Characterisation of Organic Compounds III: Nuclear Magnetic Resonance (NMR) Spectroscopy

NMR Spectrometer at the University of Sheffield

This is the last part of characterisation of organic compounds as in this section we will discuss about nuclear magnetic resonance (NMR) spectroscopy. In this last part, we will focus on the fundamental concepts of NMR spectroscopy, and also on H NMR and C-13 NMR. Furthermore, an exercise for this part will be given in part IV.

NMR spectroscopy is a spectroscopic method that is even more important to the organic chemist than IR spectroscopy as many nuclei can be studied by NMR techniques, but H and C atom are most commonly available. The basic principles of NMR is based on nuclear spin states, as the atomic nuclei behave as if they were spinning. In fact, any atomic nucleus that possesses either odd mass, odd  atomic number, or both has a quantised spin angular momentum and a magnetic moment. The more common nuclei that possess spin include H-1, H-2, C-13, N-14, O-17, and F-19. Notice that the nuclei of the ordinary (most abundant) isotopes of C and O, C-12 and O-16, are not included among those the spin property.

The 2 allowed spin states of a proton

Spin states are not equivalent energy in an applied magnetic field, because the nucleus is a charged particle, and any moving charge generates a magnetic field of its own. Thus, nucleus has a magnetic moment, μ, generated by its charge and spin. A hydrogen nucleus may have a clockwise (+1/2) or counterclockwise (-1/2) spin, and the nuclear magnetic moments in the 2 cases are pointed in opposite directions.

Hydrogen nuclei can adopt only one or the other of these orientations with respect to the applied field. The spin state +1/2 of lower energy since it is aligned with the field, while the spin state -1/2 is of higher energy since it is opposed to the applied filed.

The nuclear magnetic resonance phenomenon occurs when nuclei aligned with an applied field are induced to absorb energy and change their spin orientation with respect to the applied field.

The NMR absorption process (above) and the spin-state energy separation as a function
of the strength of the applied magnetic field

The energy absorption is a quantised process, and the energy absorbed must equal the energy difference between the two states involved. In practice, this energy difference is a function of the strength of the applied magnetic field, B_o, so the stronger the applied magnetic field, the greater energy difference between the possible spin states.

The magnetic of the energy-level separation also depends on the particular nucleus involved. Each nucleus has a different ratio of magnetic moment to angular momentum, since each has different charge and mass. The ratio is called the gyromagnetic ratio, γ, is a constant for each nucleus and determines the energy dependence on the magnetic field. Hence, we can equate the energy difference as:

Where h is the Planck's constant. This small difference in energy can be used to probe a protons environment. Furthermore, an NMR spectrometer consists of the magnetic field, detector, and recorder.

The basic elements of the classical NMR spectrometer

In general, to interpret the structure of an organic compound from NMR spectra, the signals are important. There are 4 points from the signal that basically help to interpret the structure. Firstly, the number of signals shows how many different kinds (environments) of protons are present. Secondly, the position of the signals shows how shielded or deshielded the proton is. After that, the intensity of the signal shows the number of protons with the same environment. Lastly, the signal splitting shows the number of protons on adjacent atoms.

Diamagnetic anisotropy

The basic principle of NMR spectroscopy is the protons are shielded by the electrons that surround them and in an applied magnetic field, the valence electrons of the protons are caused to circulate. This circulation is called a local diamagnetic current, generates a counter magnetic field which opposes the applied magnetic field, the figure illustrates this effect which is called diamagnetic shielding or diamagnetic anisotropy. The circulation of electrons around a nucleus can be viewed as being similar to the flow of an electric current in an electric wire. In atom, the local diamagnetic current generates a secondary, induced magnetic field which has a direction opposite that of the applied magnetic field. As a result of diamagnetic anisotropy, each proton in a molecule is shielded from the applied magnetic field to an extent that depends on the electron density surrounding it. The greater the electron density around a nucleus, the greater the induced counter field that opposes the applied field. Hence, the magnetic field strength must be increased for a shielded proton to flip at the same frequency. Moreover, depending on their chemical environment, protons in a molecules are shielded by different amounts. As the molecule is attached to more electronegative, it becomes less shielded.

