{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basis set in quantum chemistry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Examples of atomic orbitals and plane waves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###### Germain Salvato-Vallverdu (germain.valverdu@univ-pau.fr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is divided in X parts which have different purpose. The reader interested in atomic orbitals or plane waves basis could skip the first part which load python modules and define several functions used in the following.\n", "\n", "* [Atomic orbitals](#Atomic-orbitals)\n", "* [Plane waves basis set](#Plane-waves-basis-set)\n", "* [Fit a 3s atomic orbital](#Fit-a-3s-atomic-orbital)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Python stuff" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numpy and Scipy routines are used here and need to be imported." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.misc import factorial\n", "from scipy.optimize import curve_fit\n", "import scipy.constants as cst" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matplotlib is used in order to make plots" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bhor radius is defined in angstrom from scipy.constants module." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a0 = 0.52917721092 A\n" ] } ], "source": [ "ao = cst.physical_constants[\"Bohr radius\"][0] / cst.angstrom\n", "print(\"a0 = {} A\".format(ao))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A root mean square function is defined in order to measure the quality of the fit with plane waves." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def rms(y_th, y):\n", " \"\"\" compute the root mean square between y and y_th values \"\"\"\n", " return np.sqrt(((np.array(y) - np.array(y_th))**2).mean())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Atomic orbitals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the radial part of a 4s AO of an hydrogen like specie.\n", "\n", "\\begin{equation}\n", " \\varphi_{4,0,0}(r) = \n", " \\frac{1}{96} \\left(\\frac{Z}{a_o}\\right)^{3/2} \n", " \\left(24 - \\frac{18 Z r}{a_o} + \\frac{3 Z^2 r^2}{a_o^2} - \\frac{Z^3 r^3}{8 a_o^3}\\right) \n", " \\exp\\left(-\\frac{Z r}{4 a_o}\\right)\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def OA4s(r, z=19, ao=ao):\n", " \"\"\" \n", " Return values of the radial part of a 4s AO of an hydrogen like specie\n", " \n", " Args:\n", " r : float or ndarray of float in the same unit as ao (A by default)\n", " z (int) : atomic number\n", " ao (float): Bohr radius (in A by default)\n", " \"\"\"\n", " poly = 24 - 18 * z * r / ao + 3 * z**2 * r**2 / ao**2 - z**3 * r**3 / (8 * ao**3)\n", " return (z / ao)**(3/2) / 96 * poly * np.exp(- z * r / (4 * ao))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the radial part of a 4s AO of an hydrogen like specie.\n", "\n", "\\begin{equation}\n", " \\varphi_{3,0,0}(r) = \n", " \\frac{1}{9\\sqrt{3}} \\left(\\frac{Z}{a_o}\\right)^{3/2} \n", " \\left(6 - \\frac{4 Z r}{a_o} + \\frac{4 Z^2 r^2}{9 a_o^2}\\right) \n", " \\exp\\left(-\\frac{Z r}{4 a_o}\\right)\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def OA3s(r, z=11, ao=ao):\n", " \"\"\" \n", " Return values of the radial part of a 3s AO of an hydrogen like specie\n", " \n", " Args:\n", " r : float or ndarray of float in the same unit as ao (A by default)\n", " z (int) : atomic number\n", " ao (float): Bohr radius (in A by default)\n", " \"\"\"\n", " poly = 6 - 4 * z * r / ao + 4 * z**2 * r**2 / (9 * ao**2)\n", " return (z / ao)**(3/2) / (9. * np.sqrt(3)) * poly * np.exp(-z * r / (3 * ao))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison we define also a slater type orbital :\n", "\n", "\\begin{equation}\n", " \\varphi_{n,0,0}^{slater}(r) = \\frac{1}{\\sqrt{(2n)!