The band structure of Silicon is calculated using the empirical pseudopotential method implemented in the Python programming language. A generalized routine is able to calculate the band structure of diamond and zincblende lattices. The energy splittings for Silicon at symmetry points appear to be very accurate with accepted values by diagonaliz…

Pseudopotential-Derived Band Structure of Silicon.ipynb

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    "<center>\n",
    "<h1>Pseudopotential-Derived Band Structure of Silicon</h1>\n",
    "<br> William M. Medlar <br>\n",
    "*Department of Physics, University of North Texas, Denton, Texas*\n",
    "<br><br> The band structure of Silicon is calculated using the empirical pseudopotential method implemented in the Python programming <br> language.\n",
    "A generalized routine is able to calculate the band structure of diamond and zincblende lattices. The energy splittings <br> for Silicon at symmetry points appear to be very accurate with accepted values by diagonalizing a 343 x 343 Hamiltonian matrix.<br>\n",
    "    \n",
    "</center>"
   ]
  },
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   "metadata": {},
   "source": [
    "## I. Introduction\n",
    "\n",
    "The empirical pseudopotential method was developed as a tool to solve Schrodinger's equation of bulk crystals without the exact potential of an electron in a lattice -- a many body problem. Because of its simplicity and accuracy, the pseudopotential method still sees use today.\n",
    "\n",
    "A pseudopotential mimics the potential felt by valence and conduction band electrons, well beyond the nucleus. This potential can be Fourier expanded in plane waves, giving a large eigenvalue problem. Fourier coefficients can be fitted to calculations, as in Cohen and Bergstresser$^1$, or experimentally determined.\n",
    "\n",
    "In this paper I will form the pseudopotential Hamiltonian and implement it in the Python programming language to calculate the electronic band structure of Silicon. Calculated values are plotted and compared to accepted values, and the usefulness of the pseudopotential method is discussed."
   ]
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    "## II. Pseudopotential Method\n",
    "\n",
    "The pseudopotential Hamiltonian operator for an electron in a crystal takes the form:\n",
    "\n",
    "$$\n",
    "\\hat{H} = \\hat{T} + \\hat{V} = -\\frac{\\hbar^2}{2m^*} \\nabla^2 + V(\\vec{r})\n",
    "$$\n",
    "\n",
    "Where the potential $V(\\vec{r})$ is the crystal pseudopotential, and is given by a linear combination of atomic potentials. The potential is periodic and can be expanded into a Fourier series of plane waves and split into symmetric and antisymmetric parts:\n",
    "\n",
    "$$\n",
    "V(\\vec{r}) = \\sum\\limits_{\\vec{G}}^{\\infty} V_{\\vec{G}} \\: e^{-\\mathrm{i} \\: \\vec{G} \\cdot \\vec{r}}\n",
    "= \\sum\\limits_{\\vec{G}}^{\\infty} \\: \\left(V_G^S \\cos{\\vec{G} \\cdot \\vec{\\tau}} + \\mathrm{i} V_G^A \\sin{\\vec{G} \\cdot \\vec{\\tau}} \\right) \\: e^{-\\mathrm{i} \\: \\vec{G} \\cdot \\vec{r}}\n",
    "$$\n",
    "\n",
    "where $V_G^S$ and $V_G^A$ are the symmetric and asymmetric form factors, respectively, unique to the pseudopotential. Following Brust's$^2$ method, form factors will only be nonzero for reciprocal lattice vectors $\\vec{G}$ with magnitudes 0, 3, 4, 8, or 11.\n",
    "\n",
    "The form factors can be interpreted by slight adjustment until the calculated band splittings match that of experimental data. Luckily these values are readily available for Silicon; I will take Cohen and Bergstresser's$^{1}$ to be accurate.\n",
    "\n",
    "Meanwhile our kinetic component can be expressed as a summation over the reciprocal lattice vectors at any point $\\vec{k}$ in the first Brillouin zone:\n",
    "\n",
    "$$\n",
    "T = \\sum\\limits_{\\vec{G}}^{\\infty} \\frac{\\hbar^2}{2m^*} \\|\\vec{k} + \\vec{G}\\|^2\n",
    "$$\n",
    "\n",
    "Substituting these back into the Schrodinger equation and noting that the wavefunction is a Bloch function of the form:\n",
    "\n",
    "$$\n",
    "\\Psi_{\\vec{k}}(\\vec{r}) = e^{\\mathrm{i} \\: \\vec{k} \\cdot \\vec{r}} \\: u_k (\\vec{r})\n",
    "= e^{\\mathrm{i} \\: \\vec{k} \\cdot \\vec{r}} \\sum\\limits_{\\vec{G'}}^{\\infty} \\: U({\\vec{G'}}) \\: e^{\\mathrm{i} \\: \\vec{G'} \\cdot \\vec{r}}\n",
    "$$\n",
    "\n",
    "we're left with the matrix equation:\n",
    "\n",
    "$$\n",
    "\\sum\\limits_{\\vec{G}}^{\\infty} \\left[ \\left( \\frac{\\hbar^2}{2m^*} \\|\\vec{k} + \\vec{G}\\|^2 - E \\ \\right) U({\\vec{G}})\n",
    "+ \\sum\\limits_{\\vec{G'}}^{\\infty} \\: U({\\vec{G'}}) \\: \\left(V_G^S \\cos{\\left( \\vec{G} - \\vec{G'} \\right) \\cdot \\vec{\\tau}} + \\mathrm{i} V_G^A \\sin{\\left( \\vec{G} - \\vec{G'} \\right) \\cdot \\vec{\\tau}} \\right) \\right] = 0\n",
    "$$\n",
    "\n",
    "The energy eigenvalues of which can be found by diagonalizing our Hamiltonian."
