def setup_spin_system():
site = Site(
isotope="87Rb",
isotropic_chemical_shift=-9,
shielding_symmetric=SymmetricTensor(zeta=110, eta=0),
quadrupolar=SymmetricTensor(Cq=3.5e6,
eta=0.36,
beta=70 * 3.14159 / 180),
)
return SpinSystem(sites=[site])
def coupled_spin_system(j_coup=0, dipole=0):
S1 = Site(
isotope="1H",
isotropic_chemical_shift=10, # in ppm
shielding_symmetric=SymmetricTensor(zeta=-80, eta=0.25), # zeta in ppm
)
S2 = Site(isotope="1H", isotropic_chemical_shift=-10)
S12 = Coupling(
site_index=[0, 1],
isotropic_j=j_coup,
dipolar=SymmetricTensor(D=dipole, eta=0),
)
return SpinSystem(sites=[S1, S2], couplings=[S12])
def add_site(doctest_namespace):
doctest_namespace["np"] = np
doctest_namespace["plt"] = plt
doctest_namespace["SpinSystem"] = SpinSystem
doctest_namespace["Simulator"] = Simulator
doctest_namespace["Site"] = Site
doctest_namespace["Coupling"] = Coupling
doctest_namespace["SymmetricTensor"] = SymmetricTensor
doctest_namespace["st"] = SymmetricTensor
doctest_namespace["pprint"] = pprint
doctest_namespace["Isotope"] = Isotope
doctest_namespace["sp"] = sp
doctest_namespace["Method2D"] = Method2D
site1 = Site(
isotope="13C",
isotropic_chemical_shift=20,
shielding_symmetric=SymmetricTensor(zeta=10, eta=0.5),
)
site2 = Site(
isotope="1H",
isotropic_chemical_shift=-4,
shielding_symmetric=SymmetricTensor(zeta=2.1, eta=0.1),
)
site3 = Site(
isotope="27Al",
isotropic_chemical_shift=120,
shielding_symmetric=SymmetricTensor(zeta=2.1, eta=0.1),
quadrupolar=SymmetricTensor(Cq=5.1e6, eta=0.5),
)
doctest_namespace["spin_system_1H_13C"] = SpinSystem(sites=[site1, site2])
doctest_namespace["spin_systems"] = SpinSystem(sites=[site1, site2, site3])
spin_systems = [SpinSystem(sites=[site]) for site in [site1, site2, site3]]
sim = Simulator()
sim.spin_systems += spin_systems
doctest_namespace["sim"] = sim
# Transitions
t1 = Transition(initial=[0.5, 0.5], final=[0.5, -0.5])
doctest_namespace["t1"] = t1
t2 = Transition(initial=[0.5, 0.5], final=[-0.5, 0.5])
doctest_namespace["t2"] = t2
path = TransitionPathway([t1, t2])
doctest_namespace["path"] = path
def rvs(self, size: int):
"""Draw random variates of length `size` from the distribution.
Args:
size: The number of random points to draw.
Returns:
A list of two NumPy array, where the first and the second array are the
anisotropic/quadrupolar coupling constant and asymmetry parameter,
respectively.
Example:
>>> Cq_dist, eta_dist = ext_cz_model.rvs(size=1000000)
"""
# czjzek_random_distribution model
tensors = _czjzek_random_distribution_tensors(1, size)
symmetric_tensor = self.symmetric_tensor
if isinstance(symmetric_tensor, dict):
symmetric_tensor = SymmetricTensor(**symmetric_tensor)
zeta = symmetric_tensor.zeta or symmetric_tensor.Cq
eta = symmetric_tensor.eta
# the traceless second-rank symmetric Cartesian tensor in PAS
T0 = [0.0, 0.0, 0.0]
if zeta != 0 and eta != 0:
T0 = get_principal_components(zeta, eta)
# 2-norm of the tensor
norm_T0 = np.linalg.norm(T0)
# the perturbation factor
rho = self.eps * norm_T0 / np.sqrt(30)
# total tensor
total_tensors = np.diag(T0) + rho * tensors
if not self.polar:
return get_Haeberlen_components(total_tensors)
return x_y_from_zeta_eta(*get_Haeberlen_components(total_tensors))