}} \\left(\\frac{2 Z}{n a_o}\\right)^{n+\\frac{1}{2}}\n", " r^{n-1} \\exp\\left(-\\frac{Z r}{n a_o}\\right)\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def slater_ns(r, n=3, z=11, ao=ao):\n", " \"\"\" \n", " Return values of the radial part of a slater type AO of an hydrogen like specie\n", " \n", " Args:\n", " r : float or ndarray of float in the same unit as ao (A by default)\n", " z (int) : atomic number\n", " ao (float): Bohr radius (in A by default)\n", " \"\"\"\n", " fact = 1 / np.sqrt(factorial(2 * n)) * (2 * z / (n * ao))**(n + 0.5)\n", " return fact * r**(n-1) * np.exp(- z * r / (n * ao))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A smooth AO is defined for comparison, without oscillations closed to the nuclei." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def smooth_3s(r, c=14, alpha=1.9, ao=ao):\n", " \"\"\" \n", " Return values of the radial part of a smooth AO without any oscillation closed to the nuclei.\n", " \n", " Args:\n", " r : float or ndarray of float in the same unit as ao (A by default)\n", " z (int) : atomic number\n", " ao (float): Bohr radius (in A by default)\n", " \"\"\"\n", " return c * np.exp(- alpha * r / ao)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make some simple plots for comparison. As expected, the slater type orbital is smoother than the solution of the hydrogen like one." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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pqWHcuHGUlpbyyCOP7BDGBw4cyF133dVgWewfqAMPPLDFeiSl3ujRoxk+fDgP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\nWl1tbjc1mXKgj+sIWK3m80vkQlCRUlBghvqvWdP1eOfHejz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r = np.linspace(0, 1.4, 200)\n", "plt.plot(r, OA3s(r, z=11), \"b-\", label=\"OA 3s\", lw=2)\n", "#plt.plot(r, smooth_3s(r), \"m-\", label=\"3s smooth\", lw=2)\n", "ymin, ymax = plt.ylim()\n", "plt.title(\"Atomic orbitals\")\n", "plt.xlabel(\"r / $\\AA$\")\n", "plt.ylabel(\"wavefunction\")\n", "plt.legend()\n", "plt.savefig(\"orbitals_1.pdf\")\n", "plt.plot(r, slater_ns(r, n=3, z=11), \"r-\", label=\"Slater 3s\", lw=2)\n", "plt.vlines(0.5, ymin, ymax, lw=2)\n", "plt.fill_between(x=[0, .5], y1=[ymin, ymin], y2=[ymax, ymax], color=\"k\", alpha=.15)\n", "plt.annotate(\"Core part\", xy=(0.25, 27), horizontalalignment=\"center\")\n", "plt.annotate(\"Valence part\", xy=(0.9, 27), horizontalalignment=\"center\")\n", "plt.savefig(\"orbitals_2.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plane waves basis set" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Definition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plane waves basis functions are used in conjunction with periodic boundary conditions. In such case, one define a direct lattice $\\left\\lbrace \\vec{a}_i\\right\\rbrace_{i=1,3}$ corresponding to the cell into which calculations is done. Direct vectors are expressed as :\n", "\n", "\\begin{align}\n", " \\vec{r} & = r_1 \\vec{a}_1 + r_2 \\vec{a}_2 + r_3 \\vec{a}_3 \\\\ & = x \\vec{i} + y \\vec{j} + z \\vec{l}\n", "\\end{align}\n", "\n", "where $(r_1, r_2, r_3)$ are the fractional coordinates, $(\\vec{i}, \\vec{j}, \\vec{l})$ are cartesian unit vectors and $(x, y, z)$ are the cartesian coordinates. The plane waves basis functions $\\varphi_{\\alpha}(\\vec{r})$ read :\n", "\n", "\\begin{equation}\n", " \\varphi_{\\alpha}(\\vec{r}) = \\frac{1}{\\sqrt{\\Omega}} \\exp \\left( i \\vec{G}_{\\alpha}\\cdot\\vec{r}\\right)\n", "\\end{equation}\n", "\n", "where $\\Omega$ is the volume of the cell and we can show that $\\vec{G}_{\\alpha}$ are vectors of the reciprocal space corresponding to the box. Indeed, assuming periodic boundary conditions :\n", "\n", "\\begin{equation}\n", " \\varphi_{\\alpha}(\\vec{r})= \\varphi_{\\alpha}(\\vec{r} + \\vec{R})\n", "\\end{equation}\n", "\n", "where $\\vec{R}$ is a translation vector from one cell to one other, $\\vec{R}=h\\vec{a}_1 + k\\vec{a}_2 + l\\vec{a}_3$ with $(h,k,l)\\in\\mathbb{Z}^3$. Thus one has\n", "\n", "\\begin{align}\n", " \\exp \\left[ i \\vec{G}_{\\alpha}\\cdot\\vec{r}\\right] & = \\exp \\left[ i \\vec{G}_{\\alpha}\\cdot(\\vec{r} + \\vec{R})\\right] \\\\\n", " 1 & = \\exp \\left[ i \\vec{G}_{\\alpha}\\cdot\\vec{R}\\right] \\\\\n", " 2 \\pi & = \\vec{G}_{\\alpha}\\cdot\\vec{R}\n", "\\end{align}\n", "\n", "This condition could be achieve if vector $\\vec{G}$ reads $\\vec{G} = u\\vec{b_1}+v\\vec{b_2}+w\\vec{b_3}$ with $(u,v,w)\\in\\mathbb{Z}^3$ and $\\vec{a}_i \\cdot \\vec{b}_j = 2\\pi \\delta_{ij}$. Vectors $\\left\\lbrace \\vec{b}_i\\right\\rbrace_{i=1,3}$ defined the reciprocal space.