1. Introduction 

NMR stands for Nuclear Magnetic Resonance which involves the interaction between an oscillating magnetic field of electromagnetic radiation and the magnetic energy of any nucleus which are placed in an external static magnetic field. This is the most powerful tool available for structural determination. A nucleus with an odd number of protons, an odd number of neutrons, or both, has a nuclear spin that can be observed by the NMR spectrometer. The NMR active nuclei include: 1H, 13C, 15N, 19F, and 31P which have nuclear spin of ½. Carbon exists in three isotopic forms:

As per the information given in above table, the most common isotope of carbon is carbon-12 (12C) and the next heaviest carbon isotope is carbon-13 (13C). The 12C and 13C are called stable isotopes since they do not decay into other forms or elements over a period of time. The highly abundant isotopes of carbon i.e. 12C is NMR inactive because it has net zero nuclear spin (I = 0). The NMR spectrum of 1H NMR and 13C NMR are different, however the theoretical background is exactly the same. The different in spectrum is attributed to difference in their natural abundance and gyromagnetic ratio. The natural abundance of 13C, an NMR active nucleus is only 1.11% than that of 12C. Also its sensitivity is only about 1.6% than that of 1H. This shows that the overall sensitivity of 13C absorption is very very less in comparison to the 1H. With such a low sensitivity, 13C gives very weak signal. To overcome the problem of weak signal, 13C NMR requires:

? Continuous wave

? Slow scan technique

? Large sample quantity and

? Long scan time.

The gyromagnetic ratio and resonance frequency of 13C is about one fourth of the 1H. Hence, the nuclear magnetic resonance of 13C in the magnetic field of 14,092 gauss is four times less than it is observed for 1H. For example, in 13C it is observed at 15.1 MHz, while for proton it is observed at 60 MHz in the same applied magnetic field. Some other related values are given in table below. 

The 13C –NMR spectrum helps us by giving following information’s: a) The number of signals gives information about the number of equivalent carbons. The presence of less number of signals than the total number of carbons present in the molecule, signify that in the molecule, there is at least one pair of equivalent carbons. b) The position of chemical shift gives information about the environment of carbon atom. c) The integration of peak gives the ratios of equivalent carbons. d) The 13C-NMR splitting is limited to nuclei separated by just one sigma (?) bond. This suggests that the hydrogen(s) directly attached to carbons also plays role in splitting patters. There are only 5 splitting patterns in 13C –NMR (Figure 1 & 2): 

2. Resolution and multiplicity of 13C NMR

Resolution is the clarity with which a spectrum appears. The chemical shift difference in the 13C spectrum is about 20 times in comparison to those shown by 1H NMR spectrum. The 13C spectrum is much simpler and is highly resolved. For example, each of seven lines in the 13C spectrum in figure 3 represents one carbon atom of 1-methyl-3- nitrobenzene. This spectrum is simpler than its 1H NMR spectrum.

The spin number of both 13C and 1H nuclei is ½, so that one can expect the coupling in the spectrum taking place between same nuclei and different nuclei: (i) 13C ? 13C and (ii) 13C ? 1H The probability of the first case is very low because of very less natural abundance i.e. of only 1.11% of 13C. However these couplings make the 13C spectrum extremely complex. These couplings need to be removed by decoupling.

3 Coupling and Decoupling in 13C NMR

3.1 Decoupling in 13C NMR NMR

decoupling is a method used to analyze a sample which is irradiated at a certain frequency or frequency range to eliminate fully or partially the effect of coupling between certain NMR active nuclei. The decoupling for 13C NMR is: (i) Proton-noise decoupling (ii) Off- resonance decoupling (iii) Gated decoupling 

(i) Proton-Noise Decoupling

The proton-noise decoupling is also known by noise decoupling or proton decoupling or broadband decoupling. This is the most common mode of operation. This is an example of heteronuclear decoupling. In this method of sample analysis all the protons present in the sample are decoupled from the carbons. This is done by irradiation of the sample with a noise decoupler at the 1H frequency, while observing the spectrum at the 13C frequency. Due to the strong radiation in the range of all the proton frequencies in the sample, the protons change their spin states too rapidly and are effectively decoupled from the carbons. The proton-noise decoupling simplifies the 13C spectrum and increases the intensities of signals. Thus, the carbon atoms bearing no proton exhibit low intensity peaks, whereas intensity increases with increase in number of hydrogen. A proton-noise decoupled 13C NMR spectrum exhibits a single sharp peak for each kind of chemically nonequivalent carbon atom present in a molecule (Figure 4). In this spectrum, the heights of peaks are not proportional to the number of carbon atoms causing them. Some peaks appear larger than the others even though each may be due to a single carbon (Figure 3). This may occur due to the following reasons:

