# Patent

## Title
Quadrupolar nuclei NMR using residual dipolar splittings in solids

## Abstract

A method for obtaining NMR (=nuclear magnetic resonance) spectra of quadrupolar nuclei having spin I>1⁄2 using magic angle spinning (=MAS) in solid powders and transfer of coherences from a neighboring nucleus with spin S= 1/2  to single- or double-quantum transitions of quadrupolar nuclei having spin I>1⁄2, is characterized in that the transfer of coherences occurs through a combination of scalar and residual dipolar splittings. With the inventive method improved NMR-spectra can be obtained from which parameters can be extracted, which can be related to the structure and internal dynamics of solids containing the quadrupolar nuclei.

## Background
This application claims Paris Convention priority of EP 05 015 334.5 filed Jul. 14, 2005 the entire disclosure of which is hereby incorporated by reference
BACKGROUND OF THE INVENTION
The invention concerns a method for obtaining NMR (=nuclear magnetic resonance) spectra of quadrupolar nuclei having spin I>1⁄2 using magic angle spinning (=MAS) in solid powders and transfer of coherences from a neighboring nucleus with spin S=1⁄2 to single- or double-quantum transitions of quadrupolar nuclei having spin I>1⁄2.
A method for obtaining NMR (=nuclear magnetic resonance) spectra of quadrupolar nuclei having spin I>1⁄2 is known from [32]-[36].
Although nitrogen is of universal importance in virtually all branches of biology, chemistry, and material science, and although nitrogen-14 is a very abundant isotope (99.4%), nitrogen-14 NMR has enjoyed relatively little popularity so far. In liquids, nitrogen-14 line-widths are very broad because of rapid quadrupolar relaxation, except in rapidly-tumbling molecules or in highly symmetrical environments such in tetraalkyl ammonium ions.[1] In solids, nitrogen-14 quadrupole interactions can be characterized in the absence of external magnetic fields by nuclear quadrupole resonance (NQR).[2, 3] In a static magnetic field, the strong quadrupole interaction between the nuclear quadrupole moment of a spin I=1 and the electric field gradient (EFG) at the site of the nucleus leads to very broad spectra (up to a few MHz) that are difficult to excite and observe.[4-8] The interaction of a nucleus with a quadrupole moment Q with the electric field gradient V at the site of the nucleus can be characterized by the quadrupole coupling constant CQ=eQVZZlh and the asymmetry parameter ηQ=(VXX−VYY)/VZZ, where the principal components of the electric field gradient tensor are ordered VZZ>VXX>VYY. The asymmetry parameters ηQ can cover the full range 0<ηQ<1.
Early examples of direct detection of 14N NMR used single crystals,[4-8] where one obtains a doublet for each 14N site, with reasonably narrow spectral lines (on the order of 1.5 kHz for CQ≈3-4 MHz), provided that there are no significant crystal imperfections. The signals are spread over spectral ranges of several MHz, requiring very broad band-widths (or re-tuning of the circuits) for both excitation and signal acquisition. In static polycrystalline powders, the 14N signal intensity is spread over many MHz, so that it is difficult to recognize the singularities of the powder patterns. When the powders are spun at the magic angle, one observes families of spinning sidebands. Although for moderate spinning frequencies the signal intensity can be spread over hundreds of sidebands, quadrupole couplings up to CQ=1.5 MHz have been observed by direct 14N MAS.[9-13] Not surprisingly, the envelopes of the spinning sidebands depend not only on the accurate adjustment of the magic angle, but also on the amplitude of the 14N radio-frequency pulses and on the bandwidth of the probe and receiver systems.
The frequencies of double-quantum transitions between the |m=+1> and |m=−1> levels in I=1 systems are not affected by first-order quadrupolar interactions, as shown for 2H NMR by Pines and co-workers.[14] In combination with cross-polarization between 14N (I=1) and suitable S nuclei, one can excite 14N double-quantum coherences.[15-17] By transferring coherence back and forth between 14N double-quantum coherences and S nuclei, one can achieve indirect detection.
The 14N double-quantum transitions can also be detected directly by overtone spectroscopy, [18-22] where a radio-frequency field centered at twice the 14N Larmor frequency. This exploits the fact that double-quantum transitions are weakly allowed. Second-order quadrupole couplings, as shown in single crystals and powders, determine the line-shapes in overtone spectra.[18-22] Compounds with several 14N sites may lead to overlapping overtone patterns, which can in principle be separated by combining overtone spectroscopy with dynamic-angle spinning or with double sample rotation.[23-27]
It is possible to achieve indirect detection of 14N in spinning samples by recoupling heteronuclear dipolar interactions with a suitable spin S such as 13C.[28-30] By applying pulses at ω0N in synchronism with sample rotation, one can interfere with the averaging of heteronuclear dipolar interactions. This leads to a dephasing of the signals of the S nuclei, thus providing information on the strength of the dipolar interaction. Recoupling can also be achieved by 14N irradiation near the overtone frequency.[31, 32] By stepping the RF frequency in the vicinity of ω0N or 2ω0N, one obtains line shapes determined by first- or second-order quadrupole interactions respectively.[31] This may be regarded as continuous-wave approach to indirect detection of 14N spectra.
Another class of experiments exploits residual dipolar splitting (RDS), also known as second-order quadrupole-dipole cross term, between 14N (I=1) and S=1⁄2 nuclei such as 13C. [32-36] Since the IS dipolar interactions are not averaged out completely by magic angle spinning, because the large quadrupole coupling of the I nucleus prevents its quantization along the direction of the static field, the S resonances are split into 1:2 doublets (each component featuring a narrow powder pattern) with a splitting D, which depends on the orientation of the C-N bond with respect to the quadrupole tensor. The largest peak corresponds to the superposition of the |m=+1> and |m=−1> states of the S=1 spin, while the smaller peak corresponds to the |m=0> state. The former is further split into a doublet 2J due to the heteronuclear J coupling. Inhomogeneous broadening or relaxation may of course mask these splittings. Residual dipolar splittings have been used by Clare et al.,[29] who stepped an RF field in the vicinity of ω0N while observing two-dimensional exchange spectra of the S (13C) nuclei. If the RF field is applied for a duration comparable to the rotor period, the populations of the 14N levels are partly interchanged. As a result, the two components of the doublet in the S (13C) spectrum are swapped.[29]
It is the object of the invention to present a method for obtaining NMR spectra of quadrupolar nuclei having spin I>1⁄2 which overcomes the above mentioned problems.
SUMMARY OF THE INVENTION
This object is achieved, according to the invention, by a method mentioned above, characterized in that the transfer of coherences occurs through a combination of scalar and residual dipolar splittings. The inventive method enables one to achieve NMR-spectra that reveal patterns of quadrupolar couplings of the quadrupolar nuclei with extremely narrow line widths. Therefore improved NMR-spectra can be obtained from which parameters can be extracted, which can be related to the structure and internal dynamics of solids containing the quadrupolar nuclei.
The quadrupolar nuclei having spin I>1⁄2 are preferably chosen from the group 14N, 17O, 35Cl, 37Cl. Because of its great importance in biology, chemistry and material science 14N is highly preferred.
In a highly preferred variant the inventive method includes the following steps:

