def quad_MAS_method():
return BlochDecayCentralTransitionSpectrum(
channels=["17O"],
rotor_frequency=14000,
spectral_dimensions=[{
"spectral_width": 50000
}],
)
# %%
# **Step 2:** Create the spin systems from these sites. For optimum performance, we
# create five single-site spin systems instead of a single five-site spin system. The
# abundance of each spin system is taken from above reference.
abundance = [0.83, 1.05, 2.16, 2.05, 1.90]
spin_systems = [
SpinSystem(sites=[s], abundance=a) for s, a in zip(sites, abundance)
]
# %%
# **Step 3:** Create a central transition selective Bloch decay spectrum method.
method = BlochDecayCentralTransitionSpectrum(
channels=["17O"],
rotor_frequency=14000, # in Hz
spectral_dimensions=[{
"count": 2048,
"spectral_width": 50000, # in Hz
"label": r"$^{17}$O resonances",
}],
)
# %%
# The above method is set up to record the :math:`^{17}\text{O}` resonances at the
# magic angle, spinning at 14 kHz and 9.4 T (default, if the value is not provided)
# external magnetic flux density. The resonances are recorded over 50 kHz spectral
# width using 2048 points.
# %%
# **Step 4:** Create the Simulator object and add the method and spin system objects.
sim = Simulator()
sim.spin_systems = spin_systems # add the spin systems
def quad_static_method():
return BlochDecayCentralTransitionSpectrum(channels=["17O"],
spectral_dimensions=[{
"spectral_width":
50000
}])
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
"alpha": 5 * np.pi / 180,
"beta": np.pi / 2,
"gamma": 70 * np.pi / 180,
},
)
spin_system = SpinSystem(sites=[site])
# %%
# **Step 2:** Create a central transition selective Bloch decay spectrum method.
method = BlochDecayCentralTransitionSpectrum(
channels=["17O"],
magnetic_flux_density=11.74, # in T
rotor_frequency=0, # in Hz
spectral_dimensions=[
{
"count": 1024,
"spectral_width": 1e5, # in Hz
"reference_offset": 22500, # in Hz
"label": r"$^{17}$O 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
# Since the spin system have non-zero Euler angles, set the integration_volume to
# hemisphere.
systems = single_site_system_generator(isotopes="71Ga",
quadrupolar={
"Cq": cq_dist * 1e6,
"eta": e_dist
},
abundance=amp)
# %%
# Create a simulator object and add the above system.
sim = Simulator()
sim.spin_systems = systems # add the systems
sim.methods = [
BlochDecayCentralTransitionSpectrum(
channels=["71Ga"],
magnetic_flux_density=4.8, # in T
spectral_dimensions=[{
"count": 2048,
"spectral_width": 1.2e6
}],
)
] # add the method
sim.run()
# %%
# The following is the static spectrum arising from a Czjzek distribution of the
# second-rank traceless EFG tensors.
plt.figure(figsize=(4.25, 3.0))
ax = plt.gca(projection="csdm")
ax.plot(sim.methods[0].simulation, color="black", linewidth=1)
ax.invert_xaxis()
plt.tight_layout()
plt.show()
def test_DAS():
B0 = 11.7
das = Method2D(
channels=["17O"],
magnetic_flux_density=B0, # in T
spectral_dimensions=[
{
"count":
912,
"spectral_width":
5e3, # in Hz
"reference_offset":
0, # in Hz
"label":
"DAS isotropic dimension",
"events": [
{
"fraction": 0.5,
"rotor_angle": 37.38 * 3.14159 / 180
},
{
"fraction": 0.5,
"rotor_angle": 79.19 * 3.14159 / 180
},
],
},
# The last spectral dimension block is the direct-dimension
{
"count": 2048,
"spectral_width": 2e4, # in Hz
"reference_offset": 0, # in Hz
"label": "MAS dimension",
"events": [{
"rotor_angle": 54.735 * 3.14159 / 180
}],
},
],
)
sim = Simulator()
sim.spin_systems = spin_systems # add spin systems
sim.methods = [das] # add the method.