   ]
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    "## III. Implementation\n",
    "\n",
    "Our Hamiltonian matrix's size is given by the number of reciprocal lattice vectors ( $\\vec{G}$  and $\\vec{G'}$ ) that we use, where each vector takes the form:\n",
    "\n",
    "$$\n",
    "\\vec{G} = h \\: \\vec{b_1} + k \\: \\vec{b_2} + l \\: \\vec{b_3}\n",
    "$$\n",
    "\n",
    "Where $\\vec{b_n}$ are is our reciprocal lattice basis and $h$, $k$, and $l$ are a set of integers centered around zero. For ```states=5``` they are given by the set {-2, -1, 0, 1, 2}. The calculation of $h$, $k$, and $l$ is incremented about the center of the matrix a la the Cartesian product, and was translated from Danner's$^3$ Mathematica notebook into Python.\n",
    "\n",
    "Note that the coefficients can be, and often are, outside of their defined set, however any attempt to reimplement the calculations to their defined values was met with very strange band structures. Ultimately I conceded defeat and simply used his implementation."
   ]
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   "source": [
    "def coefficients(m, states):\n",
    "    \n",
    "    n = (states**3) // 2\n",
    "    s = m + n\n",
    "    floor = states // 2\n",
    "\n",
    "    h = s // states**2 - floor\n",
    "    k = s % states**2 // states - floor\n",
    "    l = s % states - floor\n",
    "\n",
    "    return h, k, l"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The kinetic term of the Hamiltonian does not depend on $\\vec{G'}$, only on $\\vec{G}$. Translating this to matrix notation, our kinetic term is nonzero only along the diagonal:\n",
    "\n",
    "$$\n",
    "T_{i,j} = \\frac{\\hbar^2}{2m^*} \\|\\vec{k} + \\vec{G_i}\\|^2 \\delta_{i,j}\n",
    "$$\n",
    "\n",
    "where $i$ and $j$ are our row and column indices, respectively, and $\\delta_{i,j}$ is the Kronecker delta. For $\\vec{k}$ and $\\vec{G_i}$ values in units of $\\frac{2 \\pi}{a}$ the kinetic term is given by:"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
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   "source": [
    "from scipy import constants as c\n",
    "\n",
    "# remove constant from function definition so it is not recalculated every time\n",
    "KINETIC_CONSTANT = c.hbar**2 / (2 * c.m_e * c.e)\n",
    "\n",
    "def kinetic(k, g):\n",
    "    \n",
    "    v = k + g\n",
    "    \n",
    "    return KINETIC_CONSTANT * v @ v"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With two atoms in the unit cell of the diamond (or zincblende) lattice our potential component must include both of their contributions. As per Cohen and Bergstresser$^{1}$ I will use an origin halfway between the two atoms, with one situated at $\\vec{r_1} = \\frac{a}{8} \\left(\\begin{array}{ccc}1, \\ 1, \\ 1\\end{array}\\right) = \\vec{\\tau}$ and the other at $\\vec{r_2} = - \\vec{\\tau}$. The potential component is then given by:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "V_{i,j} = V_G^S \\cos{\\vec{G} \\cdot \\vec{\\tau}} + \\mathrm{i} V_G^A \\sin{\\vec{G} \\cdot \\vec{\\tau}}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The unit cell of Silicon is composed only of Silicon atoms, however, and thus has no asymmetric term. I've left it commented out in the function to avoid unnecessary calculations of 0, however it can easily be uncommented to work for zincblende configurations."
