{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This cell is added by sphinx-gallery\n\n%matplotlib inline\n\nimport mrsimulator\nprint(f'You are using mrsimulator v{mrsimulator.__version__}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n# 17O DAS NMR of Coesite\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Coesite is a high-pressure (2-3 GPa) and high-temperature (700\u00b0C) polymorph of silicon\ndioxide $\\text{SiO}_2$. Coesite has five crystallographic $^{17}\\text{O}$\nsites. The experimental dataset used in this example is published in\nGrandinetti `et. al.` [#f1]_\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\nimport csdmpy as cp\nimport matplotlib as mpl\nimport matplotlib.pyplot as plt\nimport mrsimulator.signal_processing as sp\nimport mrsimulator.signal_processing.apodization as apo\nfrom mrsimulator import Simulator\nfrom mrsimulator.methods import Method2D\nfrom mrsimulator.utils import get_spectral_dimensions\nfrom mrsimulator.utils.collection import single_site_system_generator\nfrom mrsimulator.utils.spectral_fitting import LMFIT_min_function, make_LMFIT_params\nfrom lmfit import Minimizer, report_fit\n\n\n# global plot configuration\nmpl.rcParams[\"figure.figsize\"] = [4.5, 3.0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import the dataset\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "filename = \"https://sandbox.zenodo.org/record/687656/files/DASCoesite.csdf\"\nexperiment = cp.load(filename)\n\n# For spectral fitting, we only focus on the real part of the complex dataset\nexperiment = experiment.real\n\n# Convert the coordinates along each dimension from Hz to ppm.\n_ = [item.to(\"ppm\", \"nmr_frequency_ratio\") for item in experiment.dimensions]\n\n# Normalize the spectrum\nexperiment /= experiment.max()\n\n# plot of the dataset.\nlevels = (np.arange(10) + 0.3) / 15 # contours are drawn at these levels.\nax = plt.subplot(projection=\"csdm\")\ncb = ax.contour(experiment, colors=\"k\", levels=levels, alpha=0.5, linewidths=0.5)\nplt.colorbar(cb)\nax.invert_xaxis()\nax.set_ylim(30, -30)\nplt.tight_layout()\nplt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create a fitting model\nThe fitting model includes the Simulator and SignalProcessor objects. First,\ncreate the Simulator object.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Create the guess sites and spin systems.\n# default unit of isotropic_chemical_shift is ppm and Cq is Hz.\nshifts = [29, 41, 57, 53, 58] # in ppm\nCq = [6.1e6, 5.4e6, 5.5e6, 5.5e6, 5.1e6] # in Hz\neta = [0.1, 0.2, 0.1, 0.1, 0.3]\nabundance = [1, 1, 2, 2, 2]\n\nspin_systems = single_site_system_generator(\n isotopes=\"17O\",\n isotropic_chemical_shifts=shifts,\n quadrupolar={\"Cq\": Cq, \"eta\": eta},\n abundance=abundance,\n)\n\n# Create the DAS method.\n# Get the spectral dimension paramters from the experiment.\nspectral_dims = get_spectral_dimensions(experiment)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "das = Method2D(\n channels=[\"17O\"],\n magnetic_flux_density=11.7, # in T\n spectral_dimensions=[\n {\n **spectral_dims[0],\n \"events\": [\n {\"fraction\": 0.5, \"rotor_angle\": 37.38 * 3.14159 / 180},\n {\"fraction\": 0.5, \"rotor_angle\": 79.19 * 3.14159 / 180},\n ],\n },\n # The last spectral dimension block is the direct-dimension\n {**spectral_dims[1], \"events\": [{\"rotor_angle\": 54.735 * 3.14159 / 180}]},\n ],\n experiment=experiment, # also add the measurement to the method.\n)\n\n# Optimize the script by pre-setting the transition pathways for each spin system from\n# the das method.\nfor sys in spin_systems:\n sys.transition_pathways = das.get_transition_pathways(sys)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Create the Simulator object and add the method and spin system objects.\nsim = Simulator()\nsim.spin_systems = spin_systems # add the spin systems\nsim.methods = [das] # add the method\nsim.run()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Add Post simulation processing.\nprocessor = sp.SignalProcessor(\n operations=[\n # Gaussian convolution along both dimensions.\n sp.IFFT(dim_index=(0, 1)),\n apo.Gaussian(FWHM=\"0.15 kHz\", dim_index=0),\n apo.Gaussian(FWHM=\"0.15 kHz\", dim_index=1),\n sp.FFT(dim_index=(0, 1)),\n sp.Scale(factor=1 / 8),\n ]\n)\n# Apply post simulation operations.\nprocessed_data = processor.apply_operations(data=sim.methods[0].simulation).real" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# The plot of the simulation after signal processing.\nax = plt.subplot(projection=\"csdm\")\nax.contour(processed_data, colors=\"r\", levels=levels, alpha=0.75, linewidths=0.5)\ncb = ax.contour(experiment, colors=\"k\", levels=levels, alpha=0.5, linewidths=0.5)\nplt.colorbar(cb)\nax.invert_xaxis()\nax.set_ylim(30, -30)\nplt.tight_layout()\nplt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Least-squares minimization with LMFIT\nFirst, create the fitting parameters.\nUse the :func:`~mrsimulator.utils.spectral_fitting.make_LMFIT_params` for a quick\nsetup.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "params = make_LMFIT_params(sim, processor)\n\n# Here, we fix the abundance parameters to their initial value.\nfor i in range(5):\n params[f\"sys_{i}_abundance\"].vary = False\n\nparams.pretty_print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the minimization using LMFIT\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "minner = Minimizer(LMFIT_min_function, params, fcn_args=(sim, processor))\nresult = minner.minimize()\nreport_fit(result)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulate the spectrum corresponding to the optimum parameters\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sim.run()\nprocessed_data = processor.apply_operations(data=sim.methods[0].simulation).real" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the spectrum\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ax = plt.subplot(projection=\"csdm\")\nax.contour(processed_data, colors=\"r\", levels=levels, alpha=0.75, linewidths=0.5)\ncb = ax.contour(experiment, colors=\"k\", levels=levels, alpha=0.5, linewidths=0.5)\nplt.colorbar(cb)\nax.invert_xaxis()\nax.set_ylim(30, -30)\nplt.tight_layout()\nplt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ".. [#f1] Grandinetti, P. J., Baltisberger, J. H., Farnan, I., Stebbins, J. F.,\n Werner, U. and Pines, A.\n Solid-State $^{17}\\text{O}$ Magic-Angle and Dynamic-Angle Spinning NMR\n Study of the $\\text{SiO}_2$ Polymorph Coesite, J. Phys. Chem. 1995,\n **99**, *32*, 12341-12348.\n `DOI: 10.1021/j100032a045 `_\n\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 0 }