sim.config.decompose_spectrum = "spin_system"
sim.run(pack_as_csdm=False)
data_das = sim.methods[0].simulation
data_das_coords_ppm = das.spectral_dimensions[0].coordinates_ppm()
# Bloch decay central transition method
bloch = BlochDecayCentralTransitionSpectrum(
channels=["17O"],
magnetic_flux_density=B0, # in T
rotor_frequency=1e9, # in Hz
rotor_angle=54.735 * 3.14159 / 180,
spectral_dimensions=[
{
"count": 2048,
"spectral_width": 2e4, # in Hz
"reference_offset": 0, # in Hz
"label": "MAS dimension",
},
],
)
sim = Simulator()
sim.spin_systems = spin_systems
sim.methods = [bloch]
sim.config.decompose_spectrum = "spin_system"
sim.run(pack_as_csdm=False)
data_bloch = sim.methods[0].simulation
larmor_freq = das.channels[0].gyromagnetic_ratio * B0 * 1e6
spin = das.channels[0].spin
for i, sys in enumerate(spin_systems):
for site in sys.sites:
Cq = site.quadrupolar.Cq
eta = site.quadrupolar.eta
iso = site.isotropic_chemical_shift
factor1 = -(3 / 40) * (Cq / larmor_freq)**2
factor2 = (spin * (spin + 1) - 3 / 4) / (spin**2 *
(2 * spin - 1)**2)
factor3 = 1 + (eta**2) / 3
iso_obs = factor1 * factor2 * factor3 * 1e6 + iso
# get the index where there is a signal
id1 = data_das[i] / data_das[i].max()
index = np.where(id1 == id1.max())[0]
iso_spectrum = data_das_coords_ppm[
index[0]] # x[1].coords[index[0]]
# test for the position of isotropic peaks.
np.testing.assert_almost_equal(iso_obs, iso_spectrum, decimal=1)
# test for the spectrum across the isotropic peaks.
data_bloch_i = data_bloch[i] / data_bloch[i].max()
assert np.allclose(id1[index[0]], data_bloch_i)
def test_MQMAS():
spin_system = SpinSystem(sites=[
Site(
isotope="87Rb",
isotropic_chemical_shift=-9,
shielding_symmetric={
"zeta": 100,
"eta": 0
},
quadrupolar={
"Cq": 3.5e6,
"eta": 0.36,
"beta": 70 / 180 * np.pi
},
)
])
method = Method2D(
channels=["87Rb"],
magnetic_flux_density=9.4,
spectral_dimensions=[
{
"count": 128,
"spectral_width": 20000,
"events": [{
"transition_query": {
"P": [-3],
"D": [0]
}
}],
},
{
"count": 128,
"spectral_width": 20000
},
],
)
sim = Simulator()
sim.spin_systems = [spin_system]
sim.methods = [method]
sim.config.integration_volume = "hemisphere"
sim.run()
# process
k = 21 / 27 # shear factor
processor = sp.SignalProcessor(operations=[
sp.IFFT(dim_index=1),
aft.Shear(factor=-k, dim_index=1, parallel=0),
aft.Scale(factor=1 + k, dim_index=1),
sp.FFT(dim_index=1),
])
