polycrystalline powders of l - alanine and calcium formate with natural isotopic abundance , and of uniformly 13 c , 15 n - labelled l - alanine and l - glycine , were used without further purification . all experiments were performed on a bruker spectrometer operating at 9 . 4 t ( larmor frequency 400 . 2 mhz for protons ), equipped with a 2 . 5 mm triple resonance mas probe . in all experiments , cross - polarization ( cp ) was used to enhance the carbon - 13 magnetization , and the spinning frequency was set to ν rot = 30 khz . the carrier frequency ν 0 i of the decoupling rf field applied to the protons i was systematically placed on - resonance for the protons that are directly attached to the 13 c nuclei under observation . starting from the original scheme employing simple π phase shifts [ 1 ], a new supercycled scheme aimed at attenuating rotary resonance interferences during heteronuclear decoupling has been developed . the phase - inverted supercycled sequence for attenuation of rotary resonance ( pissarro ) is composed of pulse pairs ( τ p ) x ( τ p ) − x , ( τ p ) − x ( τ p ) x , ( τ p ) − y ( τ p ) y and ( τ p ) y ( τ p ) − y each of which is repeated n times ( typically n = 5 , see below ) to form a block . in the pissarro scheme shown in fig1 four blocks are combined , but other numbers of blocks can also be used . after the combination of phase inverted blocks ( τ p ) x ( τ p ) − x , and ( τ p ) − x ( τ p ) x a phase shift , for example 90 °, is carried out , thereby shifting the phase from x to y ( phase shifts other than 90 ° are also possible ). by constructing such supercycles [ 9 , 23 ], rotary resonance interferences can be attenuated and higher order heteronuclear terms can be minimized [ 9 ]. the decoupling efficiency of the new scheme has been compared with well - known decoupling methods such as cw , tppm [ 3 ], spinal - 64 [ 24 ] and xix [ 1 , 2 ] over a wide range of nutation frequencies 40 & lt ; ν 1 i & lt ; 140 khz . for the tppm sequence , the pulse duration τ p and phase angle φ were optimized for each nutation frequency ν 1 i , τ p being varied in the vicinity of the duration of an ideal π pulse , the phase angles φ being varied around ± 15 °. for a given nutation frequency ν 1 i , the optimal pulse durations for the spinal - 64 experiments were found to be close to those for tppm . for xix decoupling , the pulse duration τ p has been optimized around the recommended condition τ p = 2 . 85 · τ rot [ 2 ]. for the pissarro sequence , the pulse duration τ p was optimized for each nutation frequency ν 1 i in the interval 0 . 1 · τ rot & lt ; τ p & lt ; 1 . 1 · τ rot . to simulate the 13 c spectrum of calcium formate with xix and pissarro decoupling at the n = 2 rotary resonance condition , isolated 13 c - 1 h spin pairs with an internuclear distance of 1 . 09 å have been assumed , neglecting chemical shift anisotropies . all simulations used the simpson program [ 25 ]. powder averaging was achieved with 17 γ - angles and 615 α , β - orientations using the zaremba - conroy - wolfsberg ( zcw ) scheme [ 25 ]. to illustrate how rotary resonance recoupling can interfere destructively with decoupling in rapidly spinning powders , fig2 shows plots of 13 c signals of l - alanine in natural abundance recorded with cw decoupling as a function of the nutation frequency ν 1 i . besides a dramatic collapse of all peaks in the vicinity of the rotary resonance conditions ν 1 i = nν rot with n = 1 and 2 , the plots reveal that the ‘ dips ’ around these recoupling conditions extend symmetrically over a wide range of nutation frequencies ν 1 i . although their breadth can be in part ascribed to the inhomogeneity of the rf - field , since rotary resonance is very sensitive to this parameter [ 15 ( a )], the fact that the dips are the broadest for the ch group must be due to the strength of the heteronuclear dipolar interactions . note that for the methyl ch 3 and carboxyl cooh groups , the two dips for n = 1 and 2 are much broader than would be expected from the magnitudes of the corresponding heteronuclear couplings . this strongly suggests that homonuclear proton - proton dipolar interactions