from mrsimulator.methods import Method2D
from mrsimulator import signal_processing as sp
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension, SpectralEvent
# sphinx_gallery_thumbnail_number = 3
# %%
# Generate the site and spin system objects.
site_Ni = Site(
isotope="2H",
isotropic_chemical_shift=-97, # in ppm
shielding_symmetric=SymmetricTensor(
zeta=-551, # in ppm
eta=0.12,
alpha=62 * 3.14159 / 180, # in rads
beta=114 * 3.14159 / 180, # in rads
gamma=171 * 3.14159 / 180, # in rads
),
quadrupolar=SymmetricTensor(Cq=77.2e3, eta=0.9), # Cq in Hz
)
site_Cu = Site(
isotope="2H",
isotropic_chemical_shift=51, # in ppm
shielding_symmetric=SymmetricTensor(
zeta=146, # in ppm
eta=0.84,
alpha=95 * 3.14159 / 180, # in rads
beta=90 * 3.14159 / 180, # in rads
gamma=0 * 3.14159 / 180, # in rads
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.method.lib import ThreeQ_VAS
from mrsimulator import signal_processor as sp
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension
# sphinx_gallery_thumbnail_number = 3
# %%
# Generate the site and spin system objects.
Rb87_1 = Site(
isotope="87Rb",
isotropic_chemical_shift=-27.4, # in ppm
quadrupolar=SymmetricTensor(Cq=1.68e6, eta=0.2), # Cq is in Hz
)
Rb87_2 = Site(
isotope="87Rb",
isotropic_chemical_shift=-28.5, # in ppm
quadrupolar=SymmetricTensor(Cq=1.94e6, eta=1.0), # Cq is in Hz
)
Rb87_3 = Site(
isotope="87Rb",
isotropic_chemical_shift=-31.3, # in ppm
quadrupolar=SymmetricTensor(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]
# as tools in creating a model for the least-squares fitting.
#
# **Step 1:** Create initial guess sites and spin systems.
#
# The initial guess is often based on some prior knowledge about the system under
# investigation. For the current example, we know that Cuspidine is a crystalline silica
# polymorph with one crystallographic Si site. Therefore, our initial guess model is a
# single :math:`^{29}\text{Si}` site spin system. For non-linear fitting algorithms, as
# a general recommendation, the initial guess model parameters should be a good starting
# point for the algorithms to converge.
# the guess model comprising of a single site spin system
site = Site(
isotope="29Si",
isotropic_chemical_shift=-82.0, # in ppm,
shielding_symmetric=SymmetricTensor(zeta=-63, eta=0.4), # zeta in ppm
)
spin_system = SpinSystem(
name="Si Site",
description="A 29Si site in cuspidine",
sites=[site], # from the above code
abundance=100,
)
# %%
# **Step 2:** Create the method object.
#
# The method should be the same as the one used
# in the measurement. In this example, we use the `BlochDecaySpectrum` method. Note,
# when creating the method object, the value of the method parameters must match the
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.set_xlim(200, -200)
plt.grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Spin System**
P_31 = Site(
isotope="31P",
isotropic_chemical_shift=5.0, # in ppm,
shielding_symmetric=SymmetricTensor(zeta=-80, eta=0.5), # zeta in Hz
)
spin_systems = [SpinSystem(sites=[P_31])]
# %%
# **Method**
# Get the spectral dimension parameters from the experiment.
spectral_dims = get_spectral_dimensions(experiment)
static1D = BlochDecaySpectrum(
channels=["31P"],
magnetic_flux_density=9.395, # in T
rotor_frequency=0, # in Hz
spectral_dimensions=spectral_dims,
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.set_xlim(600, -700)
plt.grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Spin System**
H_2 = Site(
isotope="2H",
isotropic_chemical_shift=-57.12, # in ppm,
quadrupolar=SymmetricTensor(Cq=3e4, eta=0.0), # Cq in Hz
)
spin_systems = [SpinSystem(sites=[H_2])]