\n", "\n", "Then the $\\phi_i(\\vec{r})$ wave functions are expanded in term of plane waves as :\n", "\n", "\\begin{equation}\n", " \\phi_i(\\vec{r}) = \\frac{1}{\\Omega} \\sum_{\\vec{G}} c_i(\\vec{G}) \\exp\\left( i \\vec{G}\\cdot\\vec{r}\\right)\n", "\\end{equation}\n", "\n", "If we considered a one dimensionnal lattice with a box length $a$, the direct and reciprocal lattice are generated by the vectors $\\vec{a}$ and $\\vec{b}$ respectively :\n", "\n", "\\begin{align}\n", " \\vec{a} & = a\\vec{i} &\n", " \\vec{b} & = \\frac{2 \\pi}{a} \\vec{i} &\n", " \\vec{a}\\cdot\\vec{b} & = 2 \\pi\n", "\\end{align}\n", "\n", "where $\\vec{i}$ is a unit vector. In such simple case, $\\vec{r} = \\frac{x}{a} \\vec{a} = x\\vec{i}$ with $x\\in\\mathbb{R}$ and $\\vec{G} = u \\vec{b}$ with $u \\in \\mathbb{Z}^*$. Thus, the plane waves read :\n", "\n", "\\begin{equation}\n", " \\varphi_u = \\frac{1}{a} \\exp\\left(\\frac{2 i \\pi u}{a} x\\right)\n", "\\end{equation}\n", "\n", "In the following we will only consider the real part of the plane waves which reads :\n", "\n", "\\begin{equation}\n", " \\Re\\left[\\varphi_u\\right] = \\frac{1}{a} \\cos\\left(\\frac{2 \\pi u}{a} x\\right) \n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Python functions" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def pw_1D(x, u, box=1, phi=0):\n", " \"\"\" \n", " Compute the real part of a 1D plane wave at position x. The length of the box is assume to be a.\n", " \n", " Args:\n", " x: float or array of float\n", " u: coordinate of the wave vector in reciprocal space\n", " box: length of the box\n", " phi: phase\n", " \"\"\"\n", " return 1 / np.sqrt(box) * np.cos(2 * np.pi * u * x / box + phi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "kinetic energy of a plane waves :\n", "\n", "\\begin{equation}\n", " E_c = \\frac{\\hbar^2 G^2}{2 m_e} = \\frac{h^2 u^2}{2 m_e a^2}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def e_kinet_pw(u, box=1):\n", " \"\"\" \n", " Return the kinetic energy of a plane wave in electron volt defined by its reciprocal space vectors G.\n", " \n", " Args:\n", " u (int): plane waves index\n", " \"\"\"\n", " g = 2 * np.pi * u / (box * cst.angstrom)\n", " return cst.hbar**2 * g**2 / (2 * cst.m_e) / cst.eV" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot a set of plane waves for a givent box length." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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f4GAeqV07b9nk+vX59sIFTkjKRsnS0/Vt2s8+g4ceYkNiIiPr1MHTeOXP9Mm6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\nGM3Dw2nh4xMyAFJS9Ink/fe7t4K5ZYvuCDl2rNemVp1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "BOXLENGTH = 5\n", "r = np.linspace(0, BOXLENGTH, 200)\n", "spw = np.zeros(200)\n", "for u in range(1, 9):\n", " pw = pw_1D(r, u, box=BOXLENGTH)\n", " spw += pw\n", " if u in [1, 2, 4, 8]:\n", " plt.plot(r, pw, label=\"{:5.1f} eV\".format(e_kinet_pw(u, box=BOXLENGTH)), lw=1)\n", "\n", "plt.plot(r, spw/7, label=\"sum\", lw=3)\n", "plt.title(\"Plane waves\")\n", "plt.xlabel(\"r / $\\AA$\")\n", "plt.ylabel(\"wavefunction\")\n", "plt.legend()\n", "plt.savefig(\"planewaves.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit on a 3s atomoc orbital" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### General parameters and tools in order to do the fit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parameters used for the fit." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "BOXLENGTH = 5\n", "rmax = 2\n", "r = np.linspace(0, rmax, 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit function is defined such as the number of parameters set the number of used plane waves." