{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Wannierization using Wannier.jl or Wannier90\n",
    "\n",
    "DFTK features an interface with the programs\n",
    "[Wannier.jl](https://wannierjl.org) and [Wannier90](http://www.wannier.org/),\n",
    "in order to compute maximally-localized Wannier functions (MLWFs)\n",
    "from an initial self consistent field calculation.\n",
    "All processes are handled by calling the routine `Wannier.Model` (for Wannier.jl)\n",
    "or `run_wannier90` (for Wannier90).\n",
    "\n",
    "> **No guarantees on Wannier interface**\n",
    ">\n",
    "> This code is at an early stage and has so far not been fully tested.\n",
    "> Bugs are likely and we welcome issues in case you find any!\n",
    "\n",
    "This example shows how to obtain the MLWFs corresponding\n",
    "to the first five bands of graphene. Since the bands 2 to 11 are entangled,\n",
    "15 bands are first computed to obtain 5 MLWFs by a disantanglement procedure."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n     Energy            log10(ΔE)   log10(Δρ)   Diag   Δtime\n",
      "---   ---------------   ---------   ---------   ----   ------\n",
      "  1   -11.14943081262                   -0.67    9.0    541ms\n",
      "  2   -11.15007303296       -3.19       -1.40    1.0    228ms\n",
      "  3   -11.15010738316       -4.46       -2.77    3.6    278ms\n",
      "  4   -11.15010938088       -5.70       -3.32    4.4    361ms\n",
      "  5   -11.15010943002       -7.31       -4.30    2.8    265ms\n",
      "  6   -11.15010943371       -8.43       -4.99    4.2    349ms\n",
      "  7   -11.15010943376      -10.38       -5.35    3.8    312ms\n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "using DFTK\n",
    "using Plots\n",
    "using Unitful\n",
    "using UnitfulAtomic\n",
    "using PseudoPotentialData\n",
    "\n",
    "d = 10u\"Å\"\n",
    "a = 2.641u\"Å\"  # Graphene Lattice constant\n",
    "lattice = [a  -a/2    0;\n",
    "           0  √3*a/2  0;\n",
    "           0     0    d]\n",
    "\n",
    "C = ElementPsp(:C, PseudoFamily(\"cp2k.nc.sr.pbe.v0_1.semicore.gth\"))\n",
    "atoms     = [C, C]\n",
    "positions = [[0.0, 0.0, 0.0], [1//3, 2//3, 0.0]]\n",
    "model = model_DFT(lattice, atoms, positions; functionals=PBE())\n",
    "basis = PlaneWaveBasis(model; Ecut=15, kgrid=[5, 5, 1])\n",
    "nbandsalg = AdaptiveBands(basis.model; n_bands_converge=15)\n",
    "scfres = self_consistent_field(basis; nbandsalg, tol=1e-5);"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "Plot bandstructure of the system"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=123}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "cell_type": "code",
   "source": [
    "bands = compute_bands(scfres; kline_density=10)\n",
    "plot_bandstructure(bands)"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Wannierization with Wannier.jl\n",
    "\n",
    "Now we use the `Wannier.Model` routine to generate a Wannier.jl model\n",
    "that can be used to perform the wannierization procedure.\n",
    "For now, this model generation produces file in the Wannier90 convention,\n",
    "where all files are named with the same prefix and only differ by\n",
    "their extensions. By default all generated input and output files are stored\n",
    "in the subfolder \"wannierjl\" under the prefix \"wannier\" (i.e. \"wannierjl/wannier.win\",\n",
    "\"wannierjl/wannier.wout\", etc.). A different file prefix can be given with the\n",
    "keyword argument `fileprefix` as shown below.\n",
    "\n",
    "We now produce a simple Wannier model for 5 MLFWs.\n",
    "\n",