# %%
# **Method**
# Get the spectral dimension parameters from the experiment.
spectral_dims = get_spectral_dimensions(experiment)
MAS = BlochDecaySpectrum(
channels=["2H"],
magnetic_flux_density=9.395, # in T
rotor_frequency=4517.1, # in Hz
spectral_dimensions=spectral_dims,
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.method.lib import ThreeQ_VAS
from mrsimulator import signal_processor as sp
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension
# sphinx_gallery_thumbnail_number = 2
# %%
# Generate the site and spin system objects.
site = Site(
isotope="27Al",
isotropic_chemical_shift=64.7, # in ppm
quadrupolar=SymmetricTensor(Cq=3.25e6, eta=0.68), # Cq is in Hz
)
spin_systems = [SpinSystem(sites=[site])]
# %%
# 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=["27Al"],
magnetic_flux_density=7, # in T
spectral_dimensions=[
SpectralDimension(
count=256,
spectral_width=1e4, # in Hz
reference_offset=-3e3, # in Hz
import numpy as np
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.method import Method, SpectralDimension, SpectralEvent
from mrsimulator.spin_system.tensors import SymmetricTensor
# sphinx_gallery_thumbnail_number = 2
# %%
# Create a single-site arbitrary spin system.
site = Site(
name="27Al",
isotope="27Al",
isotropic_chemical_shift=35.7, # in ppm
quadrupolar=SymmetricTensor(Cq=2.959e6, eta=0.98), # Cq is in Hz
)
spin_system = SpinSystem(sites=[site])
# %%
# Selecting the triple-quantum transition
# ---------------------------------------
#
# For single-site spin-5/2 spin system, there are three triple-quantum transition
#
# - :math:`|1/2\rangle\rightarrow|-5/2\rangle` (:math:`P=-3, D=6`)
# - :math:`|3/2\rangle\rightarrow|-3/2\rangle` (:math:`P=-3, D=0`)
# - :math:`|5/2\rangle\rightarrow|-1/2\rangle` (:math:`P=-3, D=-6`)
#
# To select one or more triple-quantum transitions, assign the respective value of P and
# D to the symmetry query object of `transition_queries`. Refer to the
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Guess model**
#
# Create a guess list of spin systems.
site = Site(
isotope="2H",
isotropic_chemical_shift=-90, # in ppm
shielding_symmetric=SymmetricTensor(
zeta=-610, # in ppm
eta=0.15,
alpha=0.7, # in rads
beta=2.0, # in rads
gamma=3.0, # in rads
),
quadrupolar=SymmetricTensor(Cq=75.2e3, eta=0.9), # Cq in Hz
)
spin_systems = [SpinSystem(sites=[site])]
# %%
# **Method**
#
# Use the generic 2D method, `Method2D`, to generate a shifting-d echo method. The
# reported shifting-d 2D sequence is a correlation of the shielding frequencies to the
# first-order quadrupolar frequencies. Here, we create a correlation method using the
# :attr:`~mrsimulator.method.event.freq_contrib` attribute, which acts as a switch
from mrsimulator.methods import BlochDecaySpectrum
from mrsimulator import signal_processing as sp
from mrsimulator.spin_system.tensors import SymmetricTensor
# sphinx_gallery_thumbnail_number = 1
# %%
# **Spin Systems**
#
# Create a 13C-1H coupled spin system.
spin_system = SpinSystem(
sites=[
Site(isotope="13C", isotropic_chemical_shift=0.0),
Site(isotope="1H", isotropic_chemical_shift=0.0),
],
couplings=[Coupling(site_index=[0, 1], dipolar=SymmetricTensor(D=-2e4))],
)
# %%
# **Methods**
#
# Create a BlochDecaySpectrum method.
method = BlochDecaySpectrum(
channels=["13C"],
magnetic_flux_density=9.4, # in T
spectral_dimensions=[dict(count=2048, spectral_width=8.0e4)],
)