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def pw_vector(x, *args):\n", " \"\"\" return the linear combination of plane waves \"\"\"\n", " npar = len(args)\n", " return np.sum([args[u] * pw_1D(x, u + 1, box=BOXLENGTH, phi=0) for u in range(npar)], axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Hydrogen like atomic orbital" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, the case of a 3s hydrogen-like atomic orbital is considered." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1 plane waves, ENCUT = 6.02 eV rms = 4.6601\n", " 5 plane waves, ENCUT = 150.41 eV rms = 4.5154\n", " 10 plane waves, ENCUT = 601.65 eV rms = 3.6326\n", " 20 plane waves, ENCUT = 2406.59 eV rms = 1.9772\n", " 40 plane waves, ENCUT = 9626.37 eV rms = 0.9070\n", " 50 plane waves, ENCUT = 15041.21 eV rms = 0.7022\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Q6eOMa66oAKB03Trq6uq6onZJkiQpJ3pCi/uVtNdq3mI5cGZ0yU55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\nCoXMUuBVVYRWreI9wHXTTVinnprsEEVERERSmhL3FFAwbhz+p582s6j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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rp = np.linspace(0, rmax, 50)\n", "for umax in [1, 5, 10, 20, 40, 50]:\n", " popt, pcov = curve_fit(pw_vector, r, OA3s(r), p0=np.ones(umax))\n", " ek = e_kinet_pw(umax, box=BOXLENGTH)\n", " valrms = rms(OA3s(r), pw_vector(r, *popt))\n", " print(\"{:3d} plane waves, ENCUT = {:8.2f} eV rms = {:8.4f}\".format(umax, ek, valrms))\n", " \n", " plt.plot(rp, pw_vector(rp, *popt), \"r-\", label=\"{} plane waves\".format(umax), lw=2)\n", " plt.plot(rp, OA3s(rp), \"ko--\", label=\"AO 3s\", alpha=.75)\n", " plt.legend()\n", " plt.title(\"Fit a 3s hydrogen like AO with plane waves\")\n", " plt.xlabel(\"r / $\\AA$\")\n", " plt.ylabel(\"wavefunction\")\n", " plt.ylim(-10, 40)\n", " plt.savefig(\"fit_AO3s_{}.pdf\".format(umax))\n", " plt.clf()\n", "\n", "plt.plot(rp, pw_vector(rp, *popt), \"r-\", label=\"{} plane waves\".format(umax), lw=2)\n", "plt.plot(rp, OA3s(rp), \"ko--\", label=\"AO 3s\", alpha=.75)\n", "plt.legend()\n", "plt.ylim(-10, 40)\n", "plt.title(\"Fit a 3s hydrogen like AO with plane waves\")\n", "plt.xlabel(\"r / $\\AA$\")\n", "plt.ylabel(\"wavefunction\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### smooth 3s atomic orbital" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1 plane waves, ENCUT = 6.02 eV r^2 = 2.5843\n", " 5 plane waves, ENCUT = 150.41 eV r^2 = 0.7922\n", " 10 plane waves, ENCUT = 601.65 eV r^2 = 0.3621\n", " 15 plane waves, ENCUT = 1353.71 eV r^2 = 0.2102\n" ] }, { "data": { "image/png": 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YSUlJVmxsrBUVFWVddNFF1q233mr98MMPlmVZ1vLly61rrrnGat68uRUREWG1\natXKuu2226x9+/aV+rzK2reppNFUatv1Ve3XxlteXh7Dhg1j/vz5xMbGOhCWiDmJJTEx0ekwRErQ\nvikV4XK5zurCN+eyjIwM2rRpw8svv8wtt9zidDjiR1n7tl1eVOFcutaPpgIQFhbGnXfeSX5+vtOh\niIiIiIgUOidqxsHUKImIiIiIBJNzJhkXERERCQYJCQkUFBQ4HYYEiXOiTEVEREREJBgpGRcRERER\ncYiScRERERERh5xTyfjRo0d56KGHnA5DRERERAQ4x5Lx2NhYNm/ezIEDB5wORURERESkFibjeXl+\nZ7lcLn75y1+yadOmagxIRERERMS32peMDxkCOTl+Z3fo0EHJuIiIiIgEhdqXjK9cCT17ws6dPme7\nk3FduldERERKc/vttxMSEsLUqVP9LpOfn09qaipdunQhNjaWmJgYunTpQmpqakBjiR8/fpzRo0dz\n0UUXUa9ePRo2bEjXrl2ZN29eZT4VCWK1Lxm/5BLYvBm6doXPPisxu0WLFgDs2bOnuiMTERGRAOTn\n55OZmUlmZib5+fmOxJCbm8uCBQuoW7cur7/+us84zpw5w9ChQ7n33nvp1asXixYt4u2336ZXr15M\nmTKFYcOGlRn/6dOnCQ8P5/777+edd95h/vz5tGvXjptuuolnnnmmqp6eSJWxrCNHLOvqqy0LLCsy\n0rIWLLCKy87OtgoKCkq0i1SlNWvWOB2CiE/aN6UigEpd36FDh6wRI0ZY3bt3t7p3726NGDHCOnjw\nYKVuIxCvv/665XK5rJkzZ1oul8tatmxZiWUefvhhy+VyWUuXLi0xb8mSJZbL5bIeeeSRs9p+9+7d\nrSuuuOKsHiuVo6x9G6iUMova1zPeoAG8+y7cfjv8/DOMHg3Tp4NHWUrDhg1xuVwOBikiIiLF5efn\nM3HiRLKzs4mIiCAiIoLs7GzGjBnDokWLqjWWtLQ02rVrx+TJkznvvPNIS0vzmn/q1ClmzJjBoEGD\nGDJkSInHDx06lGuvvZYZM2Zw+vTpcm+/UaNGhIaGerU988wztGvXjqioKBo1akTnzp15++23y71u\nCS61LxkHCA+HWbPgiSfA5YL774dbboGz+DCIiIhI9di3bx/79+/36jBzuVzk5eWRmppKTikDNFSm\nvXv38uGHH3L99dfjcrkYPXo077zzDj/99FPhMl9++SU5OTkMHTrU73qGDBnCTz/9FPDAEXl5eRw+\nfJgXX3x03qyVAAAgAElEQVSR999/n7vvvrtw3rx58/jd737H2LFjeffdd3n99de57rrrOHLkyNk/\nUQkKYU4HUGVcLvjd7+DCC2HsWJg9G3bsgEWLoFEjp6MTERGp9WbPnl2iRxlg3LhxjB8/vkT7ggUL\n+O677wgJ8e4rjI+Pp2XLlhVef6Dmzp1Lfn4+N9xwAwA33HADM2bM4I033mDSpEkA7N69G4CEhAS/\n63HP2717N127di11m88991xh8h0aGspTTz3l9Rw2bNjAFVdcwYMPPljYNmDAgPI+NQlCtTcZdxsx\nAj76yAx5uHYtdOsGy5fDRRc5HZmIiEitNn78+HIlxffccw/r168nOzu7sHfcsizCw8NJSUkhNja2\nQusPVFpaGu3bt6dt27YAdOnShdatW5OWllaYjFe2G264gR49epCVlcWSJUuYMmUKERERTJw4sTCG\n1NRU7r77boYOHUqPHj2IioqqkliketXOMpXiOnaEzz+H9u1h2zbo1g1r7VoOHTrkdGQiIiJiCw0N\nZdasWYSHhxe2hYeHM3fuXJKTk6slhi+++IIffviBwYMH89NPPxVOQ4YM4dNPP2Xbtm0AhT31GRkZ\nftflnteqVasyt9ukSROuvPJK+vfvz/PPP89NN93E7373u8LRWG6++WZSU1P57LPPGDBgAI0bN2bk\nyJHs9DOUs9Qc50YyDtCyJaxfD4MHQ3Y2R/r25Zb+/QMaA1RERESqR1xcHCkpKYSFhREWFkZKSgrN\nmjWrtu27y14effRRGjVqVDg9++yzALz22msAdOrUidjYWJYsWeJ3XUuXLqVBgwZceeWV5Y6jY8eO\nHD9+nAMHDhS2TZw4kc8++4zDhw+TlpbG559/zvXXX1/udUtwOXeScYB69eDtt+Hee2mUl0eTr79m\n++TJoIRcREQkaCQnJ7Nw4UIWLlxYbT3iYMb8nj9/Pt26dSM9Pd1rWrNmDb/85S+ZM2cOABEREdx9\n992sWLGCpUuXlljXkiVLWLlyJffcc49XT3+g1q5dS0xMDE2bNi0xr379+owePZpRo0axefPm8j9R\nCSq1v2a8uNBQePppuOgiOtx5J1+98AJtc3PNCZ4iIiISFIrXh1eH5cuXk52dTUpKCr169Soxf9Kk\nSaSkpJCenk5iYiIPPfQQX3zxBaNHj2by5MkMGDAAl8vFypUree6557j22mu9Trj0ZdasWXz22Wf0\n7duXFi1acPjwYRYsWMDChQt57LHHCAszqdrEiROJjY2lW7duNG3alK1btzJ37lyuueaaKnkt5NzQ\nEpgJbABOAgXA+cWW6Qu8DvzPXmY78E8gzs86yzWY+5rHH7dSwsKs3WDlffxxBYaFFymbLqwiwUr7\nplREeb97g9nw4cOt+vXrW7m5uT7nHz161IqKirImTJhQ2JaXl2c9//zzVufOna3o6GgrOjra6ty5\ns/X8889b+fn5ZW7zk08+sQYOHGg1b97cioiIsFq0aGH169fPWrFihddyaWlpVmJiotW0aVMrIiLC\nat26tTV16lTr2LFjFXvS4ldZ+zaVdNEfJ698kwj8G/gC00PfH0gAdnksswCoD7wBbAPaAo8Ap4Ar\ngBPF1mm/NmXLyspiwoQJrP/gAy45dYrmrVox68sviYvzl+eLVIy7J0Uk2GjflIpwuVwE+t0rUpOU\ntW/bI/5UOJd2smZ8LRAPDAbe8rPMHcA1wKvAR8ArwI1Aa2D02W7YfYWvY8eO0ahZM0KB7N27GTNy\nZLVf4UtEREREzl1OJuOBHEZn+Wj7wr4972w37HmFr/PbtCG8SRNcQN6uXdV6hS8RERERObfVxNFU\netu3P1TaGt1X9dq7VyOriIiIiEi1qWnJeAwwA/geePtsV9K8eXPi4+OL6oAaNMCKiiLszBlSLr3U\nkTO4RUREROTcU5OGNgwD5gPNgZ6Y0VdKcF8+15dx48YVXjb31ltvZdGiRYUX/Qlp0oQRWVnUy8oi\nfc0aKGU9ImcjIyOD9PR0p8MQKUH7poiIb6XllZWlpiTjIUAa0AcYBPgd4b48Z3SfOnWK1NRUAFJu\nvZXBd94J6elw553Qo0eFAhYpTiNWSLDSviki4lsAo6lUWE0pU3kBM3rKDcCaylqp+wpfb731Flk5\nOZy59VYzw77krYiIiIhIVaoJPeNPArcCNwMlrzdbQe768P/85z98M3AgHZ98Et56CzIzi07sFBER\nEZ8aNmxYLT/li1S3hg0bVst2nE7Gr7NvO9q3AzHDGR4E1gF/BKZgxhnfDnTzeOxBzJU5K0X37t3Z\nsGMHHUeOhAULIDUVHn20slYvIiJSK2VnZ1fp+lVGJbWd02UqC+xpEmbc8X/a96fZ8wfY7bcAG4BP\nPKYHKzOQ7t27s2HDBqy77jINs2ZBbm5lbkJERERExIvTyXiIxxTq8Xcfe35SsXbP6ZbKDKRNmzac\nOXOG3a1awZVXwuHD8O9/V+YmRERERES8OJ2MBw2Xy2V6xz/9FO65xzQ++yyUY3QWEREREZHycLpm\nPKjceOONhIWFQUwM/P738PXX8NFH0KuX06GJiIiISC2knnEP8fHxNGnSBCIiYNIk06hhDkVERESk\niigZ9+c3v4GwMFi8GHbtcjoaEREREamFlIz7c955MHo0FBTAP//pdDQiIiIiUgspGS/N3Xeb2xdf\nhJMnnY1FRERERGodJeM+FBQUkJubC127QpcucOQIzJvndFgiIiIiUssoGfdh3rx5zJkzx9zRMIci\nIiIiUkWUjPvQqVMnNmzYYO5cdx3Ex8PmzZCe7mhcIiIiIlK7KBn34eKLL+bo0aPs3bsX6tSBlBQz\n45lnnA1MRERERGoVJeM+hISE0K1bNz799FPTMGmSScqXLoUdO5wNTkRERERqDSXjfnTv3r0oGW/W\nDG64wdSMP/+8s4GJiIiISK2hZNyPjh07EhYWhuU+adM9zOHLL8Px484FJiIiIiK1hpJxP6Kiovjb\n3/6Gy+UyDR07Qo8ecPQouEdaERERERGpACXj5eHuHdcwhyIiIiJSCZSMl0dyMrRoAVu2wKpVTkcj\nIiIiIjWckvHyCA+HO+4wf2uYQxERERGpICXj5XX77RARAcuXw7ZtTkcjIiIiIjWYkvEyHDt2jNde\ne62oIS4Oxo41f6emOhOUiIiIiNQKSsbLEBUVxcKFC8nKyipqnDjR3L75pk7kFBEREZGzpmS8DKGh\noXTp0qXoAkAAnTubEzkzM+HLL50LTkRERERqNCXjAejWrRsbNmwoaggJgeHDzd9vv+1MUCIiIiJS\n4ykZD0Dnzp35+uuvOXXqVFGjknERERERqSAl4wGIjY3loosu4uuvvy5q7N0b6teH777TqCoiIiIi\nclaUjAfo3nvvpV27dkUN4eEweLD5W73jIiIiInIWlIwHKCEhgdjYWO/GESPMrZJxERERETkLSsYr\n4pprzAWANmyA/fudjkZEREREahgl4xVRrx7062fGGl+61OloRERERKSGUTJeURpVRURERETOkpLx\ncjpz5gynT58uahg61Iw7/uGHkJPjXGAiIiIiUuMoGS+nxx57jPT09KKGuDjo2RNOn4Z333UsLhER\nERGpeZSMl1OnTp345JNPvBtVqiIiIiIiZ0HJeDl17dqVL7/8kjNnzhQ1upPx5cvB8yqdIiIiIiKl\nUDJeTg0bNqRly5asWrWKzMxM8vPzoU0buOIKOHYM1qxxOkQRERERqSGUjJdTVlYWGzduZPLkyYwe\nPZpRo0Zx6NAhlaqIiIiISLkpGS+H/Px8Jk6cSGhoKKGhoURERJCdnc2YMWNY5L4655IlUFDgbKAi\nIiIiUiMoGS+Hffv2sX//fqKiomjZsiUALpeLvLw8UleuJKdVK3Mlzs8/dzhSEREREakJlIxXpkGD\nzO3ixc7GISIiIiI1gpLxcmjevDnx8fFYllXYZlkWYWFhpKSkEHv99aZx8WLwWEZERERExBcl4+UQ\nGhrKrFmzCA8PL2wLDw9n7ty5JCcnw1VXQePGsG0bbNniYKQiIiIiUhMoGS+nuLg4UlJSCAsLK+wR\nb9asmZkZFgZDhpi/VaoiIiIiImVQMn4WkpOTWbhwIfPmzWP37t1eZSsa4lBEREREAuVkMt4SmAls\nAE4CBcD5PpZrCLwMHAKOAx8Al1VTjH7FxsYSFxfHV199xQ8//FA0o18/qFsXNm6EzEznAhQRERGR\noOdkMv4LYBRwGFjnZxkX8A7QH7gTGAmEA2uAFtUQY6lcLhd9+vRh9erVRY1RUTBggPl7yRJnAhMR\nERGRGsHJZHwtEA8MBt7ys8xQoAdwE/AG8J7dFgL8oRpiLFNSUhLp6ekUeF7oR