    "For a good MLWF, we need to provide initial projections that resemble the expected shape\n",
    "of the Wannier functions.\n",
    "Here we will use:\n",
    "- 3 bond-centered 2s hydrogenic orbitals for the expected σ bonds\n",
    "- 2 atom-centered 2pz hydrogenic orbitals for the expected π bands"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using Wannier # Needed to make Wannier.Model available"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "From chemical intuition, we know that the bonds with the lowest energy are:\n",
    "  - the 3 σ bonds,\n",
    "  - the π and π* bonds.\n",
    "We provide relevant initial projections to help Wannierization\n",
    "converge to functions with a similar shape."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "5-element Vector{DFTK.HydrogenicWannierProjection}:\n DFTK.HydrogenicWannierProjection([0.16666666666666666, 0.3333333333333333, 0.0], 2, 0, 0, 6)\n DFTK.HydrogenicWannierProjection([0.16666666666666666, -0.16666666666666669, 0.0], 2, 0, 0, 6)\n DFTK.HydrogenicWannierProjection([-0.33333333333333337, -0.16666666666666669, 0.0], 2, 0, 0, 6)\n DFTK.HydrogenicWannierProjection([0.0, 0.0, 0.0], 2, 1, 0, 6)\n DFTK.HydrogenicWannierProjection([0.3333333333333333, 0.6666666666666666, 0.0], 2, 1, 0, 6)"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "C_Z = charge_nuclear(C)\n",
    "s_guess(center)  = DFTK.HydrogenicWannierProjection(center, 2, 0, 0, C_Z)\n",
    "pz_guess(center) = DFTK.HydrogenicWannierProjection(center, 2, 1, 0, C_Z)\n",
    "projections = [\n",
    "    # Note: fractional coordinates for the centers!\n",
    "    # 3 bond-centered 2s hydrogenic orbitals to imitate σ bonds\n",
    "    s_guess((positions[1] + positions[2]) / 2),\n",
    "    s_guess((positions[1] + positions[2] + [0, -1, 0]) / 2),\n",
    "    s_guess((positions[1] + positions[2] + [-1, -1, 0]) / 2),\n",
    "    # 2 atom-centered 2pz hydrogenic orbitals\n",
    "    pz_guess(positions[1]),\n",
    "    pz_guess(positions[2]),\n",
    "]"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "Wannierize:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ Info: Reading win file: wannier/graphene.win\n",
      "  num_wann  = 5\n",
      "  num_bands = 15\n",
      "  mp_grid   = 5 5 1\n",
      "\n",
      "b-vector shell   1    weight =  1.10422\n",
      "    1      -0.47582   -0.27471    0.00000\n",
      "    2       0.47582    0.27471    0.00000\n",
      "    3       0.00000   -0.54943    0.00000\n",
      "    4       0.00000    0.54943    0.00000\n",
      "    5       0.47582   -0.27471    0.00000\n",
      "    6      -0.47582    0.27471    0.00000\n",
      "b-vector shell   2    weight =  1.26651\n",
      "    1       0.00000    0.00000   -0.62832\n",
      "    2       0.00000    0.00000    0.62832\n",
      "\n",
      "Finite difference condition satisfied\n",
      "\n",
      "[ Info: Reading win file: wannier/graphene.win\n",
      "  num_wann  = 5\n",
      "  num_bands = 15\n",
      "  mp_grid   = 5 5 1\n",
      "\n",
      "b-vector shell   1    weight =  1.10422\n",
      "    1      -0.47582   -0.27471    0.00000\n",
      "    2       0.47582    0.27471    0.00000\n",
      "    3       0.00000   -0.54943    0.00000\n",
      "    4       0.00000    0.54943    0.00000\n",
      "    5       0.47582   -0.27471    0.00000\n",
      "    6      -0.47582    0.27471    0.00000\n",
      "b-vector shell   2    weight =  1.26651\n",
      "    1       0.00000    0.00000   -0.62832\n",
      "    2       0.00000    0.00000    0.62832\n",
      "\n",
      "Finite difference condition satisfied\n",
      "\n",