processed_data = processor.apply_operations(
data=sim.methods[0].simulation).real
# Since there is a single site, after the shear and scaling transformations, there
# should be a single perak along the isotropic dimension at index 70.
# The isotropic coordinate of this peak is given by
# w_iso = (17.8)*iso_shift + 1e6/8 * (vq/v0)^2 * (eta^2 / 3 + 1)
# ref: D. Massiot et al. / Solid State Nuclear Magnetic Resonance 6 (1996) 73-83
iso_slice = processed_data[40, :]
assert np.argmax(iso_slice.dependent_variables[0].components[0]) == 70
# calculate the isotropic coordinate
spin = method.channels[0].spin
w0 = method.channels[0].gyromagnetic_ratio * 9.4 * 1e6
wq = 3 * 3.5e6 / (2 * spin * (2 * spin - 1))
w_iso = -9 * 17 / 8 + 1e6 / 8 * (wq / w0)**2 * ((0.36**2) / 3 + 1)
# the coordinate from spectrum
w_iso_spectrum = processed_data.dimensions[1].coordinates[70].value
np.testing.assert_almost_equal(w_iso, w_iso_spectrum, decimal=2)
# The projection onto the MAS dimension should be the 1D block decay central
# transition spectrum
mas_slice = processed_data.sum(axis=1).dependent_variables[0].components[0]
# MAS spectrum
method = BlochDecayCentralTransitionSpectrum(
channels=["87Rb"],
magnetic_flux_density=9.4,
rotor_frequency=1e9,
spectral_dimensions=[{
"count": 128,
"spectral_width": 20000
}],
)
sim = Simulator()
sim.spin_systems = [spin_system]
sim.methods = [method]
sim.config.integration_volume = "hemisphere"
sim.run()
data = sim.methods[0].simulation.dependent_variables[0].components[0]
np.testing.assert_almost_equal(data / data.max(),
mas_slice / mas_slice.max(),
decimal=6,
err_msg="not equal")
def test_MQMAS_spin_5halves():
spin_system = SpinSystem(sites=[
Site(
isotope="27Al",
isotropic_chemical_shift=64.5, # in ppm
quadrupolar={
"Cq": 3.22e6,
"eta": 0.66
}, # Cq is in Hz
)
])
method = ThreeQ_VAS(
channels=["27Al"],
magnetic_flux_density=7,
spectral_dimensions=[
{
"count": 1024,
"spectral_width": 5000,
"reference_offset": -3e3
},
{
"count": 512,
"spectral_width": 10000,
"reference_offset": 4e3
},
],
)
sim = Simulator()
sim.spin_systems = [spin_system]
sim.methods = [method]
sim.run()
data = sim.methods[0].simulation
dat = data.dependent_variables[0].components[0]
index = np.where(dat == dat.max())[0]
# The isotropic coordinate of this peak is given by
# v_iso = -(17/31)*iso_shift + 8e6/93 * (vq/v0)^2 * (eta^2 / 3 + 1)
# ref: D. Massiot et al. / Solid State Nuclear Magnetic Resonance 6 (1996) 73-83
spin = method.channels[0].spin
v0 = method.channels[0].gyromagnetic_ratio * 7 * 1e6
vq = 3 * 3.22e6 / (2 * spin * (2 * spin - 1))
v_iso = -(17 / 31) * 64.5 - (8e6 / 93) * (vq / v0)**2 * ((0.66**2) / 3 + 1)
# the coordinate from spectrum along the iso dimension must be equal to v_iso
v_iso_spectrum = data.dimensions[1].coordinates[index[0]].value
np.testing.assert_almost_equal(v_iso, v_iso_spectrum, decimal=2)
# The projection onto the MAS dimension should be the 1D block decay central
# transition spectrum
mas_slice = data.sum(axis=1).dependent_variables[0].components[0]
# MAS spectrum
method = BlochDecayCentralTransitionSpectrum(
channels=["27Al"],
magnetic_flux_density=7,
rotor_frequency=1e9,
spectral_dimensions=[{
"count": 512,
"spectral_width": 10000,
"reference_offset": 4e3
}],
)
sim = Simulator()
sim.spin_systems = [spin_system]
sim.methods = [method]
sim.config.integration_volume = "hemisphere"
sim.run()
data = sim.methods[0].simulation.dependent_variables[0].components[0]
assert np.allclose(data / data.max(), mas_slice / mas_slice.max())
def test_ThreeQ_VAS_spin_3halves():
spin_system = SpinSystem(sites=[
Site(
isotope="87Rb",
isotropic_chemical_shift=-9,
shielding_symmetric={
"zeta": 100,
"eta": 0
},
quadrupolar={
"Cq": 3.5e6,
"eta": 0.36,
"beta": 70 / 180 * np.pi
},
)
])
method = ThreeQ_VAS(
channels=["87Rb"],
magnetic_flux_density=9.4,
spectral_dimensions=[
{
"count": 1024,
"spectral_width": 20000
},
{
"count": 512,