Secondly, as mentioned before, the number of signals means the number of types or environments of proton in a molecule. Therefore, we should the number of equivalent protons in a molecule. For example from the spectrum of methyl acetoacetate, we can determine there are 3 different protons environments in that molecule. Hence, the spectrum would appear with 3 signals.

H-1 NMR spectrum of methyl acetoacetate

Furthermore, we can predict the number of protons environments from an NMR spectrum from the number of signals and we also should aware that the molecule has possible symmetry.

If all protons absorbed the same amount of energy in a given magnetic field, not much information could be obtained. Not only do different types of protons have different chemical shifts (signal position), but each also has a characteristic value of chemical shift and each type of proton has only a limited range of chemical shift, δ, over which it gives resonance. Hence, the numerical value of the chemical shift (in δ units or ppm) of the chemical shift for a proton gives a clue as to the type of proton originating the signal.

It is important to learn the ranges of chemical shifts over which the most common types of protons have resonance. In figure below is a correlation char that contains the most essential and frequently encountered types of protons.

A simplified correlation chart for proton chemical shift values

In chemical shifts, to ensure all the measurement will give the same chemical shifts even the frequency of the NMR spectrometer is different, an internal reference is required. The internal reference of NMR spectroscopy is tetramethylsilane, Si(CH₃)₄. Since Si is less electronegative than C, TMS protons are highly shielded, so the signal is defined as 0. Therefore, when another compound is measured, the resonances of its protons are reported in terms of how far they are shifted from those of TMS.

Diamagnetic anisotropy in benzene (left), acetylene (centre), and vinylic proton (right)

The ratio shift downfield (goes to left to the scale) from TMS (in Hz) to total spectrometer frequency (in Hz) is known as chemical shifts. The chemical shifts are measured in parts per million (ppm) and it would give the same value for 60, 100, or even 300 MHz NMR spectrometer. The delta scale of chemical shifts are in range from 0-12. As we mentioned before for electronegative effect, the anisotropy effect could also affect the chemical shifts such as in aromatic (δ 7-8 ppm), vinyl (δ 5-6 ppm), or acetylinic (δ 2.5 ppm) protons.

The protons on heteroatoms such as alcohols and amines have variable chemical shifts, meanwhile the protons in carboxylic acids show very deshielded signal ( δ 11-12 ppm) due to acidic protons. The chemical shifts of O-H and N-H depend concentration, solvent, temperature, and presence of water or acid or basic impurities. O-H peak can be found anywhere in the range of 0.5 - 5.0 ppm (δ 4.5 ppm) and N-H can be found at the same range as O-H (δ 3.5 ppm). The variability of this absorption is dependant on the rates of -OH and -NH proton exchange and the amount of of hydrogen bonding in the solution. In ultrapure samples of ethanol, it shows splitting signal. However, ethanol with a small amount of acidic or basic impurities will not show splitting. Meanwhile, -NH proton has moderate rate of proton exchange which gives broad peak. Another characteristic of -NH and hydroxyl protons, the sample can be shaken with D₂O and the signal will dissapear or less intense because deuterium will exchange with -OH or -NH protons. In carboxylic acid, the highly deshielded is due to hydrogen bonding interactions. Hydrogen bonding interactions polarise the electrons from H, so this polarisation removes electrons from H. Hence, it changes its chemical shift (around +3 ppm). 

Another properties of the NMR spectrum signal is the intensity of the signal which tell us the number of protons. In the NMR spectrum, the are under each peak is proportional to the number of hydrogen generating that peak. The NMR spectrometer has the capability to electronically integrate the are under each peak. It does this by tracing over each peak a vertically rising line, called the integral, which rises in height by an amount proportional to the area under the peak. For example, in benzyl acetate the integration 2.52: 1.00: 1.48, which is roughly 2.5: 1: 1.5 (5: 2: 3) as shown below.

H-1 NMR spectrum of benzyl acetate and the integration

One of the characteristic of NMR spectrum is the signal has spin-spin splitting pattern which tell us the environment. Nonequivalent protons on adjacent carbons have magnetic fields that may align with or oppose the external field. This magnetic coupling causes the proton to absorb slightly downfield when the external field is reinforced and slightly upfield when the external field is opposed. This splitting is known as coupling.

