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Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning
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10.1063/1.3496407
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Affiliations:
1 Department of Chemistry, Indian Institute of Technology Madras, Chennai 600 036, India
a) Author to whom correspondence should be addressed. Electronic mail: mangal@iitm.ac.in.
J. Chem. Phys. 133, 174121 (2010)
/content/aip/journal/jcp/133/17/10.1063/1.3496407
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/17/10.1063/1.3496407

## Figures

FIG. 1.

Simulated MAS spectra for a single spin-1/2 system at 100 MHz frequency. The following CSA parameters were employed in the simulations: , , and equal to 35, 50, and 65 ppm, respectively; CSA orientations , , and equal to 70°, 60°, and 122°, respectively. Gaussian line broadening of 70 Hz was employed in the simulations.

FIG. 2.

and represent simulated MAS spectra for a homonuclear dipolar-coupled two spin-1/2 system obtained at two different spinning frequencies. The following CSA parameters were employed: CSA orientations , , , , and equal to 160°, 33°, 90°/119°, 94°, and −13°, asymmetry parameters equal to 1.0/0.91, isotropic chemical shifts (denoted by asterisk) equal to 21.87 kHz/5.25 kHz and chemical shift anisotropies equal to 8.54 kHz/1.41 kHz. The dipolar coupling strength was set to 457 Hz .

FIG. 3.

, , and represent the simulated MAS spectra for a three-spin dipolar-coupled system at different spinning frequencies. The following chemical shift parameters were employed: , , , , , , , , , , , and , , , , , . The dipolar parameters employed were , , and ( dipolar coupling strength at 1 Å internuclear distance is equal to 7.5859 kHz). The asterisks denote the position of the center-band associated with the isotropic chemical shifts of the three spins.

FIG. 4.

, , and represent the simulated MAS spectra for a four-spin dipolar-coupled system at different spinning frequencies. The following chemical shift parameters were employed: , , , , , , , , , , , , , , , , , and , , , , , . The dipolar parameters employed were , , , , , and ( dipolar coupling strength at 1 Å internuclear distance is equal to 7.5859 kHz). The asterisks represent the position of the center-band associated with the isotropic chemical shifts of the four spins.

FIG. 5.

Comparison of MAS spectrum for a dipolar-coupled spin-1/2 system (top panel) and the corresponding spectrum at the matching condition (lower panel). The spectrum at matching condition is broad due to the reintroduction of the dipolar interactions resulting in lower sensitivity. Input parameters employed for the simulation are similar to that used in Fig. 2.

FIG. 6.

, , , , , and represent simulated MAS spectra for a single spin-1 system obtained by varying the quadrupolar coupling strength keeping spinning frequency fixed. The following parameters were employed in the simulations: , , , and ; CSA orientations , , and are equal to 40°, 128°, and 122°, respectively. Quadrupolar orientations , , and equal to 30°, 60°, and 120°, respectively.

FIG. 7.

, , , , , and represent simulated MAS spectra for a single spin-1 system obtained by varying spinning frequency keeping quadrupolar coupling strength fixed. Input parameters employed for the simulation are similar to that used in Fig. 6.

## Tables

Table I.

States connected by the flip-flop operators for spins and . The indices and represent the spin states and depend on the spin topology. In the case of a two-spin system, , , , and , while , , and , , in the cases of three and four spins, respectively.

/content/aip/journal/jcp/133/17/10.1063/1.3496407
2010-11-04
2014-04-17

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