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Investigation of complex networks of spin-spin coupling by two-dimensional NMR

Proton-proton couplings in a sample of 9-hydroxytricyclodecan-2,5-dione were studied by the two-dimensional Fourier transform method proposed by Jeener. Various techniques were tested for reshaping the two-dimensional responses to remove the long dispersion-mode tails, and to emphasize cross-peaks at the expense of diagonal peaks. Operation with a mixing pulse of relatively small flip angle allows relative signs of coupling constants to be determined by inspection of the two-dimensional spectrum. Weak long-range couplings, normally hidden within the linewidth, may be detected, although their magnitudes can only be estimated very approximately. A simple modification of the pulse sequence permits broadband decoupling in one frequency dimension, giving proton spectra without any J splittings.

An improved method for heteronuclear chemical shift correlation by two-dimensional NMR

Since the use of two-dimensional NMR for correlating the spectra of coupled heteronuclei was first proposed in 1977 (I), a considerable number of papers have appeared describing different techniques for heteronuclear correlation (2-8). The most widely used method (5, 9-12) produces a two-dimensional spectrum in which one signal appears for each directly bonded carbon-hydrogen pair in a molecule. The fi domain of the spectrum is governed by the proton resonance frequencies and thef, by the carbon-13, so that the correlation signal for a given CH, group appears at frequency coordinates which are just the proton chemical shift in fi, and the carbon-13 chemical shift in fi. Heteronuclear couplings are absent from both frequency domains, although proton-proton scalar coupling structure remains in fi. Such experiments are relatively simple to perform, and show good sensitivity; data for a typical shift correlation two-dimensional spectrum may be obtained in about 10 times the time required to produce a good protondecoupled carbon13 spectrum. A number of chemical applications of such shift correlation experiments have been published (9-ZZ), all using the basic pulse sequence of Ref. (5). This sequence generates proton-decoupled carbon-13 free-induction decays which are modulated as a function of r1 by the frequency difference between the proton chemical shift and the proton transmitter frequency. Since the signals are amplitude modulated with respect to t,, it is not possible to distinguish between positive and negative fi frequencies (13), so that to avoid ambiguity it is necessary to position the proton transmitter either to low field or to high field of the proton spectrum. This is unfortunate in that much of the proton transmitter power is thus wasted, which can lead to severe heating problems with ionic samples if the same proton frequency is used for pulses and for decoupling, as is usually the case. A second problem is that twice as many t1 samples are needed to digitize thef, domain of the spectrum if the proton transmitter lies to one side of the proton spectrum. Both from the point of view of optimum decoupling and from that of minimizing data storage needs and complexity of data processing, it would be desirable to be able to place the proton transmitter in the middle of the proton spectrum. This communication suggests the use of phase cycling of the proton and carbon-13 transmitter pulses, similar to that recently introduced in homonuclear correlation experiments (14-16). This converts amplitude modulation as a function oft, into phase modulation, allowing positive and negativef, frequencies to be distinguished. Thus in the usual experiment (5), examination off2 spectra for successive r1 values would show the amplitudes of individual signals oscillating while their phases remained fixed. The proposed modification would lead tof, spectra with signals oscillating between absorption and dispersion mode while