    
    
        (i) excitation of the neighboring nucleus single quantum coherence by cross polarization from protons,
        (ii) applying a delay of Texc≈1⁄2D, where D is the splitting due to a combination of scalar and residual dipolar splittings,
        (iii) applying an RF-pulse of duration τP to the quadrupolar nuclei having spin l>1⁄2,
        (iv) applying a π-RF-pulse to the neighboring nucleus in the middle of an evolution interval t1,
        (v) applying an RF-pulse at t1 of duration τP to the quadrupolar nuclei having spin I>1⁄2, and
        (vi) recording the signal of the neighboring nucleus with spin S=1⁄2 after a duration τrec≈1⁄2D.
    
    


The neighboring nucleus with spin S=1⁄2 is preferably chosen from the group 13C, 31P, 15N, 29Si, 1H.
Advantageously the steps (i) to (vi) are repeated for N rotor-synchronized increments t1=nΔt1 with Δt1=1/vrot and n=1, 2,3 . . . N in the manner of 2-dimensional spectroscopy.
In a preferred variant the time domain signals S(t1, t2) are Fourier transformed with respect to t1 to yield a spectrum of the quadrupolar nuclei having spin I>1⁄2 in the ω1 domain and with respect to t2 to yield a spectrum of the neighboring nucleus with S=1⁄2 in the ω2 domain.
A variant of the NMR method according to the invention is characterized in that (π/2)φ pulses are applied to the neighboring nucleus with S=1⁄2 at the beginning and at the end of an evolution interval t1. Therewith the heteronuclear coherences can be converted into coherences of the I=1⁄2 nucleus .
Also in accordance with the invention is a variant of the method wherein a z-filter is used before the detection period. The excitation and reconversion are then symmetrical in time domain, which improves the spectra.
Further it is preferred, that from the obtained NMR spectra the quadrupolar coupling constant CQ, the asymmetry parameter ηQ of the quadrupolar nuclei having spin I>1⁄2 and the relative orientation of the quadrupolar tensor with respect to the bond between the quadrupolar nuclei having spin I>1⁄2 and the neighboring nucleus with S=1⁄2 are extracted.
It is shown that nuclear magnetic resonance (NMR) spectra of nitrogen-14 (spin I=1, with quadrupole couplings up to a few MHz) can be obtained by indirect detection in powders spinning at the magic angle (MAS). The method relies on the transfer of coherence from a neighboring nucleus with S=1⁄2 such as carbon-13 to single- or double-quantum transitions of nitrogen-14 nuclei. The transfer of coherence occurs through a combination of scalar and residual dipolar splittings, the latter being also known as second-order quadrupole-dipole cross terms. The two-dimensional (2D) NMR spectra reveal powder patterns determined by second-order quadrupolar couplings of nitrogen-14, which have line-widths that are about three orders of magnitude narrower than the first-order quadrupolar interaction.
Analysis of the spectra yields the quadrupolar coupling constant CQ and asymmetry parameter ηQ of nitrogen-14 and the relative orientation of the quadrupolar tensor with respect to the bond between the nitrogen-14 and S nuclei. These parameters, which can be subject to motional averaging, can be related to the structure and internal dynamics of nitrogen-containing solids.
Further advantages can be extracted from the description and the enclosed drawing. The features mentioned above and below can be used in accordance with the invention either individually or collectively in any combination. The embodiments mentioned are not to be understood as exhaustive enumeration but rather have exemplary character for the description of the invention.



The invention is shown in the drawings.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 shows a pulse sequence and coherence transfer pathways for the excitation of 14N single- or double-quantum coherences according to the invention;
FIG. 2 shows simulations of 14N single-quantum (SQ) powder patterns that result from the pulse sequence of FIG. 1 for different excitation intervals and 14N pulse lengths;
FIG. 3 shows simulations of 14N double-quantum (DQ) powder patterns with the same parameters as in FIG. 2;
FIG. 4a shows an experimental 13C CPMAS in L-alanine;
FIG. 4b shows an experimental 13C CPMAS in glycine;
FIG. 4c shows a 2-dimensional 14N/13C correlation spectrum in L-alanine with single-quantum signals;
FIG. 4d shows a 2-dimensional 14N/13C correlation spectrum in glycine with single-quantum signals;
FIG. 4e shows a 2-dimensional 14N/13C correlation spectrum in L-alanine with double-quantum signals
FIG. 4f shows a 2-dimensional 14N/13C correlation spectrum in glycine with double-quantum signals
FIG. 4g-j shows projections of the 14N single- and double-quantum coherences of FIG. 4c-f onto the δ1 axis;
FIG. 5a shows an experimental 13C CPMAS of L-leucine;
FIG. 5b shows a two-dimensional 14N/13C correlation spectra obtained with single-quantum methods of L-leucine;
FIG. 5c shows a two-dimensional 14N/13C correlation spectra obtained with double-quantum methods of L-leucine;
FIG. 6a shows an experimental 13C CPMAS for the tripeptide L-ala-L-ala-gly;
FIG. 6b shows a two-dimensional 14N/13C correlation spectra obtained with single-quantum methods for the tripeptide L-ala-L-ala-gly;
FIG. 6c shows a two-dimensional 14N/13C correlation spectra obtained with double-quantum methods for the tripeptide L-ala-L-ala-gly;
FIG. 7 shows simulations of single-quantum and double-quantum 14N spectra; and
FIG. 8 shows simulations of single-quantum and double-quantum 14N spectra at different polar angles.



