RbNO3, 87Rb (I=3/2) 3QMAS

87Rb (I=3/2) triple-quantum magic-angle spinning (3Q-MAS) simulation.

The following is an example of the 3QMAS simulation of \(\text{RbNO}_3\), which has three distinct \(^{87}\text{Rb}\) sites. The \(^{87}\text{Rb}\) tensor parameters were obtained from Massiot et. al. 1. In this simulation, a Gaussian broadening is applied to the spectrum as a post-simulation step.

import matplotlib as mpl
import matplotlib.pyplot as plt
import mrsimulator.signal_processing as sp
import mrsimulator.signal_processing.apodization as apo
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.methods import ThreeQ_VAS

# global plot configuration
font = {"size": 9}
mpl.rc("font", **font)
mpl.rcParams["figure.figsize"] = [4.25, 3.0]

Generate the site and spin system objects.

Rb87_1 = Site(
    isotope="87Rb",
    isotropic_chemical_shift=-27.4,  # in ppm
    quadrupolar={"Cq": 1.68e6, "eta": 0.2},  # Cq is in Hz
)
Rb87_2 = Site(
    isotope="87Rb",
    isotropic_chemical_shift=-28.5,  # in ppm
    quadrupolar={"Cq": 1.94e6, "eta": 1.0},  # Cq is in Hz
)
Rb87_3 = Site(
    isotope="87Rb",
    isotropic_chemical_shift=-31.3,  # in ppm
    quadrupolar={"Cq": 1.72e6, "eta": 0.5},  # Cq is in Hz
)

sites = [Rb87_1, Rb87_2, Rb87_3]  # all sites
spin_systems = [SpinSystem(sites=[s]) for s in sites]

Select a Triple Quantum variable-angle spinning method. You may optionally provide a rotor_angle to the method. The default rotor_angle is the magic-angle.

method = ThreeQ_VAS(
    channels=["87Rb"],
    magnetic_flux_density=9.4,  # in T
    spectral_dimensions=[
        {
            "count": 128,
            "spectral_width": 7e3,  # in Hz
            "reference_offset": -7e3,  # in Hz
            "label": "Isotropic dimension",
        },
        {
            "count": 256,
            "spectral_width": 1e4,  # in Hz
            "reference_offset": -4e3,  # in Hz
            "label": "MAS dimension",
        },
    ],
)

Create the Simulator object, add the method and spin system objects, and run the simulation.

sim = Simulator()
sim.spin_systems = spin_systems  # add the spin systems
sim.methods = [method]  # add the method.
sim.run()

The plot of the simulation.

data = sim.methods[0].simulation
ax = plt.gca(projection="csdm")
cb = ax.imshow(data / data.max(), aspect="auto", cmap="gist_ncar_r")
plt.colorbar(cb)
ax.invert_xaxis()
ax.invert_yaxis()
plt.tight_layout()
plt.show()

Add post-simulation signal processing.

processor = sp.SignalProcessor(
    operations=[
        # Gaussian convolution along both dimensions.
        sp.IFFT(dim_index=(0, 1)),
        apo.Gaussian(FWHM="0.08 kHz", dim_index=0),
        apo.Gaussian(FWHM="0.22 kHz", dim_index=1),
        sp.FFT(dim_index=(0, 1)),
    ]
)
processed_data = processor.apply_operations(data=sim.methods[0].simulation)
processed_data /= processed_data.max()

The plot of the simulation after signal processing.

ax = plt.subplot(projection="csdm")
cb = ax.imshow(processed_data.real, cmap="gist_ncar_r", aspect="auto")
plt.colorbar(cb)
ax.set_ylim(-40, -70)
ax.set_xlim(-20, -60)
plt.tight_layout()
plt.show()

1

Massiot, D., Touzoa, B., Trumeaua, D., Coutures, J.P., Virlet, J., Florian, P., Grandinetti, P.J. Two-dimensional magic-angle spinning isotropic reconstruction sequences for quadrupolar nuclei, ssnmr, (1996), 6, 1, 73-83. DOI: 10.1016/0926-2040(95)01210-9

See also

Simulating site disorder (crystalline) for RbNO3.