"spectral_width": 20000
},
],
)
sim = Simulator()
sim.spin_systems = [spin_system]
sim.methods = [method]
sim.config.integration_volume = "hemisphere"
sim.run()
data = sim.methods[0].simulation
dat = data.dependent_variables[0].components[0]
index = np.where(dat == dat.max())[0]
# The isotropic coordinate of this peak is given by
# v_iso = (17/8)*iso_shift + 1e6/8 * (vq/v0)^2 * (eta^2 / 3 + 1)
# ref: D. Massiot et al. / Solid State Nuclear Magnetic Resonance 6 (1996) 73-83
spin = method.channels[0].spin
v0 = method.channels[0].gyromagnetic_ratio * 9.4 * 1e6
vq = (3 * 3.5e6) / (2 * spin * (2 * spin - 1))
v_iso = -9 * 17 / 8 + 1e6 / 8 * ((vq / v0)**2) * ((0.36**2) / 3 + 1)
# the coordinate from spectrum along the iso dimension must be equal to v_iso
v_iso_spectrum = data.dimensions[1].coordinates[index[0]].value
np.testing.assert_almost_equal(v_iso, v_iso_spectrum, decimal=2)
# The projection onto the MAS dimension should be the 1D block decay central
# transition spectrum
mas_slice = data.sum(axis=1).dependent_variables[0].components[0]
# MAS spectrum
method = BlochDecayCentralTransitionSpectrum(
channels=["87Rb"],
magnetic_flux_density=9.4,
rotor_frequency=1e9,
spectral_dimensions=[{
"count": 512,
"spectral_width": 20000
}],
)
sim = Simulator()
sim.spin_systems = [spin_system]
sim.methods = [method]
sim.config.integration_volume = "hemisphere"
sim.run()
data = sim.methods[0].simulation.dependent_variables[0].components[0]
assert np.allclose(data / data.max(), mas_slice / mas_slice.max())
"Cq": 2.3e6,
"eta": 0.03
}, # Cq in Hz
)
spin_systems = [SpinSystem(sites=[B11])]
# %%
# **Method**
# Get the spectral dimension paramters from the experiment.
spectral_dims = get_spectral_dimensions(experiment)
method = BlochDecayCentralTransitionSpectrum(
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.
)
# Optimize the script by pre-setting the transition pathways for each spin system from
# the das method.
for sys in spin_systems:
sys.transition_pathways = method.get_transition_pathways(sys)
# %%
# **Guess Spectrum**
# Simulation
# ----------
sim = Simulator()
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()
systems = single_site_system_generator(isotopes="71Ga",
quadrupolar={
"Cq": cq_dist * 1e6,
"eta": e_dist
},
abundance=amp)
# %%
# Create a simulator object and add the above system.
sim = Simulator()
sim.spin_systems = systems # add the systems
sim.methods = [
BlochDecayCentralTransitionSpectrum(
channels=["71Ga"],
magnetic_flux_density=9.4, # in T
spectral_dimensions=[{
"count": 2048,
"spectral_width": 2e5
}],
)
] # add the method
sim.run()
# %%
# The following is a static spectrum arising from an extended Czjzek distribution of
# the second-rank traceless EFG tensors.
plt.figure(figsize=(4.25, 3.0))
ax = plt.gca(projection="csdm")
ax.plot(sim.methods[0].simulation, color="black", linewidth=1)
ax.invert_xaxis()
plt.tight_layout()
plt.show()
# Use the :func:`~mrsimulator.utils.collection.single_site_system_generator` utility
# function to generate single-site spin systems.
spin_systems = single_site_system_generator(
isotopes="27Al",
isotropic_chemical_shifts=iso,
quadrupolar={"Cq": Cq * 1e6, "eta": eta}, # Cq in Hz
abundance=pdf,
)
# %%
# Static spectrum
# ---------------
# Observe the static :math:`^{27}\text{Al}` NMR spectrum simulation. First,
# create a central transition selective Bloch decay spectrum method.
static_method = BlochDecayCentralTransitionSpectrum(
channels=["27Al"], spectral_dimensions=[{"spectral_width": 80000}]
)
# %%
# Create the simulator object and add the spin systems and method.
sim = Simulator()
sim.spin_systems = spin_systems # add the spin systems
sim.methods = [static_method] # add the method
sim.run()
# %%
# The plot of the corresponding spectrum.
ax = plt.subplot(projection="csdm")
ax.plot(sim.methods[0].simulation, color="black", linewidth=1)
ax.invert_xaxis()
plt.tight_layout()