6UqIiIiIhIAJ5Px\nQMb+GwrswSTubjmY3vJhVRFUeZ1//vk0bNiQb775pqhx0CAIDYX0dDhyxLHYRERERCS4BfsJnJcC\nm320f4+pL4+q3nB869OnD+np6UUNjRtDr16QlwcrVjgWl4iIiIgEt2BPxhsBvrqWs+3bhtUYi19D\nhw5l0qRJ3o0jRphbDXEoIiIiIn4EezJeIy5jGR0dTd26db0bh9lVNCtXQm5u9QclIiIiIkEvzOkA\nynAE0zteXCOP+V5cLpfflY0bN47x48dXSmABufFG2LcP5syBtm2rb7sSlDIyMrzLmUSChPZNCWba\nP8Ups2fPJi0trcq3E+zJ+HeYYQ2L+z9gJ2Z8ci9eF+Bx2kcfwfz50KYNTJzodDTisPT0dBITE50O\nQ6QE7ZsSzLR/ilMSExOZPXu23/mldQCXR7CXqSzFjCfey6MtFhhizwtu7rrxpUshP9/ZWEREREQk\n6DidjF9nTx3t+wPt++7keynmCp1zgeuBa+w2C3i8WiMNwOnTp9m82WPwl0svhQsvhKws+OQT5wIT\nERERkaDkdDK+wJ4mYRLsf9r3p9nzLcxFgT6w5y0CzgBJmPHHg0pubi733XcfP//8s2lwuYouAKRR\nVURERESkGKeT8RCPKdTj7z4eyxwBbgUaA9FAP+Db6g0zMPXr1+fSSy/lE89ecM+rcQZTPbuIiIiI\nOM7pZLzW6dOnD6tXry5q6N4dmjaFHTvg26A8hhARERERhygZr2Q9e/bk66+/5vjx46YhNBSGDjV/\nv/22c4GJiIiISNBRMl7JoqOjufLKK/noo4+KGlU3LiIiIiI+BPs44zXS6NGjvcc7v/pqqFcPvv4a\nMjIgIcGp0EREREQkiKhnvApcdtllXH755UUNkZFw7bXm7yVLnAlKRERERIKOkvHqolIVERERESlG\nyXh1GTgQwsLgo4/MRYBERERE5JynZLy6NGgAffpAQQEsW+Z0NCIiIiISBJSMV7GCgoKiO+4hDt95\nx5lgRERERCSoKBmvQtu3b2fq1KlFDYMHm9v334dTp5wJSkRERESChpLxKtS6dWt27drF3r17TcMF\nF8AVV8Dx45Ce7mhsIiIiIuI8JeNVKDQ0lN69e7NmzZqixiFDzO3Spc4EJSIiIiJBQ8l4FUtKSvJO\nxj3rxj0vDCQiIiIi5xwl41XssssuIycnh4yMDNPQqRPEx8Pu3fDNN47GJiIiIiLOUjJexUJCQhg4\ncCC7du1yN8CgQeZvjaoiIiIick5TMl4Nxo8fT69evYoaVDcuIiIiIigZd0bfvhAZCRs3wr59Tkcj\nIiIiIg5RMl5N8vPzyczMJDMzk/zISLj6ajNj+XJnAxMRERERx4Q5HcC5ICsri4kTJ7J//34A4uPj\nmZWYSNzy5aZu/LbbHI5QRERERJygnvEqlp+fz8SJE8nOziYiIoKIiAiys7MZs2QJiwA++AByc50O\nU0REREQcoGS8iu3bt4/9+/fjcrnIzc3l8OHDuFwu8sLCSI2JISc3Fz780OkwRURERMQBSsarUUhI\nCPv27cNyX+ynSRNzqyEORURERM5JSsarWPPmzYmPj8eyLCIiIoiMjOSnn34iLCyMlDvuIBZg2TJd\njVNERETkHKRkvIqFhoYya9YswsPDAWjcuDFHjhxh7ty5JP/2t9CiBezdC1995XCkIiIiIlLdlIxX\ng7i4OFJSUggLC6Nx48Y0a9aM/Px8cLlg8GCzkC4AJCIiInLOUTJeTZKTk1m4cCGLFy9mwoQJvP/+\n+2bG0KHmVnXjIiIiIuccjTNejWJjYwG4+eabiYiIMI19+kBUFGzaBJmZ0LKlgxGKiIiISHVSz7gD\noqOjCQuzj4MiI6FfP/P3smXOBSUiIiIi1U7JeDAYMsTcqlRFRERE5JyiZDwYDB5sTub88EM4ccLp\naERERESkmigZDwbNmkGXLnDqFHzwgdPRiIiIiEg1UTLuIMuyWLZsGXl5eSpVERERETkHKRl3kMvl\n4v333+fTTz8tSsaXLYOCAmcDExEREZFqoWTcYYMHD2bZsmVw+eVwwQVw8CB8/rnTYYmIiIhINVAy\n7rDevXuzZcsWDhw8qFIVERERkXOMknGHRURE0LdvX1asWKFkXEREROQco2Q8CAwaNIgVK1aQf9VV\nUK8efPstZGQ4HZaIiIiIVDEl40GgdevW/PWvfyWkbl0YMMA0qndcREREpNZTMh4kLr74Ylwul0pV\nRERERM4hSsaDzcCBEBIC6emQk+N0NCIiIiJShZSMB5smTaB7dzhzBt5/3+loRERERKQKKRkPRkOH\nmluVqoiIiIjUakrGg0xWVha7O3Uyd5Yvh/x8ZwMSERERkSpTE5LxXwEfAAeBHOBLYIKjEVWhjRs3\n8sKqVXDhhXD4MGzY4HRIIiIiIlJFgj0Z74BJxEOAW4ERwEbgFeA3DsZVZZKSkvh282YOXX21aVCp\nioiIiEitFezJ+Gj7dgjwDvAhJgn/FLjZqaCqUmRkJH369OHdRo1Mg5JxERERkVor2JPxUOAMkFus\nPQdwVX841WPw4MEs376dgthY+OEH2L7d6ZBEREREpAoEezL+CpAPPAs0BxoAtwN9gKcdjKtK/eIX\nv6BRkyZs7NrVNKh3XERERKRWCvZk/EfgGmAUsAfIBp4DJgELHIyryk2ePJmWGuJQREREpFYL9mT8\nMmAZsAkYDFwNvADMAsY4GFeVu+yyy2gxdiyEhsK6dXDkiNMhiYiIiEglC/a668WYhLwdkOfRPhfT\nYx5XbHmrtJWNGzeO8ePHV2Z8VS8tDTIyIDkZLr/c6WikAjIyMkhISHA6DJEStG9KMNP+KU6ZPXs2\naWlpZS1W4Vw62JPxH4HNwMhi7fdgasbjMeOPu1mWVWo+XvM89RT89rdw443w+utORyMVkJ6eTmJi\notNhiJSgfVOCmfZPCVYulwsqIZcO9jKVTKA9EF6svStmhJXsao+omuUPHEgmkLl8Ofm5xQeVERER\nEZGaLNiT8WeBNpgxxocC/TEncN4ApOJdulLrZGVlMer++xkRGcnonBxG9enDoUOHnA5LRERERCpJ\nWDmWvRBzEZ5WQKSP+bdUSkTelmBqw+8DXra3ux24A3ixCrYXNPLz85k4cSJZWVnsCAnhEiD7v/9l\nzJgxpKSkkJyc7HSIIiIiIlJBgSbjw4E3MXUxB4FTHvNclHHiZAV9YE/nlH379rF//34iIiJoEBfH\n4Z07iT98mLxTp0hNTaVv377ExsY6HaaIiIiIVECgZSp/AdZgLrxzHtDaY0qwb6WKxDVvTlZYGAUF\nBZCV5XQ4IiIiIlJJAk3G2wBPAipYribNmzcnPj4ey7KIjIwkKiaGbCDs4EFSUlLUKy4iIiJSCwSa\njP8INK7KQMRbaGgos2bNIjzcDCTT9IILyAJey84m+aqrnA1ORERERCpFoMn4H4D7MSdxSjWJi4sj\nJSWFsLAwGjRpwvg2bWhkWfDmm06HJiIiIiKVINATOB8GGgHfA9vwHt/bfQJnr8oNTQCSk5Pp27cv\nALHLlsHYsebiP5MnOxyZiIiIiFRUoMl4PqZUxd9VhmrZZS+DS2F9+NChEBUFn3wCO3ZAa503KyIi\nIlKTBZqMJ1ZlEBKgevVg2DCYP99M99/vdEQiIiIiUgHBfgVOKW7sWHM7bx5Y+kFCREREpCYrTzJ+\nHmZ4wy+A/wEbgSeA+CqIS/zp3x+rUSN2fP89fPut09GIiIiISAUEmoy3Bb4G7gKOAZ8DJ4B7gP8A\nF1VJdFJSeDgnR4zgXuDgiy86HY2IiIiIVECgyfhjwFFMUp4E3ICpI7/Ibn+8KoIT36LHj2cAsPD1\n16GgwOlwREREROQsBZqMJwEPARnF2ndihj1MqsSYpCw9enBdixa8e+QIxz74wOloREREROQsBZqM\n18GUp/hy3J4v1SUkhLhf/5oewNLH9aOEiIiISE0VaDL+H0y9ePHlQ4AUTD25VKexY7keWPTRR5w+\nftzpaERERETkLAQ6zvgjwHLgB+ANYB9mFJXRmLrxQVUSnfh3+eW0vuwyfrt5M65Vq2D4cKcjEhER\nEZFyCrRnfCUm4T4GPAA8Dzxo3x8EvFcl0UnpxoyhBxD+xhtORyIiIiIiZ6E844yvBDoBscD59m0X\nlIg758Ybze2SJaBSFREREZEa52yuwHkCyLRvxUkJCdCzJ+TmmoRcRERERGqU0mrGHwJeBvZihi8s\n69rrf66soKQcxoyBjz+GefNg7FinoxERERGRcigtGZ+GKU1xJ+NlUTLuhNGj4Z57yHvvPf6zahUd\n+/Z1OiIRERERCVBpZSohmMveu/8uaxInNGkC/ftTUFDA337/e3bs2OF0RCIiIiISoECT6PPxf2Gf\ncHu+OGXMGOoAySdO8IZGVhERERGpMQJNxjOAX/qZ1x5Qd6yThg2DqCiGbtvGJ6tWcejQIacjEhER\nEZEAVEZ5SThln9wpValePRg2jBhgQHQ0b731ltMRiYiIiEgASkvGGwJtgAvt+y3t+57TZcDNwP4q\njFECMWYMANf9+CMrV67k2LFjDgckIiIiImUpbTSVezDDG7qV1t06rVKikbN3zTXQuDFNf/yRxx9/\nnMjISDIzMwFo3rw5oaGhDgcoIiIiIsWVloy/jakVB3gV+Cvwv2LLnAK+B/5T6ZFJ+YSHw6hR8MIL\nNF61iutnz2b/fvODRXx8PLNmzSIuLs7hIEVERETEU2nJ+Nf25LYMyKracKRCxowh/4UXmPjyy2R3\n6UJERAQA2dnZjBkzhpSUFJKTkx0OUkRERETcAj2BcwNwqZ95vYGLKiccqZCePdl33nnsz83FlZNT\n2OxyucjLyyM1NZUcj3YRERERcVagyfgMYIifeYOBpysnHKmQkBAzzCHAgQPOxiIiIiIiZQo0Ge8I\nfORn3jqgS+WEIxXV/PbbiQesAwegoIBDhw5RUFBAWFgYKSkpxMbGOh2iiIiIiNhKqxn3FAPk+pl3\nBqhfOeFIRYV26MCsSy5hzJYt5B05Qk5ODqGhobz//vs0a9bM6fBERERExEOgPeM7gL5+5iVRNOqK\nBIG4m28mBQg7eJBWrVpRt25d9YiLiIiIBKFAk/E0YApwJxBht0Xa96fY8yVY3HgjycDCnBzeffNN\nBg0apKtyioiIiAShQJPxJ4ElwLPASeAQcMK+vwR4rEqik7OTkAA9exKbm0vsmjXccsstLFy4kKNH\njzodmYiIiIh4CDQZzwOuw5SqPIG5INDjQB9gFJBfJdHJ2Rszxty++CItWrQgKSmJNWvWOBuTiIiI\niHgJ9AROt9X2JMHu17+GBx6Adevgo4+44447CA8PdzoqEREREfEQaM+4p6bA+T4mCSaxsXD33ebv\nRx9VIi4iIiIShAJNxusDszHDG+7HjJ7iOe2o7MCkEtx9N9SrB++9Bxs3Oh2NiIiIiBQTaJnKc8BI\n4GVgM3CqyiKSytO4MdxxBzz+ODz6KLz9ttMRiYiIiIiHQJPxAcAfMEm51CRTp8Kzz8KSJfDNN3DF\nFQBYloXL5XI4OBEREZFzW3lqxrdUWRRSdZo1g4kTzd9/+xsAW7du5Y9//COWZTkYmIiIiIgEmoy/\nAQypykCkCv3+9xAeDgsWwI8/8otf/IJDhw7x+eefOx2ZiIiIyDkt0GT8PUwy/i/MeON9fExVaSCw\nDjgGHAU2AklVvM3ao2VLmDABLAv+/ndCQkK47bbbeOmllygoKHA6OhEREZFzVqDJ+BIgARgHLABW\nFZs+qIrgbJMwFxnaCAzHXGRoAVC3CrdZ+/zxjxAaCnPmQEYGPXr0IDIykg8//NDpyERERETOWYGe\nwFnVPd/+JAAzgN8Bz3q0v+9INDVZmzYwdiy89ho89hiu1FRuv/12/v73v5OYmKhxyEVEREQcEGgy\nnl6VQZTiFiAPeMGh7dcu991nesZffRUefJD27dszePBgTpw4QYMGDZyOTkREROScczZX4KxOVwE/\nAmOA/wJngG3AHU4GVWNdcglcdx2cPg3/+AcAY8eOVSIuIiIi4pBAe8bXAP7GwXPZ86qilOU8oDnw\nOHAfJiEfjRnvPAzv0hUJxAMPwJtvwqxZpqe8aVOnIxIRERE5ZwXaM+6ypxCPKQ7Tc93WnlcVQoAY\nYCLwCqZc5g5gJSY5l/Jq3x6GDIHcXHj6aaejERERETmnVTSJvhAz0skUzKgqlW0D0AWIBU54tE8B\nnsT0mh/waC/1Kjbjxo1j/PjxlRxiDZSZCa+8AnXqwL33Ql0NTFMdMjIySEhIcDoMkRK0b0ow0/4p\nTpk9ezZpaWllLVbhDunK6NEeixntpEMlrKu4lzEnccYQYDKuq0oGqH9/+OADeOQReOghwPzDO3r0\nKI0bN6Z58+aEhoY6HGTtkp6eTmJiotNhiJSgfVOCmfZPCVYulwsqIZeujBM4s4CLK2E9viyybwcU\nax8A7MY7EZfyePBBcztjBhw7RlZWFiNHjmTIkCGMHj2aUaNGcejQIWdjFBEREanlKpqMN8H0Uv+3\nEmLxZQXm5NFZmIv/9AdeAvoB/6+Ktnlu6NULfvUrOHKE/OefZ+LEiURFRZGbm0tBQQHZ2dmMGTOG\nRYsWlb0uERERETkrgSbjO4D/2bfuaQ+wH7gaeLBKojOGA/8GHgHeATpjhjp8rQq3eW6we8f3/eMf\n7P+13OEAACAASURBVN+zh7CwMJo1a8a+fftwuVzk5eWRmppKTk6Ow4GKiIiI1E6BDm241kfbz8BO\nzKXpq6pnHOAYcKc9SWXq1w86d4aNGyEmBhISaNKkCVlZWRw9epT69es7HaGIiIhIrVZaMj4UWAf8\nBIyvlmikerlc8OCDNB82jPj9+8lu1QpXaCitWrVi9+7dNGrUiJSUFGJjY52OVERERKRWKq1M5W3M\nGOIA+ZghBqW2GTyY0MsvZ9bPPxNun7BZr1492rVrx7x580hOTnY4QBEREZHaq7Rk/Bjgvk56VV3U\nR5wWEgIPPEAckHL4MGEhIYSFhXHXXXfRrFkzp6MTERERqdVKK1P5EngBU6oCZvSS0sa6u6WygpJq\ndt110LYtyVu30nf0aLjxRpWmiIiIiFSD0pLxO4CngN72/S7AaR/LuSjjypcS5EJD4f77Yfx4YmfM\ngNtuczoiERERkXNCaWUqW4CBQGv7/lCglY+ppX0rNdmYMZCQAFu2QLGxxS3L4tSpU87EJSIiIlKL\nBTrOeB/g+6oMRBwWHg5/+pP5+69/Bavox45ly5bx5JNPOhSYiIiISO0VaDKejjmhsz1wF/Aw0Nye\ndxGgAuPaYPx4OO88+OYbeK3omkr9+vXjm2++YdOmTc7FJiIiIlILBZqMRwBvAZuAZ4CHKErGHwPu\nr/zQpNpFRMCjj5q/J0+GbdsAiIyM5O677+bpp5/mzJkzDgYoIiIiUrsEmow/irns/a+BZngPdfgu\nMKCS4xKnjBsHN9wAJ06YW7tWvEePHpx//vnMnz/f4QBFREREao9Ak/EbMUMbvg4cKTYvA0iovJDE\nUS4XvPACtGkDX31VVEcO3HXXXSxatIg9e/Y4GKCIiIhI7RFoMt4Y/ydwhmDKWKS2qF8f5s+HsDCY\nMQPeeQeAZs2aMX36dJo2bepwgCIiIiK1Q6DJeAbQw8+8zsCPlRKNBI8uXWD6dPP3hAmQmQlAu3bt\nCA8PdzAwERERkdoj0GQ8DfgTMBbwzMT6AFOBVys5LgkGU6fCgAFw+DD8+teQn+90RCIiIiK1SqDJ\n+BPAMmAORTXj64FVmBM4Z1Z+aOK4kBBIS4P4eFj7/9u78/ioqvv/4687SyYhySQsk0wQZBFRBLEq\nrnVBCFVscYkGNFVwwdhRW6VuVdt+EZdKrUsLmqZa60JVtCAupValgv6su0AFEVlkGUggYSAhe2b5\n/XGTECBAIJPcmeT9fDzuI8mduXc+Ew43n3vmc85ZtGumFRERERGJitYm40HgMuBs4BHgr8CfgHMw\ne8sj+z5U4lpGBsyaZQ7svPde+OADqyMSERER6TRam4w3+hC4B7gOs