{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aca254eb-6658-4688-89f0-311c4043ba9e",
   "metadata": {},
   "source": [
    "# The basics: bonding descriptors in diamond"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e0e78760-ffb0-4a7d-8585-c1f917815e9f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9572527c-13d2-4091-8e55-2f6a3a7f6a68",
   "metadata": {},
   "source": [
    "![The structure of diamond with a single Wannier function plotted](images/structure.png)\n",
    "\n",
    "This example demonstrates how `pengwann` can be used to calculate the Wannier orbital Hamilton population (WOHP) and the Wannier orbital bond index (WOBI) for the C-C bond in diamond. We will also integrate these descriptors to (roughly speaking) measure the bond strength and bond order.\n",
    "\n",
    ":::{note}\n",
    "As referenced in the title above, this example is designed to showcase the **basics** of `pengwann` as applied to a simple system. This should be enough to get you started, but for more information regarding additional functionality and alternative workflows, please see the other [examples](../../examples) and the [API reference](../../api).\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d7ec48d-784b-4706-9a02-cb7c4751a5bb",
   "metadata": {},
   "source": [
    "## Step 1: Identifying interatomic interactions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68a4ee83-77b4-4c1e-9a61-810eafe35937",
   "metadata": {},
   "source": [
    "Within `pengwann`, the interaction between a given pair of atoms *i* and *j* is the sum total of all interactions between the Wannier functions associated with atom *i* and the Wannier functions associated with atom *j*. In order to compute bonding descriptors for the C-C bond in diamond, we must therefore first figure out which Wannier functions should be assigned to each carbon atom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2c0b90a4-4e8b-4538-a323-948268dfe409",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Geometry\n",
      "========\n",
      "Cell\n",
      "----\n",
      "[[-1.780373 -1.780373  0.      ]\n",
      " [-1.780373  0.       -1.780373]\n",
      " [ 0.       -1.780373 -1.780373]]\n",
      "\n",
      "Assignments\n",
      "-----------\n",
      "X0 => (8,)\n",
      "X1 => (9,)\n",
      "X2 => (8,)\n",
      "X3 => (9,)\n",
      "X4 => (9,)\n",
      "X5 => (8,)\n",
      "X6 => (8,)\n",
      "X7 => (9,)\n",
      "C8 <= (0, 2, 5, 6)\n",
      "C9 <= (1, 3, 4, 7)\n",
      "\n",
      "Site(symbol='X', index=0, coords=array([ 0.26424442,  0.57858402, -0.4214136 ]))\n",
      "Site(symbol='X', index=1, coords=array([0.17141581, 0.48575541, 0.1714149 ]))\n",
      "Site(symbol='X', index=2, coords=array([-0.42141344,  0.26424353,  0.57858404]))\n",
      "Site(symbol='X', index=3, coords=array([0.4857563 , 0.1714135 , 0.17141418]))\n",
      "Site(symbol='X', index=4, coords=array([0.17141464, 0.17141484, 0.48575593]))\n",
      "Site(symbol='X', index=5, coords=array([-0.42141478, -0.42141459, -0.4214143 ]))\n",
      "Site(symbol='X', index=6, coords=array([ 0.57858386, -0.42141294,  0.26424387]))\n",
      "Site(symbol='X', index=7, coords=array([0.17141299, 0.17141598, 0.17141483]))\n",
      "Site(symbol='C', index=8, coords=array([0.49999989, 0.49999989, 0.49999989]))\n",
      "Site(symbol='C', index=9, coords=array([0.24999994, 0.24999994, 0.24999994]))\n"
     ]
    }
   ],
   "source": [
    "from pengwann.geometry import Geometry\n",
    "\n",
    "geometry = Geometry.from_xyz(seedname='wannier90', path='inputs')\n",
    "\n",
    "print(geometry)\n",
    "\n",
    "for site in geometry:\n",
    "    print(site)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "124e599e-18a1-46d3-8cbe-ed67d0f7da3d",
   "metadata": {},
   "source": [
    "Above, we have initialised a {py:class}`~pengwann.geometry.Geometry` object using the {py:meth}`~pengwann.geometry.Geometry.from_xyz` classmethod, which parses the Wannier90 seedname_centres.xyz and seedname.wout files to extract the coordinates of atoms and Wannier centres as well as the cell vectors. As indicated by the output above, each atom or Wannier centre is represented by an individual {py:class}`~pengwann.geometry.Site` object and associated with a `symbol`, `index` and set of `coords` (fractional coordinates). For atomic sites, the `symbol` is just an elemental symbol such as `C` for carbon, whereas for the sites defined by Wannier centres, the `symbol` is always `X`.\n",
