Scaling and labeling the high-resolution isotropic axis of two-dimensional multiple-quantum magic-angle-spinning spectra of half-integer quadrupole spins

The dynamics of half-integer quadrupole spins ~I5 3 2 , 5 2 , 7 2 , and 9 2 ! during the multiple-quantum ~MQ! magic-angle spinning experiment with the two-pulse sequence, a recent NMR method, is analyzed in order to scale in frequency unit and label in ppm ~the chemical shift unit! the high-resolution isotropic axis of a two-dimensional ~2D! spectrum. Knowledge of the two observed chemical shifts ~dG1 (obs) and dG2 ! of the center of gravity of an MQ-filtered central-transition peak in the two dimensions allows us to determine the true isotropic chemical shift of an absorption line, which is related to the mean bond angle in a compound. Only the isotropic chemical shift and the second-order quadrupole interaction for a sample rotating at the magic angle at a high spinning rate are considered during the free precession of the spin system. On the other hand, only the first-order quadrupole interaction for a static sample is considered during the pulses. The hypercomplex detection method is used to obtain a pure 2D absorption spectrum. The pulse program and the successive stages of data processing are described. For simplicity, only the density matrix for a spin I5 3 2 at the end of the first pulse of phase w is calculated in detail, which allows us to deduce the phase cycling of the pulse sequence that selectively detects the 63-quantum coherences generated by the first pulse. The positions of the echo and antiecho relative to the second pulse, and that of the MQ-filtered central-transition peak relative to the carrier frequency (v0) along the F1 dimension are derived for the four half-integer quadrupole spins. The frequency offset of v0 relative to an external aqueous solution in the F1 dimension is linearly related to that in the F2 dimension. The shearing transformation, whose main interest is to shift the beginning of the acquisition period from the end of the second pulse to the echo position and to yield a high-resolution spectrum along the F1 dimension, is presented in great detail. In the literature, two conventions are used to define the evolution period. Convention Cz takes the experimental evolution period as the evolution period, whereas convention Ck considers the echo position relative to the first pulse as the evolution period. The true isotropic chemical shift, the second-order quadrupole shift of the center of gravity of a peak, and the parameter CQh relating the quadrupole coupling constant with the asymmetry parameter are functions of dG1 (obs) and dG2 (obs) ; their relationships depend on the conventions. In fact, convention Ck introduces a scaling factor ~depending on the spin and the coherence order! that modifies not only the spectral width and the linewidth, but also the positions of the spinning sidebands in the F1 dimension. Convention Cz is recommended for linewidth comparison. The analytical expressions are checked using Rb (I5 3 2 ) in the extensively studied RbNO3 powder with two carrier frequencies: 98.2 and 163.6 MHz. Our data are in agreement with those of the literature. @S0163-1829~98!01429-5#