must also contribute to the breadth of these dips [ 21 ] by playing an indirect role in the recoupling conditions at n = 1 and 2 . quenching of interference of rotary resonance recoupling ( r 3 ) with heteronuclear decoupling the efficiency of different decoupling sequences for the ch 3 , ch 2 and ch groups of uniformly labelled alanine and glycine is shown in fig3 over a wide range of nutation frequencies ν 1 i that include rotary resonance conditions ν 1 i = nν rot with n = 2 , 3 and 4 . for each resonance , the signal intensities were normalized to s = 1 for the pissarro scheme using the highest nutation frequency ν 1 i . besides the obvious improvement in performance of all phase - modulated schemes compared to cw decoupling , the pissarro sequence proved to be the most effective in quenching rotary resonance effects in the range 40 & lt ; ν 1 i & lt ; 100 khz . for ch 3 and ch groups , it turned out to be the most efficient method over the whole range 40 & lt ; ν 1 i & lt ; 140 khz that has been explored . indeed , for both ch 3 and carboxyl groups ( the latter not shown ), the new scheme using ν 1 i = 90 khz is more efficient than tppm with ν 1 i = 140 khz , and for ch 3 and ch groups the new method , again using ν 1 i = 90 khz , reaches ˜ 80 % of the performance of xix with ν 1 i = 140 khz . for the ch 2 group of glycine , the pissarro scheme was only inferior to the tppm sequence in the range of 110 & lt ; ν 1 i & lt ; 130 khz , while for ν 1 i = 140 khz the new method showed the same performance as xix and tppm . obviously , a high decoupling efficiency with moderate nutation frequencies ν 1 i & lt ; 100 khz is particularly attractive for heat - sensitive samples , such as proteins with high water and salt content , where high rf power levels can be harmful . fig4 a allows one to appreciate how sensitive various decoupling schemes are to rotary resonance interference at the n = 2 condition ( ν 1 i = 60 khz and ν rot = 30 khz ). the relative intensities of the ch 3 signals using pissarro , xix , spinal - 64 , tppm and cw decoupling are 100 , 33 , 27 , 18 and 8 % respectively . the ch 3 linewidths are 83 , 126 , 163 , 250 and 730 hz for the five methods that have been compared . note that areas of the signals are not conserved , since the signal amplitudes are partly transferred to modulation sidebands , as discussed below . for the ch resonance , the relative intensities in fig4 a are 100 , 18 , 14 , 8 and 7 %, and the corresponding linewidths are 135 , 218 , 285 , 760 and 1250 hz . for the ch 2 resonance , the relative intensities are 100 , 12 , 12 , 13 and 9 %, and the corresponding linewidths 250 , 440 , 1100 , 710 and 1230 hz . although at the n = 2 rotary resonance condition , the amplitude of the ch 2 signal observed with pissarro remains humble compared to high amplitude decoupling ( the efficiency of decoupling at ν 1 i = 100 khz is shown in fig4 b ), the ch 2 intensity could be increased by a factor of at least 8 compared to other decoupling schemes at n = 2 . it should be pointed out that for xix decoupling , an improved efficiency was observed at n = 2 with τ p = 0 . 85 · τ rot , much shorter that the recommended duration τ p = 2 . 85 · τ rot . however , the intensities recorded under such unusual conditions are significantly below those observed with the new decoupling scheme . another remarkable advantage of the new pissarro scheme is its unique capacity to suppress spurious modulation sidebands , which arise from the interference between the decoupling field and the modulation of dipolar couplings by mas [ 3 ]. fig5 shows spectra recorded at the n = 2 rotary resonance condition , with different decoupling schemes optimized for signal intensity . the modulation sidebands show up dramatically for all known techniques except for the new scheme , which offers a remarkably clean spectrum . because of the complexity of the evolution of the magnetization under phase - modulated irradiation and mas close to the rotary resonance conditions , the combined effects of homo - and heteronuclear dipolar interactions are difficult to handle analytically . to gain a better insight into some basic features of xix and pissarro decoupling , the behaviour of calcium formate ca ( chcoo ) 2 with natural 13 c abundance , which contains reasonably isolated 13 c - 1 h spin pairs , has been studied by experiments and simulations . very similar effects could be observed for the ( less well isolated ) ch group in uniformly 13 c enriched l - alanine . as shown in fig6 , both the experimental and simulated spectra clearly show the dependence of the modulation sidebands that appear at ν ms = n (± ν rot ∓ 1 / τ p ) on the pulse duration τ p of xix decoupling . thus for ν rot = 30 khz and τ p = 31 . 