Introduction

NMR spectroscopy is a technique used most frequently for verification or structure determination of medium sized and small bio and organic molecules. There are two parameters that majorly determine NMR spectra’s quality: resolution and sensitivity.  In the last few decades, many advances of significance have been achieved in the sensitivity enhancement field. With the usage of higher magnetic fields, small volume tubes (Grimes and O’Connell, 2011), improvement in electronics and particularly of cooled probes done cryogenically; there has been increase of sensitivity by greater than one magnitude order. Contrastingly,  the improvement of basic resolution that can only be done by the usage of higher magnetic fields, has had the increase by around a factor of 2 when highest magnetic fields have been compared with that having the availability today than with the ones two decades ago. Thus, the need is there for techniques in improving the NMR spectra resolution, especially for ¹H NMR.

The characteristics of proton spectra have been rather poor dispersion of signal. This has been the result from a conjunction of shift range (_10–15 ppm) in relation to limited chemical and extensively done signal spitting because of scalar coupling of proton–proton. When there can be obtainment of structural information that is very useful potentially from the derived coupling constants and multiplicity, there is overlapping of heavy signal preventing this information’s extraction (Molinski, 2010). The resultant condition of the scalar coupling is the presence of signal overlapping in virtually all ¹H NMR spectra, which also include the small molecules. Contrasting to the proton NMR, at natural isotopic abundance, ¹³C NMR spectra, for instance have shown much superior separation of signal, as there is presence of only singlets. Homonuclear ¹³C–¹³C couplings have been hidden typically in the noise, and due to ¹³C nuclei of low percentage (_1.1%), and scalar coupling to ¹H have been suppressible easily by the decoupling sequences of the heteronuclear broadband.

The ¹H NMR spectra resolution can be enhanced significantly if there can be conversions of all signals to singlets. This forms the pure shift NMR’s aim, also known as ‘‘homonuclear broadband decoupling’’ or the ‘‘chemical shift spectra’’. The ¹³C NMR spectra’s analogy helps pure shifting of ¹H spectra that have been featuring molecules which are highly deuterated. For instance, in the Fig. 1a 99% deuterated glucose of ¹H NMR spectrum has been shown. As there is likelihood for the residual ¹H nucleus being surrounded by deuterium spins only, ¹H–¹H coupling are, thus, been removed. There is much smaller size of the couplings to deuterium and thus in this spectrum there is no visibility (Kovacs et al., 2005). Deuteration has been leading to the significantly downgrading of the signal-to-noise ratio.  

The signal intensities’ variation are mostly determined by different levels of deuteration at various sites, and changes of chemical shift in relation to the protonated glucose are the causation of the secondary isotope effect of deuterium. In a converse way, there is presence of homonuclear ¹³C–¹³C scalar coupling in ¹³C-enriched molecules of carbon spectra as shown in Fig. 1d. The way to pure shift spectra in terms of deuteration has not been feasible for most technical and/or economic reasons in most cases.

The resolution’s reduction in the proton NMR spectra’s conventional form because of overlapping among scalar-coupled multiplets has more severity at magnetic fields in the lower level. Therefore, proton spectra are fully proton-decoupled and its desirability have been notable in the NMR’s early days. There is no possibility of using decoupling sequences of conventional broadband in removing homonuclear scalar couplings because the polarization would be destroyed and disallowing the observation of the decoupled nuclei (Shaka and Keeler, 1987). Thus, another 13 years was taken till the first method in relation to indirect obtainment of the presentation of the fully-decoupled NMR spectrum was tabled by Ernst and co-workers. With the use of specially created 2D J-resolved spectra projections, there is invisibility of the scalar couplings. The results of the broad lines, because of the necessary use of magnitude-mode calculation, can be compensated partially. There have been several methods that followed through the decades offering various strategies to obtain NMR spectra that are broadband decoupled and fully homonuclear.

However, techniques like these can be applied to the NMR spectra of two dimensional natures in terms of indirect dimension. They require data processing of complicated nature and in some significant reduction of sensitivity takes place in comparison to the regular spectra. In addition, multidimensional NMR’s progress and magnetic fields that are ever increasing has availability to provide relief somewhat in overcoming the proton NMR spectra’s limited resolution. 

In the recent decades, there has been several experiments related to the homonuclear broadband-decoupled innovations which in part has been driven by path breaking work conducted by Morris and coworkers (Aguilar et al., 2012). These have been on the basis of works done earlier leading to pure shift experiments which are fully decoupled and much easier in its usage. There is applicability of these generally with high increase of its sensitivity.  The pure shift spectra like these of the generation are usable finally as routine experiments of NMR.  A resolution advantage’s example related to the pure shift spectra have been shown in the Fig. 2.