    "\n",
    "In addition to the basic geometric information encoded by `Geometry` objects, they also assign Wannier centres to atoms based on a closest distance criterion. This is represented in the output above by the `Assignments` table, which contains indices that associate each Wannier centre with its closest atom. The indices refer to the order of sites in the `Geometry` object itself, for example, looking at the last site in the structure (a carbon atom at site #9), we read `C9 <= (1, 3, 4, 7)`, meaning that the Wannier centres at sites #1, #3, #4 and #7 have been assigned to this atom. Vice versa, if we look at the first site in the structure (a Wannier centre at site #0), we read `X0 => (8,)`, meaning that this Wannier centre has been assigned to the carbon atom at site #8.\n",
    "\n",
    ":::{warning}\n",
    "The seedname_centres.xyz file read by the `from_xyz` classmethod should always be generated by [Wannier90](https://wannier.org/) with `translate_home cell = false`. If a seedname_centres.xyz file generated with `translated_home_cell = true` is used, then the Wannier centre assignments will still be accurate, but the interatomic interactions (specifically the Bravais lattice vectors associated with the interacting Wannier functions) identified in subsequent steps **may not be accurate**.\n",
    ":::\n",
    "\n",
    "Now that we have the geometry of the system and its Wannier centres available to us, we can identify interatomic interactions according to a radial distance cutoff:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "36b2bf2d-eaf7-4520-878a-bc216e4934b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atomic interactions\n",
      "===================\n",
      "C8 <=> C9\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from pengwann.geometry import identify_interatomic_interactions\n",
    "\n",
    "# Find all C-C bonds that are < 1.6 Å.\n",
    "cutoffs = {('C', 'C'): 1.6}\n",
    "\n",
    "interactions = identify_interatomic_interactions(geometry, cutoffs)\n",
    "\n",
    "print(interactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1486df84-f263-4523-84f6-2bd67da869f3",
   "metadata": {},
   "source": [
    "Sure enough, because we are here using the primitive cell of diamond (which contains only 2 carbon atoms), we find just a single C-C interaction between atoms #8 and #9 (with reference to the `Geometry` generated prior).\n",
    "\n",
    "The object returned by the {py:func}`~pengwann.geometry.identify_interatomic_interactions` function is an {py:class}`~pengwann.interactions.AtomicInteractionContainer`. As the name suggests, this object is designed to collect multiple {py:class}`~pengwann.interactions.AtomicInteraction` objects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a65f916b-b7a2-4a33-84d9-a0138bc03335",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atomic interaction C8 <=> C9\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, 1] <=> 1[0, 0, 0]\n",
      "0[0, 0, 1] <=> 3[0, 0, 0]\n",
      "0[0, 0, 1] <=> 4[0, 0, 0]\n",
      "0[0, 0, 1] <=> 7[0, 0, 0]\n",
      "2[1, 0, 0] <=> 1[0, 0, 0]\n",
      "2[1, 0, 0] <=> 3[0, 0, 0]\n",
      "2[1, 0, 0] <=> 4[0, 0, 0]\n",
      "2[1, 0, 0] <=> 7[0, 0, 0]\n",
      "5[1, 1, 1] <=> 1[0, 0, 0]\n",
      "5[1, 1, 1] <=> 3[0, 0, 0]\n",
      "5[1, 1, 1] <=> 4[0, 0, 0]\n",
      "5[1, 1, 1] <=> 7[0, 0, 0]\n",
      "6[0, 1, 0] <=> 1[0, 0, 0]\n",
      "6[0, 1, 0] <=> 3[0, 0, 0]\n",
      "6[0, 1, 0] <=> 4[0, 0, 0]\n",
      "6[0, 1, 0] <=> 7[0, 0, 0]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for interaction in interactions:\n",
    "    print(interaction)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17d4a3fa-df09-4437-840d-e642abf180c8",
   "metadata": {},
   "source": [
    "As we only have one interaction, iterating over `interactions` just yields one `AtomicInteraction` object. We can also access the interaction between `C8` and `C9` via [numpy](https://numpy.org/)-style indexing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "80fc9b7a-974a-4214-adc2-6f0c894b96ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atomic interaction C8 <=> C9\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, 1] <=> 1[0, 0, 0]\n",
      "0[0, 0, 1] <=> 3[0, 0, 0]\n",
      "0[0, 0, 1] <=> 4[0, 0, 0]\n",
