Solid-state MAS correlation spectra involving cross polarization cross polarization will always provide spectra which are will generally provide spectra which are asymmetric about the asymmetric about the main diagonal. This effect, which is main diagonal. A quantitative treatment of this effect is provided due to the nonuniform nonequilibrium initial conditions inand is demonstrated experimentally with examples of two-dimenduced by cross polarization, is usually very pronounced, sional spin-diffusion spectra. The effect, which is due to the noncannot be eliminated simply, and must be taken into account uniform nonequilibrium initial coherent state induced by cross in quantitative analysis.
polarization, is usually pronounced, and cannot be eliminated sim-
The possibility of liquid-state correlation spectra being ply. It must be taken into account when quantifying solid-state asymmetric is well recognized (5). In general it is sufficient
CPMAS correlation spectra. α§ 1998 Academic Press
that the preparation of the magnetization is nonuniform, and it has been remarked that this occurs whenever selective pulses are used, or if the delay between successive experi-Nuclear magnetic resonance correlation spectroscopy apments is too short to allow full recovery to thermal equilibplied to powders has recently experienced a rapid expansion. rium in the presence of different relaxation rates. This second A promising route toward structure determination in solids mechanism, originally exploited by Bremer et al. (10), has by NMR (1) appears to be the combination of magic-angle recently been discussed in some detail by Griesinger and sample spinning (MAS) (2, 3), which yields high-resolution co-workers (11, 12). In most liquid-state correlation experispectra during the detection periods of a two-dimensional ments, however, asymmetry can be avoided by simply using experiment, with different methods of reintroducing dipolar a sufficiently long relaxation delay. This is not the case in interactions during the mixing time. These experiments all solid-state experiments in which cross polarization is used conform to the basic spin-exchange scheme shown in Fig. to prepare the initial coherent state, since the cross-polariza-1 (4, 5) and encompass a wide variety of mixing schemes tion step always results in a state which is normally not varying from simply waiting long enough for exchange to uniformly proportional to the equilibrium condition. This is occur spontaneously (in the original spin-diffusion experia well-known effect which is at the origin of the fact that it ment) (6, 7), to sophisticated recoupling schemes using rois difficult to obtain ''quantitative'' CPMAS spectra in which tor-synchronized RF pulses. Usually, the experiments are the integrals are simply proportional to the number of carperformed on fully or partially isotopically enriched carbonbons. The consequences of this situation on two-dimensional 13 or nitrogen-15 samples, in which sensitivity is enhanced correlation spectra can be easily appreciated if we consider by cross polarization (once again using some sort of more the predicted cross-peak intensities in two possible versions or less sophisticated sequence of RF pulses) (8, 9). The of the MAS exchange experiment (4, 13, 14) shown in Figs. spectra that can be recorded are currently of sufficient quality 1b and 1c. Using standard procedures one finds that in the that attention can be given to detailed quantification and case of Fig. 1b where excitation is achieved by a single interpretation of the observed correlations in terms of molecnonselective carbon pulse, the time-domain signal is (neular geometry.
glecting relaxation during t 1 and t 2 ) (5) In this article we point out that contrary to their liquidstate cousins such as COSY and NOESY, which under cons(t 1 , t m , t 2 ) ditions of complete relaxation yield symmetric correlation spectra (5), solid-state MAS correlation spectra involving Γ
0 β k,l exp(iv k t 2 )[exp(Lt m )] kl exp(iv l t 1 )M l 0 , [1]