      "[ Info: Reading mmn file: wannier/graphene.mmn\n",
      "  header  = Generated by DFTK at 2025-03-15T15:29:34.617\n",
      "  n_bands = 15\n",
      "  n_bvecs = 8\n",
      "  n_kpts  = 25\n",
      "\n",
      "[ Info: Reading wannier/graphene.amn\n",
      "  header  = Generated by DFTK at 2025-03-15T15:29:31.105\n",
      "  n_bands = 15\n",
      "  n_wann  = 5\n",
      "  n_kpts  = 25\n",
      "\n",
      "[ Info: Reading wannier/graphene.eig\n",
      "  n_bands = 15\n",
      "  n_kpts  = 25\n",
      "\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "lattice: Å\n  a1:  2.64100  0.00000  0.00000\n  a2: -1.32050  2.28717  0.00000\n  a3:  0.00000  0.00000 10.00000\n\natoms: fractional\n   C:  0.00000  0.00000  0.00000\n   C:  0.33333  0.66667  0.00000\n\nn_bands: 15\nn_wann : 5\nkgrid  : 5 5 1\nn_kpts : 25\nn_bvecs: 8\n\nb-vectors:\n         [bx, by, bz] / Å⁻¹                weight\n  1      -0.47582   -0.27471    0.00000    1.10422\n  2       0.47582    0.27471    0.00000    1.10422\n  3       0.00000   -0.54943    0.00000    1.10422\n  4       0.00000    0.54943    0.00000    1.10422\n  5       0.47582   -0.27471    0.00000    1.10422\n  6      -0.47582    0.27471    0.00000    1.10422\n  7       0.00000    0.00000   -0.62832    1.26651\n  8       0.00000    0.00000    0.62832    1.26651"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "wannier_model = Wannier.Model(scfres;\n",
    "    fileprefix=\"wannier/graphene\",\n",
    "    n_bands=scfres.n_bands_converge,\n",
    "    n_wannier=5,\n",
    "    projections,\n",
    "    dis_froz_max=ustrip(auconvert(u\"eV\", scfres.εF))+1) # maximum frozen window, for example 1 eV above Fermi level"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "Once we have the `wannier_model`,\n",
    "we can use the functions in the Wannier.jl package:\n",
    "\n",
    "Compute MLWF:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ Info: Initial spread\n",
      "  WF     center [rx, ry, rz]/Š             spread/Ų\n",
      "   1    -0.00000     0.76239    -0.00000     0.62113\n",
      "   2     0.66025    -0.38120    -0.00000     0.62113\n",
      "   3    -0.66025    -0.38120    -0.00000     0.62113\n",
      "   4    -0.00000    -0.00000     0.00000     1.19369\n",
      "   5     0.00000     1.52478     0.00000     1.19369\n",
      "Sum spread: Ω = ΩI + Ω̃, Ω̃ = ΩOD + ΩD\n",
      "   ΩI  =     3.81157\n",
      "   Ω̃   =     0.43920\n",
      "   ΩOD =     0.43823\n",
      "   ΩD  =     0.00097\n",
      "   Ω   =     4.25077\n",
      "\n",
      "\n",
      "[ Info: Initial spread (with states freezed)\n",
      "  WF     center [rx, ry, rz]/Š             spread/Ų\n",
      "   1    -0.00000     0.76239    -0.00000     0.64218\n",
      "   2     0.66025    -0.38120    -0.00000     0.64218\n",
      "   3    -0.66025    -0.38120    -0.00000     0.64218\n",
      "   4    -0.00000    -0.00000     0.00000     1.13078\n",
      "   5     0.00000     1.52478    -0.00000     1.13078\n",
      "Sum spread: Ω = ΩI + Ω̃, Ω̃ = ΩOD + ΩD\n",
      "   ΩI  =     3.46548\n",
      "   Ω̃   =     0.72262\n",
      "   ΩOD =     0.71487\n",
      "   ΩD  =     0.00775\n",
      "   Ω   =     4.18810\n",
      "\n",
      "\n",
      "Iter     Function value   Gradient norm \n",
      "     0     4.188100e+00     1.401803e+00\n",
      " * time: 0.001074075698852539\n",
      "     1     3.807536e+00     8.825704e-02\n",
      " * time: 1.1336090564727783\n",
      "     2     3.768223e+00     2.015969e-02\n",
      " * time: 1.1379899978637695\n",
      "     3     3.765770e+00     2.446952e-03\n",
      " * time: 1.1423261165618896\n",