   ]
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   "execution_count": 3,
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   "source": [
    "import numpy as np\n",
    "\n",
    "def potential(g, tau, sym, asym=0):\n",
    "    \n",
    "    return sym * np.cos(2 * np.pi * g @ tau) # + 1j * asym * np.sin(2 * np.pi * g @ tau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total Hamiltonian size will be given by $states^3 \\times states^3$ where $states$ is the odd number of integer states our $h$, $k$, and $l$ coefficients can take. The ```coefficients``` function has been reimplemented in the ```hamiltonian``` function with a cache to improve the performance of our calculation."
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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   "source": [
    "import functools\n",
    "import itertools\n",
    "\n",
    "def hamiltonian(lattice_constant, form_factors, reciprocal_basis, k, states):\n",
    "    \n",
    "    # descriptive names are good for reading function signatures\n",
    "    # but a bit of a pain for writing\n",
    "    a = lattice_constant\n",
    "    ff = form_factors\n",
    "    basis = reciprocal_basis\n",
    "    \n",
    "    # some constants that don't need to be recalculated\n",
    "    kinetic_c = (2 * np.pi / a)**2\n",
    "    offset = 1 / 8 * np.ones(3)\n",
    "    \n",
    "    # states determines size of matrix\n",
    "    # each of the three reciprocal lattice vectors can\n",
    "    # take on this many states, centered around zero\n",
    "    # resulting in an n**3 x n**3 matrix\n",
    "    \n",
    "    n = states**3\n",
    "    \n",
    "    # internal cached implementation\n",
    "    @functools.lru_cache(maxsize=n)\n",
    "    def coefficients(m):\n",
    "        n = (states**3) // 2\n",
    "        s = m + n\n",
    "        floor = states // 2\n",
    "\n",
    "        h = s // states**2 - floor\n",
    "        k = s % states**2 // states - floor\n",
    "        l = s % states - floor\n",
    "\n",
    "        return h, k, l\n",
    "    \n",
    "    # initialize our matrix to arbitrary elements\n",
    "    # from whatever's currently in the memory location\n",
    "    # these will be filled up anyway and it's faster than initializing to a value\n",
    "    h = np.empty(shape=(n, n))\n",
    "    \n",
    "    # cartesian product over rows, cols; think an odometer\n",
    "    for row, col in itertools.product(range(n), repeat=2):\n",
    "        \n",
    "        if row == col:\n",
    "            g = coefficients(row - n // 2) @ basis\n",
    "            h[row][col] = kinetic_c * kinetic(k, g)\n",
    "            \n",
    "        else:\n",
    "            g = coefficients(row - col) @ basis\n",
    "            factors = ff.get(g @ g)\n",
    "            # potential is 0 for g**2 != (3, 8, 11)\n",
    "            h[row][col] = potential(g, offset, *factors) if factors else 0\n",
    "    \n",
    "    return h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally a function that will calculate the first eight eigenvalues of our Hamiltonian for each point along our k-path. The actual eigenvalues are calculated by the NumPy library using routines from the open-source Fortran 90 linear algebra package LAPACK."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
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   "source": [
    "def band_structure(lattice_constant, form_factors, reciprocal_basis, states, path):\n",
    "    \n",
    "    bands = []\n",
    "    \n",
    "    # vstack concatenates our list of paths into one nice array\n",
    "    for k in np.vstack(path):\n",
    "        h = hamiltonian(lattice_constant, form_factors, reciprocal_basis, k, states)\n",
    "        eigvals = np.linalg.eigvals(h)\n",
    "        eigvals.sort()\n",
    "        # picks out the lowest eight eigenvalues\n",
    "        bands.append(eigvals[:8])\n",
    "    \n",
    "    \n",
    "    return np.stack(bands, axis=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```linpath``` is a function taken from an earlier project of mine, and will be useful in creating a path of n k-points across the first Brillouin zone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linpath(a, b, n=50, endpoint=True):\n",
    "    '''\n",
    "    Creates an array of n equally spaced points along the path a -> b, inclusive.\n",