In the strychnine mixture’s 1D ¹H spectrum and the degradation product being unknown, the strychnine’s two H-15a signals and its form of degradation at 1.36 ppm, separable by 4 Hz at 500 MHz only, show multiplets in both width of signal of _24 Hz because of scalar coupling. In the spectrum of pure shift, there clear separation of the two signals. For a proton spectrum that is coupled and regular, an increase of six fold in the strength of magnetic field (to 3 GHz or greater to the least) will have necessity for separating those signals. 

The NMR experiments’ pure shift generally has the usage of elements of pulse sequence refocusing selectively the evolution’s effects under the couplings. Zangger and Sterk (ZS) suggested an elegant method using the frequency selective and spatially 1801pulse, and bilinear rotation decoupling (BIRD) method exploiting the sparse heteronuclei and one-bond couplings for refocusing on all but geminal couplings, which currently are a couple of J-refocusing elements used most commonly in pure NMR shift. These approaches can be obtained from HSQC, 2D J spectroscopy, NOESY, and TOCSY in the 2D experiments; along with DOSY and 1D NMR (Bruschweiler et al., 1987). It is unfortunate that the incurring of the ZS method is associated with penalty of very large sensitivity when there is shift difference in the chemicals between resonances for decoupling to be small as signals then will require originating from a sample’s small fraction that is corresponding. The use of BIRD largely usable with protons bonded directly at natural abundance to 13C. This generally gives a minimal sensitivity penalty of the magnitude’s two orders.

In the recent times, the sequence element of pure and new shift pulse, PSYCHE (Pure Shift Yielded by Chirp Excitation) has had the introduction relying on the spin populations’ statistical separation by using the swept-frequency chirp pulses with low flip angle. The offerings of PSYCHE with respect to magnitude improvement order in performance over the methods existing been demonstrated for 2D ¹H–¹H TOCSY and 1D ¹H NMR. In the current time, BASHD (band-selective homodecoupling) methods are the PSYCHE’s only competitors in sensitivity terms, although these cease to be the broadband and only the spectrum’s decoupling part.

The NMR’s pure shift can facilitate greatly the crowded spectra assignment. This is accomplished by eliminating or hiding the structure of homonuclear multiplet and bonding. The multiplet structure can be an annoyance in the crowded 1D spectra because it reduces and cannot be disentangled. Where there cannot be any reliable recovery of the multiplet structure, it can be made available by the coupling constant which may have high usefulness (McCoy and Mueller, 1992). The case that would be ideal is an experiment producing spectrum’s pure shift and for each chemical site with a singlet. However, it makes multiplet structure of high resolution having availability in a second dimension.  

2D J (J-resolved) spectroscopy is one such experiment showing in F₂, normal coupled spectrum although in F₁, it has been coupling structure. In such experiments, the phase-twist line shape complicates matters severely extending to the extent of sacrificing majority of advantage pertaining to potential resolution of technique with the use severe value mode display and functions of time domain weighing (Mccoy and Mueller, 1993). The phase-twist lineshape’s projection at 45 degree in zero in frequency space, the generated pure shift spectra by2D J spectroscopy has the requirement of calculation of value mode and therefore has a resolution that is degraded and distorted intensities severely. 

Several attempts have been made in producing pure NMR spectra shift and extraction of multiplet structure absorption mode from 2D J spectra. This use manipulation of the combined data and the recognition of the pattern, pulse sequences modified, and approaches related to the data post processing. Thus far, the practical applications have not been reached by these and questions in relation to their sensitivity, suitability, and reliability for complex spin systems that have been without satisfactory responses or been unanswered.

The need is clear for 2D J method providing reliable and clean spectra and good sensitivity. Such method’s great strength has been that the resolution’s ideal limit is approached as F2’s multiplet structure is suppressible and F1’s line widths have closeness with natural line widths that are limiting, B_o have been refocused with respect to inhomogenity contributions. 

Pell and Keeler present till date the most successful method. They have shown that 2D J spectrum, the pure absorption mode, is obtainable with the use of element of ZS J-refocusing pulse in reversing the 2D J pulse sequence’s t1 evolution. The combination of reversed and normal datasets with the analogy of antiecho/echo processing in the experiments of 2D correlation has the allowance of phase-twist line shape’s dispersive components subject to cancellation and obtainment of absorption mode peaks. The entailing pertinent to loss of sensitivity in a significant way has been the usage of the ZS element. This has severity particularly in second-order spin systems, requiring the usage bandwidth that is very narrow and in ZS element, the highly selective pass (Carnevale et al., 2012). The unwanted responses are also given by such systems in F1 and thereby complicating analysis.    