      "     4     3.765731e+00     2.711486e-04\n",
      " * time: 1.1466350555419922\n",
      "     5     3.765730e+00     3.155843e-05\n",
      " * time: 1.1527681350708008\n",
      "     6     3.765730e+00     1.434268e-05\n",
      " * time: 1.1587610244750977\n",
      "     7     3.765730e+00     1.359838e-06\n",
      " * time: 1.2077560424804688\n",
      "[ Info: Final spread\n",
      "  WF     center [rx, ry, rz]/Š             spread/Ų\n",
      "   1    -0.00000     0.76239    -0.00000     0.64174\n",
      "   2     0.66025    -0.38120    -0.00000     0.64174\n",
      "   3    -0.66025    -0.38120    -0.00000     0.64174\n",
      "   4    -0.00000    -0.00000     0.00000     0.92025\n",
      "   5    -0.00000     1.52478    -0.00000     0.92025\n",
      "Sum spread: Ω = ΩI + Ω̃, Ω̃ = ΩOD + ΩD\n",
      "   ΩI  =     3.02222\n",
      "   Ω̃   =     0.74351\n",
      "   ΩOD =     0.73886\n",
      "   ΩD  =     0.00465\n",
      "   Ω   =     3.76573\n",
      "\n",
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": " * Status: success\n\n * Candidate solution\n    Final objective value:     3.765730e+00\n\n * Found with\n    Algorithm:     L-BFGS\n\n * Convergence measures\n    |x - x'|               = 1.07e-05 ≰ 0.0e+00\n    |x - x'|/|x'|          = 1.07e-05 ≰ 0.0e+00\n    |f(x) - f(x')|         = 2.58e-09 ≰ 0.0e+00\n    |f(x) - f(x')|/|f(x')| = 6.86e-10 ≤ 1.0e-07\n    |g(x)|                 = 1.36e-06 ≤ 1.0e-05\n\n * Work counters\n    Seconds run:   1  (vs limit Inf)\n    Iterations:    7\n    f(x) calls:    17\n    ∇f(x) calls:   18\n"
     },
     "metadata": {}
    }
   ],
   "cell_type": "code",
   "source": [
    "U = disentangle(wannier_model, max_iter=200);"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "Inspect localization before and after Wannierization:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "  WF     center [rx, ry, rz]/Å              spread/Ų\n   1    -0.00000     0.76239    -0.00000     0.64174\n   2     0.66025    -0.38120    -0.00000     0.64174\n   3    -0.66025    -0.38120    -0.00000     0.64174\n   4    -0.00000    -0.00000     0.00000     0.92025\n   5    -0.00000     1.52478    -0.00000     0.92025\nSum spread: Ω = ΩI + Ω̃, Ω̃ = ΩOD + ΩD\n   ΩI  =     3.02222\n   Ω̃   =     0.74351\n   ΩOD =     0.73886\n   ΩD  =     0.00465\n   Ω   =     3.76573\n"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "omega(wannier_model)\n",
    "omega(wannier_model, U)"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "Build a Wannier interpolation model:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "\nrecip_lattice: Å⁻¹\n  a1:  2.37909  1.37357 -0.00000\n  a2:  0.00000  2.74714  0.00000\n  a3:  0.00000 -0.00000  0.62832\nkgrid  : 5 5 1\nn_kpts : 25\n\nlattice: Å\n  a1:  2.64100  0.00000  0.00000\n  a2: -1.32050  2.28717  0.00000\n  a3:  0.00000  0.00000 10.00000\ngrid    = 5 5 1\nn_rvecs = 31\nusing MDRS interpolation\n\nKPath{3} (6 points, 3 paths, 12 points in paths):\n points: :M => [0.5, 0.0, 0.0]\n         :A => [0.0, 0.0, 0.5]\n         :H => [0.333333, 0.333333, 0.5]\n         :K => [0.333333, 0.333333, 0.0]\n         :Γ => [0.0, 0.0, 0.0]\n         :L => [0.5, 0.0, 0.5]\n  paths: [:Γ, :M, :K, :Γ, :A, :L, :H, :A]\n         [:L, :M]\n         [:H, :K]\n  basis: [1.258962, 0.726862, -0.0]\n         [0.0, 1.453724, 0.0]\n         [0.0, -0.0, 0.332492]"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "kpath = irrfbz_path(model)\n",
    "interp_model = Wannier.InterpModel(wannier_model; kpath=kpath)"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "And so on...\n",