# %%
# **Simulator**
#
# Create the Simulator object and add the method and the spin system object.
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Guess model**
#
# Create a guess list of spin systems. There are two spin systems present in this
# example,
# - 1) an uncoupled :math:`^{119}\text{Sn}` and
# - 2) a coupled :math:`^{119}\text{Sn}`-:math:`^{117}\text{Sn}` spin systems.
sn119 = Site(
isotope="119Sn",
isotropic_chemical_shift=-210,
shielding_symmetric=SymmetricTensor(zeta=700, eta=0.1),
)
sn117 = Site(
isotope="117Sn",
isotropic_chemical_shift=0,
)
j_sn = Coupling(
site_index=[0, 1],
isotropic_j=8150.0,
)
sn117_abundance = 7.68 # in %
spin_systems = [
# uncoupled spin system
SpinSystem(sites=[sn119], abundance=100 - sn117_abundance),
# coupled spin systems
plt.grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Guess model**
#
# Create a guess list of spin systems. For fitting the sideband profile at an isotropic
# chemical shift cross-section from PASS/MAT datasets, set the isotropic_chemical_shift
# parameter of the site object as zero.
site = Site(
isotope="13C",
isotropic_chemical_shift=0, #
shielding_symmetric=SymmetricTensor(zeta=-70, eta=0.8),
)
spin_systems = [SpinSystem(sites=[site])]
# %%
# **Method**
#
# For the sideband-only cross-section, use the BlochDecaySpectrum method.
# Get the dimension information from the experiment.
spectral_dims = get_spectral_dimensions(pass_cross_section)
PASS = BlochDecaySpectrum(
channels=["13C"],
magnetic_flux_density=9.395, # in T
rotor_frequency=1500, # in Hz
import numpy as np
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.method import Method, SpectralDimension, SpectralEvent
from mrsimulator.spin_system.tensors import SymmetricTensor
# sphinx_gallery_thumbnail_number = 4
# %%
# Create a single-site arbitrary spin system.
site = Site(
name="27Al",
isotope="27Al",
isotropic_chemical_shift=35.7, # in ppm
quadrupolar=SymmetricTensor(Cq=5.959e6, eta=0.32), # Cq is in Hz
)
spin_system = SpinSystem(sites=[site])
# %%
# Selecting spin transitions for simulation
# -----------------------------------------
#
# The arguments of the Method object are the same as the arguments of the
# BlochDecaySpectrum method; however, unlike a BlochDecaySpectrum method, the
# :ref:`spectral_dim_api` object in Method contains an additional argument---`events`.
#
# The :ref:`event_api` object is a collection of attributes, which are local to the
# event. It is here where we define `transition_queries` to select one or more
# transitions for simulating the spectrum. Recall, a TransitionQuery object holds a
# channel wise SymmetryQuery. For more information, refer to the
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.set_xlim(1200, -1200)
plt.grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Guess model**
#
# Create a guess list of spin systems.
Al_1 = Site(
isotope="27Al",
isotropic_chemical_shift=76, # in ppm
quadrupolar=SymmetricTensor(Cq=6e6, eta=0.0), # Cq in Hz
)
Al_2 = Site(
isotope="27Al",
isotropic_chemical_shift=1, # in ppm
quadrupolar=SymmetricTensor(Cq=5e5, eta=0.3), # Cq in Hz
)
spin_systems = [
SpinSystem(sites=[Al_1], name="AlO4"),
SpinSystem(sites=[Al_2], name="AlO6"),
]
# %%
# **Method**
# were obtained from Hansen `et al.` [#f1]_
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator import signal_processing as sp
from mrsimulator.methods import BlochDecaySpectrum
from mrsimulator.spin_system.tensors import SymmetricTensor
# sphinx_gallery_thumbnail_number = 3
# %%
# **Step 1:** Create the sites.
Si29_1 = Site(
isotope="29Si",
isotropic_chemical_shift=-89.0, # in ppm
shielding_symmetric=SymmetricTensor(zeta=59.8, eta=0.62), # zeta in ppm
)
Si29_2 = Site(
isotope="29Si",
isotropic_chemical_shift=-89.5, # in ppm
shielding_symmetric=SymmetricTensor(zeta=52.1, eta=0.68), # zeta in ppm
)
Si29_3 = Site(
isotope="29Si",
isotropic_chemical_shift=-87.8, # in ppm
shielding_symmetric=SymmetricTensor(zeta=69.4, eta=0.60), # zeta in ppm
)
# %%
# **Step 2:** Create the spin systems from these sites. Again, we create three
# single-site spin systems for better performance.
ax.set_xlim(200, -200)
ax.set_ylim(75, -120)