There have been several methods in couplings’ selective measurement in 2D J experiments. This experiment uses either ZS method or band-selective

Pulses, but these approaches cease to be broadband and/or suffering from significant penalties of sensitivity. Cotte and Jeannerat, in recent years, have reported significantly increased sensitivity of a ZS experiment with the use of multi-slice irradiation’s selective pulse and the use of nemo ZS (non-equidistant phase modulation) in reducing the accidental recoupling chances. The recovered sensitivity, however, can be secured at the cost of enhanced experimental complexity and spectral artefacts.

The heteronuclear 2D NMR experiments that are proton detected have been on the basis of two separate pulse schemes known as HSQC (Heteronuclear Single Quantum Correlation) and HMQC (Heteronuclear Multiple Quantum Correlation). These have been the most important tools of NMR, where the biochemists and the chemists do provision of valuable structure on ¹H-¹⁵N and ¹H-¹³C chemical bonds. These experiments have the provision of information pertaining to dynamics, conformation, and structure of flexible and rigid molecules in solution (Hammarstroem and Otting, 1994). They can also be serving for several other interests such as RDCs (Residual Dipolar Couplings) which are measured or have been under intermolecular interactions’ determination. And along with it are also structural validation methods in molecules dissolving in weakly aligned media. In the recent times, the performance of experiments is usually with automation mode in both processing steps and acquisition of data, without intervention need of the direct user. The 2D maps that results have simplicity to analyze and interpreting, even for the NMR users who are non-experienced. They display typically with cross peaks that are well dispersed correlating with ¹³C and ¹H chemical shifts through transfer medium of ¹J^CH directly between attached groups ¹H-¹³C.

Band-selective and selective homonuclear decoupling

Following the discovery of the NMR’s scalar coupling, the techniques that come first as continuous wave to remove selectively is this signal splitting.  Bloom and Shoolery (1955), gave description of the effect pertinent to the second radiofrequency field perturbing on the fluorine spectra that are weakly scalar coupled, immediately following the double-irradiation experiment discussed first by Bloch.

There was later establishment of a theoretical formalism which is inclusive of strong coupled spin systems. There can also be introduction of selective homonuclear decoupling to dimensions of indirect nature of two- and multidimensional experiments (Mccoy and Mueller, 1993). The selective pulse, for this purpose, is subject to application in the t1time’s middle part. The evolving of the scalar coupling in the time of first half is t1/2, and in the second half has been refocused of the evolution time. The band selective pulses are also needed to be used instead of signal selective pulse in suppressing couplings from all spins in a range of frequency that is well defined.  For example, this is employable in decoupling all a-proteins in peptides’ 2D NMR spectra (21). In an alternative way, the signals can be decoupled with certain range of frequency from every signal in the outer surface of this region with the use of a conjunction of a non-selective and band selective 180_ pulse in the time of t1 evolution. The signals falling under the excitation bandwidth pertaining to the experience of selective pulse with a 360_ rotation gives rise to the spins of all other have been subject to inversion and thus been decoupled.  The decoupling which is band selective during the 2D experiments of indirect dimension is usable for both 13C homonuclear and proton decoupling. For reducing decoupling sidebands, there can be amplitude modulation of the pulses usable for decoupling in incorporating the composite decoupling sequences’ elements, such as GARP, WALTZ, and MLEV.  

The applicability of the homonuclear decoupling in the time of direct dimensions’ acquisition of FT NMR spectra have had more difficulty. Here, there is need of perturbing radiofrequency field needing for coordination with NMR data sampling. The alternation of decoupling field has been the stroboscopic fashion’s receiver. The selectivity of the 1H homodecoupling has been usable in a routine way in identifying the partners of individual coupling and/or for the simplification of partial spectral. Instead of single signal been decoupled, there is possibility of using multiply-selective pulses, obtainable with the addition of a number of selective pulses that are phase shifted. During the acquisition, such polychromatic decoupling is usable in simplifying a few signals selected in a spectrum although it retains the information pertaining to the scalar coupling for other peaks (Carnevale et al., 2012). The extension of homodecoupling concept in the time of acquisition that switches the decoupler between the two data points that have been acquired allows the implementation, during the acquisition, of the band-selective decoupling. The semi selective acquisition modulated (SESAM) decoupling has been described by Hammarstrom and Otting in 1994.  In the experiment of band-selective decoupling, the inversion pulse of band-selective G³ is been sliced to minute fragments applicable in the mode of time share where the decoupler and the receiver are subject to activation alternately. In other words, the band selective pulse is applicable similar to pulse cluster of amplitude-modulated DANTE. During the acquisition, band selective decoupling is been a method very useful heteronuclear RDCs (residual dipolar couplings) are been measured.

