Potassium Sulfate, 33S (I=3/2)

33S (I=3/2) quadrupolar spectrum simulation.

The following example is the \(^{33}\text{S}\) NMR spectrum simulation of potassium sulfate (\(\text{K}_2\text{SO}_4\)). The quadrupole tensor parameters for \(^{33}\text{S}\) is obtained from Moudrakovski et. al. 1

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 BlochDecayCentralTransitionSpectrum

# global plot configuration
mpl.rcParams["figure.figsize"] = [4.5, 3.0]

Step 1: Create the spin system

site = Site(
    name="33S",
    isotope="33S",
    isotropic_chemical_shift=335.7,  # in ppm
    quadrupolar={"Cq": 0.959e6, "eta": 0.42},  # Cq is in Hz
)
spin_system = SpinSystem(sites=[site])

Step 2: Create a central transition selective Bloch decay spectrum method.

method = BlochDecayCentralTransitionSpectrum(
    channels=["33S"],
    magnetic_flux_density=21.14,  # in T
    rotor_frequency=14000,  # in Hz
    spectral_dimensions=[
        {
            "count": 2048,
            "spectral_width": 5000,  # in Hz
            "reference_offset": 22500,  # in Hz
            "label": r"$^{33}$S resonances",
        }
    ],
)

Step 3: Create the Simulator object and add method and spin system objects.

sim = Simulator()
sim.spin_systems += [spin_system]  # add the spin system
sim.methods += [method]  # add the method

Step 4: Simulate the spectrum.

sim.run()

# The plot of the simulation before signal processing.
ax = plt.subplot(projection="csdm")
ax.plot(sim.methods[0].simulation.real, color="black", linewidth=1)
ax.invert_xaxis()
plt.tight_layout()
plt.show()

Step 5: Add post-simulation signal processing.

processor = sp.SignalProcessor(
    operations=[sp.IFFT(), apo.Exponential(FWHM="10 Hz"), sp.FFT()]
)
processed_data = processor.apply_operations(data=sim.methods[0].simulation)

# The plot of the simulation after signal processing.
ax = plt.subplot(projection="csdm")
ax.plot(processed_data.real, color="black", linewidth=1)
ax.invert_xaxis()
plt.tight_layout()
plt.show()

1

Moudrakovski, I., Lang, S., Patchkovskii, S., and Ripmeester, J. High field \(^{33}\text{S}\) solid state NMR and first-principles calculations in potassium sulfates. J. Phys. Chem. A, 2010, 114, 1, 309–316. DOI: 10.1021/jp908206c