DESCRIPTION OF THE PREFERRED EMBODIMENT
The method presented in this work exploits residual dipolar splittings between 14N (I=1) and a “spy” nucleus with S=1⁄2 such as 13C, in combination with scalar J couplings. The residual splitting D(14N, 13C), which decreases in inverse proportion to the static field strength B0, is on the order of D≈30 Hz for 14NH3+13CαHRCOO− in zwitterionic amino acids at B0=9.4 T (400 MHz for protons), while J(14N, 13C) couplings in L-alanine are about 3.1 and 4.0 Hz for 14NH3+R and 14NH2R respectively, and around 8 Hz in peptide bonds.[37] If the magic angle is adjusted very accurately,[38] and if proton decoupling is optimized,[39, 40] the 13Cα lines of amino acids can be as narrow as 18 Hz, so that the residual dipolar splitting can readily be observed.[38] Even when the splittings are masked by inhomogeneous broadening, due to slight errors in the adjustment of the magic angle, temperature gradients, or magnetic susceptibility effects, the residual dipolar splittings can still be exploited, provided that they are larger than the homogeneous (‘refocusable’) line-width 1/(πT2′). In amino acids, the time constant T2′(13Cα) of spin-echo decays can be as long as 50 ms, so that 1/(πT2′)=6 Hz is not exceptional for 13Cα.
The pulse sequence and coherence transfer pathways for the novel two-dimensional correlation NMR methods are illustrated in FIG. 1. After exciting carbon-13 single-quantum coherence Cx=(TC11+TC1−1)/2 in the usual manner by cross-polarization from protons, a delay τ≈1⁄2D leads to a state that can be described by a product of irreducible tensor operators TC11TN20. This state can also be represented by a product of Cartesian operators Cx(Nz2−2EN/3), where the unity operator EN ensures that the product operator is traceless and orthonormal. For simplicity, we can loosely speak of a doubly-antiphase operator CxNz2. However, it turns out that irreducible tensor operators are more convenient to describe heteronuclear multiple-quantum coherences. A radio-frequency pulse applied in the center of the 14N spectrum can lead to a partial conversion into TC11TN1±1 and TC11TN2±1 (corresponding to 14N single-quantum coherences) or into TC11TN2±2, corresponding to 14N double-quantum coherences. Henceforth, we shall speak of nitrogen-14 single-uantum (SQ) or double-quantum (DQ) spectroscopy, which are distinct in their coherence transfer pathways (FIG. 1), and of course in the appearance of the spectra. In either case, a π pulse applied to 13C in the middle of the evolution interval t1 not only interconverts TC1+1 and TC1−1 to refocus the carbon chemical shifts, but also eliminates the effects of inhomogeneous decay, so that the attenuation of the signal by irreversible dephasing of the carbon-13 coherences is determined by the factor exp{-(τexc+t1+τrec)/T2′(C)}. Terms containing TC1−1 are converted into TC1+1 by the π pulse at t1/2 and therefore cannot contribute to any observable pathways, unless a z-filter is inserted prior to signal observation. Note that in the fixed intervals τexc and τrec, the inhomogeneous decay with a time constant T2*<<T2′ does not contribute to signal losses.
The heteronuclear coherences TC11TN1±1 and TC11TN2±1 or TC11TN2±2 are allowed to evolve freely during the evolution interval t1 prior to symmetrical reconversion into observable single quantum coherence TC1−1. The experiment is repeated for N rotor-synchronized increments t1=nΔt1 with Δt1=1/νrot and n=1, 2, 3, . . . , N, in the manner of two-dimensional spectroscopy. The time-domain signals S(t1,t2) are Fourier transformed with respect to t1 to yield a 14N spectrum in the ω1 domain, and with respect to t2 to produce a 13C spectrum in the ω2 domain. The coherence transfer pathways in FIG. 1 show that both single- and double quantum experiments lead to pure two-dimensional absorption line shapes since they retain two mirror-image pathways with respect to the 14N coherence order ρN. Note that, in contrast to most other 2D experiments, the t1 period is defined as the interval between the centers of the two 14N pulses, rather than as a period of free precession. Its initial duration corresponds to one rotor period, so that a first-order phase correction must be applied to the ω1 domain. The initial free evolution interval between the pulses is 1/νrot−τp.
