Relative Intensities in Nuclear Spin Multiplets

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DOI: It is often used as an internal standard. However, TMS has low solubility in aqueous solution, therefore, it is often necessary to use a secondary standard such as DSP. The chemical shifts of functional groups in many molecules have been measured and they provide a basis for identification of functional groups in novel molecules. The area of a signal is proportional to the total number of contributing nuclei.

In the 1H NMR spectrum of a pure compound containing a single methyl group and a single methylene group, the relative areas of the corresponding signals will be in the ratio , because there are 3 protons in the methyl group and 2 in the methylene group. If the pure compound can exist in multiple conformations, and if the transitions between the different conformational states occur on a time scale that is slow with reference to the relevant NMR time scale typically msec then it may be possible to observe separate signals corresponding to the different conformations in the NMR spectrum.

In such a case, the relative areas of the signals corresponding to different conformations will be proportional to the fractions of the molecules that exist in each conformational state during the time that the NMR spectrum was acquired.

Nuclear spin in a magnetic field

Many small molecules can exist in multiple conformations due to rotation about single bonds, however, such rotation is generally rapid at room temperature and hence separate signals are usually not observed for the different rotational isomers that exist at equilibrium. For large molecules, e. Such restricted rotation about single bonds results in separate NMR signal for each conformer and the areas of the NMR signals are again proportional to the populations of the conformers. In the NMR spectra of mixtures, the relative areas of signals can be used to deduce information regarding the relative concentration of each compound.

The very high resolution of NMR spectra enables us to resolve a very large number of compounds, and hence determine the relative concentrations of a large number of chemical species.

Supplementary files

This is of particular use in vivo spectroscopy and NMR-based metabolomics studies in which blood plamsa or serum, urine, cerebral spinal bluid, or tissue extracts can be studied for metabolic disorders or chemical injury. Systems undergoing physical and chemical changes can also be monitored by NMR spectroscopy as the interconverting species usually have different chemical shifts.

The changes in the relative areas of the reactants and products can be used to obtain information regarding the time course of the reaction. This is possible if the time scale of the conversion is slow with respect to the NMR time scale. Systems which interconvert very fast compared to the NMR data acquisition time are observed as a single, averaged single entity, while those exchanging at about the same time frame can be broadened out so that no direct signal is observed. J-coupling, also known as scalar coupling, causes splitting of NMR signals due to the interactions between different nuclei in the same molecule that iare mediated through electrons in chemical bonds [10] [11] [12].

Usually, the J-coupling interaction is observable between nuclei that are separated from each other by three or fewer bonds. If the coupling is weak the resulting pattern is a function of the number of neighboring nuclei, and this information plays a critical role in structural elucidation of small organic molecules.

Proton nuclear magnetic resonance

In addition, the magnitude of the line-splitting coupling constant provides information regarding the molecular conformation. In addition, the relative intensities of the peaks within a multiplet is given by the coefficients of the binomial expansion. In this case the pairs of nuclei that have observable J-coupling are separated by three bonds. Note that interactions between magnetically equivalent nuclei, such as interactions between the different protons of the same methyl group separated by only two bonds , need not be considered when predicting the multiplicity.

In this example the three protons in the methyl group are treated as magnetically equivalent and the two protons in the methylene group are treated as magnetically equivalent by assuming that free rotation occurs about the single bond separating the methyl and methylene groups. If this is not the case, e.

If this is not the case, then the multiplet structure can still be predicted by considering first the coupling to one set of equivalent J-coupled nuclei and predicting that the effect of the remaining nuclei will cause additional splitting of the multiplet generated by interaction with the first set.

The magnitude of the J-coupling depends on the number of bonds separating the interacting nuclei as well as on the geometry. For 3 J coupling, i. The values of A,B and C depend on the chemical nature of the fragment. The Karplus equation is useful for conformational analysis of molecules, particurly biopolymers such as polypeptides [13] and nucleic acids. The parameters A,B and C of the Karplus equation have been determined for most combinations of nuclei that occur in organic compounds, by comparing experimental NMR and X-ray crystallographic data.

