{ "cells": [ { "cell_type": "markdown", "id": "61e39717-da1a-4476-93fd-599f27b4ff1e", "metadata": {}, "source": [ "# The Wannier-projected density of states, populations and charges" ] }, { "cell_type": "code", "execution_count": 1, "id": "3266eb37-399f-463b-8c49-c3e3d5524589", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "%config InlineBackend.figure_format = 'retina'" ] }, { "cell_type": "markdown", "id": "d9c32afd-89b7-4095-83f0-40c449397499", "metadata": {}, "source": [ "![The structure of rutile with a single Wannier function plotted](images/structure.png)" ] }, { "cell_type": "markdown", "id": "afce749e-e9bc-40fc-8696-d72e6aef86db", "metadata": {}, "source": [ "As well as enabling the calculation of bonding descriptors from Wannier functions, `pengwann` also allows for the computation of a Wannier-projected density of states which can be integrated to derive atomic populations and charges. This example demonstrates the calculation of these quantities in rutile TiO$_{2}$." ] }, { "cell_type": "markdown", "id": "61d34e52-15ae-412a-9db1-2c5dfae1e4c6", "metadata": {}, "source": [ "## The Wannier-projected density of states" ] }, { "cell_type": "code", "execution_count": 2, "id": "85f710dc-ac9d-4c06-ac65-07351f672468", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Geometry\n", "========\n", "Cell\n", "----\n", "[[4.587891 0. 0. ]\n", " [0. 4.587891 0. ]\n", " [0. 0. 2.938132]]\n", "\n", "Assignments\n", "-----------\n", "X0 => (28,)\n", "X1 => (28,)\n", "X2 => (28,)\n", "X3 => (28,)\n", "X4 => (28,)\n", "X5 => (28,)\n", "X6 => (29,)\n", "X7 => (29,)\n", "X8 => (29,)\n", "X9 => (29,)\n", "X10 => (29,)\n", "X11 => (29,)\n", "X12 => (30,)\n", "X13 => (30,)\n", "X14 => (30,)\n", "X15 => (30,)\n", "X16 => (31,)\n", "X17 => (31,)\n", "X18 => (31,)\n", "X19 => (31,)\n", "X20 => (32,)\n", "X21 => (32,)\n", "X22 => (32,)\n", "X23 => (32,)\n", "X24 => (33,)\n", "X25 => (33,)\n", "X26 => (33,)\n", "X27 => (33,)\n", "Ti28 <= (0, 1, 2, 3, 4, 5)\n", "Ti29 <= (6, 7, 8, 9, 10, 11)\n", "O30 <= (12, 13, 14, 15)\n", "O31 <= (16, 17, 18, 19)\n", "O32 <= (20, 21, 22, 23)\n", "O33 <= (24, 25, 26, 27)\n", "\n" ] } ], "source": [ "from pengwann.geometry import Geometry\n", "\n", "geometry = Geometry.from_xyz(seedname='wannier90', path='inputs')\n", "\n", "print(geometry)" ] }, { "cell_type": "markdown", "id": "a26591c5-6810-4225-8ec6-7487aff5c185", "metadata": {}, "source": [ "In previous [examples](../../examples), we have used the {py:func}`~pengwann.geometry.identify_interatomic_interactions` function to find bonds and describe them in terms of the interacting atoms' assigned Wannier functions. To instead calculate local atomic properties such as the Wannier pDOS, we make use of the {py:func}`~pengwann.geometry.identify_onsite_interactions` function:" ] }, { "cell_type": "code", "execution_count": 3, "id": "bc047f97-e40a-4f34-a088-217451fc84dd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Atomic interactions\n", "===================\n", "Ti28 <=> Ti28\n", "Ti29 <=> Ti29\n", "O30 <=> O30\n", "O31 <=> O31\n", "O32 <=> O32\n", "O33 <=> O33\n", "\n" ] } ], "source": [ "from pengwann.geometry import identify_onsite_interactions\n", "\n", "# The atomic species for which to obtain interactions.