      "0[0, 0, 1] <=> 7[0, 0, 0]\n",
      "2[1, 0, 0] <=> 1[0, 0, 0]\n",
      "2[1, 0, 0] <=> 3[0, 0, 0]\n",
      "2[1, 0, 0] <=> 4[0, 0, 0]\n",
      "2[1, 0, 0] <=> 7[0, 0, 0]\n",
      "5[1, 1, 1] <=> 1[0, 0, 0]\n",
      "5[1, 1, 1] <=> 3[0, 0, 0]\n",
      "5[1, 1, 1] <=> 4[0, 0, 0]\n",
      "5[1, 1, 1] <=> 7[0, 0, 0]\n",
      "6[0, 1, 0] <=> 1[0, 0, 0]\n",
      "6[0, 1, 0] <=> 3[0, 0, 0]\n",
      "6[0, 1, 0] <=> 4[0, 0, 0]\n",
      "6[0, 1, 0] <=> 7[0, 0, 0]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(interactions[8, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0575007-a24b-4d34-b5b2-b11973af0374",
   "metadata": {},
   "source": [
    "As we can see from the output above, the interaction between `C8` and `C9` is internally represented by the interactions between their respective Wannier functions. The notation used to refer to each Wannier function can be understood as $\\ket{w_{iR}} =$ `i[R_1, R_2, R_3]`, where `i` is a band-like index and `R_1`, `R_2` and `R_3` are the components of a Bravais lattice vector."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "253cbba4-3dad-4aa0-9ecd-d1e2b4c053ee",
   "metadata": {},
   "source": [
    "## Step 2: Building a `DescriptorCalculator`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2b4e817-1f0f-4f4b-9eae-904511bc982e",
   "metadata": {},
   "source": [
    "To actually calculate the WOHP and the WOBI for the C-C bond, we will need to parse a few more Wannier90 input and output files. This can be easily accomplished with the {py:func}`~pengwann.io.read` function, which parses the Wannier90 seedname.eig, seedname_u.mat and seedname_hr.dat files to yield the k-point mesh, the Kohn-Sham eigenvalues, the unitary matrices that define the Wannier functions and the Wannier Hamiltonian:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "63caa14b-166f-4f01-ab7f-8cdd6d485ae4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pengwann.io import read\n",
    "\n",
    "kpoints, eigenvalues, u_matrices, hamiltonian = read(seedname='wannier90',\n",
    "                                                     path='inputs')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f800ba8e-7109-4344-9a00-53feabeb4f7a",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "The seedname.eig, seedname_u.mat and seedname_hr.dat files can also be parsed separately by various functions in the {py:mod}`~pengwann.io` module, the `read` function is just a convenient wrapper for most use cases.\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a674178-0f33-4e16-8edb-fc50ef581dc3",
   "metadata": {},
   "source": [
    "### Optional: Obtain the occupation matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d29145c-2243-43e6-bdaf-7690d2ca6d56",
   "metadata": {},
   "source": [
    "As we would like to calculate the WOBI as well as the WOHP for the C-C bond, we are also in need of the occupation matrix, which is required to compute elements of the Wannier density matrix. Ideally, the occupation matrix should be read directly from the ab initio code, in our case from VASP. Due to the fact that different ab initio codes output the occupation matrix in different formats, `pengwann` does not provide a generic I/O function for this purpose. We recommend that users look towards larger and more general-use Python packages such as [pymatgen](https://pymatgen.org) or [ase](https://wiki.fysik.dtu.dk/ase/) for this functionality, and use these to read the occupation matrix from their ab initio calculations.\n",
    "\n",
    "If for whatever reason, the occupation matrix cannot be read directly from the ab initio code, then the {py:class}`~pengwann.occupations.get_occupation_matrix` function can be used to reconstruct it from the Kohn-Sham eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2d99431d-62f5-457d-aad3-32c3715a0c9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pengwann.occupations import get_occupation_matrix\n",
    "\n",
    "mu = 10.5 # The Fermi level\n",
    "nspin = 2 # The number of electrons per fully-occupied state.\n",
    "\n",