The nitrogen-14 single- and double-quantum coherences evolve in the t1 interval under the effect of the quadrupolar interaction and the chemical shift. The single-quantum coherences are affected by both first- and second-order quadrupole interactions, while the double-quantum coherences are affected only by second-order quadrupole effects. Synchronization of the increments Δt1 with the spinner period 1/νrot leads to aliasing in the ω1 domain, so that the spinning sidebands coincide with the center bands. The spinning sidebands can be observed separately if smaller time increments are chosen.
Many variants of the experiments can be conceived. For example, optional (π/2)φ pulses applied to 13C at the beginning and at the end of the evolution period can convert TS11TI22 into TS10TI22 and back. Complementary experiments with different phases φ of the 13C pulse can be used. This variant allows one to avoid the T2-decay of the TS11 term in the t1 interval. Another variant uses a z-filter before the detection period so that the excitation and reconversion are symmetrical even when there is a distribution of residual dipolar splittings. This improves the spectra if τrec<1⁄2D, so that the reconversion into in-phase Cx coherence is not complete.
FIG. 2 and FIG. 3 show simulations of SQ and DQ powder patterns as a function of the excitation and reconversion intervals τexc=τrec and of the 14N pulse length τp. The thick lines show the spectra expected for ideal single- and double-quantum excitation. For quadrupole parameters that are typical for amino acids, the optimum τp for SQ excitation is about half as for DQ excitation.
In the experimental SQ and DQ spectra of FIG. 4, the 14N patterns have line-widths on the order of a few kHz, determined by the anisotropy of the second order quadrupole interaction. The SQ spectra are about twice as narrow at the DQ spectra. For L-alanine in FIG. 4a, the residual dipolar splitting D(14N, 13C) is barely resolved at 9.4 T. The fact that 14N coherences can be excited efficiently even in the absence of a resolved residual dipolar splitting is demonstrated in FIG. 4b for glycine.
FIG. 5 shows how the two crystallographic ally inequivalent 13C sites I and II in powdered L-leucine correlate with non-degenerate 14N quadrupole parameters estimated to CQI=1.2 MHz, ηQI=0.3, CQII=1.1 MHz, ηQII=0.1. Again, the SQ spectra are about twice as narrow at the DQ spectra.
FIG. 6 shows a challenging example of a tripeptide L-ala-L-ala-gly. The terminal 14NH3+ group (site II) has similar parameters as in FIG. 4, except that is this case the SQ spectrum is broader than the DQ spectrum, which indicates motional broadening.[41] On the other hand, the amide groups —CO14 NH13Cα— have quadrupole parameters CQI and CQIII of at least 3 MHz. It is remarkable that signals could be excited and observed with a 14N RF strength of only 60 kHz for such large quadrupole interactions.
The sensitivity is largely determined by the quantum yield of two-way coherence transfer. The efficiency of the conversion of TC11TN20 into TC11TN2±1 or TC11TN2±2 and back under MAS is determined by the amplitude ω1N N and duration τp of the 14N pulse. Numerical calculations (neglecting relaxation) with integration over all crystallite orientations show that with CQ=1.2 MHz, ηQ=0, νRFN=60 kHz, τp=15 μs, D=30 Hz, and τexc=τrec=15 ms, the efficiency of the two-way coherence transfer to SQ or DQ and back is about 5%. Experiments indicate an efficiency of 2% for SQ or DQ spectra for the first t1 increment, compared with a simple 13C CPMAS spectrum.
The experiments work in principle with 13C in natural abundance. The sensitivity can be boosted by a factor of about 100 by 13C enrichment, as we have done to optimize the experimental conditions. In principle, the experiment can work with any S=1⁄2 “spy” nucleus such as phosphorus-31, nitrogen-15, silicon-29, etc., provided that there is a non-vanishing residual dipolar splitting and/or scalar coupling between the spy nucleus and 14N. In some cases, the J coupling may be larger than D. Even protons could be used as spy nuclei, provided the broadening due to homonuclear dipolar proton-proton couplings does not mask the residual dipolar splittings. It is possible to contemplate the indirect detection of other quadrupolar nuclei with S=3/2, 5/2 etc., such as 35Cl, 17O, etc., provided that one can exploit a residual dipolar splitting with suitable spy nuclei.
FIG. 7 and FIG. 8 show how the line shapes depend on the quadrupole asymmetry parameter ηQ and on the relative orientation θQD, φQD of the internuclear nitrogen-carbon vector with respect to the principal axis system of the quadrupole tensor. It is possible to determine these parameters by analysis of the line-shapes. Indeed, the efficiency of the 14N single- or double-quantum excitation (and hence the line-shapes) depends on the magnitude of the quadrupole tensor and on its relative orientation with respect to the 13C-14N dipole-dipole interaction.