\n", "symbols = ('Ti', 'O')\n", "\n", "interactions = identify_onsite_interactions(geometry, symbols)\n", "\n", "print(interactions)" ] }, { "cell_type": "markdown", "id": "7cdbed59-b85b-4e8a-bf52-304ff7c4097d", "metadata": {}, "source": [ "The meaning of \"on-site\" interactions in this context is made slightly clearer if we examine a specific {py:class}`~pengwann.interactions.AtomicInteraction`:" ] }, { "cell_type": "code", "execution_count": 4, "id": "82741fb7-b71f-497d-b431-cfbe9a159665", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Atomic interaction Ti28 <=> Ti28\n", "================================\n", "DOS matrix => Not calculated\n", "WOHP => Not calculated\n", "WOBI => Not calculated\n", "IWOHP => Not calculated\n", "IWOBI => Not calculated\n", "Population => Not calculated\n", "Charge => Not calculated\n", "\n", "\n", "Associated Wannier interactions\n", "-------------------------------\n", "0[0, 0, 0] <=> 0[0, 0, 0]\n", "1[0, 0, 0] <=> 1[0, 0, 0]\n", "2[0, 0, 0] <=> 2[0, 0, 0]\n", "3[0, 0, 0] <=> 3[0, 0, 0]\n", "4[0, 0, 0] <=> 4[0, 0, 0]\n", "5[0, 0, 0] <=> 5[0, 0, 0]\n", "\n" ] } ], "source": [ "print(interactions[28, 28])" ] }, { "cell_type": "markdown", "id": "1fed1e61-6e7c-40f3-8029-ff428d43d200", "metadata": {}, "source": [ "As seen above, an on-site interaction in `pengwann` refers to all of the diagonal terms, in which the coefficients used to calculate the DOS matrix are related by complex conjugation, yielding the Wannier-projected density of states:\n", "\n", "$$\\mathrm{pDOS}_{\\alpha}(E) = \\sum_{nk}\\mathrm{Re}\\left[\\left(C^{\\alpha}_{nk}\\right)^{*}C^{\\alpha}_{nk}\\right]\\cdot\\delta(E - \\epsilon_{nk}).$$\n", "\n", ":::{note}\n", "For more details regarding the mathematical formalism employed in `pengwann`, please see the [methodology](../../methodology) page and the [API reference](../../api).\n", ":::" ] }, { "cell_type": "code", "execution_count": 5, "id": "18dfd56a-2c82-4280-893d-456668f2ed6a", "metadata": {}, "outputs": [], "source": [ "from pengwann.descriptors import DescriptorCalculator\n", "from pengwann.io import read\n", "\n", "kpoints, eigenvalues, u_matrices, _ = read(seedname='wannier90',\n", " path='inputs')\n", "\n", "mu = 9.5\n", "nspin = 2\n", "\n", "num_wann = 28\n", "energy_range = (-20, 20)\n", "resolution = 0.1\n", "sigma = 0.1\n", "\n", "dcalc = DescriptorCalculator.from_eigenvalues(eigenvalues,\n", " num_wann,\n", " nspin,\n", " energy_range,\n", " resolution,\n", " sigma,\n", " kpoints,\n", " u_matrices)" ] }, { "cell_type": "markdown", "id": "93255097-d78e-442b-b31d-63515e83e74d", "metadata": {}, "source": [ "Having initialised a {py:class}`~pengwann.descriptors.DescriptorCalculator` in much the same way as we would to calculate bonding descriptors, we can now obtain the pDOS by calling the {py:meth}`~pengwann.descriptors.DescriptorCalculator.assign_descriptors` method on our on-site `interactions`:" ] }, { "cell_type": "code", "execution_count": 6, "id": "bf2df6eb-0aaf-4d9d-862b-f305e16cdb17", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a146550e5b404eafa4863bae6cb73e69", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/28 [00:00" ] }, "metadata": { "image/png": { "height": 433, "width": 567 } }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "# Colours for plots\n", "ti_colour = '#79a9d1'\n", "o_colour = '#ff4365'\n", "\n", "shifted_energies = dcalc.energies - mu\n", "\n", "fig, ax = plt.subplots()\n", "\n", "pdos = interactions[28, 28].dos_matrix\n", "ax.plot(shifted_energies, pdos, color=ti_colour)\n", "ax.axvline(x=0, color='black', ls='--', lw=1)\n", "\n", "ax.set_xlim(-20, 8)\n", "\n", "ax.set_xlabel(r'$E - E_{\\mathrm{F}}$ / eV')\n", "ax.set_ylabel('pDOS')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9ae1b7bb-8564-4992-8865-8e21f7d34345", "metadata": {}, "source": [ ":::{note}\n", "In much the same way that bonding descriptors such as the Wannier orbital Hamilton population (WOHP) can be resolved with respect to individual Wannier functions (see this [example](../diamond/orbital_and_k_resolution)), the same is true of the pDOS.