plt.grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Guess model**
#
# Create a guess list of spin systems.
Rb_1 = Site(
isotope="87Rb",
isotropic_chemical_shift=16, # in ppm
quadrupolar=SymmetricTensor(Cq=5.3e6, eta=0.1), # Cq in Hz
)
Rb_2 = Site(
isotope="87Rb",
isotropic_chemical_shift=40, # in ppm
quadrupolar=SymmetricTensor(Cq=2.2e6, eta=0.95), # Cq in Hz
)
spin_systems = [SpinSystem(sites=[s]) for s in [Rb_1, Rb_2]]
# %%
# **Method**
#
# Create the SSB2D method.
# Get the spectral dimension parameters from the experiment.
from mrsimulator import Simulator, SpinSystem, Site, Coupling
from mrsimulator.methods import Method1D
from mrsimulator.method import SpectralDimension, SpectralEvent, MixingEvent
from mrsimulator.spin_system.tensors import SymmetricTensor
# sphinx_gallery_thumbnail_number = 2
# %%
# For demonstration, we will create two spin systems, one with a single site and other
# with two spin 1/2 sites.
S1 = Site(
isotope="1H",
isotropic_chemical_shift=10, # in ppm
shielding_symmetric=SymmetricTensor(zeta=-80, eta=0.25), # zeta in ppm
)
S2 = Site(isotope="1H", isotropic_chemical_shift=-10)
S12 = Coupling(site_index=[0, 1],
isotropic_j=100,
dipolar=SymmetricTensor(D=2000, eta=0, alpha=0))
spin_system_1 = SpinSystem(sites=[S1], label="Uncoupled system")
spin_system_2 = SpinSystem(sites=[S1, S2],
couplings=[S12],
label="Coupled system")
# %%
# **Create a custom method**
#
# Writing a custom method is simply specifying an appropriate list of event objects per
def add_site(doctest_namespace):
doctest_namespace["np"] = np
doctest_namespace["plt"] = plt
doctest_namespace["SpinSystem"] = SpinSystem
doctest_namespace["Simulator"] = Simulator
doctest_namespace["Site"] = Site
doctest_namespace["SymmetricTensor"] = SymmetricTensor
doctest_namespace["st"] = SymmetricTensor
doctest_namespace["pprint"] = pprint
doctest_namespace["Isotope"] = Isotope
doctest_namespace["sp"] = sp
doctest_namespace["apo"] = apo
site1 = Site(
isotope="13C",
isotropic_chemical_shift=20,
shielding_symmetric=SymmetricTensor(zeta=10, eta=0.5),
)
doctest_namespace["site1"] = site1
site2 = Site(
isotope="1H",
isotropic_chemical_shift=-4,
shielding_symmetric=SymmetricTensor(zeta=2.1, eta=0.1),
)
doctest_namespace["site2"] = site2
site3 = Site(
isotope="27Al",
isotropic_chemical_shift=120,
shielding_symmetric=SymmetricTensor(zeta=2.1, eta=0.1),
quadrupole=SymmetricTensor(Cq=5.1e6, eta=0.5),
)
doctest_namespace["site3"] = site3
spin_system_1H_13C = SpinSystem(sites=[site1, site2])
doctest_namespace["spin_system_1H_13C"] = spin_system_1H_13C
spin_system_1 = SpinSystem(sites=[site1])
doctest_namespace["spin_system_1"] = spin_system_1
doctest_namespace["spin_systems"] = SpinSystem(sites=[site1, site2, site3])
spin_systems = [SpinSystem(sites=[site]) for site in [site1, site2, site3]]
sim = Simulator()
sim.spin_systems += spin_systems
doctest_namespace["sim"] = sim
# coesite
O17_1 = Site(
isotope="17O",
isotropic_chemical_shift=29,
quadrupolar=SymmetricTensor(Cq=6.05e6, eta=0.000),
)
O17_2 = Site(
isotope="17O",
isotropic_chemical_shift=41,
quadrupolar=SymmetricTensor(Cq=5.43e6, eta=0.166),
)
O17_3 = Site(
isotope="17O",
isotropic_chemical_shift=57,
quadrupolar=SymmetricTensor(Cq=5.45e6, eta=0.168),
)
O17_4 = Site(
isotope="17O",
isotropic_chemical_shift=53,
quadrupolar=SymmetricTensor(Cq=5.52e6, eta=0.169),
)
O17_5 = Site(
isotope="17O",
isotropic_chemical_shift=58,
quadrupolar=SymmetricTensor(Cq=5.16e6, eta=0.292),
)
sites = [O17_1, O17_2, O17_3, O17_4, O17_5]
abundance = [0.83, 1.05, 2.16, 2.05, 1.90] # abundance of each spin system
spin_systems = [
SpinSystem(sites=[s], abundance=a) for s, a in zip(sites, abundance)
]
method = BlochDecayCentralTransitionSpectrum(
channels=["17O"],
rotor_frequency=14000,
spectral_dimensions=[{"count": 2048, "spectral_width": 50000}],
)
sim_coesite = Simulator()
sim_coesite.spin_systems += spin_systems
sim_coesite.methods += [method]
doctest_namespace["sim_coesite"] = sim_coesite
ax.set_xlim(100, -50)