•  Carbon atoms with large spin-lattice relaxation time may not completely return to a Boltzmann’s distribution between pulses. Due to this, the resulting signal is considerably weaker than expected from the number of carbon atoms causing those signals.
• Some carbon atoms give rise to exceptionally small signals due to weak NOE enhancement. Hence, wrong relative intensities of the signal depend on the mode of spectrometer operation. 

(ii) Off-Resonance Decoupling

The off-resonance decoupling is only applicable to the protons (or hydrogens) directly attached to 13C atom. In other words, the couplings due to 13C-H coupling are only observed. The other couplings like 13C-C-H, 13C-C-C-H etc. are removed or not observed. In this mode of decoupling, 13C signals are split into a multiplet consisting of “n+1” component peaks, where n is the number of protons directly attached to 13C atom (Figure 1 & 2). For example,

a) The methyl carbon atoms (CH3-) appear as a quartet (3+1 = 4). Here, three hydrogens are attached with carbon, hence n = 3.

b) The methylene carbon atoms (-CH2-) appear as triplet (2+1 = 3). Here, two hydrogens are attached with carbon, hence n = 2. In this case, a pair of doublets may also obtained if the protons are not equivalent and their coupling constant are sufficiently different.

c) The methine carbon atoms (>CH-) appear as doublet (1+1 = 2). Here, one hydrogen is attached with carbon, hence n = 1.  

d) The quaternary carbon atoms (>C<) appear as singlet (0+1 = 1). Here, no hydrogen is attached with carbon, hence n = 0.

A typical off-resonance decoupled 13C NMR spectrum of 1,2,2-trichloropropane is given in figure 5. The information regarding the number of CH3-, -CH2- and –CH- groups present in a molecule, one can count protons. Also, this number is sometimes mislead; as the number of protons obtained from the off-resonance decoupled 13C NMR does not tally with the molecular formula. This is possible in case of compounds containing two or more equivalent carbons bearing protons. In the off-resonance decoupled 13C NMR spectrum of 1,2,2-trichloropropane (Figure 5), peak 1 is for -CH2- group. Here, two protons are attached with carbon, hence it exists as triplet. Peak 2 is for quaternary carbon atom and appears as singlet as there is no hydrogen is attached with it. Similarly, peak 3 is for –CH3 group. Here, three protons are attached with carbon, hence it exists as quartet. The method of off-resonance decoupling is achieved by irradiating the sample at a frequency near to the resonance frequency of protons but not coinciding with it. Due to this, residual couplings beyond one proton directly bonded to 13C atoms are retained, while couplings beyond one bond are usually removed. This removal simplifies the spectrum. 

Figure 5. Off-resonance decoupled 13C NMR spectrum of 1,2,2-trichloropropane

In another example, the off-resonance decoupled 13C NMR spectrum of 1-propanol (Figure 6), the methyl carbon atom having three protons attached is split into a quartet and each of the methylene carbons appears as a triplet as they are attached with two protons each. We can see that the observed multiplet patterns are in accordance with the “n+1” rule. The solvent peak appeared at 77 ppm and TMS at 0 ppm. 

(iii) Gated Decoupling The gated decoupling in 13C NMR gives information about the number of carbon atoms present in any molecule. In this mode of operation, the area under each peak is directly proportional to the number of carbon atoms causing that peak. The integration of the area under each peak gives the relative number of carbon atoms represented by each peak. The major disadvantage with this mode of 13C NMR recording is that this is more time taking and requires large amount of samples.