5 μs , i . e ., 1 / τ p = 31 . 746 khz , one obtains sidebands at multiples of 1 . 746 khz . these modulation sidebands cannot be avoided when optimizing the τ p values for the best efficiency of xix decoupling . on the other hand , experimental and simulated spectra obtained with the pissarro scheme with optimized τ p values are remarkably free of any spurious sideband signals . further simulations ( not shown ) reveal that the magnitudes of the dipolar and csa interactions , the proton offset as well as the decoupling frequency affect the intensity of the modulation sidebands under xix decoupling . extensive numerical simulations will be necessary to probe the influence of homonuclear proton - proton couplings when quenching rotary resonance effects . indeed , the relevance of such interactions for heteronuclear decoupling in fast spinning solids has been recognized early on [ 1 ], and studied experimentally and theoretically under different conditions [ 1 , 9 , 26 - 28 ]. it is worth noting that the modulation sidebands overlap with their parent signals when τ p corresponds to a full rotor period ( ν rot = 1 / τ p ), thus fulfilling one of the recoupling conditions for phase - modulated decoupling [ 1 , 2 ]. finally , it should be noted that a simplified , truncated version of the pissarro scheme , using only the first half of the decoupling sequence in fig1 , without any 90 ° phase shifts , also exhibits a significantly improved decoupling efficiency at n = 2 compared with other pulse sequences . for 70 & lt ; ν 1 i & lt ; 80 khz , it is actually superior to the complete untruncated pissarro scheme . the supercycled pissarro sequences with odd numbers of pulse pairs n = 3 , 5 , 7 . . . ( usually , n = 5 ) perform significantly better than those with even numbers n = 2 , 4 , . . . . this appears to open further opportunities to improve the quenching of rotary resonance interferences . destructive interference due to rotary resonance recoupling also occurs when very fast spinning frequencies ν rot & gt ; 30 khz are combined with commonly used rf - decoupling schemes . for ch and ch 2 resonances observed with spinning frequencies ν rot = 40 khz , rotary resonance interferences can extend beyond ν 1 i = 200 khz [ 8 ] while at ν rot = 70 khz such effects occur at ν 1 i = 350 khz [ 22 ]. all previously known decoupling methods therefore entail the use of ever - increasing rf - amplitudes with increasing nutation frequencies . of course , low - amplitude decoupling with ν 1 i & lt ;& lt ; ν rot can be used to avoid interference effects . except for ch 2 resonances , this simple approach can compete in efficiency with high amplitude decoupling , provided ν rot & gt ; 40 khz [ 8 , 29 ]. a novel heteronuclear decoupling scheme for fast mas that offers improved decoupling efficiency over a wide range of nutation frequencies ν 1 i has been introduced . the - pissarro decoupling sequence using a single adjustable τ p parameter proved to be more effective that the xix , tppm , spinal - 64 and cw methods in quenching rotary resonance interference effects . the new method yields improved resolution and sensitivity for all solid - state nmr spectra recorded with fast spinning with nutation frequencies ν 1 i close to the n = 2 rotary resonance condition . numerical simulations of pissarro decoupling using an experimentally optimized pulse duration τ p corroborate the experimental observation that spurious signals due to modulation sidebands are efficiently eliminated . for ch 3 , cooh and ch groups , pissarro decoupling proved to be