plt.grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
#
# A fitting model is a composite of ``Simulator`` and ``SignalProcessor`` objects.
#
# **Step 1:** Create initial guess sites and spin systems
O1 = Site(
isotope="17O",
isotropic_chemical_shift=60.0, # in ppm,
quadrupolar=SymmetricTensor(Cq=4.2e6, eta=0.5), # Cq in Hz
)
O2 = Site(
isotope="17O",
isotropic_chemical_shift=40.0, # in ppm,
quadrupolar=SymmetricTensor(Cq=2.4e6, eta=0.0), # Cq in Hz
)
spin_systems = [
SpinSystem(sites=[O1], abundance=50, name="O1"),
SpinSystem(sites=[O2], abundance=50, name="O2"),
]
# %%
# **Step 2:** Create the method object. Create an appropriate method object that closely
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator import signal_processor as sp
from mrsimulator.method.lib import BlochDecayCTSpectrum
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension
# sphinx_gallery_thumbnail_number = 2
# %%
# Create the sites.
# default unit of isotropic_chemical_shift is ppm and Cq is Hz.
O17_1 = Site(
isotope="17O",
isotropic_chemical_shift=29,
quadrupolar=SymmetricTensor(Cq=6.05e6, eta=0.000),
)
O17_2 = Site(
isotope="17O",
isotropic_chemical_shift=41,
quadrupolar=SymmetricTensor(Cq=5.43e6, eta=0.166),
)
O17_3 = Site(
isotope="17O",
isotropic_chemical_shift=57,
quadrupolar=SymmetricTensor(Cq=5.45e6, eta=0.168),
)
O17_4 = Site(
isotope="17O",
isotropic_chemical_shift=53,
quadrupolar=SymmetricTensor(Cq=5.52e6, eta=0.169),
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.methods import Method2D
from mrsimulator import signal_processing as sp
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension, SpectralEvent
# sphinx_gallery_thumbnail_number = 3
# %%
# Generate the site and spin system objects.
site = Site(
isotope="87Rb",
isotropic_chemical_shift=-9, # in ppm
shielding_symmetric=SymmetricTensor(zeta=110, eta=0),
quadrupolar=SymmetricTensor(
Cq=3.5e6, # in Hz
eta=0.36,
alpha=0, # in rads
beta=70 * 3.14159 / 180, # in rads
gamma=0, # in rads
),
)
spin_system = SpinSystem(sites=[site])
# %%
# Use the generic 2D method, `Method2D`, to simulate a COASTER spectrum by customizing
# the method parameters, as shown below. Note, the Method2D method simulates an infinite
# spinning speed spectrum.
coaster = Method2D(
# Here, we create three 13C-1H spin systems with different relative orientations
# between the shielding and dipolar tensors. The Euler angle orientations
# :math:`\alpha=\gamma=0` and :math:`\beta` values are listed below.
beta_orientation = [np.pi / 6, 5 * np.pi / 18, np.pi / 2]
# The `variable` spin_systems is a list of three coupled 13C-1H spin systems with
# different relative shielding and dipolar tensor orientation.
spin_systems = [
SpinSystem(
sites=[
Site(
isotope="13C",
isotropic_chemical_shift=0.0, # in ppm
shielding_symmetric=SymmetricTensor(
zeta=18.87562, # in ppm
eta=0.4,
beta=beta,
),
),
Site(
isotope="1H",
isotropic_chemical_shift=0.0, # in ppm
),
],
couplings=[
Coupling(
site_index=[0, 1], isotropic_j=200.0, dipolar=SymmetricTensor(D=-2.1e4)
)
],
)
