{ "cells": [ { "cell_type": "markdown", "id": "81c543e7", "metadata": {}, "source": [ "# Model masking" ] }, { "cell_type": "markdown", "id": "4bef1d38", "metadata": {}, "source": [ "This tutorial explores some of ramannoodle's masking features. These features are useful when analyzing simulated Raman spectra. \n", "\n", " [InterpolationModel](../generated/ramannoodle.pmodel.html#ramannoodle.pmodel.interpolation.InterpolationModel), as well it's subclasses (such as [ARTModel](../generated/ramannoodle.pmodel.html#ramannoodle.pmodel.art.ARTModel)), can be modified by \"masking\" specified degrees of freedom (DOFs). When a DOF is masked, it is excluded when calculating polarizabilities and therefore will not be accounted for when calculating Raman spectra. Raman spectra computed with masking should be regarded as *partial Raman spectra*. By choosing the masks wisely, quite a bit can be learned about which atom (or groups of atoms) correspond to which features in the simulated Raman spectra." ] }, { "cell_type": "markdown", "id": "0b8f3299-8cf3-4c00-b2b2-fb514c3aeb0f", "metadata": {}, "source": [ "First, our usual imports." ] }, { "cell_type": "code", "execution_count": 1, "id": "3956373a-63a1-4128-b0f2-e2711b5a5213", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import matplotlib_inline\n", "\n", "matplotlib_inline.backend_inline.set_matplotlib_formats('png')\n", "plt.rcParams['figure.dpi'] = 300\n", "plt.rcParams['font.family'] = 'sans-serif'\n", "plt.rcParams[\"mathtext.default\"] = 'regular'\n", "plt.rcParams['axes.linewidth'] = 0.5\n", "plt.rcParams['xtick.major.width'] = 0.5\n", "plt.rcParams['xtick.minor.width'] = 0.5\n", "plt.rcParams['lines.linewidth'] = 1.5\n", "\n", "import ramannoodle as rn" ] }, { "cell_type": "markdown", "id": "d7da690f-f4db-4509-8c89-014e7a49c83b", "metadata": {}, "source": [ "### Setup of model\n", "\n", "We will be computing TiO2's Raman spectrum using data available in `tests/data/TiO2` (see [Github repo](https://github.com/wolearyc/ramannoodle)). We will be basing this spectrum on frozen phonon calculations and use [ARTModel](../generated/ramannoodle.pmodel.html#ramannoodle.pmodel.art.ARTModel) to estimate polarizabilities." ] }, { "cell_type": "code", "execution_count": 2, "id": "6102769c-0416-497a-b6a9-e451b66ca71d", "metadata": {}, "outputs": [], "source": [ "data_dir = \"../../../test/data/TiO2\"\n", "# phonon_OUTCAR contains phonons (duh) as well as the reference TiO2 structure.\n", "phonon_outcar = f\"{data_dir}/phonons_OUTCAR\"\n", "\n", "# Read the phonons\n", "phonons = rn.io.vasp.outcar.read_phonons(phonon_outcar)\n", "# Read the reference structure. This might take a few moments...\n", "ref_structure = rn.io.vasp.outcar.read_ref_structure(f\"{data_dir}/ref_eps_OUTCAR\")\n", "\n", "# We'll need the polarizability of the reference structure. \n", "_, ref_polarizability = rn.io.vasp.outcar.read_positions_and_polarizability(\n", " f\"{data_dir}/ref_eps_OUTCAR\"\n", ")\n", "model = rn.pmodel.ARTModel(ref_structure, ref_polarizability)" ] }, { "cell_type": "code", "execution_count": 3, "id": "147f6a26-a22a-4cff-9659-336d6316e0b1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "╭──────────────┬─────────────────────────────────────────────┬─────────────┬────────────────────╮\n", "│ Atom index │ Directions │ Specified │ Equivalent atoms │\n", "├──────────────┼─────────────────────────────────────────────┼─────────────┼────────────────────┤\n", "│ 0 │ [-1. -0. +0.], [-0. -1. -0.], [-0. -0. +1.] │ \u001b[1;32;49m3/3\u001b[0m │ 35 │\n", "│ 36 │ [+0. +0. +1.], [+1. +0. +0.], [+0. +1. +0.] │ \u001b[1;32;49m3/3\u001b[0m │ 71 │\n", "╰──────────────┴─────────────────────────────────────────────┴─────────────┴────────────────────╯" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# OUTCARS are polarizability calculation where atom 5 (Ti) \n", "# was displaced +0.1 and +0.2 angstrom in the x direction\n", "model.add_art_from_files(\n", " [f\"{data_dir}/Ti5_0.1x_eps_OUTCAR\"], file_format = 'outcar'\n", " )\n", "model.add_art_from_files(\n", " [f\"{data_dir}/Ti5_0.1z_eps_OUTCAR\"],file_format = 'outcar'\n", " )\n", "model.add_art_from_files(\n", " [f\"{data_dir}/O43_0.1z_eps_OUTCAR\", f\"{data_dir}/O43_m0.1z_eps_OUTCAR\"], \n", " file_format=\"outcar\"\n", ")\n", "model.add_art_from_files(\n", " [f\"{data_dir}/O43_0.1x_eps_OUTCAR\"], file_format = 'outcar'\n", ")\n", "model.add_art_from_files([f\"{data_dir}/O43_0.1y_eps_OUTCAR\"],file_format = 'outcar')\n", "model" ] }, { "cell_type": "markdown", "id": "a6c70688", "metadata": {}, "source": [ "All degrees of freedom have been specified. We are now ready to do some Raman calculations!\n", "\n", "### Calculating the full Raman spectrum" ] }, { "cell_type": "code", "execution_count": 4, "id": "b1f2cb2c-8444-4b6a-ae8e-f1ac6c6a6e98", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute and plot spectrum\n", "spectrum = phonons.get_raman_spectrum(model)\n", "wavenumbers, total_intensities = spectrum.measure(\n", " laser_correction = True, \n", " laser_wavelength = 532, \n", " bose_einstein_correction = True, \n", " temperature = 300\n", ")\n", "wavenumbers, total_intensities = rn.spectrum.utils.convolve_spectrum(wavenumbers, total_intensities)\n", "fig = plt.figure(constrained_layout = True, figsize = (8, 3))\n", "axis = fig.add_subplot(111)\n", "axis.plot(wavenumbers, total_intensities)\n", "axis.set_ylabel(\"Intensity (a.u.)\")\n", "l = axis.set_xlabel(r\"Raman shift ($\\mathregular{cm^{-1}}$)\")" ] }, { "cell_type": "markdown", "id": "049753d4", "metadata": {}, "source": [ "### Isolating atomic contributions\n", "\n", "One question we could ask is which parts of the Raman spectrum are associated with motion of Ti atoms and which parts are associated more with O atoms. In this case, we can produce two masked `ARTModel`'s, one with the Ti atoms masked and other with the O atoms masked." ] }, { "cell_type": "code", "execution_count": 5, "id": "e0806350-ac5d-4f09-826d-b9dc85ec471b", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(constrained_layout = True, figsize = (8, 4))\n", "axis = fig.add_subplot(111)\n", "\n", "total_model = model\n", "O_dof_indexes = total_model.get_dof_indexes('O')\n", "Ti_model = total_model.get_masked_model(O_dof_indexes) # Mask O to leave only Ti\n", "Ti_dof_indexes = total_model.get_dof_indexes('Ti')\n", "O_model = total_model.get_masked_model(Ti_dof_indexes) # Mask Ti to leave only O\n", "\n", "offset = 0\n", "models = [Ti_model, O_model, total_model]\n", "labels = ['Ti contribution', 'O contribution', 'Total spectrum']\n", "for plot_model, label in zip(models, labels):\n", "\n", " spectrum = phonons.get_raman_spectrum(plot_model)\n", " wavenumbers, intensities = spectrum.measure(\n", " laser_correction = True, \n", " laser_wavelength = 532, \n", " bose_einstein_correction = True, \n", " temperature = 300\n", " )\n", " wavenumbers, intensities = rn.spectrum.utils.convolve_spectrum(wavenumbers, intensities)\n", " axis.plot(wavenumbers, intensities + offset, label = label)\n", " offset += np.max(intensities) + 0.02\n", "\n", "axis.set_ylabel(\"Intensity (a.u.)