The samples were packed in 2.5 mm outer diameter ZrO2 rotors (sample volume ca. 11 μl), and spun at 30 kHz in a Bruker triple resonance CP-MAS probe where one channel was adapted for nitrogen-14 resonance, using the 9.4 T wide-bore magnet (13C and 14N Larmor frequencies of 100.6 and 28.9 MHz) of an Advance 400 spectrometer. The magic angle was adjusted within 0.004°.[38] Cross-polarization (CP) was used with a constant proton RF amplitude νRFH=85 kHz while νRFC was ramped. Two-pulse phase-modulation (TPPM) proton decoupling was used during the entire experiment with an RF amplitude 100 kHz, pulse-widths of 3.9 μs, and a phase difference between two successive pulses of 35°. The RF amplitude of the 14N pulses was calibrated by direct detection of 14NH4NO3, which has a very small quadrupole splitting. The 14N pulses had an amplitude of νRFN=60 kHz using a 500 W amplifier. The samples of L-alanine (14NH4+13CαHCH3COO−), glycine (14NH4+13CαH2COO−), L-leucine (14NH4+13CαHRCOO−) with R=CH2CH(CH3)2 and the tri-peptide L-ala-L-ala-gly, all enriched in the 13Cα positions, were purchased from Cambridge Isotope Laboratories, and used without further purification.
FIG. 1 shows pulse sequence and coherence transfer pathways for the excitation of 14N single- or double-quantum coherences in two-dimensional correlation experiments for solids rotating at the magic angle. The sequence starts with cross-polarization from protons to carbon-13 to generate CX magnetization, followed by an interval τexc≈1⁄2D where the residual dipolar splitting D and the scalar coupling J between 14N and 13C lead to anti-phase coherences TC11TN10 and TC11TN20. In the 14N single-quantum experiment (SQ), these are converted into heteronuclear coherences TC11TN11 and TC11TN21 by applying an RF pulse of duration τp to the 14N nuclei, while in the 14N double-quantum experiment (DQ), one excites heteronuclear coherences TC11TN22. The evolution period t1 is defined as the separation between the centers of the two RF pulses applied to the 14N nuclei, with a duration t1=ntrot(n=1, 2, . . . N). In this interval, the coherences evolve chiefly under the second-order quadrupole interaction, before being converted back into observable CX magnetization. The coherence transfer pathway diagrams show that pure two-dimensional line shapes are obtained. The SQ experiment uses a simple phase alternation of the first 14N pulse with addition and subtraction of the 13C signals, while the DQ experiments requires a 4-step cycle of the phase of the first 14N pulse (0, 90, 180, 270°), again with addition and subtraction of the 13C signals. In addition, the first 1H pulse may be phase-alternated, and the 13C π pulse may be exorcycled.
FIG. 2 shows simulations of 14N single-quantum (SQ) powder patterns that result from the pulse sequence of FIG. 1 for different excitation intervals τexc and 14N pulse lengths τp. The radio-frequency (RF) field amplitude is νRF=60 kHz, the quadrupolar parameters are CQ=1.2 MHz and ηQ=0.2, the dipolar interaction corresponds to a typical 14N-13C bond length (dCN=667 Hz) leading to a residual dipolar splitting D≈25 Hz at 9.4 T. The powder pattern drawn with a thick line represents the ideal line-shape of the single-quantum 14N MAS spectrum obtained with ideal excitation and rotor synchronized acquisition.
FIG. 3 shows simulations of 14N double-quantum (DQ) powder patterns with the same parameters as in FIG. 2. The powder pattern drawn with a thick line represents the ideal line shape for the double-quantum 14N MAS spectrum obtained with ideal excitation and rotor synchronized acquisition.
FIG. 4 shows (a, b) experimental 13C CPMAS and two-dimensional 14N/13C correlation spectra showing isotropic 13C chemical shifts along the horizontal ω2 axis (δ2 labeled in ppm with respect to TMS) and 14N (c, d) single- and (e, f) double-quantum signals along the vertical ω1 axis (δ1 labeled in ppm with respect to 14NH4NO3). (a) In L-alanine (14NH4+13CαHCH3COO−) the 13C CPMAS spectrum reveals an ill-resolved residual dipolar splitting (see expansion); (b) in glycine (14NH4+13CαH2COO−) there is no visible residual dipolar splitting. Nevertheless, the 14 N single- and double-quantum coherences can be excited efficiently and the projections onto the δ1 axis (g-j) reveal characteristic second-order quadrupolar powder patterns. For L-alanine CQ≈1.2 MHz and ηQ≈0.3; for glycine CQ≈1.2 MHz and ηQ≈0.5. Under our experimental conditions the T2′(13Cα) values are found to be 28 and 23 ms for L-alanine and glycine, respectively. The CPMAS spectra (a, b) result from averaging 8 transients with relaxation intervals of 5 s. The two-dimensional spectra result from averaging (c, d) 32 and (e, f) 96 transients for each of (c, d) 512 and (e, f) 170 t1 increments Δt1=1/νrot=33.33 μs, with a relaxation interval of 3 s. The intervals τexc=τrec were 16 ms, while τp was (c, d) 11 μs and (e, f) 15 μs. The CP contact times for L-ala and gly were 0.5 and 1 ms, respectively.
