Rational reduction of periodic propagators for off-period observations.

Many common solid-state nuclear magnetic resonance problems take advantage of the periodicity of the underlying Hamiltonian to simplify the computation of an observation. Most of the time-domain methods used, however, require the time step between observations to be some integer or reciprocal-integer multiple of the period, thereby restricting the observation bandwidth. Calculations of off-period observations are usually reduced to brute force direct methods resulting in many demanding matrix multiplications. For large spin systems, the matrix multiplication becomes the limiting step. A simple method that can dramatically reduce the number of matrix multiplications required to calculate the time evolution when the observation time step is some rational fraction of the period of the Hamiltonian is presented. The algorithm implements two different optimization routines. One uses pattern matching and additional memory storage, while the other recursively generates the propagators via time shifting. The net result is a significant speed improvement for some types of time-domain calculations.

Investigations of low-amplitude radio frequency pulses at and away from rotary resonance conditions for I = 5/2 nuclei.

Additional experimental evidence of rotary resonance effects for multiple-quantum coherence conversion in a spin-5/2 system is presented. Two-dimensional plots of the relative efficiency of MQ excitation and conversion are given as a function of radio frequency (rf) amplitude and pulse width. Data are presented for the excitation of five-quantum coherence (5QC), as well as for 5QC to three-quantum coherence (3QC) conversion, 5QC to IQC (the central transition coherence) conversion, and 3QC to IQC conversion. A two-fold increase in the signal-to-noise ratio is achieved by substituting low amplitude rf pulses in place of hard rf pulses for 5QC excitation and 5QC to 3QC conversion in a mixed multiple-quantum magic angle spinning (MAS) (MMQMAS) experiment. The anisotropic line shape for the low-amplitude rf pulse version of the MMQMAS experiment was observed to be distorted from the MAS line shape. The cause and implications of the distortion are discussed.