The biomolecular sample’s partial orientation has also been leading to severe 1H line that broadens because of the homonuclear proton RDCs been unresolved. By the aliphatic protons’ band-selective homonuclear decoupling, the contributions which are line broadening to amide protons may be subjected to reduction significantly.

Molecules’ (isotopically enriched) ¹³C–¹³C decoupling

The ¹³C NMR spectra, at natural abundance, have not shown any homonuclear coupling usually as the lower percentage of ¹³C. Nonetheless, there are ¹³C–¹³C scalar coupling constants that are fairly large one-bond in ¹³C-enriched molecules of approximately _35–55 Hz. Because of the relative uniformity of multiplicity of various carbon nuclei and coupling constants, there is common use of constant-time decoupling in the multidimensional spectra belonging to the indirect dimension (33).  In the recent years, the experiments that is ¹³C-detected directly have indicated to be offering several biomolecular NMR’s advantages (Felli and Pierattelli, 2014). There is particular usefulness of these experiments when there is heavy overlapping of the proton signals as in proteins of intrinsic disorder. This can be very broad as well in the presence of pragmatic center in the chemical or molecule exchange.

The ¹³C detection, in perdeuterated proteins, has been only possible in directly observing non-exchangeable nuclei. Because of the big ¹³C–¹³C couplings of one bond, the results has been the experiments detecting ¹³C needing to be subject to decoupling in the carbon dimension’s direct acquisition and making best of the carbon signal’s direct acquisition. The methods usable for the labeled biomolecules’ decoupling pertain to the groups of three separate approaches: spin-state-selective decoupling, band-selective decoupling, and maximum entropy deconvolution.   

Maximum deconvolution of entropy

The consideration of an NMR spectrum can be pertinent to the actual frequency spectrum’s (purely shift spectrum with infinite lines of narrow sizes) convolution with a function that is blurring and corresponds to the physical or instrumental line with split signals describing the function and broadened by scalar coupling. The MEM (maximum entropy method) is usable to deconvulate a coupled spectrum if certain information regarding coupled signals is available.  In case there is no availability of any information regarding coupling constants, there can be variation in a deconvolution of two dimensional forms. The use of maximum entropy deconvolution has been on certain occasions for experiments of ¹³C-detected decoupling, where it is expected of known ¹³C–¹³C coupling constants with doublets.

The deconvolution of maximum entropy gets benefitted from the narrowly formed range of carbon coupling constants to one bond carbon and thus, does uniform patterns of the multiplet. Additionally, the final step of refocusing may be subject to elimination as anti-phase doublets are also usable for maximum deconvolution of entropy. The working of this method was especially well for C-detected experiments. Here, the only one thing which must be removed is the coupling to Ca (Hoch and Stern, 2002). However, the patterns of coupling, often overlapped, and complicated with coupling constants of varying degree has presence in ¹H NMR spectra that has impossibility of being successfully analyzed by MEM.

¹³C-decoupling – Band selective

In the time of acquisition, ¹³C-decoupling that is band selective are usable on nucleic acids and proteins conveniently as certain carbon signal types preferentially found in distinguishing spectral region. For proteins, methyl carbons, Ca, C_aromatic, and C’ are usable in decoupling band selectively. Even, there is possibility of better signal for RNA, C⁵’, C²’-C³’, C⁴’, C¹’, C5 ^{(U, C)} are distinguishable (Richter et al., 2010).  

During the acquisition, band selective decoupling is implementable in the method of Hammarstrom–Otting with the use of adiabatic decoupling pulses that is band selective interleaving with the acquisition of data point. The resultant band selective pulses looking like DANTE are generally embedded in a super cycle of decoupling, in the form of p5m4 in reducing artifacts of decoupling.  If a number of separate regions have the need of decoupling, band selective pulses, double or triple, are usable. This has necessity when the experiments of ¹³C–¹³C TOCSY have the need of decoupling (Vogeli et al., 2005). It is notable that during the band selective pulse application, there cannot be any acquiring of the data point leading to decrease of signal-to-noise ratio in the spectrum of decoupling.  The band selective decoupling, as an example, include an experiment of ¹³C-detected, a spectrum of 2D ¹³C–¹³C COCAMQ in relation to superoxide dismutase of protein superoxide as indicated in Fig. 3. In regular spectrum, for all signals doublets are found, while Ca-protons decoupling during carbonyl carbons collapses’ detection have been with the doublets singlets as shown in Fig. 3.