Correlation of proton chemical shifts by two-dimensional Fourier transform NMR

The first two-dimensional Fourier transform NMR experiment of Jeener (1) has proved to be of considerable historical importance in the development of twodimensional NMR spectroscopy (2,3) but in its original form (a 90”-t,-90”~t, sequence) it has been surprisingly little used. On the other hand, the corresponding heteronuclear chemical shift correlation experiments (4) have been quite popular (S-8). Recently Nagayama et at. (9) have proposed a modification of the Jeener experiment in which acquisition is delayed by a further period t1 so that it starts at the peak of the spin echo. They have demonstrated that this “spin-echo correlated spectroscopy” technique (SECSY) can be extremely useful in the assignment of proton spectra of fairly large molecules, since it identifies the resonances connected by a scalar spin-spin coupling. The purpose of the present communication is to show that the original Jeener experiment can have some advantages in this application. For the proton spectroscopy of large molecules, the refocusing effect which occurs at time 2t, is not usually an important consideration since the linewidths are largely determined by T2 relaxation; sensitivity can thus be improved by starting acquisition immediately after the second 90” pulse. The size of the data matrix can be reduced by the equivalent of quadrature phase detection in the F1 dimension. It is also possible that the form of the two-dimensional spectrum obtained in the Jeener experiment is better suited to the task of sorting out the complicated correlation networks appropriate to large molecules. A detailed theoretical analysis of the Jeener experiment has been given by Aue ef al. (3), showing that in general the spectrum S(F1,F2) contains three kinds of resonance response: axial, diagonal, and cross peaks. Axial peaks appear along the F2 axis and arise from transverse nuclear magnetization created by the second 90” pulse from longitudinal magnetization; they are weak when t1 % T,. Consider the simple example of a first-order AX spin system with chemical shift difference 6 and coupling constant J. The second 90” pulse (called a mixing pulse) interchanges transverse nuclear magnetization between the four resonance frequencies. If the resulting frequency change is only zero or ?J Hz, the corresponding responses lie on or near the diagonal F1 = Ft. With the convention that all responses of a two-dimensional spin multiplet constitute a “peak,” these are diagonal peaks. The frequency change may, however, be of the order of 6, and then there are responses far away from the diagonal; these “cross peaks” are of particular interest because they correlate the shifts of groups of ‘spincoupled nuclei. One of the factors governing the efficiency of magnetization transfer from A to X is a term sin (27rJf,) sin (2mJtZ), which implies that both time dimensions should extend to at least 1/(4J). Another way of visualizing this requirement notes that the cross peaks in the frequency-domain spectrum consist of two pairs of

Assignment of carbon-13 NMR spectra via double-quantum coherence

The spin-spin coupling between carbon-13 nuclei is a particularly useful property on which to base a determination of the network of linkages within an organic molecule. One-bond carbon-carbon couplings are readily distinguished from long-range couplings on the basis of their magnitudes, identifying adjacent carbon atoms in an unambiguous manner. For materials with the natural isotopic abundance (l%), it is sufficient to consider only pairs of interacting carbon-13 nuclei in any given molecule, so the corresponding spin systems are very simple: AX, AB, or AZ. Recent experiments (Z-3) have exploited this principle through a technique which suppresses the strong resonances from isolated carbon-13 spins, revealing the weak satellite spectrum from molecules with two coupled carbon-13 spins. Good discrimination is achieved by excitation of double-quantum coherence (d-8), which exhibits a characteristic dependence on the phase of a radiofrequency pulse, different from that of single-quantum coherence or longitudinal magnetization. A phase-cycling procedure suppresses the unwanted strong signals leaving only signals derived from double-quantum coherence. Only the coupled carbon spins can generate such double-quantum signals. Each carbon site may be directly coupled to as many as four other sites, and since the coupling constants are often very similar in magnitude, assignment to specific pairs of carbon atoms cannot always be made on the basis of coupling constants alone. Fortunately the coupled spins can be identified by means of a different criterion-the frequency of the double-quantum coherence, which is equal to the sum of the chemical shifts of the two carbon sites, measured with respect to the transmitter frequency. Since double-quantum coherence may not be observed directly (5) it is converted into transverse nuclear magnetization and its frequency is determined by means of a two-dimensional Fourier transform experiment (5, 9). This method has recently been used to establish the connectivity of the carbon atoms in Sa-androstane (3). In its simple form the experiment uses the pulse sequence shown in Fig. la. The first three pulses serve to excite double-quantum coherence, which is allowed to evolve for a variable period tl, when the fourth pulse converts it back into detectable transverse nuclear magnetization. In this reconversion process, only the imaginary component of double-quantum coherence is recovered, leaving an ambiguity about the sense of precession of the doublequantum coherence during tl. In the resulting two-dimensional spectrum S(F,, F2), the signs of the double-quantum frequencies are not determined, and this could be a critical problem for spectra of any complexity. The purpose of the present communication is to describe an extension of the method which allows the sense of this precession to be determined by detecting the