If relevant experiment data is not available the magnitude of the J coupling may be calculated by using quantum chemical calculations [14] ; however the prediction accuracy of ab initio calculations is often lower than that obtained from empirical parametrization. In the presence of an external magnetic field B , the distribution of the number of nuclei in the different allowed nuclear spin states follows the Boltzmann distribution at equilibrium.

However, since the energy difference between these two states is small the population difference is quite small and the macroscopically observable net magnetization vector for the entire population will be the vectorial sum of the magnetic moments of all the nuclei present in the sample. At equilibrium, in a homogeneous magnetic field, although the orientation of the spin magnetic moments of individual nuclei is restricted to certain directions with respect to the applied magnetic field which usually defines the z axis , there is no preference for any direction for the projection of the magnetic moment onto the x-y plane.

The X- and Y-components of the net magnetization vector of the sample should be zero at equilibrium because the X- and Y-components of the spin magnetic moments of individual nuclei are randomly oriented and the net magnetization vector is the vectorial sum of the spin magnetic moments of individual nuclei. Therefore, the equilibrium magnetization will be. However, there are more nuclei in the lower energy state at the temperature of the experiment T, hence the numerator in the sum above is nonzero.

Therefore, at equilibrium, the net magnetization vector has only one non-zero component the M z , e q u i l -component when the system is placed in a static homogeneous magnetic field. In the presence of homogeneous magnetic field possibly time dependent , represented by the vector B , the magnetization vector experiences a torque and the time dependence of the net magnetization vector M neglecting relaxation effects is.

The Bloch equations describe the time dependence of the different components of the net magnetization vector subject to relaxation, in the presence of a time dependent magnetic field. After a collection of nuclei in a magnetic field that is at equilibrium with its surroundings is perturbed in some manner usually by a pulse of electromagnetic radiation the system requires a certain amount of the time to return to equilibrium. If this process is exponential, the rate constant is called relaxation rate. The relaxation rate is inversely proportional to relaxation time [15] [16] [17].

T1 relaxation time characterizes the return to equilibrium of the longitudinal component of the magnetization of the collection of nuclei. Similarly, T2 relaxation time characterizes the return to equilibrium of the transverse component of the magnetization of the collection of nuclei that are being studied. In a static homogeneous magnetic field, the transverse component of the net magnetization vector for a sufficiently large collection of nuclei is always zero, at equilibrium.

The dominant mechanism of relaxation is usually the dipolar interaction with the closest neighbor. For a pair of identical spins separated by a distance r , in a homogeneous magnetic field, undergoing isotropic rotational motion in solution, the relaxation rates are:.

For a pair of nonidentical spins I and S, separated by a distance r, the time dependence of the expectation values of the z-components of magnetization are given by the Solomon equations:. A homogeneous magnetic field, isotropic rotational motion and negligible chemical shift anisotropy are assumed in the derivation of the equations described above.

NMR - Interpretation

Irradiation at the resonance frequency of one nucleus in the molecule may cause changes in the intensity of a signal at a different frequency corresponding to another nucleus - this is called the Nuclear Overhauser effect [18] Noe. The Nuclear Overhauser effect is due to dipole-dipole interactions between the magnetic moments of a pair of nuclei. Unlike J-coupling, this interaction is not mediated through bonds.

Hence, it may be possible to observe the Nuclear Overhauser effect between pairs of nuclei separated by many bonds provided that they are in spatial proximity. The strength of the observable Nuclear Overhauser effect for molecules in solution is proportional to the inverse of the sixth power of the distance between the two nuclei due to averaging caused by rotational motion.

Both the magnitude as well as the sign of the Nuclear Overhauser effect depend on the rotational frequencies of the pair of nuclei with respect to the applied magnetic field. This happens for rigid molecules with relative molecular mass about at room temperature e. For most molecules in isotropic media, at room temperature direct observation of dipolar coupling in solution NMR spectra as a separation of the components of a signal is not possible, because dipolar interactions are averaged over all orientations of the molecule.