FIG. 5 shows (a) experimental 13C CPMAS and two-dimensional 14N/13C correlation spectra obtained with (b) single- and (c) double-quantum methods of L-leucine that has two magnetically inequivalent sites I and II for 14N and 13Cα. The projections onto the δ1 axis (right) reveal second-order quadrupolar powder patterns that resembles simulated patterns with CQI≈1.2 MHz, CQII≈1.1 MHz, ηQI≈0.3, and ηQII≈0.1. The T2′ values of the two 13Cα sites in L-leu are found to be (I) 26 and (II) 22 ms. The CPMAS spectrum (a) results from averaging 8 transients with a relaxation interval of 5 s. The two-dimensional spectra result from averaging (b) 32 and (c) 96 transients for each of (b) 400 and (c) 190 t1 increments of Δt1=1/νrot=33.33 μs, with a relaxation interval of 3 s. The intervals τexc=τrec were 16 ms, while τp was (b) 11 μs and (c) 23 μs. The CP contact time was 0.6 ms.
FIG. 6 shows (a) experimental 13C CPMAS and two-dimensional 14N/13C correlation spectra obtained with (b) single- and (c) double-quantum methods for the tripeptide L-ala-L-ala-gly where all 13Cα are enriched. For the amide sites (I) and (III), 14N SQ and DQ signals can be observed (projections on the right) despite very large first-order quadrupole couplings (CQI≈CQIII≈3 MHz) and very short T2′(13Cα)=14, 11 and 8 ms for sites I, II and III respectively. The projections of the NH3+ group of the first L-alanine onto the δ1 axis (d, e) reveal powder patterns that correspond to CQII≈1.3 MHz, and ηQII≈0.3. The line widths of all three sites in the SQ spectrum are broadened, most probably by local molecular motions. The CPMAS spectrum (a) results from averaging 8 transients with a relaxation interval of 5 s. The two-dimensional spectra result from averaging (b) 4096 and (c) 8192 transients for each of (b) 16 and (c) 20 t1 increments Δt1=1νrot=33.33 μs, with a relaxation interval of 2.5 s. The intervals τexc=τrec were 6 ms, while τp was (b) 11 μs and (c) 24 μs. The CP contact time was 0.5 ms. The projections of the N-terminal 14N resonances onto δ1 axis (d, e) were extracted from two-dimensional spectra recorded with (d) 64 (e) 96 t1 increments each with (d) 128 and (e) 1024 transients.
FIG. 7 shows simulations of SQ and DQ 14N spectra for CQ=1.2 MHz and ηQ=0, 0.5 and 1, appropriate for B0=9.4 T, τexc=15 ms, νRFN=60 kHz, νrot=30 kHz, τp=10 μs for SQ and τp=20 μs for DQ. The powder patterns drawn with thick lines represent spectra assuming ideal single- or double-quantum excitation and rotor synchronized acquisition.
FIG. 8 shows simulations of SQ and DQ 14N spectra for CQ=1.2 MHz and η=0.5, appropriate for B0=9.4 T, τexc=15 ms, νRFN=60 kHz, νrot=30 kHz, τp=10 μs for SQ and τp=20 μs for DQ, as a function of the polar angles θQD, φQD of the internuclear vector r(14N, 13C) with respect to the principal axis system of the quadrupole tensor. For larger values of θQD, the sensitivity of the line shapes to φQD is more pronounced.
To summarize, we have shown that by transferring coherence between 14N and 13C in solid powdered samples, one can indirectly detect the single- or double-quantum transitions of 14N nuclei. Under fast magic-angle spinning, the spectra are determined predominantly by second-order quadrupole interactions. The orientation of the principal components of the quadrupole tensor can be readily rationalized in terms of electronic charge distributions. In many respects, quadrupole tensors are more straightforward to relate to the local environment than chemical shift tensors.[42] Quadrupole tensors can give direct insight into the electronic charge distribution in molecules. For example, the extent of “pyramidalisation” of nitrogen atoms in peptide bonds would be much easier to assess if one could determine nitrogen-14 quadrupole tensors instead of nitrogen-15 chemical shift tensors. Nitrogen-14 NMR could become an important tool for biology, chemistry and material science. The new method bears a close analogy to earlier work on the indirect detection of nitrogen-15 NMR,[43] which was originally published without a catchy name, but later dubbed Heteronuclear Single Quantum Correlation (HSQC).
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## Claims