Spin-spin splitting arises because hydrogens on adjacent carbon atoms can "sense" one another. The hydrogen on carbon A can sense the spin direction of the hydrogen on carbon B. In some molecules of the solution, the hydrogen on carbon B has spin +1/2 (X-type molecules); in other molecules of the solution, the hydrogen on carbon B has spin -1/2 (Y-type molecules).

2 different molecules in a solution with differing spin relationships between protons.

The chemical shift of proton A is influenced by the direction of the spin in proton B. Proton A is said to be coupled to proton B. Its magnetic environment is affected by whether proton B has a +1/2 or a -1/2 spin state. Thus, proton A absorbs at a slightly different chemical shift value in type X molecules than in type Y-molecules. In fact, in X-type molecules, proton A is slightly deshielded because the field of proton B is aligned with the applied field and its magnetic moment adds to the applied field. In Y-molecules, proton A is slightly shielded with respect to what its chemical shift would be in the absence of coupling. Since, in a given solution there are approximately equal numbers of X- and Y-type molecules at any given time, 2 absorptions of nearly equal intensity are observed. The resonance of proton A is said to have been split by proton B, and the general phenomenon is called spin-spin splitting.

The origin of spin-spin splitting in proton A's NMR spectrum

Another example, now we consider ethyl iodide. In this case, there are eight possible spin arrangement are identical to each other, since one methyl proton is indistinguishable from another and since there is free rotation in a methyl group. Hence, there are 3 possible ways to obtain the arrangements with net spins of +1/2 or -1/2. Thus, one notes in splitting pattern of the methylene protons that the centre of 2 peaks are more intense than the outer one, in fact the intensity ratio is 1: 3: 3: 1 as shown below. 

The splitting pattern of methylene protons due to the presence of an adjacent methyl group

Moreover, the equivalent protons do not split each other and protons bonded to the same carbon will split each other only if they are not equivalent. Besides that, protons separated by 4 or more bonds will not couple.

H-1 NMR spectrum of 1,1,2 trichloroethane

For example in 1,1,2-trichloroethane, the signal appeared on the spectrum has five peaks: a group of three peaks (called triplet) and a group of 2 peaks (called doublet). This phenomenon is called spin-spin splitting can be explained empirically by the so-called n+1 Rule. Each type of proton "senses" the number of equivalent protons (n) on the carbon atom(s) next to the one to which it is bonded, and its resonance peak is split into (n +1) components.

H-1 NMR spectrum of 2-nitropropane and its splitting pattern

Another example is 2-nitropropane which has the spectrum given in figure above. Notice that in the case of 2-nitropropane there are 2 adjacent carbons that bear hydrogens (2 carbons, each with 3 hydrogens) and that all six hydrogens as a group split the methine hydrogen into a septet.

This splitting pattern has distinct separation between each peaks in a signal and this distance is called coupling constants (J). The coupling constant is a measure how strongly a nucleus affected by the spin states of its neighbour. The spacing between the multiplet peaks is measured on the same scale as the chemical shift, and the coupling constant is always expressed in Hertz (Hz). Moreover, the coupling constants of the groups of protons that split one another must be identical, and this is extremely useful in interpreting a spectrum that may have several multiplets, each with a different coupling constant.

An illustration of the relationship between the chemical shift and the coupling constant

In table below is shown some representative coupling constants and their approximate values (Hz).

Besides that, the coupling requires orbital overlap - i.e. hydrogen on adjacent carbons and there is relationship between dihedral angle and the coupling constant. This coupling constant is known as the vicinal coupling constant (³J_HH). The parameter ³J_HH measures the magnitude of the splitting. This coupling measures the separation in Hz between the multiplet peaks. The actual magnitude of the coupling constant between 2 adjacent C-H bonds can be shown to depend directly on the dihedral angle α between these 2 bonds as shown below.

The definition of a dihedral angle

 The magnitude of the splitting between H_A and H_B is greatest at α= 0° or 180° and is smallest when α= 90°. The side-side overlap of the 2 C-H bonds orbitals is at maximum at 0°, where the C-H bond orbitals are parallel, and at a minimum at 90°, where they are perpendicular. At α= 180°, overlap with the back lobes of the orbital occurs.

