH | JHH | JHH | Measurement of JHH | 0.25/1 | Easy |
JRES (hetero) | δC | JCH | JCH | Measurement of JCH and number of attached Hs | 5/10 | Moderate |
INADEQUATE | δC | δCa + δCb | 1JCC | C–C connectivity | 15/100 | 1 in 104 molecules, difficult |
13C NMR spectroscopy
An example of molecular structure determination –ibuprofen

Figure 1. 600 MHz 1H NMR spectrum and molecular structure with numbering system of the non–steroidal anti–inflammatory drug ibuprofen dissolved in DMSO–d6. Assignments are as marked.

Figure 2. Two–dimensional 600 MHz 1H–1H COSY NMR spectrum and molecular structure of the non–steroidal anti–inflammatory drug ibuprofen dissolved in DMSO–d6. The spin–spin coupling connectivities for the CH2(10)–CH(11)–CH3(12,13) and CH(7)–CH3(8) spin systems are shown as dotted lines. Assignments are as marked.

Figure 3. 125 MHz 13C NMR spectrum with broadband 1H decoupling, and molecular structure of the non–steroidal anti–inflammatory drug ibuprofen dissolved in DMSO–d6. Assignments are as marked.

Figure 4. Two–dimensional 1H–13C HSQCNMR spectrum and molecular structure of the non–steroidal anti–inflammatory drug ibuprofen dissolved in DMSO–d6. A peak is seen at the intersection of the 1H and 13C NMR chemical shifts of each CH, CH2 and CH3 group. Assignments are as marked by the peaks on the axes.
Quantitative analysis
Directly–coupled HPLC–NMR–MS

Figure 5. The experimental arrangement for directly coupled HPLC–NMR–MS. The bold lines indicate sample flow and the thinner lines are the electronic control and data signals.
Examples of the use of NMR spectroscopy in the British Pharmacopoeia
NMR spectroscopy of intact biofluids and tissues

Figure 6. 800 MHz 1H NMR spectra of a typical control human urine sample showing successive horizontal and vertical expansions, and illustrating the complexity of the biochemical profile. The vertical arrow points to a very minor peak from the axial methyl group of a bile acid, a substance known to be elevated in certain types of hepatotoxicity. This demonstrates the ability of 1H NMR spectroscopy of biofluids to detect very subtle changes in minor components.
Last modified: 20 May, 2017