    "Refer to the Wannier.jl documentation for further examples."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(Delete temporary files when done.)"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "rm(\"wannier\", recursive=true)"
   ],
   "metadata": {},
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Custom initial guesses\n",
    "\n",
    "We can also provide custom initial guesses for Wannierization,\n",
    "by passing a callable function in the `projections` array.\n",
    "The function receives the basis and a list of points\n",
    "(fractional coordinates in reciprocal space),\n",
    "and returns the Fourier transform of the initial guess function evaluated at each point.\n",
    "\n",
    "For example, we could use Gaussians for the σ and pz guesses with the following code:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "pz_guess (generic function with 1 method)"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "cell_type": "code",
   "source": [
    "s_guess(center) = DFTK.GaussianWannierProjection(center)\n",
    "function pz_guess(center)\n",
    "    # Approximate with two Gaussians offset by 0.5 Å from the center of the atom\n",
    "    offset = model.inv_lattice * [0, 0, austrip(0.5u\"Å\")]\n",
    "    center1 = center + offset\n",
    "    center2 = center - offset\n",
    "    # Build the custom projector\n",
    "    (basis, ps) -> DFTK.GaussianWannierProjection(center1)(basis, ps) - DFTK.GaussianWannierProjection(center2)(basis, ps)\n",
    "end\n",
    "# Feed to Wannier via the `projections` as before..."
   ],
   "metadata": {},
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "source": [
    "This example assumes that Wannier.jl version 0.3.2 is used,\n",
    "and may need to be updated to accommodate for changes in Wannier.jl.\n",
    "\n",
    "Note: Some parameters supported by Wannier90 may have to be passed to Wannier.jl differently,\n",
    "for example the max number of iterations is passed to `disentangle` in Wannier.jl,\n",
    "but as `num_iter` to `run_wannier90`."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Wannierization with Wannier90\n",
    "\n",
    "We can use the `run_wannier90` routine to generate all required files and perform the wannierization procedure:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using wannier90_jll  # Needed to make run_wannier90 available\n",
    "run_wannier90(scfres;\n",
    "              fileprefix=\"wannier/graphene\",\n",
    "              n_wannier=5,\n",
    "              projections,\n",
    "              num_print_cycles=25,\n",
    "              num_iter=200,\n",
    "              #\n",
    "              dis_win_max=19.0,\n",
    "              dis_froz_max=ustrip(auconvert(u\"eV\", scfres.εF))+1, # 1 eV above Fermi level\n",
    "              dis_num_iter=300,\n",
    "              dis_mix_ratio=1.0,\n",
    "              #\n",
    "              wannier_plot=true,\n",
    "              wannier_plot_format=\"cube\",\n",
    "              wannier_plot_supercell=5,\n",
    "              write_xyz=true,\n",
    "              translate_home_cell=true,\n",
    "             );"
   ],
   "metadata": {},
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "source": [
    "As can be observed standard optional arguments for the disentanglement\n",
    "can be passed directly to `run_wannier90` as keyword arguments."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(Delete temporary files.)"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "rm(\"wannier\", recursive=true)"
   ],
   "metadata": {},
   "execution_count": 12
  }
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