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Two-dimensional One Pulse (TOP) experiment is a data processing approach where a 1D MAS spectrum containing spinning sidebands is mapped into a 2D spectrum correlating frequency and spinning sideband order. It was first described in the context of spin 1/2 and spin 1 nuclei by Blumich and coworkers. For half-integer quadrupolar nuclei the TOP representation of MAS data is particularly advantageous over the conventional one-dimensional spectrum. The TOP spectrum provides a rapid determination of the number of sites as well as size of their quadrupolar coupling. Additionally, synchronous acquisition spectra of the central and satellites transition resonances can be separated by different projections of the TOP spectrum, with higher resolution spectra often found in the satellite transitions projection.

For example, shown below is the TOP transformation of a one dimensional 27Al NMR spectrum of A9B2 (9Al2O3-2B2O3), a crystalline compound with four different Al sites, acquired at 17.6 T with ΩR/2 π = 31248 Hz.


Processing Approach

Time Domain

In a one pulse NMR experiment with a rotating sample, rotational echoes are obtained in the time domain with the coordinate definitions and timings shown below.


This data falls along the sampling trajectory (blue lines) of the sample spinning data in the 2D t-Θ and k-Ξ coordinate systems shown below.


The slope of the sampling trajectory in the t-Θ coordinate system is the inverse rotor frequency. Identical data sets run parallel in the 2D plane and are separated by tR and 2 π, respectively, t-Θ coordinate system. After shearing, a 2D data that correlates time and rotor pitch is obtained. A double Fourier transform of this data with respect to time and rotor pitch yields a 2D spectrum correlating frequency and spinning sideband order.

Frequency Domain

Alternatively, one can perform the TOP processing starting with the one-dimensional Frequency domain spectrum with spinning sideband using the coordinate definitions and spacings shown below.


The one dimensional frequency domain spectrum is stacked identically in a 2D ω1'-N' coordinate system as shown below.


By applying a shearing transformation, the 2D spectrum in ω1-N coordinate system, shown below, which correlates frequency to sideband order, of 2D spectrum, is obtained.


References and Related Resources from our Lab