The Karplus relationship (right) and the orbital overlap at certain dihedral angle (left)

Martin Karplus was the first study the variation of the coupling constant ³J_HH with α. He was the first worker to develop an equation that gave a good fit to the experimental data shown in graph below. In short, Karplus relationship states better orbital overlapping provides higher coupling constant.

A more complex splitting than we saw before can happen in alkene (e.g. styrene) or in a saturated cyclic compound. For example in styrene, signals may be split by adjacent protons, different from each other, with different coupling constant. H_A of styrene which is split by an adjacent H trans to it (J = 17 Hz) and an adjacent H cis to it (J = 11 Hz).

Another complex splitting also happens if there are protons that stereochemically nonequivalent. Usually, 2 protons on the same C are equivalent and do not split each other. If the replacement of a -CH₂- group with an imaginary "Z" gives stereoisomers, then the protons are nonequivalent and will split each other. This figure below shows an example about stereochemical nonequivalence splitting in 4-t-butylcyclohexanol.

H-1 NMR spectrum of 4-t-butylhexanol

Another types of NMR spectroscopy that is commonly used in organic chemistry is C-13 NMR spectroscopy. The reason behind the used of C-13 is because the most abundant C isotopes, C-12, is has silent spin (even number of atomic number and mass number), but C-13 has a magnetic spin despite is only 1% of the carbon sample. Moreover, the gyromagnetic ratio C-13 is 1/4 of H-1, so the signals are weak and getting lost in noise.

A simplified correlation chart of C-13 NMR

An important parameter derived from C-13 spectra is the chemical shift. The correlation chart below shows typical C-13 chemical shifts, listed in ppm from TMS, where carbons of the methyl groups of TMS are used for reference. Notice that chemical shifts appear over a range (0 to 220 ppm) much larger than observed protons (0 to 12 ppm). Because of the very large range of values, nearly every nonequivalent carbon atom in an organic molecule gives rise to a peak with a different chemical shift. The differences in C-13 techniques firstly is the resonance frequency which is 1/4 than proton NMR (15.1 MHz instead of 60 MHz). Secondly, the peaks area are not proportional to the number of carbons. Lastly, carbon atoms with more hydrogens absorb more strongly.

In C-13 NMR, it is unlikely that C-13 would be adjacent to another C-13, so splitting by carbon is negligible. However, C-13 will magnetically couple with attached protons and adjacent protons and this complex splitting patterns are difficult to interpret.

Therefore, to simplify the spectrum, protons are continuously irradiated with "noise", so they are rapidly flipping. The carbon nuclei see an average of all the possible proton spin state. Thus, each different kind of carbon gives a single, unsplit peak. As mentioned before, C-13 nuclei are split only by the protons attached directly to them, so the n +1 rule can be applied: a carbon with n number of protons gives a signal with n + 1 peaks.

The way of C-13 spectrum interpretation is almost the same as H-1 NMR. The number of different signals indicates the number of different kinds of carbon. The location of signal indicate the type of functional group. Lastly, the splitting pattern of off-resonance decoupled spectrum indicates the number of protons attached to the carbon. The example of C-13 NMR is shown below.

C-13 NMR spectrum of methyl acetoacetate

Another types of C-13 NMR is called Distortionless Enhancement by Polarisation Transfer or better known as DEPT. The DEPT technique requires an FT-pulsed spectrometer and it is more complicated than off resonance decoupling and it requires a computer, but it gives the same information more reliably and more clearly. There are three types of DEPT spectrometer, DEPT-45, DEPT-90, and DEPT-135. DEPT-45 signals are arisen from protonated carbon. Besides that, DEPT-90 only detects for those carbons that bear a single hydrogen. Lastly, DEPT-135 detects all carbons that have hydrogen attached, but signal arising from carbon that bears odd number of hydrogens (CH₃ or CH)will give positive peaks and carbon that bears even number of hydrogens (CH₂)will form negative peaks. An example of DEPT spectra is shown below.

DEPT signals of 4-methoxy cinnamaldehyde