\n", ":::\n", "\n", "To plot the pDOS in terms of atomic species rather than individual atoms, we simply sum over atoms of the same species. Accessing all interactions involving a certain subset of atomic species/elemental symbols is easily accomplished using the {py:meth}`~pengwann.interactions.AtomicInteractionContainer.filter_by_species` method:" ] }, { "cell_type": "code", "execution_count": 8, "id": "df4f3a25-cbde-4c52-8102-125dd8b61870", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 433, "width": 554 } }, "output_type": "display_data" } ], "source": [ "ti_pdos = sum(\n", " interaction.dos_matrix for interaction in \n", " interactions.filter_by_species(['Ti'])\n", ")\n", "o_pdos = sum(\n", " interaction.dos_matrix for interaction in \n", " interactions.filter_by_species(['O'])\n", ")\n", "\n", "fig, ax = plt.subplots()\n", "\n", "ax.plot(shifted_energies, ti_pdos, color=ti_colour, label='Ti')\n", "ax.plot(shifted_energies, o_pdos, color=o_colour, label='O')\n", "ax.axvline(x=0, color='black', ls='--', lw=1)\n", "\n", "ax.set_xlim(-20, 8)\n", "\n", "ax.set_xlabel(r'$E - E_{\\mathrm{F}}$ / eV')\n", "ax.set_ylabel('pDOS')\n", "\n", "ax.legend(frameon=False)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c831eb51-8b58-4b5a-befd-89c49a2b6ef0", "metadata": {}, "source": [ "## Populations and charges" ] }, { "cell_type": "markdown", "id": "e296f491-9900-48d5-b9d5-49202459d778", "metadata": {}, "source": [ "The pDOS can be integrated to derive a Löwdin-style population for a particular Wannier function or atom." ] }, { "cell_type": "code", "execution_count": 9, "id": "17acedbc-c8e5-4b66-be9c-17e4f4089859", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Population for Ti28 <=> Ti28 = 1.88\n", "Population for Ti29 <=> Ti29 = 1.88\n", "Population for O30 <=> O30 = 7.06\n", "Population for O31 <=> O31 = 7.06\n", "Population for O32 <=> O32 = 7.06\n", "Population for O33 <=> O33 = 7.06\n" ] } ], "source": [ "interactions = interactions.with_integrals(dcalc.energies, mu)\n", "\n", "for interaction in interactions:\n", " print(f'Population for {interaction.tag} = {interaction.population:.2f}')" ] }, { "cell_type": "markdown", "id": "f7ee2a7b-4266-4248-a63e-bd50c5007983", "metadata": {}, "source": [ "If we also provide `valence_counts` to the {py:meth}`~pengwann.interactions.AtomicInteractionContainer.with_integrals` method, then we will also have access to charges for each atom too:" ] }, { "cell_type": "code", "execution_count": 10, "id": "2f4c4e33-bd2c-4271-9d33-7cfcb7b28ab5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Charge for Ti28 <=> Ti28 = 2.12\n", "Charge for Ti29 <=> Ti29 = 2.12\n", "Charge for O30 <=> O30 = -1.06\n", "Charge for O31 <=> O31 = -1.06\n", "Charge for O32 <=> O32 = -1.06\n", "Charge for O33 <=> O33 = -1.06\n" ] } ], "source": [ "valence_counts = {'Ti': 4, 'O': 6}\n", "\n", "interactions = interactions.with_integrals(dcalc.energies,\n", " mu,\n", " valence_counts=valence_counts)\n", "\n", "for interaction in interactions:\n", " print(f'Charge for {interaction.tag} = {interaction.charge:.2f}')" ] }, { "cell_type": "markdown", "id": "a8ec4b29-f862-4d29-886e-efcc5251a79b", "metadata": {}, "source": [ "The relationship between populations and charges in this instance is trivial, the charge is simply the difference between the number of valence electrons associated with an atom (according to the pseudopotential used in the ab initio calculation) and its population." ] } ], "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": "3.12.0" } }, "nbformat": 4, "nbformat_minor": 5 }