    "\n",
    "    args:\n",
    "        a: An iterable of numbers that represents the starting position.\n",
    "        b: An iterable of numbers that represents the ending position.\n",
    "        n: The integer number of sample points to calculate. Defaults to 50.\n",
    "        \n",
    "    returns:\n",
    "        A numpy array of shape (n, k) where k is the shortest length of either\n",
    "        iterable -- a or b.\n",
    "    '''\n",
    "    # list of n linear spacings between the start and end of each corresponding point\n",
    "    spacings = [np.linspace(start, end, num=n, endpoint=endpoint) for start, end in zip(a, b)]\n",
    "    \n",
    "    # stacks along their last axis, transforming a list of spacings into an array of points of len n\n",
    "    return np.stack(spacings, axis=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we set up our lattice parameters and sample points between each symmetry point. With ```n=100``` we will create and diagonalize 325 Hamiltonians, 100 each along the $\\Lambda$, $\\Delta$, and $\\Sigma$ paths, and 25 along the path from $X$ to $U$/$K$. I don't suggest attempting to use much more than 100 points, as this is more than enough to look nice on a large graph and will significantly increase the calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# lattice constant in meters\n",
    "A = 5.43e-10\n",
    "\n",
    "rytoev = lambda *i: np.array(i) * 13.6059\n",
    "\n",
    "# symmetric form factors are commonly given in Rydbergs\n",
    "# however we've implemented our functions to use eV\n",
    "FORM_FACTORS = {\n",
    "    3.0: rytoev(-0.21),\n",
    "    8.0: rytoev(0.04),\n",
    "   11.0: rytoev(0.08)\n",
    "}\n",
    "\n",
    "# in units of 2 pi / a\n",
    "RECIPROCAL_BASIS = np.array([\n",
    "        [-1, 1, 1],\n",
    "        [1, -1, 1],\n",
    "        [1, 1, -1]\n",
    "])\n",
    "\n",
    "# sample points per k-path\n",
    "n = 100\n",
    "\n",
    "# symmetry points in the Brillouin zone\n",
    "G = np.array([0, 0, 0])\n",
    "L = np.array([1/2, 1/2, 1/2])\n",
    "K = np.array([3/4, 3/4, 0])\n",
    "X = np.array([0, 0, 1])\n",
    "W = np.array([1, 1/2, 0])\n",
    "U = np.array([1/4, 1/4, 1])\n",
    "\n",
    "# k-paths\n",
    "lambd = linpath(L, G, n, endpoint=False)\n",
    "delta = linpath(G, X, n, endpoint=False)\n",
    "x_uk = linpath(X, U, n / 4, endpoint=False)\n",
    "sigma = linpath(K, G, n, endpoint=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we run the actual calculation of the band structure, making use of the high symmetry of the diamond lattice with a path $L \\rightarrow \\Gamma \\rightarrow X \\rightarrow U/K \\rightarrow \\Gamma$. Diagonalizing 325 7-state (343 x 343) Hamiltonians took about two minutes on my machine. Uncomment the ```%%timeit``` line to see how yours compares."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# %%timeit -n 1 -r 1\n",
    "bands = band_structure(A, FORM_FACTORS, RECIPROCAL_BASIS, states=7, path=[lambd, delta, x_uk, sigma])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we manipulate and plot the data into a lovely graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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Sko0VikhXdGLLQfYUHiRomCQ741n1nddJyUm3uyyRDscKWjR8UkzjgVKwIDw7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\n24d+A29FZZFbJ10Pcpk0P/jcZ5gcGmDN7W/njt/+dLGbJF2C2GSaro4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DbgEagXIgBYwD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0998de5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "# offset the bands so that the top of the valence bands is at zero\n",
    "bands -= max(bands[3])\n",
    "\n",
    "plt.figure(figsize=(15, 9))\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "# remove plot borders\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['bottom'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['left'].set_visible(False)\n",
    "\n",
    "# limit plot area to data\n",
    "plt.xlim(0, len(bands))\n",
    "plt.ylim(min(bands[0]) - 1, max(bands[7]) + 1)\n",
    "\n",
    "# custom tick names for k-points\n",
    "xticks = n * np.array([0, 0.5, 1, 1.5, 2, 2.25, 2.75, 3.25])\n",
    "plt.xticks(xticks, ('$L$', '$\\Lambda$', '$\\Gamma$', '$\\Delta$', '$X$', '$U,K$', '$\\Sigma$', '$\\Gamma$'), fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "\n",