¹³C decoupling – spin-state selective

This approach is the one that is used most often to homonuclear decoupling in the experiments of ¹³C-detected with respect to the acquisition dimension on the basis of methods of spin state selective (Ottiger et al., 1998).  The linear combination is used by it of anti phase and in phase signals, a method called IPAP, or single quantum coherences’ direct excitation as in spin state selective excitation (S3E). For homonuclear decoupling of experiments of ¹³C-detected, the techniques of spin state selective have been on the review of biomolecules. The experiments performed at natural abundance on small molecules, although being similar to the decoupling techniques of the state spin selective are usable on ¹³C-labeled biomolecules has been INADEQUATE-CR (57). The experiment predating IPAP ¹³C-decoupling, the coherence of double-quantum convertible to two separate subspectra containing only the doublet’s right or left component. The datasets merged do delivering homodecoupled INADEQUATE spectrum.

The techniques usable for ¹³C-detected spectra’s homonuclear decoupling rely entirely on the coupling patterns and J values’ presence or may be usable only band selectively and requiring the separation of spectral of coupling partners. The decoupled spectra that is band selective cease to be a spectra that is strictly pure, as all resonances are not decoupled and neither spin state selective method nor maximum entropy deconvolution are usable for nuclei showing an array of multiplet patterns and coupling constants. This has been the case for proton NMR, suffering from the spectral crowding most which has been caused by scalar coupling. 

¹H NMR experiments – pure shift

While band selective and selective proton spectra’s homonuclear decoupling are usable for a long period of time, there is no possibility of achieving whole spectrum’s broadband decoupling with these methods or the application of the decoupling sequences of  heteronuclear broadband in the homonuclear case. There are several methods to obtain pure shift spectra not usable in real time. They can be implemented most easily for _x1-decoupling of spectra which is two or multidimensional or is usable in obtaining a decoupled spectrum by processing that is sophisticated of special 2D spectra. Generally, all decoupling that is homonuclear broadband works well with techniques for weakly coupled protons. However, they also lead to the risen artifacts when strong coupling occurs. In systems that are strongly coupled, the scalar coupling behavior and the chemical shift cannot be separated completely by any method. However, certain techniques that are available have been more robust for strong coupling compared to others. Certain techniques in achieving pure shift spectra are employable for the acquisition domain’s decoupling either via real time decoupling which is interrupted acquisition or via data chunking which is individual pieces’ concatenation.    

Decoupling methods – homonuclear broadband

There are various different physical principles exploitable in achieving broadband homonuclear decoupling. Many implementations of theirs are describable in chronological order of the report published first as below.

4.1.1. Experiments – 2D J-resolved

The report of Ernst and co-workers published in 1976 took the first route of experiment to the decoupled proton spectra of homonuclear broadband (6). During those period it has been known already that spinecho amplitudes of weak coupling has not been affected with chemical shift, but with the evolution of scalar coupling. In the experiment of 2D J-resolved with 90_-t1/2-180_-t1/2-FID pulse sequence, only scalar coupling remains. However, there is no evolution of chemical shift in the time of t1 period although during detection both are active. The displaying of the resultant 2D spectrum does displaying tilted multiplets. Here, the multiplet’s component(s) of the low frequency in _x2 make its appearance in low frequency at _x1. A projection of 2D spectrum at 45 degree does yielding of 1D ¹H spectrum from where there is removal of scalar coupling. However, there is arising of problems due to the exhibition of 2D J-resolved spectrum complicating line shape (Nagayama et al., 1978).  

There is phase modulation of the signals as t1 function. Therefore, after Fourier transformation which are two dimensional in nature can be yielding a mixture of 2D dispersion and 2D absorption modes called ‘‘phase twist’’ lineshape. A projection of 45 degree of such a lineshape can be leading to canceling of the signal completely. Therefore, calculation of the absolute value mode related to the spectrum needing its usage before the projection of 45 degree. This can be leading to broad peaks with long tails in the resultant absolute value mode as shown in Fig. 4. There has been description of a number of approaches in circumventing this problem. Almost all additionally required software tools and these methods are needed for data analysis and implementation.