\")\n", "axis.set_xlabel(r\"Raman shift ($\\mathregular{cm^{-1}}$)\")\n", "axis.set_yticks([])\n", "l = axis.legend()" ] }, { "cell_type": "markdown", "id": "32f6be86", "metadata": {}, "source": [ "Convince yourself that this makes sense. Hint: consider the vibrational frequencies of the heavier Ti atoms vs the lighter O atoms.\n", "\n", "Although this a very simple example, model masking is extremely powerful. By isolating the influence of individual atomic motions on the Raman spectrum, we can gain deep insight into the factors regulating the Raman shifts and Raman intensities of certain motions. In addition, masking gives us a straightforward way to isolate the Raman spectra of specific atoms or groups of atoms. This is useful in many cases, for example when considering defects." ] }, { "cell_type": "markdown", "id": "a4824320", "metadata": {}, "source": [ "### Pitfalls" ] }, { "cell_type": "markdown", "id": "645a83d5", "metadata": {}, "source": [ "It is important of a model's mask, lest you unintentionally use a masked model and believe the results represent the total spectrum. You can check a model's masking status using its `__repr__` string:" ] }, { "cell_type": "code", "execution_count": 6, "id": "3ee61b25", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "╭──────────────┬─────────────────────────────────────────────┬─────────────┬────────────────────╮\n", "│ Atom index │ Directions │ Specified │ Equivalent atoms │\n", "├──────────────┼─────────────────────────────────────────────┼─────────────┼────────────────────┤\n", "│ 0 │ [-1. -0. +0.], [-0. -1. -0.], [-0. -0. +1.] │ \u001b[1;32;49m3/3\u001b[0m │ 35 │\n", "│ 36 │ [+0. +0. +1.], [+1. +0. +0.], [+0. +1. +0.] │ \u001b[1;32;49m3/3\u001b[0m │ 71 │\n", "╰──────────────┴─────────────────────────────────────────────┴─────────────┴────────────────────╯\n", " \u001b[1;33;49m ATTENTION: 108/324 atomic Raman tensors are masked. \u001b[0m\n" ] }, { "data": { "text/plain": [ "╭──────────────┬─────────────────────────────────────────────┬─────────────┬────────────────────╮\n", "│ Atom index │ Directions │ Specified │ Equivalent atoms │\n", "├──────────────┼─────────────────────────────────────────────┼─────────────┼────────────────────┤\n", "│ 0 │ [-1. -0. +0.], [-0. -1. -0.], [-0. -0. +1.] │ \u001b[1;32;49m3/3\u001b[0m │ 35 │\n", "│ 36 │ [+0. +0. +1.], [+1. +0. +0.], [+0. +1. +0.] │ \u001b[1;32;49m3/3\u001b[0m │ 71 │\n", "╰──────────────┴─────────────────────────────────────────────┴─────────────┴────────────────────╯\n", " \u001b[1;33;49m ATTENTION: 108/324 atomic Raman tensors are masked. \u001b[0m" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(repr(O_model))\n", "\n", "# OR (in Jupyter notebooks)\n", "O_model " ] }, { "cell_type": "markdown", "id": "f7288549", "metadata": {}, "source": [ "If in doubt, you can always use `unmask` to remove the mask." ] }, { "cell_type": "code", "execution_count": 7, "id": "42d653d5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "╭──────────────┬─────────────────────────────────────────────┬─────────────┬────────────────────╮\n", "│ Atom index │ Directions │ Specified │ Equivalent atoms │\n", "├──────────────┼─────────────────────────────────────────────┼─────────────┼────────────────────┤\n", "│ 0 │ [-1. -0. +0.], [-0. -1. -0.], [-0. -0. +1.] │ \u001b[1;32;49m3/3\u001b[0m │ 35 │\n", "│ 36 │ [+0. +0. +1.], [+1. +0. +0.], [+0. +1. +0.] │ \u001b[1;32;49m3/3\u001b[0m │ 71 │\n", "╰──────────────┴─────────────────────────────────────────────┴─────────────┴────────────────────╯" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "O_model.unmask()\n", "O_model" ] }, { "cell_type": "code", "execution_count": null, "id": "d769efda", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 5 }