1. A method for obtaining a two-dimensional NMR (=nuclear magnetic resonance) spectrum of quadrupolar nuclei of 14N having spin I=1 using magic angle spinning (=MAS) of a solid powder sample and transfer of coherence from a neighboring nucleus with spin S=1⁄2 to single- or double-quantum transitions of said quadrupolar nuclei of 14N having spin I=1, wherein the detection of the spectrum occurs indirectly via the spin S=1⁄2 nuclei, wherein the transfer of coherence occurs through residual dipolar splittings, the method comprising the steps of:
a) exciting the neighboring nucleus single quantum coherence;
b) applying a delay of τexc≈1/(2D), wherein D is a splitting between the quadrupolar nuclei of 14N and the nuclei with spin S=1⁄2 due to residual dipolar splittings, leading to antiphase coherence;
c) applying a first 14N RF-pulse of duration τp the quadrupolar nuclei of 14N having spin I=1 for transferring anti-phase coherence into heteronuclear coherence;
d) applying a π-RF-pulse to the neighboring nucleus with spin S=1⁄2 in a middle of an evolution interval t1;
e) applying a second 14N RF-pulse at t1 of duration τp to the quadrupolar nuclei of 14N having spin I=1, wherein to is an interval between centers of the first and the second 14N pulses; and
f) recording the signal of the neighboring nucleus with spin S=1⁄2 after a duration τrec≈1/(2D) in t2, wherein t2 is the detection time interval.