    "occupation_matrix = get_occupation_matrix(eigenvalues, mu, nspin)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89deb0c9-3561-443d-98c9-41e47a200af0",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "By default, the `get_occupation_matrix` function uses a heaviside function to build the occupation matrix: occupation numbers are 1 below the Fermi level and 0 above it (with a sharp cutoff). In the case of diamond, an insulator, this is perfectly appropriate, but for systems in which thermal smearing has been applied during the ab initio calculation it may be desirable to apply a different occupation function. The `get_occupation_matrix` function has an optional `occupation_function` keyword argument that can be used to apply any arbitary occupation function, several of which are available in the {py:mod}`~pengwann.occupations` module.\n",
    ":::\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f5b6c4a-749c-4cb7-8870-b5940bb31d72",
   "metadata": {},
   "source": [
    "The actual calculation of bonding descriptors is accomplished in `pengwann` via the {py:class}`~pengwann.descriptors.DescriptorCalculator` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1094c538-45ea-466a-9404-f33b544cd314",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pengwann.descriptors import DescriptorCalculator\n",
    "\n",
    "num_wann = 8\n",
    "energy_range = (-15, 26)\n",
    "resolution = 0.1\n",
    "sigma = 0.2 # Smearing width\n",
    "\n",
    "dcalc = DescriptorCalculator.from_eigenvalues(eigenvalues,\n",
    "                                              num_wann, \n",
    "                                              nspin, \n",
    "                                              energy_range, \n",
    "                                              resolution, \n",
    "                                              sigma, \n",
    "                                              kpoints, \n",
    "                                              u_matrices, \n",
    "                                              h=hamiltonian,\n",
    "                                              occupation_matrix=occupation_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "028199a3-52b1-4601-87cd-de3f833be3f1",
   "metadata": {},
   "source": [
    "The `energy_range`, `resolution` and `sigma` arguments all refer to the manner in which the density of states is to be evaluated: from `energy_range[0]` up to `energy_range[1]` in steps of `resolution` smeared by a Gaussian of width `sigma`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "433690bb-dea6-4d8e-aac6-e037e1adeb01",
   "metadata": {},
   "source": [
    "## Step 3: Integrating and plotting the WOHP and the WOBI"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bbe0a41-3085-41a6-8f89-aacb11fd9c8d",
   "metadata": {},
   "source": [
    "Having initialised a `DescriptorCalculator`, actually calculating the WOHP and the WOBI is very straightforward:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "44561588-a220-43e6-a359-5d801d822b67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ce0408a28d524014973a67b9f083f138",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/16 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interactions = dcalc.assign_descriptors(interactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30d8f3fa-4863-495a-af44-4907b00700af",
   "metadata": {},
   "source": [
    "Note that the {py:meth}`~pengwann.descriptors.DescriptorCalculator.assign_descriptors` method returns a new `AtomicInteractionContainer` rather than updating the original in-place - this behaviour is common throughout the `pengwann` codebase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "eefd1f75-ec8a-4c9f-b619-727010f9c11a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atomic interaction C8 <=> C9\n",
      "============================\n",
      "DOS matrix => Calculated\n",
      "WOHP => Calculated\n",
      "WOBI => 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, 1] <=> 1[0, 0, 0]\n",
      "0[0, 0, 1] <=> 3[0, 0, 0]\n",
      "0[0, 0, 1] <=> 4[0, 0, 0]\n",
      "0[0, 0, 1] <=> 7[0, 0, 0]\n",
      "2[1, 0, 0] <=> 1[0, 0, 0]\n",
      "2[1, 0, 0] <=> 3[0, 0, 0]\n",
      "2[1, 0, 0] <=> 4[0, 0, 0]\n",
      "2[1, 0, 0] <=> 7[0, 0, 0]\n",
      "5[1, 1, 1] <=> 1[0, 0, 0]\n",
      "5[1, 1, 1] <=> 3[0, 0, 0]\n",
      "5[1, 1, 1] <=> 4[0, 0, 0]\n",
      "5[1, 1, 1] <=> 7[0, 0, 0]\n",
      "6[0, 1, 0] <=> 1[0, 0, 0]\n",
      "6[0, 1, 0] <=> 3[0, 0, 0]\n",
      "6[0, 1, 0] <=> 4[0, 0, 0]\n",
      "6[0, 1, 0] <=> 7[0, 0, 0]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(interactions[8, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fdc104e-b893-4bf9-9647-418211ec8d02",