Investigation of 13C13C long-range couplings in natural-abundance samples

A recent communication (I) has suggested a method of studying 13C-13C couplings in samples with the natural 13C abundance by suppressing the strong cemral resonance from molecules containing a single isolated 13C nucleus, revealing the weak satellite signals from the coupled 13C-13C systems. Excellent suppression ratios were achieved by momentary conversion of the magnetization from coupled spins into double-quantum coherence (2,3), exploiting the characteristic phase properties of the latter. The principal restriction on the generality of this technique arises from the condition for optimum transfer into double-quantum coherence (4,5). For the case of weakly coupled spins, this condition is

Homonuclear broadband-decoupled absorption spectra, with linewidths which are independent of the transverse relaxation rate

Recently Aue ef al. (I) presented a method for obtaining a homonuclear broadband-decoupled high-resolution NMR spectrum by means of diagonal projection of a 2D J-resolved absolute-value spectrum. Resolution in such a projection is severely lim ited by the fact that resonance lines have absolute-value l ineshapes (2). As has been shown by Nagayama et al. (3) it is impossible to obtain a homonuclear broadband-decoupled spectrum via projection of a phase-sensit ive spectrum which is obtained by using the method of Aue et al. (1). Until now it was impossible to eliminate the absolute-value character in the decoupled spectrum. A new method is introduced here by which it is possible io obtain a decoupled absorption spectrum with linewidths which are independent of the transverse relaxation rate. The basic schemes of the method described by Aue et al. (1) and our new method are the same: spin echoes are created by means of 90-180” pulse sequences, for different intervals t/2 between the 90 and 180” pulses (Fig. 1). In our method the magnetization is measured at a fixed time r after the initial 90” pulse, as a function of time t. Following the arguments of Aue et al. the observed magnetization, corresponding to a resonance line k of a set j of magnetically equivalent nuclei, is given in the case of weak coupling by

Relative signs of NMR spin coupling constants by two-dimensional Fourier transform spectroscopy

Conventional high-resolution NMR spectra yield the magnitudes of the spin coupling constants but not their signs. When relative sign information is required it is necessary to set up a further experiment employing selective double resonance (1-3) or proceed to a detailed analysis of a strongly coupled spectrum (4). In certain circumstances, relative sign information can be used as a diagnostic tool, for example, in the recognition of geminal and vicinal proton-proton couplings, which normally have opposite signs. The present work describes a simple twodimensional Fourier transform experiment (5,6) in which relative signs of coupling constants are obtained directly by inspection (7). The basic requirement for any relative sign determination is a system of three c,oupled nonequivalent spins, for example, an AMX system. It is useful for this discussion to introduce the concept of a “passive” spin, say, the M spin in this case. The role of the M spin is limited to the creation of two AX subspectra, one corresponding to M in an cr spin state, the other to M in a p spin state. Apart from introducing the two couplings J AM and JMX, the passive spin M is not involved and its resonance need not be observed. Double resonance provides a method for recognizing which A and X lines belong to a given AX subspectrum, and it is well known that if the upfield A doublet is associated with the upfield X doublet, tlhen JAM and JMx have like signs (I -3). A new approach to relative sign determination is provided by magnetization t:ransfer experiments studied by two-dimensional Fourier transformation (5, 6). The magnetization of the A spin is labeled in terms of the characteristic precession frequencies by allowing transverse A magnetization to evolve during a varia.ble interval tl. A second pulse (known as a “mixing pulse”) converts this back into Z magnetization, equivalent to a disturbance of the energy level populations. These population changes affect the intensities of the X signals when the

Absorption spectra from phase-modulated spin echoes

Abstract A method is presented by which pure absorption spectra can be derived from spin echoes with a symmetric envelope amplitude, but with arbitrary phases φ in the centers of the echoes. It is shown that without any phase correction, absorption spectra can be obtained in which the amplitudes of the spectral lines are either proportional to cos φ or sin φ, or independent of φ. As an example a T2 measurement of 1,1,2-trichloroethane is given.

