Patent Document (Category 6):

the method presented in this work exploits residual dipolar splittings between 14 n ( i = 1 ) and a “ spy ” nucleus with s = ½ such as 13 c , in combination with scalar j couplings . the residual splitting d ( 14 n , 13 c ), which decreases in inverse proportion to the static field strength b 0 , is on the order of d ≈ 30 hz for 14 nh 3 + 13 c α hrcoo − in zwitterionic amino acids at b 0 = 9 . 4 t ( 400 mhz for protons ), while j ( 14 n , 13 c ) couplings in l - alanine are about 3 . 1 and 4 . 0 hz for 14 nh 3 + r and 14 nh 2 r 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 13 c α 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 /( πt 2 ′). in amino acids , the time constant t 2 ′( 13 c α ) of spin - echo decays can be as long as 50 ms , so that 1 /( πt 2 ′)= 6 hz is not exceptional for 13 c α . the pulse sequence and coherence transfer pathways for the novel two - dimensional correlation nmr methods are illustrated in fig1 . after exciting carbon - 13 single - quantum coherence c x =( t c 11 + t c 1 − 1 )/ 2 in the usual manner by cross - polarization from protons , a delay τ ≈ ½d leads to a state that can be described by a product of irreducible tensor operators t c 11 t n 20 . this state can also be represented by a product of cartesian operators c x ( n z 2 − 2e n / 3 ), where the unity operator e n ensures that the product operator is traceless and orthonormal . for simplicity , we can loosely speak of a doubly - antiphase operator c x n z 2 . 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 14 n spectrum can lead to a partial conversion into t c 11 t n 1 ± 1 and t c 11 t n 2 ± 1 ( corresponding to 14 n single - quantum coherences ) or into t c 11 t n 2 ± 2 , corresponding to 14 n 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 ( fig1 ), and of course in the appearance of the spectra . in either case , a π pulse applied to 13 c in the middle of the evolution interval t 1 not only interconverts t c 1 + 1 and t c 1 − 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 {-( τ exc + t 1 + τ rec )/ t 2 ′( c )}. terms containing t c 1 − 1 are converted into t c 1 + 1 by the π pulse at t 1 / 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 τ exc and τ rec , the inhomogeneous decay with a time constant t 2 *& lt ;& lt ; t 2 ′ does not contribute to signal losses . the heteronuclear coherences t c 11 t n 1 ± 1 and t c 11 t n 2 ± 1 or t c 11 t n 2 ± 2 are allowed to evolve freely during the evolution interval t 1 prior to symmetrical reconversion into observable single quantum coherence t c 1 − 1 . the experiment is repeated for n rotor - synchronized increments t 1 = nδt 1 with δt 1 = 1 / ν rot and n = 1 , 2 , 3 , . . . , n , in the manner of two - dimensional spectroscopy . the time - domain signals s ( t 1 , t 2 ) are fourier transformed with respect to t 1 to yield a 14 n spectrum in the ω 1 domain , and with respect to t 2 to produce a 13 c spectrum in the ω 2 domain . the coherence transfer pathways in fig1 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 14 n coherence order ρ n . note that , in contrast to most other 2d experiments , the t 1 period is defined as the interval between the centers of the two 14 n 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 ω 1 domain . the initial free evolution interval between the pulses is 1 / ν rot − τ p . the nitrogen - 14 single - and double - quantum coherences evolve in the t 1 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 δt 1 with the spinner period 1 / ν rot leads to aliasing in the ω 1 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 13 c at the beginning and at the end of the evolution period can convert t s 11 t i 22 into t s 10 t i 22 and back . complementary experiments with different phases φ of the 13 c pulse can be used . this variant allows one to avoid the t 2 - decay of the t s 11 term in the t 1 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 τ rec & lt ; ½d , so that the reconversion into in - phase c x coherence is not complete . fig2 and fig3 show simulations of sq and dq powder patterns as a function of the excitation and reconversion intervals τ exc = τ rec and of the 14 n pulse length τ p . 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 τ p for sq excitation is about half as for dq excitation . in the experimental sq and dq spectra of fig4 , the 14 n 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 fig4 a , the residual dipolar splitting d ( 14 n , 13 c ) is barely resolved at 9 . 