{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ionisation potential of a porous material\n",
    "\n",
    "In this example we use `MacroDensity` with `VASP` to align the energy levels of a porous material.\n",
    "\n",
    "The procedure involves one DFT calculaion, yielding different important values:\n",
    "\n",
    "* $\\epsilon_{vbm}$ - the valence band maximum\n",
    "* $V_{vac}$ - the vacuum potential\n",
    "\n",
    "The ionisation potential ($IP$) is then obtained from:\n",
    "\n",
    "$IP = V_{vac} - \\epsilon_{vbm}$\n",
    "\n",
    "The difference to a bulk calculation is that here the material itself has a vacuum within it. This allows us to sample the vacuum level from the vacuum region, as explained in [this paper](http://pubs.acs.org/doi/abs/10.1021/ja4110073).\n",
    "\n",
    "## Our system \n",
    "\n",
    "We will demonstrate this procedure for the porous system ZIF-8.\n",
    "\n",
    "![](./zif8.png)\n",
    "\n",
    "## Procedure\n",
    "\n",
    "1. Optimise the structure\n",
    "2. Calculate the electronic structure at your chosen level of theory, adding the `LVHAR` flag to the `INCAR` file:\n",
    "\n",
    "    ``LVHAR = .TRUE.  # This generates a LOCPOT file with the potential`` \n",
    "    \n",
    "3. Locate the centre of the largest pore - do this \"by eye\" first\n",
    "4. Plot the potential in that plane, so see if it plateaus\n",
    "5. Plot a profile of the potential across the pore, again to see the plateau\n",
    "6. Sample the potential from the pore centre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_13766/391802285.py:7: DeprecationWarning: the imp module is deprecated in favour of importlib and slated for removal in Python 3.12; see the module's documentation for alternative uses\n",
      "  import imp\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import sys\n",
    "sys.path.append('../../')\n",
    "import imp\n",
    "import macrodensity as md\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read the potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "if os.path.isfile('LOCPOT'):\n",
    "    print('LOCPOT already exists')\n",
    "else:\n",
    "    os.system('bunzip2 LOCPOT.bz2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading header information...\n",
      "Reading 3D data using Pandas...\n",
      "Average of the potential =  1.9559870102655787e-14\n"
     ]
    }
   ],
   "source": [
    "input_file = 'LOCPOT'\n",
    "\n",
    "#=== No need to edit below\n",
    "vasp_pot, NGX, NGY, NGZ, Lattice = md.read_vasp_density(input_file)\n",
    "vector_a,vector_b,vector_c,av,bv,cv = md.matrix_2_abc(Lattice)\n",
    "resolution_x = vector_a/NGX\n",
    "resolution_y = vector_b/NGY\n",
    "resolution_z = vector_c/NGZ\n",
    "grid_pot, electrons = md.density_2_grid(vasp_pot, NGX, NGY, NGZ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Look for pore centre points\n",
    "\n",
    "* For this we will use `VESTA`.\n",
    "    * Open the LOCPOT in `VESTA`.\n",
    "    * Expand to 2x2x2 cell, by choosing the Boundary option on the left hand side.\n",
    "    * Look for a pore centre - [1,1,1] is at a pore centre here.\n",
    "    * Now draw a lattice plane through that point.\n",
    "        * Choose Edit > Lattice Planes.\n",
    "        * Click New.\n",
    "        * Put in the Miller index (e.g. 1,1,1).\n",
    "        * Move the plane up and down using the d parameter, until it passes through the point you think is the centre.\n",
    "        * It should look like the picture below.\n",
    "![](./111.png)\n",
    "\n",
    "* Now we look at a contour plot of this plane to see if we are at a plateau.\n",
    "    * Utiltiy > 2D Data Display.\n",
    "    * Click Slice and enter the same parameters as in the 3D view.\n",
    "    * Now choose contours to play with the settings\n",
    "    * Z(max) and Z(min) tell you the potential max and min.\n",
    "    * Set contour max = Z(max) and contour min = 0 and the interval to 0.1.\n",
    "    * With some playing with the General settings, you can get something like this:\n",
    "    \n",
    "![](./plane.png)\n",
    "\n",
    "* We can see the [1,1,1], at the centre of the picture is a maximum and is a plateau, so we can now use it for sampling.\n",
    "\n",
    "## Sampling the potential\n",
    "\n",
    "* We now set the point to sample at [1,1,1]\n",
    "* We must also set the travelled parameter, for this type of analysis it is always [0,0,0]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "cube_origin = [1,1,1]\n",
    "travelled = [0,0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "216"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(cube_origin[0]*NGX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We want to try a range of sampling area sizes and analyse how this affects the potential.\n",
    "* We also want low variance (plateau condidtions).\n",
    "* Ideally we should have as large an area as possible, with low (< 1e-5) variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension   Potential   Variance\n",
      "--------------------------------\n",
      "   1         2.3068     0.000000\n",
      "  10         2.3068     0.000001\n",
      "  20         2.3068     0.000003\n",
      "  40         2.3068     0.000019\n",
      "  60         2.3067     0.000108\n",
      "  80         2.3048     0.001151\n",
      " 100         2.2883     0.015872\n"
     ]
    }
   ],
   "source": [
    "dim = [1, 10, 20, 40, 60, 80, 100]\n",
    "print(\"Dimension   Potential   Variance\")\n",
    "print(\"--------------------------------\")\n",
    "for d in dim:\n",
    "    cube = [d, d, d]\n",
    "    cube_potential, cube_var = md.volume_average(cube_origin, cube,grid_pot, NGX, NGY, NGZ, travelled=travelled)\n",
    "    print(\" %3i     %10.4f   %10.6f\"%(d, cube_potential, cube_var))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we take the potential value of `2.3068`. For the VBM value, we take it from the `OUTCAR` file (VBM: -2.4396 eV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IP: 4.7464 eV\n"
     ]
    }
   ],
   "source": [
    "print(\"IP: %3.4f eV\" % (2.3068 -- 2.4396 ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}