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¹³C MAS NMR of Glycine (CSA) [960 Hz]

The following is a sideband least-squares fitting example of a \(^{13}\text{C}\) MAS NMR spectrum of Glycine spinning at 960 Hz. The following experimental dataset is a part of DMFIT 1 examples. We thank Dr. Dominique Massiot for sharing the dataset.

import csdmpy as cp
import numpy as np
import matplotlib.pyplot as plt
from lmfit import Minimizer

from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.method.lib import BlochDecaySpectrum
from mrsimulator import signal_processor as sp
from mrsimulator.utils import spectral_fitting as sf
from mrsimulator.utils import get_spectral_dimensions

Import the dataset

host = "https://nmr.cemhti.cnrs-orleans.fr/Dmfit/Help/csdm/"
filename = "13C MAS 960Hz - Glycine.csdf"
experiment = cp.load(host + filename)

# For spectral fitting, we only focus on the real part of the complex dataset
experiment = experiment.real

# Convert the coordinates along each dimension from Hz to ppm.
_ = [item.to("ppm", "nmr_frequency_ratio") for item in experiment.dimensions]

# plot of the dataset.
plt.figure(figsize=(8, 4))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.set_xlim(280, -10)
plt.grid()
plt.tight_layout()
plt.show()
plot 2 13C glycine 960Hz

Estimate noise statistics from the dataset

coords = experiment.dimensions[0].coordinates
noise_region = np.where(coords < 10e-6)
noise_data = experiment[noise_region]

plt.figure(figsize=(3.75, 2.5))
ax = plt.subplot(projection="csdm")
ax.plot(noise_data, label="noise")
plt.title("Noise section")
plt.axis("off")
plt.tight_layout()
plt.show()

noise_mean, sigma = experiment[noise_region].mean(), experiment[noise_region].std()
noise_mean, sigma
Noise section
(<Quantity 0.6193483>, <Quantity 3.939941>)

Create a fitting model

Spin System

C1 = Site(
    isotope="13C",
    isotropic_chemical_shift=176.0,  # in ppm
    shielding_symmetric={"zeta": 70, "eta": 0.6},  # zeta in Hz
)
C2 = Site(
    isotope="13C",
    isotropic_chemical_shift=43.0,  # in ppm
    shielding_symmetric={"zeta": 30, "eta": 0.5},  # zeta in Hz
)

spin_systems = [SpinSystem(sites=[C1], name="C1"), SpinSystem(sites=[C2], name="C2")]

Method

# Get the spectral dimension parameters from the experiment.
spectral_dims = get_spectral_dimensions(experiment)

MAS = BlochDecaySpectrum(
    channels=["13C"],
    magnetic_flux_density=7.05,  # in T
    rotor_frequency=960,  # in Hz
    spectral_dimensions=spectral_dims,
    experiment=experiment,  # experimental dataset
)

Guess Model Spectrum

# Simulation
# ----------
sim = Simulator(spin_systems=spin_systems, methods=[MAS])
sim.config.decompose_spectrum = "spin_system"
sim.run()

# Post Simulation Processing
# --------------------------
processor = sp.SignalProcessor(
    operations=[
        sp.IFFT(),
        sp.apodization.Exponential(FWHM="20 Hz", dv_index=0),  # spin system 0
        sp.apodization.Exponential(FWHM="200 Hz", dv_index=1),  # spin system 1
        sp.FFT(),
        sp.Scale(factor=100),
    ]
)
processed_dataset = processor.apply_operations(dataset=sim.methods[0].simulation).real

# Plot of the guess Spectrum
# --------------------------
plt.figure(figsize=(8, 4))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.plot(processed_dataset, linewidth=2, alpha=0.6)
ax.set_xlim(280, -10)
plt.grid()
plt.legend()
plt.tight_layout()
plt.show()
plot 2 13C glycine 960Hz

Least-squares minimization with LMFIT

Use the make_LMFIT_params() for a quick setup of the fitting parameters.

params = sf.make_LMFIT_params(sim, processor, include={"rotor_frequency"})
print(params.pretty_print(columns=["value", "min", "max", "vary", "expr"]))

Name                                      Value      Min      Max     Vary     Expr
SP_0_operation_1_Exponential_FWHM            20     -inf      inf     True     None
SP_0_operation_2_Exponential_FWHM           200     -inf      inf     True     None
SP_0_operation_4_Scale_factor               100     -inf      inf     True     None
mth_0_rotor_frequency                       960      860     1060     True     None
sys_0_abundance                              50        0      100     True     None
sys_0_site_0_isotropic_chemical_shift       176     -inf      inf     True     None
sys_0_site_0_shielding_symmetric_eta        0.6        0        1     True     None
sys_0_site_0_shielding_symmetric_zeta        70     -inf      inf     True     None
sys_1_abundance                              50        0      100    False 100-sys_0_abundance
sys_1_site_0_isotropic_chemical_shift        43     -inf      inf     True     None
sys_1_site_0_shielding_symmetric_eta        0.5        0        1     True     None
sys_1_site_0_shielding_symmetric_zeta        30     -inf      inf     True     None
None

Solve the minimizer using LMFIT

opt = sim.optimize()
minner = Minimizer(
    sf.LMFIT_min_function,
    params,
    fcn_args=(sim, processor, sigma),
    fcn_kws={"opt": opt},
)
result = minner.minimize()
result

Fit Result



The best fit solution

best_fit = sf.bestfit(sim, processor)[0].real
residuals = sf.residuals(sim, processor)[0].real

plt.figure(figsize=(8, 4))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.plot(residuals, color="gray", linewidth=0.5, label="Residual")
ax.plot(best_fit, linewidth=2, alpha=0.6)
ax.set_xlim(280, -10)
plt.grid()
plt.legend()
plt.tight_layout()
plt.show()
plot 2 13C glycine 960Hz
1

D.Massiot, F.Fayon, M.Capron, I.King, S.Le Calvé, B.Alonso, J.O.Durand, B.Bujoli, Z.Gan, G.Hoatson, ‘Modelling one and two-dimensional solid-state NMR spectra.’, Magn. Reson. Chem. 40 70-76 (2002) DOI: 10.1002/mrc.984

Total running time of the script: (0 minutes 3.989 seconds)

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