   "metadata": {},
   "source": [
    "As seen above, the DOS matrix, the WOHP and the WOBI are now all reported as `Calculated` (the raw `numpy` arrays are not displayed because they would take up an impractical amount of screen real estate in most cases).\n",
    "\n",
    "To evaluate the IWOHP (integrated WOHP) and the IWOBI (integrated WOBI), we call the {py:meth}`~pengwann.interactions.AtomicInteractionContainer.with_integrals` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9bd5696d-3b2a-4156-a5d7-b51500d9bfc4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atomic interaction C8 <=> C9\n",
      "============================\n",
      "DOS matrix => Calculated\n",
      "WOHP => Calculated\n",
      "WOBI => Calculated\n",
      "IWOHP => Calculated\n",
      "IWOBI => Calculated\n",
      "Population => Calculated\n",
      "Charge => Not calculated\n",
      "\n",
      "\n",
      "Associated Wannier interactions\n",
      "-------------------------------\n",
      "0[0, 0, 1] <=> 1[0, 0, 0]\n",
      "0[0, 0, 1] <=> 3[0, 0, 0]\n",
      "0[0, 0, 1] <=> 4[0, 0, 0]\n",
      "0[0, 0, 1] <=> 7[0, 0, 0]\n",
      "2[1, 0, 0] <=> 1[0, 0, 0]\n",
      "2[1, 0, 0] <=> 3[0, 0, 0]\n",
      "2[1, 0, 0] <=> 4[0, 0, 0]\n",
      "2[1, 0, 0] <=> 7[0, 0, 0]\n",
      "5[1, 1, 1] <=> 1[0, 0, 0]\n",
      "5[1, 1, 1] <=> 3[0, 0, 0]\n",
      "5[1, 1, 1] <=> 4[0, 0, 0]\n",
      "5[1, 1, 1] <=> 7[0, 0, 0]\n",
      "6[0, 1, 0] <=> 1[0, 0, 0]\n",
      "6[0, 1, 0] <=> 3[0, 0, 0]\n",
      "6[0, 1, 0] <=> 4[0, 0, 0]\n",
      "6[0, 1, 0] <=> 7[0, 0, 0]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "interactions = interactions.with_integrals(dcalc.energies, mu)\n",
    "\n",
    "print(interactions[8, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcbe9c01-c636-4a38-a2ba-5f5621b6a5ae",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "The `energies` property of the `DescriptorCalculator` class simply returns the discrete energies at which the DOS and all derived descriptors have been evaluated.\n",
    ":::\n",
    "\n",
    "We are now in a position to plot the WOHP and the WOBI:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c3875342-1523-47e5-9ebf-b5455f503680",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 433,
       "width": 587
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "shifted_energies = dcalc.energies - mu\n",
    "\n",
    "wohp = interactions[8, 9].wohp\n",
    "iwohp = interactions[8, 9].iwohp\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(shifted_energies, wohp)\n",
    "ax.fill_between(shifted_energies, wohp, alpha=0.7, where=shifted_energies <= 0)\n",
    "ax.axvline(x=0, color='black', ls='--', lw=1)\n",
    "\n",
    "ax.annotate(f'IWOHP = {iwohp:.2f}', (0.25, 0.90), xycoords='axes fraction')\n",
    "\n",
    "ax.set_xlim(-25, 15)\n",
    "ax.set_ylim(-1.2, 1.2)\n",
    "\n",
    "ax.set_xlabel(r'$E - E_{\\mathrm{F}}$ / eV')\n",
    "ax.set_ylabel('WOHP')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ea9f2e89-76d8-41ca-84f5-9b8accfbdc9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fsM1SPwAAnIOZVAAAAK1ITk5Wd+mQ4K7fpb5helxcnOHJfM4yYsQIPf/880451pQpU9zy/0MAALo6ZlIBAADAdPUh1ZVXXmlyJQAAwCzMpAIAAIDpJk+erLFjx2rOnDlmlwIAAExCSAUAAADTtdTQHAAAeAaLlQX1AAAAAAAAMBk9qQAAAAAAAGA6QioAAAAAAACYjpAKAAAAAAAApiOkAgAAAAAAgOkIqQAAAAAAAGA6QioAAAAAAACYjpAKAAAAAAAApiOkAgAAAAAAgOkIqQAAAAAAAGA6QioAAAAAAACYjpAKAAAAAAAApiOkAgAAAAAAgOkIqQAAAAAAAGA6QioAAAAAAACYjpAKAAAAAAAApiOkAgAAAAAAgOkIqQAAAAAAAGA6QioAAAAAAACYjpAKAAAAAAAApiOkAgAAAAAAgOkIqQAAAAAAAGC6/x+enOgoOZxe1wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 433,
       "width": 596
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "wobi = interactions[8, 9].wobi\n",
    "iwobi = interactions[8, 9].iwobi\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(shifted_energies, wobi)\n",
    "ax.fill_between(shifted_energies, wobi, alpha=0.7, where=shifted_energies <= 0)\n",
    "ax.axvline(x=0, color='black', ls='--', lw=1)\n",
    "\n",
    "ax.annotate(f'IWOBI = {iwobi:.2f}', (0.25, 0.90), xycoords='axes fraction')\n",
    "\n",
    "ax.set_xlim(-25, 15)\n",
    "ax.set_ylim(-0.12, 0.12)\n",
    "\n",
    "ax.set_xlabel(r'$E - E_{\\mathrm{F}}$ / eV')\n",
    "ax.set_ylabel('WOBI')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "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
}