The FID’s dispersive components are suppressible with the creation of a pseudo-echo (Bax et al., 1981).  This has been on the basis of the observation in relation to the antisymmetric components yielding after Fourier transformation with the dispersive part are subjected to elimination from a function of time domain decaying in a symmetrical fashion on the mid point’s both sides. There can be creation of the a pseudo-echo from the FID with the multiplication of it first with e(t/T2⁄)  in removing the decay being induced by relaxation, and then its multiplication by a Gaussian in yielding the symmetrical pseudo-echo.

After projection of 45 degree of the 2D J-resolved spectrum, there can be appearance of isolated peaks in the mode of absorption but where there is overlapping of  the peaks where distortions remains. However, the resultant pure shift spectrum and its sensitivity have significant reduction since the FIDs first points are reduced severely in intensity.  The signals’ intensities, more importantly, in pseudo-echo processed spectra is dependent on both multiplet and linewidth structure, and thus, these spectra are not usable for a quantitative analysis.

As the phase-twist line-shape form is known, there is possibility for the individual peaks to be fitting with the ‘‘phase-twist mask’’ that are in synthetic form (Shaka et al., 1984). Once the intensities and the frequencies of all peaks being phasetwisted are determined, there is removal of the dispersive components from the spectrum with the use of this information with lineshapes and linewidths been assumed.  The pure absorptive spectrum that resulted from it may be usable for the projection of 45 degree in obtaining the pure shift spectrum. This is the way the cleaning up of the 2D J-resolved spectrum’s phase actually takes place. It is unfortunate that for practical applications these methods could not be proved to be useful.  

The sequence of 2D J-resolved pulse has been used by Freeman et al. where there is removal of dispersive components, although there complete change takes place in coupling pattern (Woodley and Freeman, 1994). The obtainment of such a spectrum can take place by different approach. The components of dispersive anti-phase, for instance, can be subject to purging by either an adiabatic pulse or a trim pulse. The signals’ appearance after 2D FT undergoes complications of greater magnitude as cancelled responses in regular 2D J-resolved spectrum have presence now and thus now four and not two are shown by doublet, peaking at its position at +/- J in _x1 and v +/- J/2 in _x2.   

These peaks’ projection would be delivering the identical pattern of multiplet observable in regular proton spectrum. These peaks’ special cross shape shapes them especially suitable for algorithms of special recognition.  Along the _x2 dimension, a search that is one dimensional is carried out where C4 symmetry patterns are located. Then the construction of synthetic spectrum uses the obtainment of chemical shifts. The peak positions in this artificial spectrum can be broadened artificially in rendering the appearance having similarity to experimental spectrum. Instead of the usage of purging pulse, the obtainment of identical spectrum with C₄ symmetry is possible by carrying out on a data set a hypercomplex Fourier-transformation from where the shifted scan of 90 degree phase in x1 has been subject to omission (Woodley and Freeman, 1994). A spectrum is again yielded where there is appearance of _x1 signals at +/- J that are screened by the algorithm of pattern recognition in constructing the artificially pure shift spectrum.  

In an alternative strategy of processing involving 2D J-resolved spectra, there can be creation of artificial pure shift spectrum from the data set of time domain not including any Fourier transformation by the FDM (filter diagonalization method) (Mandelshtam and Taylor, 1997). The time domain signal of two dimensional natures can have fittings to the function that describes the both dimension’s exponential decay with the use of parameters for width, frequency, phase, and amplitude. With the use of the parameters obtainable from a chemical shift, the calculation is done by spectrum only.

Another approach having promise in relation to the obtainment of pure shift spectra with the help of 2D J-resolved data’s special data processing has had the presentation recently by Martinez et al. (2012).  The obtainment of the symmetrical FIDs with back prediction of the data for the times – t1^max <= t1 < 0 with the algorithm of ALPESTRE. The data points subject to back calculation have been subjected to appending following experimental ones in obtaining a symmetrical FID that in the center has the lowest intensity. 

At the FID’s center, the data are needed to be enhanced that is achievable by sine-bell and apodization window function. This has resulted in the 2D spectra pure absorption with added benefits with which the identification of the strong coupling peaks can be done by their negative sign. Because of the sine-bell window function, there is reduction of the sensitivity. A processing scheme of similar nature having improved sensitivity is describable and has been done recently by Sakhaii and Bermel (2014). The FID’s right shifting has been used by them with the help of n points and with the n points back predicting is done in the gap that is newly formed from time 0 < t1 < n with increased intensity in the range of 0 and n. The echo-shaped FID results having in the center the maximum and leading to the improvement of the sensitivity of _6 in comparison to the standardized data processing with filtering of pseudo-echo.