    "# horizontal guide lines every 2.5 eV\n",
    "for y in np.arange(-25, 25, 2.5):\n",
    "    plt.axhline(y, ls='--', lw=0.3, color='black', alpha=0.3)\n",
    "\n",
    "# hide ticks, unnecessary with gridlines\n",
    "plt.tick_params(axis='both', which='both',\n",
    "                top='off', bottom='off', left='off', right='off',\n",
    "                labelbottom='on', labelleft='on', pad=5)\n",
    "\n",
    "plt.xlabel('k-Path', fontsize=20)\n",
    "plt.ylabel('E(k) (eV)', fontsize=20)\n",
    "\n",
    "plt.text(135, -18, 'Fig. 1. Band structure of Si.', fontsize=12)\n",
    "\n",
    "# tableau 10 in fractional (r, g, b)\n",
    "colors = 1 / 255 * np.array([\n",
    "    [31, 119, 180],\n",
    "    [255, 127, 14],\n",
    "    [44, 160, 44],\n",
    "    [214, 39, 40],\n",
    "    [148, 103, 189],\n",
    "    [140, 86, 75],\n",
    "    [227, 119, 194],\n",
    "    [127, 127, 127],\n",
    "    [188, 189, 34],\n",
    "    [23, 190, 207]\n",
    "])\n",
    "\n",
    "for band, color in zip(bands, colors):\n",
    "    plt.plot(band, lw=2.0, color=color)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV. Results\n",
    "\n",
    "The calculated band structure is given in Fig. 1.\n",
    "\n",
    "Convergence to within 0.1 eV for each energy splitting was acheived with seven states (within 0.15 eV with five). Subsequent odd-numbered states improved the convergence by additional orders of magnitude. All of my calculated values, save for the $\\Gamma_{25'}-X_1$ splitting, were found to be within 5% of those calculated by Cohen and Bergstresser$^1$. Calculated band splittings are given in Fig. 2.\n",
    "\n",
    "\n",
    " | $\\Gamma_{25'}-\\Gamma_{2'}$ | $\\Gamma_{25'}-\\Gamma_{15}$ | $\\Gamma_{25'}-L_1$ | $\\Gamma_{25'}-X_1$ | $L_{3'}-L_1$ | $L_{3'}-L_3$ | $X_4-X_1$\n",
    ":--- | ---: | ---: | ---: | ---: | ---: | ---: | ---:\n",
    "Calculated | 3.89 | 3.42 | 1.88 | 0.95 | 3.13 | 5.23 | 3.95\n",
    "Cohen and Bergstresser$^1$ | 3.8 | 3.4 | 1.9 | 0.8 | 3.1 | 5.2 | 4.0\n",
    "\n",
    "$$\\scriptsize \\text{Fig. 2. Energy splittings in eV between high-symmetry points of Silicon.}$$\n",
    "\n",
    "At lower values of states, there appears to be a discontinuity at the $U$/$K$ symmetry point, marked by a slight but clear shift in all eight bands at the point. With a large number of sample points along each path this may become less apparent at lower state values. The blip seems to have all but disappeared when plotted at the converging parameters.\n",
    "\n",
    "Silicon has an indirect band gap, with a valence band peak at the $\\Gamma$ point and a conduction band minimum in the direction of the $X$ point. The band gap was found to be 0.82 eV, a far cry from its accepted value of 1.11 eV. This discrepancy is likely made up in more advanced pseudopotential methods that account for the effects of spin-orbit coupling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## V. Conclusion\n",
    "\n",
    "The pseudopotential method is surprisingly accurate for the minimal computation required. The empirical approach grounds the calculations in reality, and the values derived very neatly match those from experimentation. This method has no upper limit, either -- the series expansions of the Hamiltonian extend to an infinite number of plane waves. As computational power increases, so too can the accuracy of pseudopotential calculations.\n",
    "\n",
    "Hardware is not the only useful tool; access to high-performance code is a necessity. As the availability of high-level wrappers to Fortran and C libraries increases, and numerous advancements are made in the field of computer science, your average computational physicist will experience a golden age of choices in which languages and tools they will use."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VI. References\n",
    "\n",
    "1. M.L. Cohen and T.K. Bergstresser, \"Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures,\" Phys. Rev. 141, 789 (1966)\n",
    "2. D. Brust, \"Electronic Spectra of Crystalline Germanium and Silicon,\" Phys. Rev. 134, A1337 (1964)\n",
    "3. A. Danner, \"An introduction to the empirical pseudopotential method,\" https://www.ece.nus.edu.sg/stfpage/eleadj/pseudopotential.htm, downloaded November, 2015"
   ]
  }
 ],
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