for beta in beta_orientation
# spectrum. The parameters for the simulation are obtained from Walder `et al.` [#f1]_.
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.methods import SSB2D
from mrsimulator.spin_system.tensors import SymmetricTensor
# sphinx_gallery_thumbnail_number = 2
# %%
# Generate the site and spin system objects.
sites = [
Site(
isotope="87Rb",
isotropic_chemical_shift=16, # in ppm
quadrupolar=SymmetricTensor(Cq=5.3e6, eta=0.1), # Cq in Hz
),
Site(
isotope="87Rb",
isotropic_chemical_shift=40, # in ppm
quadrupolar=SymmetricTensor(Cq=2.6e6, eta=1.0), # Cq in Hz
),
]
spin_systems = [SpinSystem(sites=[s]) for s in sites]
# %%
# Use the ``SSB2D`` method to simulate a PASS, MAT, QPASS, QMAT, or any equivalent
# sideband separation spectrum. Here, we use the method to generate a QMAT spectrum.
# The QMAT method is created from the ``SSB2D`` method in the same as a PASS or MAT
# method. The difference is that the observed channel is a half-integer quadrupolar
# spin instead of a spin I=1/2.
ax[i].plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax[i].set_xlim(280, -10)
ax[i].grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Spin System**: The objective of a multi-data fitting is to optimize the spin
# system parameters using multiple datasets. In this example, we create two single-site
# spin systems, which are then shared by three method objects.
C1 = Site(
isotope="13C",
isotropic_chemical_shift=176.0, # in ppm
shielding_symmetric=SymmetricTensor(zeta=60, eta=0.6), # zeta in Hz
)
C2 = Site(
isotope="13C",
isotropic_chemical_shift=43.0, # in ppm
shielding_symmetric=SymmetricTensor(zeta=30, eta=0.5), # zeta in Hz
)
spin_systems = [
SpinSystem(sites=[C1], name="C1"),
SpinSystem(sites=[C2], name="C2")
]
# %%
# **Method**: Create the three MAS method objects with respective MAS spinning speeds.
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, "k", alpha=0.5)
ax.set_xlim(100, -100)
plt.grid()
plt.tight_layout()
plt.show()
# %%
# Create a fitting model
# ----------------------
# **Spin System**
B11 = Site(
isotope="11B",
isotropic_chemical_shift=20.0, # in ppm
quadrupolar=SymmetricTensor(Cq=2.3e6, eta=0.03), # Cq in Hz
)
spin_systems = [SpinSystem(sites=[B11])]
# %%
# **Method**
# Get the spectral dimension parameters from the experiment.
spectral_dims = get_spectral_dimensions(experiment)
MAS_CT = BlochDecayCTSpectrum(
channels=["11B"],
magnetic_flux_density=14.1, # in T
rotor_frequency=12500, # in Hz
spectral_dimensions=spectral_dims,
experiment=experiment, # add the measurement to the method.
import numpy as np
import matplotlib.pyplot as plt
from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.method.lib import BlochDecayCTSpectrum
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension
# sphinx_gallery_thumbnail_number = 1
# %%
# Create the spin system.
site = Site(
isotope="17O",
isotropic_chemical_shift=320, # in ppm
shielding_symmetric=SymmetricTensor(zeta=376.667, eta=0.345),
quadrupolar=SymmetricTensor(
Cq=8.97e6, # in Hz
eta=0.15,
alpha=5 * np.pi / 180,
beta=np.pi / 2,
gamma=70 * np.pi / 180,
),
)
spin_system = SpinSystem(sites=[site])
# %%
# Create a central transition selective Bloch decay spectrum method.
method = BlochDecayCTSpectrum(
channels=["17O"],
magnetic_flux_density=11.74, # in T