In spite of all the laudable efforts to obtain from 2D J-resolved data the pure shift spectra, their reliance on data processing algorithms which are post acquisition and complicated and unreliable potentially having overlapping signals. Nonetheless, the pure shift spectra and its usage are obtainable from 2D J-resolved data. This approach is in all probability used most often, particularly for the compound mixture analysis, which can be in the form of metabolomic screenings (Brennan, 2014).

The NMR metabolomic studies, interestingly, is an absolute and simple processing of value mode of the usage of 2D J-resolved spectrum. Additionally, the gaining of the resolution involves the reduction the components’ intensity by spin-echo sequence for example proteins that has been done with fast T₂ relaxation. In the plasma samples that are untreated and especially the ones with underlying protein having undergone significant reduction allowing for 2D J-resolved spectra projections’ higher resolution outweighing the longer measurement times in comparison to, for example, the sequence of CPMG. However, from J-resolved spectra quantitative information, there has been the need of interpreting with caution as the intensities’ T₂ weighing which can be leading to the metabolite intensities’ variation in relation to their times of transverse relaxation.  By J-resolved experiment’s projection, homonuclear broadband decoupling has had the addition of 2D experiments such as DOSY or HSQC. These experiments yielding 3D spectrum involves J-resolved dimension which is usable in obtaining the dimension of pure shift acquisition. This has special importance in the DOSY experiments, where there is overlapping of the signal causing substantial difficulty for data analysis. Additionally, the dimension of J-resolved is being implemented in the experiment of 3D pure shift HMBC.

The keeping of the relaxation losses minimally requiring the evolution time of J-resolved accommodating  and the delay for magnetization generation’s heteronuclear antiphase. The J-resolved dimension’s absolute value mode is projected and tilted for affording the pure shift proton spectrum in 2D HMBC’s direct dimension. Because of the issues of sensitivity with other methods of homonuclear broadband decoupling, pure shift HMBC of no other are describable in the literature so far.  

4.1.2. Evolution of constant time

The method of constant time method for the decoupling of homonuclear broadband, which Bax and co-workers described first in 1979 is to an extent similar to the experiments to J-resolved. It is again the basic building block consisting of a sequence of a spin echo. However, the time after and before 180 degree pulse have variation between 2D experiment’s individual increments (Fig. 5) (Bax and Freeman, 1981).  The refocus of the 180 degree pulse has been for the evolution of chemical shift, although does not have any effect on the evolution of the scalar coupling. There is increase of t₁ within the 2D experiment, although T_d (constant-time delay) has not been subject to change. The 180 degree pulse has been at the T_d center, when t₁ = 0. Therefore, the evolution of net chemical shift does not take place during T_d. With the increase of t₁ the movement of 180 degree pulse takes place that is closer to the 90 degree pulse. The chemical shift _xI is for spin1, which is to spin S is a scalar coupled with JIS, the coupling constant in the presence of in-phase magnetization after T_d .

Although during T_d, there is evolution of scalar coupling, with respect to t₁, it is independent and ceases doing modulation and observing signal amplitude, contrasting to the evolution of chemical shift. Another constant-time evolution’s side effect that is there is no showing of the detected signal with any modulation as a t₁ functions by T₂ relaxation. This essentially means that T₂ relaxation effect has the visibility only in dimensions detected indirectly via a signal amplitude decrease rather than an increase in linewidth. In the dimension _x1 there can be obtainment of a pure shift spectrum having signals that are very sharp if there is acquiring of enough increments. However, the resultant signal decay in homogeneities magnetic field T₂ increases the linewidth. In broadening of the inhomogeneity, on modern NMR spectrometers, does not have significance and there can be expectation of the sharp signals in the indirect dimension. A problem that is more serious has been the remaining magnetization’s intensity by the T_d and scalar coupling constant(s).

The J coupling constants, for protons, and in the constant-time experiment, the intensities of the peaks can be varying considerably within a molecule. The in-phase magnetization is not left for some J values. There can be building of a 2D COSY experiment in accordance with the pulse sequence as shown in Fig. 5. The presence of anti-phase magnetization prior to the last 90 degree pulse that has been the phase shift of 90 degree in relation to inphase magnetization and modulation by sin(ΠJ_IST_d) generating increase in cross-peaks that results in 2D COSY spectrum that in indirect dimension cease to show any scalar coupling (Bax and Freeman, 1981).    