the most efficient method over the whole range 40 & lt ; ν 1 i & lt ; 140 khz that was examined . for the most challenging ch 2 groups , pissarro decoupling was less efficient than tppm only in a limited range 110 & lt ; ν 1 i & lt ; 130 khz . at ν 1 i = 140 khz the new scheme has the same performance as xix and tppm . since pisarro decoupling leads to quenching of rotary resonance interferences , one can expect an improved efficiency of low - amplitude decoupling at spinning frequencies ν rot & gt ; 40 khz . the inventive method has been exemplary explained for the resonance measurements with dilute spins s = 13 c and abundant spins i = 1 h . however , the application of the inventive method is not restricted to these nuclei , but can be carried out in analogous manner using spins of other nuclei . the proposed a new scheme for heteronuclear decoupling designed for fast magic - angle spinning ( mas ) is dubbed phase - inverted supercycled sequence for attenuation of rotary resonance ( pissarro ). its efficiency compares favourably with cw , tppm , spinal and xix decoupling methods at medium and high nutation frequencies , particularly under conditions where the efficiency of decoupling can be affected by undesired rotary resonance effects . p . tekely , p . palmas , d . canet , j . magn . reson . a 107 ( 1994 ) 129 - 133 . a . detken , e . h . hardy , m . ernst , b . h . meier , chem . phys . lett . 356 ( 2002 ) 298 - 304 . a . e . bennett , c . m . rienstra , m . auger , k . v . lakshli , r . g . griffin , j . chem . phys . 103 ( 1995 ) 6951 - 6958 . p . hodgkinson , prog . nmr spectrosc . 46 ( 2005 ) 197 - 222 and references therein . k . takegoshi , j . mizokami , t . terao , chem . phys . lett . 341 ( 2001 ) 540 - 544 r . s . thakur , n . d . kurur , p . k . madhu , chem . phys . lett . 426 ( 2006 ) 459 - 463 . m . kotecha , n . p . wickramasingbe , y . ishii , magn . reson . chem . 45 ( 2007 ) s221 - s230 . g . depaëpe , p . hodgkinson , l . emsley , chem . phys . lett . 376 ( 2003 ) 259 - 267 . g . gerbaud , f . ziarelli , s . caldarelli , chem . phys . lett . 377 ( 2003 ) 1 - 5 . s . dusold , a . sebald , ann . rep . nmr spectrosc . 41 ( 2000 ) 185 - 264 . t . g . oas , r . g . griffin , m . h . levitt , j . chem . phys , 89 ( 1988 ) 692 - 695 . n . c . nielsen , h . bildsoe , h . j . jakobsen , m . h . levitt , j . chem . phys . 101 ( 1994 ) 1805 - 1812 . ( a ) z . gan , d . m . grant , r . r . ernst , chem . phys lett . 254 ( 1996 ) 349 - 357 ; ( b ) z . gan , j . magn . reson . 183 ( 2006 ) 247 - 253 . ( a ) k . takegoshi , s . nakamura , t . terao , chem . phys . lett . 344 ( 2001 ) 631 - 637 . ( b ) k . takegoshi , s . nakamura , t . terao , j . chem . phys . 118 ( 2003 ) 2325 - 2341 . z . gan , j . p . amoureux , j . trébosc , chem . phys . lett . 435 ( 2007 ) 163 - 169 . l . odgaard , m . bak , h . j . jakobsen , n . c . nielsen ; j . magn . reson . 148 ( 2001 ) 298 - 308 . ( a ) l . duma , d . abergel , p . tekely , g . bodenhausen , chem . comm . 20 ( 2008 ) 2361 - 2363 ; ( b ) l . duma , d . abergel , f . ferrage , p . pelupessy , p . tekely , g . bodenhausen , chem phys chem . 9 ( 2008 ) 1104 - 1108 . t . nakai , c . a . mcdowell , chem . phys . lett . 227 ( 1994 ) 639 - 644 . s . j . kitchin , k . d . m . harris , a . e . aliev , d . c . apperley , chem . phys . lett . 323 ( 2000 ) 490 - 497 . m . ernst , a . samoson , b . h . meier , j . chem . phys . 123 ( 2005 ) 064102 - 1 - 10 . b . m . fung , a . k . khitrin , k . ermolaev , j . magn . reson . 142 ( 2000 ) 97 - 101 . m . bak , j . t . rasmussen , n . c . nielsen , j . magn . reson . 147 ( 2000 ) 296 . m . ernst , h . zimmermann , b . h . meier , chem . phys . lett . 317 ( 2000 ) 581 - 588 . g . depaëpe , b . elena , l . emsley , j . chem . phys . 121 ( 2004 ) 3165 - 3180 . m . leskes , r . s . thakur , p . k . madhu , n . d . kurur , s . vega , j . chem . phys . 127 ( 2007 ) 024501 - 17 . m . ernst , a . samoson , b . h . meier , chem . phys . lett . 348 ( 2001 ) 293 - 302 . y . yu , b . m . fung , j . magn . reson . 130 ( 1998 ) 317 - 320 . s - f . fiu , j - d . mao , k . schmidt - rohr , j . magn . reson . 155 ( 2002 ) 15 - 28