3.2 Coupling in 13C NMR

(1) Deuterium coupling The NMR recording requires deuterated solvents to dissolve the sample whose NMR is to be recorded. Deuterium is the 2H isotope of hydrogen. In 13C NMR, the deuterated solvents are frequently seen as part of the spectrum as they all contain carbon atom(s) (Table 1). There is a heteronuclear coupling of carbon and deuterium. Deuterium couple with 13C with the multiplicity formula: 2nI+1, where n is the number of deuterium and I is spin number of Deuterium. The molecule with one deuterium atom like CDCl3 gives 1:1:1 triplet at about 77 ppm whereas the molecule like CD3COCD3 gives seven line i.e. septet (1:3:6:7:6:3:1) at about 30 ppm and carbonyl at 206 ppm. The 13C chemical shift values of some common NMR solvents are given in table 1.

(2) Fluorine coupling Fluorine with mass number 19 (19F) has 100% abundance. It has a spin of ½. The gyromagnetic ratio of 19F is almost equal to protons hence it's almost as sensitive as proton. Hence, for recording the 19F spectra, no major modification is required in NMR instrument to work from 1H to 19F. Only, adjustment of proper radiofrequency source is required like 56.46 MHz at 1.1T. The 13C spectra are not 19F decoupled; the fluorine couplings appear in 13C NMR spectra. The couplings range for 19F is given below: 1 JC-F = 245 Hz; 2 JC-F = 21; 3 JC-F = 8; 4 JC-F = 3 The size of a heteronuclear coupling is proportional to the product of their gyromagnetic ratios, so fluorine behaves very similarly to proton (e.g., carbon-fluorine and carbon-proton couplings are similar in size).

In a typical example, 13C proton-decoupled spectrum of CF3CH2OH in CDCl3 at 75 MHz (Figure 7), suppose a quartet is observed around 120 ppm, the one-bond C-F coupling constant (1 JC-F) is 228.6 Hz by taking the two middle signals observed at 122.63 and 126.11 ppm. The coupling constant is calculated as: 126.11 – 122.63 = 3.48 ? 75 = 228.6 Hz Similarly, the second quartet which is observed due to more than one bond appeared around 60 ppm shows coupling constant of 30 Hz by taking the middle peaks at 61.02 and 61.42 ppm.

(3) Phosphorus coupling Phosphorus with mass number 31 (31F) has 100% abundance. It has a spin of ½. In comparison to 1H- or 13C-NMR spectroscopy, the coupling constants in 31P-NMR spectroscopy are generally larger in magnitude. The coupling is mainly through the ?- bonds of the molecular backbone. The coupling of phosphorus (P) to carbon (C) follows the general trends and rules observed with other nuclei. The value of n JP-C is mainly dependent on the coordination number of the phosphorus and its oxidation state. The value of n, stereochemical disposition of coupling nuclei and electronegativity of substituents on phosphorus also plays an important role in the coupling with 31P. 

In a typical example, 13C proton-decoupled spectrum of CH3PO(OCH3)2 in CDCl3 at 75 MHz (Figure 8), suppose two doublets are observed around 11 and 55 ppm. For the quartet observed around 11 ppm, the one-bond C-P coupling constant (1 JC-P) for P-CH3 is 122.3 Hz by taking the two middle signals observed at 10.63 and 9.00 ppm. The coupling constant is calculated as: 10.63 – 9.00 = 1.63 ? 75 = 122.3 Hz Similarly, the second doublet which is observed due to two-bond coupling P-OCH3 appeared around 52 ppm shows coupling constant of 9 Hz by taking the middle peaks at 52.41 and 52.42 ppm. A list of coupling constant for 13C NMR is given in table 2.

Table 2. Coupling constant for 13C NMR

4. NOE signal enhancement

The decoupling usually interferes with relaxation time and shortens the relaxation time. At this time the concept of nuclear overhauser effect (NOE) operates and helps in the signal enhancement of related 13C NMR peaks. The line intensities or heights in the usual 13C spectra are not equal due to the relaxation effects. It has been observed that the major relaxation for a 13C nucleus is due to the dipolar transfer of its excitation energy to the proton(s) directly attached to it. Hence, NOE signal enhancement is observed mainly for CH3, CH2 and CH carbons. This type of enhancement has not been observed for quaternary carbons. This also helps in inferring the presence of quaternary carbon in any 13C NMR spectra because these carbons show low-intensity signals. The NOE effect is heteronuclear in this case as this works between two dissimilar atoms such as carbon and hydrogen.