4 t . the fact that 14 n coherences can be excited efficiently even in the absence of a resolved residual dipolar splitting is demonstrated in fig4 b for glycine . fig5 shows how the two crystallographic ally inequivalent 13 c sites i and ii in powdered l - leucine correlate with non - degenerate 14 n quadrupole parameters estimated to c q i = 1 . 2 mhz , η q i = 0 . 3 , c q ii = 1 . 1 mhz , η q ii = 0 . 1 . again , the sq spectra are about twice as narrow at the dq spectra . fig6 shows a challenging example of a tripeptide l - ala - l - ala - gly . the terminal 14 nh 3 + group ( site ii ) has similar parameters as in fig4 , 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 — co 14 nh 13 c α — have quadrupole parameters c q i and c q iii of at least 3 mhz . it is remarkable that signals could be excited and observed with a 14 n 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 t c 11 t n 20 into t c 11 t n 2 ± 1 or t c 11 t n 2 ± 2 and back under mas is determined by the amplitude ω 1 n n and duration τ p of the 14 n pulse . numerical calculations ( neglecting relaxation ) with integration over all crystallite orientations show that with c q = 1 . 2 mhz , η q = 0 , ν rf n = 60 khz , τ p = 15 μs , d = 30 hz , and τ exc = τ rec = 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 t 1 increment , compared with a simple 13 c cpmas spectrum . the experiments work in principle with 13 c in natural abundance . the sensitivity can be boosted by a factor of about 100 by 13 c enrichment , as we have done to optimize the experimental conditions . in principle , the experiment can work with any s = ½ “ 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 14 n . 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 35 cl , 17 o , etc ., provided that one can exploit a residual dipolar splitting with suitable spy nuclei . fig7 and fig8 show how the line shapes depend on the quadrupole asymmetry parameter η q and on the relative orientation θ qd , φ qd 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 14 n 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 13 c - 14 n dipole - dipole interaction . the samples were packed in 2 . 5 mm outer diameter zro 2 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 ( 13 c and 14 n 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 ν rf h = 85 khz while ν rf c 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 14 n pulses was calibrated by direct detection of 14 nh 4 no 3 , which has a very small quadrupole splitting . the 14 n pulses had an amplitude of ν rf n = 60 khz using a 500 w amplifier . the samples of l - alanine ( 14 nh 4 + 13 c α hch 3 coo − ), glycine ( 14 nh 4 + 13 c α h 2 coo − ), l - leucine ( 14 nh 4 + 13 c α hrcoo − ) with r = ch 2 ch ( ch 3 ) 2 and the tri - peptide l - ala - l - ala - gly , all enriched in the 13 c α positions , were purchased from cambridge isotope laboratories , and used without further purification . fig1 shows pulse sequence and coherence transfer pathways for the excitation of 14 n 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 c x magnetization , followed by an interval τ exc ≈ ½d where the residual dipolar splitting d and the scalar coupling j between 14 n and 13 c lead to anti - phase coherences t c 11 t n 10 and t c 11 t n 20 . in the 14 n single - quantum experiment ( sq ), these are converted into heteronuclear coherences t c 11 t n 11 and t c 11 t n 21 by applying an rf pulse of duration τ p to the 14 n nuclei , while in the 14 n double - quantum experiment ( dq ), one excites heteronuclear coherences t c 11 t n 22 . the evolution period t 1 is defined as the separation between the centers of the two rf pulses applied to the 14 n nuclei , with a duration t 1 = nt rot ( n = 1 , 2 , . . . n ). in this interval , the coherences evolve chiefly under the second - order quadrupole interaction , before being converted back into observable c x 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 14 n pulse with addition and subtraction of the 13 c signals , while the dq experiments requires a 4 - step cycle of the phase of the first 14 n pulse ( 0 , 90 , 180 , 270 °), again with addition and subtraction of the 13 c signals . in addition , the first 1 h pulse may be phase - alternated , and the 13 c π pulse may be exorcycled . fig2 shows simulations of 14 n single - quantum ( sq ) powder patterns that result from the pulse sequence of fig1 for different excitation intervals τ exc and 14 n pulse lengths τ p . the radio - frequency ( rf ) field amplitude is ν rf = 60 khz , the quadrupolar parameters are c q = 1 . 2 mhz and η q = 0 . 