A constant-time COSY spectrum, as an example, of camphor has been indicated in Fig. 6, along with an _x1 projection. Differences in the constant values of the scalar coupling and multiplicities have been leading to relative intensities’ variation of diagonal and cross peaks. While, there cease to be signals’ T₂ relaxation modulation in an indirect dimension, there is activeness of the transverse relaxation during T_d. For the molecules relaxing rapidly, the problems are caused by this as the intensities of signal in all 2D COSY increments that are reduced significantly. Contrastingly, in COSY experiment done regularly, there are minimal losses of transverse relaxation during the increments in the early part and building up for evolution times of longer duration.  Additionally,  in COSY experiments, there is also use of constant-time decoupling for SECSY and COSY spectra relayed and the resolution enhancement’s advantage which has been shown in protein NMR studies done very early (Rance et al., 1984).

The avoidance of missing peaks is because of coupling constants that are unfavorable and can be done by a number of spectra with various constant-time periods which are recordable. Nonetheless, because of the variation of the signal intensity for various scalar coupling constants and the resultant quantitative evaluations’ unsuitability in these cases, there has not been extensive use of constant-time proton spectra. ¹³C–¹³C one-bond scalar coupling constants, on the other hand, have more constant-time evolution and uniformity in becoming the standard method to enhance the indirect carbon dimensions’ resolution in uniform labeling of ¹³C biomolecules and its carbon dimensions of indirect nature, particularly the 3D experiments of triple-resonance usable for the proteins’ backbone assignment (Salzmann et al., 1999).

To keep the losses of relaxation to the minimum in the constant-time period, special importance has been put for larger biomolecules. The delay in the constant-time is thus used typically not only for the evolution of carbon chemical shift but also in refocusing carbon–nitrogen or carbon–proton anti-phase magnetization having presence at the onset of constant period of time. In pulse sequence, where there is no desire of no net ¹³C–¹³C evolution of scalar coupling that is desirable during T_d, there should be duration of about 1/¹J_CC. In the constant-time dimension, the increments numbers to high level in taking advantage of increase in the theoretical resolution by the constant-time delay duration is limited.  The improvement of the resolution by the evolution of constant-time in the carbon dimension of indirect nature has special importance for spectra that display and/or carbon dimension of been band-selective with respect to ¹³C spectral range of limited nature (Shaw et al., 1997).

4.1.3. Decoupling – Bilinear rotational

At natural isotopic abundance in a molecule, there is binding of most CH protons to ¹²C nuclei and to ¹³C, there is binding of only around 1.1 percent. The bilinear rotational decoupling (BIRD) has the enablement of ¹²C-bound protons’ selective inversion while keeping unchanged protons’ magnetization to ¹³C. This is achievable by the pulse scheme indicated in Fig. 7. The fates of¹³C magnetization and ¹³C and ¹²C bound protons in the vector representation are outlined in Fig. 7. This starts with proton excitation of 90 degree and continuing with ¹³C-bound protons’ magnetization starting evolving under one-bond coupling of scalar to carbon. Delaying t of 1/¹J_HC, the ¹³C-bound protons’ magnetization is 180 degree out of phase in comparison to the ¹²C-bound protons. The evolution of chemical shift has been subject to refocus in the middle of t by the 180 degree pulse. The rotation of the final 90 degree pulse is with the ¹³C-bound protons’ magnetization ¹²Cbound protons into –z and into +z axis. In the middle of the period of evolution, t1, with the element of BIRD, is possibility of decoupling ¹³C-bound proton. This takes place from the ¹³C-bound proton’s neighbors, which at natural abundance in a molecule has the unlikeliest to be bound to ¹³C.

As the working of this decoupling scheme is only for ¹³C-bound protons, the sensitivity of it with respect to the regular spectrum is only 1.1 percent. However, the complete inversion is given by this kind of decoupling of the passive spins (these cease contributing to the signal measured, although couplings have the responsibility to cause the multiplet structure) while they leave the active spins (that have the bindings to ¹³C and contributing to the signal) untroubled and therefore an easy obtainment is possible for spectra of high quality in pure absorption mode.

The pure shift spectra are obtainable and can be subject to analysis quantitatively.  For germinal protons, there is no working of BIRD decoupling as there is binding of them to the identical ¹³C nucleus. There can also be arising of the problems for compounds where bigger differences are found with ¹J_HC. BIRD decoupling has one specific advantage in the form of very strongly coupled normal spectrum which has the¹³C isotopomer spectrum being weakly coupled normally as there is displacement of one-bond coupling with the effective shifts of chemical of protons bound to ¹³C by +/-¹J_CH/2.

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