2. The method of claim 1, wherein step a) comprises cross polarization from protons.

3. The method of claim 1, wherein the neighboring nucleus with spin S=1⁄2 is chosen from the group consisting of 13C, 31P, 15N, 29Si, and 1H.

4. The method of claim 1, wherein steps a) to f) are repeated for N rotor-synchronized increments t1=nΔt1 with Δt1=1 /νrot and n=1 , 2, 3 . . . N in a manner of two-dimensional spectroscopy, wherein νrot is a spinning frequency of the solid powder sample.

5. The method of claim 4, wherein time domain signals S(t1, t2) are Fourier transformed with respect to t1 to yield a spectrum of the quadrupolar nuclei of 14N having spin I=1 in an ω1 domain and with respect to t2 to yield a spectrum of the neighboring nucleus with S=1⁄2 in an ω2 domainI.

6. The method of claim 1, wherein (π/2)φ pulses are applied to the neighboring nucleus with S=1⁄2 at a beginning and at an end of the evolution interval t1.

7. The method of claim 1, wherein a z-filter is used before a detection period.

8. The method of claim 1, wherein a quadrupolar coupling constant CQ, an asymmetry parameter ηQ of the quadrupolar nuclei of 14N having spin I=1, and a relative orientation of the quadrupolar tensor with respect to a bond between the quadrupolar nuclei of 14N having spin I=1 and the neighboring nucleus with S=1⁄2 are extracted from the obtained NMR spectra.