However, it is possible to obtain partial alignment of macromolecules using anisotropic media, leading to incomplete averaging of the dipolar interactions - in such cases there is an 'apparent' change in the measured values of J-coupling constants because the residual dipolar coupling has the same form as the weak scalar coupling Hamiltonian. For a pair of nuclei, at a fixed distance, the magnitude and signs of the residual dipolar couplings are angle dependent.

Hence, measurements of residual dipolar couplings RDC can be used to obtain angular constraints used for structure determination. For any system at equilibrium in the absence of a magnetic field, all the nuclear spin states are equally populated and hence there is no net polarization due to the nuclear spins. Therefore, it is necessary to introduce an external magnetic field which leads to preferential population of the lower energy nuclear spin states.

The energy differences between the different nuclear spin states are proportional to the strength of the magnetic field. Therefore, higher magnetic fields lead to greater separation between the energy levels and greater polarization at equilibrium. The required magnetic field is usually provided by an external magnet.

High magnetic fields 1 Tesla to 17 Tesla are generally preferred for high resolution, high sensitivity NMR spectroscopic experiments.

NMR Spectroscopy

In general, higher magnetic fields provide higher signal to noise ratio as well as higher resolution. Most high resolution NMR spectrometers used by chemists and biologists use superconducting magnets. However, NMR spectrometers with lower resolution may use permanent magnets or electromagnets. It is also feasible to carry out certain types of NMR experiments in much weaker fields - in fact many NMR spectroscopic experiments have been conducted using the earth's Magnetic field.


The probe in an NMR spectrometer is responsible for coupling the radio frequency electromagnetic field generated by the RF electronics to the sample. It is also responsible for detecting the NMR signal through induction and passing it to the receiver. Transmitter subsystem: The transmitter subsystem is responsible for generating a radio frequency signal in the form of a sequence of pulses with specified frequency , amplitude , phase and duration for each pulse. It consists of the RF synthesizers and amplifiers. The most common modes of recording 13 C spectra are proton-noise decoupling also known as noise, proton, or broadband decoupling , off-resonance decoupling, and gated decoupling. The rapid changes in proton spin create an effective heteronuclear decoupling, increasing carbon signal strength on account of the nuclear Overhauser effect NOE and simplifying the spectrum so that each nonequivalent carbon produces a singlet peak.

The relative intensities are unreliable because some carbons have a larger spin-lattice relaxation time and others have weaker NOE enhancement. In gated decoupling, the noise decoupler is gated on early in the free induction delay but gated off for the pulse delay. This largely prevents NOE enhancement, allowing the strength of individual 13 C peaks to be meaningfully compared by integration, at a cost of half to two-thirds of the overall sensitivity. This retains couplings between protons immediately adjacent to 13 C atoms but most often removes the others, allowing narrow multiplets to be visualized with one extra peak per bound proton unless bound methylene protons are nonequivalent, in which case a pair of doublets may be observed.

Distortionless enhancement by polarization transfer DEPT [7] is a NMR method used for determining the presence of primary, secondary and tertiary carbon atoms. Signals from quaternary carbons and other carbons with no attached protons are always absent due to the lack of attached protons. The polarization transfer from 1 H to 13 C has the secondary advantage of increasing the sensitivity over the normal 13 C spectrum which has a modest enhancement from the nuclear overhauser effect NOE due to the 1 H decoupling.

Another useful way of determining how many protons a carbon in a molecule is bonded to is to use an attached proton test APT , which distinguishes between carbon atoms with even or odd number of attached hydrogens. A proper spin-echo sequence is able to distinguish between S, I 2 S and I 1 S, I 3 S spin systems: the first will appear as positive peaks in the spectrum, while the latter as negative peaks pointing downwards , while retaining relative simplicity in the spectrum since it is still broadband proton decoupled.

Even though this technique does not distinguish fully between CH n groups, it is so easy and reliable that it is frequently employed as a first attempt to assign peaks in the spectrum and elucidate the structure. It is, however, sometimes possible that a CH and CH 2 signal have coincidentally equivalent chemical shifts resulting in annulment in the APT spectrum due to the opposite phases.

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