2 , the dipolar interaction corresponds to a typical 14 n - 13 c bond length ( d cn = 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 14 n mas spectrum obtained with ideal excitation and rotor synchronized acquisition . fig3 shows simulations of 14 n double - quantum ( dq ) powder patterns with the same parameters as in fig2 . the powder pattern drawn with a thick line represents the ideal line shape for the double - quantum 14 n mas spectrum obtained with ideal excitation and rotor synchronized acquisition . fig4 shows ( a , b ) experimental 13 c cpmas and two - dimensional 14 n / 13 c correlation spectra showing isotropic 13 c chemical shifts along the horizontal ω 2 axis ( δ 2 labeled in ppm with respect to tms ) and 14 n ( c , d ) single - and ( e , f ) double - quantum signals along the vertical ω 1 axis ( δ 1 labeled in ppm with respect to 14 nh 4 no 3 ). ( a ) in l - alanine ( 14 nh 4 + 13 c α hch 3 coo − ) the 13 c cpmas spectrum reveals an ill - resolved residual dipolar splitting ( see expansion ); ( b ) in glycine ( 14 nh 4 + 13 c α h 2 coo − ) 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 δ 1 axis ( g - j ) reveal characteristic second - order quadrupolar powder patterns . for l - alanine c q ≈ 1 . 2 mhz and η q ≈ 0 . 3 ; for glycine c q ≈ 1 . 2 mhz and η q ≈ 0 . 5 . under our experimental conditions the t 2 ′( 13 c α ) 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 t 1 increments δt 1 = 1 / ν rot = 33 . 33 μs , with a relaxation interval of 3 s . the intervals τ exc = τ rec were 16 ms , while τ p 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 . fig5 shows ( a ) experimental 13 c cpmas and two - dimensional 14 n / 13 c correlation spectra obtained with ( b ) single - and ( c ) double - quantum methods of l - leucine that has two magnetically inequivalent sites i and ii for 14 n and 13 c α . the projections onto the δ 1 axis ( right ) reveal second - order quadrupolar powder patterns that resembles simulated patterns with c q i ≈ 1 . 2 mhz , c q ii ≈ 1 . 1 mhz , η q i ≈ 0 . 3 , and η q ii ≈ 0 . 1 . the t 2 ′ values of the two 13 c α 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 t 1 increments of δ t 1 = 1 / ν rot = 33 . 33 μs , with a relaxation interval of 3 s . the intervals τ exc = τ rec were 16 ms , while τ p was ( b ) 11 μs and ( c ) 23 μs . the cp contact time was 0 . 6 ms . fig6 shows ( a ) experimental 13 c cpmas and two - dimensional 14 n / 13 c correlation spectra obtained with ( b ) single - and ( c ) double - quantum methods for the tripeptide l - ala - l - ala - gly where all 13 c α are enriched . for the amide sites ( i ) and ( iii ), 14 n sq and dq signals can be observed ( projections on the right ) despite very large first - order quadrupole couplings ( c q i ≈ c q iii ≈ 3 mhz ) and very short t 2 ′( 13 c α )= 14 , 11 and 8 ms for sites i , ii and iii respectively . the projections of the nh 3 + group of the first l - alanine onto the δ 1 axis ( d , e ) reveal powder patterns that correspond to c q ii ≈ 1 . 3 mhz , and η q ii ≈ 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 t 1 increments δt 1 = 1ν rot = 33 . 33 μs , with a relaxation interval of 2 . 5 s . the intervals τ exc = τ rec were 6 ms , while τ p was ( b ) 11 μs and ( c ) 24 μs . the cp contact time was 0 . 5 ms . the projections of the n - terminal 14 n resonances onto δ 1 axis ( d , e ) were extracted from two - dimensional spectra recorded with ( d ) 64 ( e ) 96 t 1 increments each with ( d ) 128 and ( e ) 1024 transients . fig7 shows simulations of sq and dq 14 n spectra for c q = 1 . 2 mhz and η q = 0 , 0 . 5 and 1 , appropriate for b 0 = 9 . 4 t , τ exc = 15 ms , ν rf n = 60 khz , ν rot = 30 khz , τ p = 10 μs for sq and τ p = 20 μs for dq . the powder patterns drawn with thick lines represent spectra assuming ideal single - or double - quantum excitation and rotor synchronized acquisition . fig8 shows simulations of sq and dq 14 n spectra for c q = 1 . 2 mhz and η = 0 . 5 , appropriate for b 0 = 9 . 4 t , τ exc = 15 ms , ν rf n = 60 khz , ν rot = 30 khz , τ p = 10 μs for sq and τ p = 20 μs for dq , as a function of the polar angles θ qd , φ qd of the internuclear vector r ( 14 n , 13 c ) with respect to the principal axis system of the quadrupole tensor . for larger values of θ qd , the sensitivity of the line shapes to φ qd is more pronounced . to summarize , we have shown that by transferring coherence between 14 n and 13 c in solid powdered samples , one can indirectly detect the single - or double - quantum transitions of 14 n 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 . 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