Enhanced NMR resolution by restricting the effective sample volume

Since the very first experiments on the high-resolution NMR of liquid samples there has been widespread interest in the quest for enhanced resolving power to bring out the fine structure due to weak spin-spin interactions and to approach the natural width of the NMR lines. The lim iting factors are well known-spatial inhomogeneity of the static field BO and instability of B. measured with respect to the excitation frequency-but since the pioneering work of Arnold (1) and Anderson (2) technological improvements in this area have been relatively slow. There has been a steady improvement in field stability, particularly for modern superconduct ing spectrometers, and pulse excitation reduces the sensitivity to low-frequency instabilities (3). In addition there are special techniques such as double irradiation (4) and spin.-echo experiments (5-8) which can circumvent some of the problems of field inhomogeneity. Enhanced resolution may also be achieved “artificially” by data man ipulation after the acquisition of the NMR signal, either by a convolution operation on the frequency-domain spectrum (9, 10) or by a weighting function which prolongs the decay of the transient time-domain signal (IO,1 I ). Many different prescriptions are in vogue (12-16). A simple and more direct method is to use a very small NMR sample. The resulting loss of sensitivity is seldom a problem for proton NMR, and for less sensitive nuclei it can usually be retrieved by time averaging. Unfortunately this is not quite as easy as it sounds. Suppose that the sample is enclosed within a very small glass container; resolution is significantly degraded because of the field distortions due to discontinuities in magnetic susceptibility between sample, glass, and the surrounding med ium. Experiments which emp loy retaining plugs or small capillary tubes do not in practice achieve the expected resolution. This communicat ion proposes an alternative method of restricting the effecfiue sample volume without the need for the equivalent physical confinement; spinning sample tubes are used with the normal dimensions (5 m m o.d.). The idea is to excite part of the sample by selective irradiation in an imposed field gradient, a concept often used in spin-mapping experiments or zeugmatography (17). The field gradient is strong in comparison with the overall width of the mu ltiplet under investigation, and also in comparison with the residual “natural” gradients of the high-resolution magnet. Ideally several gradients m ight be used, chosen to match the dominant natural gradients, but in practice a single applied gradient is quite effective, since a linear Z gradient, for example, m inimizes the extent of excitation in the Z dimension, and automatically takes care of higher-order natural Z gradients. Frequency selectivity is achieved either by means of a “soft” radiofrequency pulse (18, 19) or by a regular sequence of very short strong pulses designed to have a cumulative effect in

A fast method for obtaining 2D J-resolved absorption spectra

Two-dimensional homonuclear J spectroscopy (1) is a useful method both for unraveling complicated spectra (2) and for the study of spin-spin coupling constants. The principle of the technique has been described by Aue er al. (I ). By means of one or more 180” pulses a spin echo is created at a time tr after an initial 90” pulse. The second half of this echo is acquired for a series of tl values. Two-dimensional Fourier transformation then generates a 2D frequency spectrum. This method needs a rather long measuring time and does not give the optimum sensitivity. Another disadvantage is that it is impossible to get 2D absorption spectra in an easy way (3,4), and therefore one usually calculates an absolute-value spectrum, which introduces line broadening, and decreases the obtainable resolution. As has been shown earlier (5), processing of complete spin echoes can remove this disadvantage. Slightly different measuring techniques are described, which allow a shorter measuring time and can also produce 2D J-resolved absorption spectra. The essence of J spectroscopy is that spin echoes are modulated by spin-spin coupling. The phase 4jk of the frequency component k of a set of magnetically equivalent nuclei j at the center of a spin echo, tl seconds after an initial 90” pulse, is given by