2xlUdQjktgzejTcdReEw5CX\nZ5atAFu3buXuu+8mpPIVERERkUPS2mR8CTAFc45x6YqmToXTT4dNm8wBnZEIHo+H2tpa/vGPf+D3\n+/H7/UrMRURERA5Ca5PxzcDvAT9mjfjlQGJ7BSUxyOmEF1+E9HRzqsMZMzAMg4kTJ3LLLbdw8cUX\nM378eHJzcykpKbE6WhEREZG40Npk/HygD3A7kAH8HdgC/A2zbly6gn794Omnze9vv53QF19w7733\nkpaWRklJCS6Xi0AgQF5eHnPnzrU2VhEREZE4cDA141uAx4ETgaHAE5hTGy4ANkQ/NIlJl1wCPh/U\n1VGUm0vxpk14vV5qamooKyvDMAyCwSAFBQWUl5dbHa2IiIhITDvYAZyNVgD3AXdjlrD0iVpEEvse\neQSOPRbWrYPvv8cwDA4//HAcDofVkYmIiIjElYNNxg1gNPAsZk/5C8BG4KbohiUxLSkJZs8mKzER\nb0kJkaIikpOTSU5OJhKJ4HA48Pl8uN1uqyMVERERiWmtTcaPBaZjlqO8C5yFWbJyFHAa8GS7RCex\na8gQ7DNnUgg4V62CqioAnE4ns2bNIicnx9r4REREROJAa5PxpUA+5kwqZwEDgd8Cq9opLokH11yD\n57LL8IXDOL75BofNhs/nIzNTM2CKiIiItEZri3wnAG8Ate0Yi8Qbw4A//5mczz4je+1aGDQI98UX\nNz0ciUQwDMPCAEVERERiW2t7xl9Fibi0JC0NXnoJt8OB+y9/gbvvhkiEBQsW8MQTT1gdnYiIiEhM\nO5jpL1zAWGAwLS/4My0qEUn8OflkmDULrrgCHnoIKis5+b77eOqppxgxYgSnnnqq1RGKiIiIxKTW\nJuO9gY+Afvt5jpLxrmzCBHOWldxcmDGD1MpK7rrjDqY98ABPPfUUPXr0sDpCERERkZjT2jKVh4ES\ndiXjpwJHAPdjDuIcGP3QJO5ccAG8+aaZlD/zDMf94Q/8+LzzmD59OuFw2OroRERERGJOa5PxM4E/\nYC7wAxACvsecUWUO8KfohyZx6Uc/gn//G1JT4aWXmPjmm1SUlfHmm29aHZmIiIhIzGltMt4TKMJM\nwiuB7s0e+w8wMrphSVw780x47z1IT8fx5pv8duVKzj7pJKujEhEREYk5rU3G/UDj5NFrgXObPXYS\nUBPNoKQTOPlkWLgQPB4yFy4k/fLLYedOq6MSERERiSmtTcYXYi72A/Bn4FbgHWA+Zt34P6IemcS/\n446DDz6A3r3Nr9nZsH271VGJiIiIxIzWJuP3ADMbvi8AbgaSAS8wHfhl9EOTTuHoo+HDD6F/f/js\nMzjnHNi61eqoRERERGJCa5Pxk4BNzX6eAfwQOAG4G5WpyP4MHGj2jA8eDEuXEjrrLHauXGl1VCIi\nIiKWa20y/k8gAPwXeAAYTcsL/4i0rG9fMyEfNoz5K1cy7ZRTqF+1Cr/fj9/vJxQKWR2hiIiISIdr\n7aI/RwGjgHOAycBdQB3wKeZsKu8DH7RHgNKJZGbCwoWcf+65zPvyS344dCiOoUMhKQmv10thYSEe\nj8fqKEVEREQ6TGt7xlcBhcBlmLOqHAvcDgSB/8NMxkUOrGdPeOcditLTWVtfT3jZMlzBIIFAgLy8\nPObOnWt1hCIiIiIdprXJeKNumNMaTmzYzgbKAa3oIq1WVFXFjsGD6ZOSwrpgkPBXX2GUlREMBiko\nKKC8vNzqEEVEREQ6RGuT8fuAj4AdmNMYDgdeAU4BegAXtUt00nnZ7XQ/4QSSk5MpDYVg6VLYssXq\nqEREREQ6VGtrxu8BqjGXvf89oLnp5JBlZWXh9XoJBAL0PfFEjLVrifj9OFeswHfCCbhTU60OUURE\nRKRDtLZn/GbMRX6uBoqAL4GHgbFASvuEJp2V3W6nsLAQp9OJYbPBoEE4jzySWUDO3/8ON94Iml1F\nREREuoDWJuMzgIsBD+ac4y8CQ4CX2TXlYUd5Gwhjls5InPJ4PPh8PhwOBw6HA99DD5H56qvgckFB\nAeTkQFWV1WGKiIiItKvWlqk0CgPLgDQgHegFnAycGuW49uVyzHp1gEgHvaa0k5ycHLKzswFwu93m\nTq8XLrgA3njDXK3zzTchI8PCKEVERETaT2t7xn8I/AZzTvEyYAFwPbABuBE4pl2i21134FFgSge8\nlnQQt9u9KxEHKo8/nkfz86nt1w8++wxOOw1WrbIwQhEREZH209pk/EPMJLgc+BXwA8z5xscDBcC3\n7RLd7qYDXwOzO+C1xCLdunWjMjmZhydMIHLCCbB2rZmQf/yx1aGJiIiIRF1rk/GTMEtSLgL+CPyP\nji0TOQO4ErMXXjoxwzC444478JeV8eINN8D558O2bTBqFMybZ3V4IiIiIlHV2mT8S8x6cSskYK7+\n+TDmSqDSyblcLu6//35e//e/+fD22+G666CmxhzUOXOm1eGJiIiIRI1hdQCt8GvgKmAoUNuwLwzc\nD/x2j+fut7d+0qRJXHXVVVEOT9pLaWkp7733Hj8+/3xSlyyB9983Hzj9dMjOBiMemu8u69ato3//\n/laHIbIXtU2JZWqfYpVnn32W55577kBPa3MyEuvZzOHASuBaYH6z/QHgD8ADwE529dpHIhFNstKZ\nfP/99/Tv3x/DMOD55+HaayEYhAkT4LnnzKkQ48TChQsZOXKk1WGI7EVtU2KZ2qfEKsPsFGxzLt3a\nMhWrDARcwCzMBLxxA7gN2A4MsyY06QgDBgxobOwwcSLMnw+pqTB7NuTmQm3t/k8gIiIiEsNiPRlf\nDIzcYzun4bEXGn5e0+FRiXXGjIFFi6BHD3MOciXkIiIiEsdiPRkvAz7YY1vU8Nj6hp8rrQlNrBAK\nhfB7PPhffJFQ9+5KyEVERCSuHewKnCKWKS0tZeLEifj9flJSUvAefzyFX32FpzEhf/XVuKohFxER\nEYn1nvF9sbH3TCrSiYVCIfLz8ykpKaGoqIhIJEIgFCLvqKOYm5KiHnIRERGJS/GajEsXU1RURHFx\nMSkpKfTu3Zu1a9cSDAYJJiVRMHQo5c1LVurqrA5XREREpFWUjEvc6dGjB7169WL16tUEg0FzdpXX\nX981qPPSS5WQi4iISFxQMi5xISsrC6/XS+M88hkZGaSnp7NmzRomT56M+8wz4b33lJCLiIhIXFEy\nLnHBbrdTWFiI0+ls2te3b19eeOEFJkyYYO44/ngl5CIiIhJXlIxL3PB4PPh8PhwOBw6HA5/Px+jR\no3d/0p4JuWrIRUREJIZpakOJKzk5OWRnZwPgdrtbflJjQj56NLzxxq5pDxMSOjBSERERkQNTz7jE\nHbfbve9EvNHxx8OCBdC9+66EXD3kIiIiEmOUjEunsmXLFh5//HFzlhUl5CIiIhLjlIxLp9KjRw+K\ni4uZPn064XB474R8/HgIBq0OU0RERARQMi6djNPp5N5772Xbtm088sgjeyfkr78OPh80TJEoIiIi\nYiUl49LpuFwuHnjgAdavX88TTzxhzk1+/PHwz39CUhI8/TRMnWp1mCIiIiJKxqVzSkpKYvr06Sxf\nvpylS5cSCoXw9+2Lf+ZMQoYB06ZBYaHVYYqIiEgXp6kNpdNKTk5mxowZlJWVkZubS3FxMQDe446j\ncMkSPDfcAF4vXHihxZGKiIhIV6WecenUbDYb+fn5BAIBXC4XLpeLQFoaeQMGMDcchssug48+sjpM\nERER6aKUjEunVlRURHFxMYZhNO0zDINgv34U9O5NeU0NjBsHK1ZYGKWIiIh0VUrGpcupr683vxky\nBMaOhe3b4bzzYPNmawMTERGRLkfJuHRqWVlZeL1ec0aVBhs3bsTv95N//fW4//EPOO002LDBTMh3\n7LAwWhEREelqlIxLp2a32yksLMTpdDbtO+KIIxg7dixffPEF1YYBb74JRx0FX38NF18MtbUWRiwi\nIiJdiZJx6fQ8Hg8+nw+Hw4HD4eCmm27iscceo1evXvzyl79kh90Ob78NWVmwcCFMnAjhsNVhi4iI\nSBegZFy6hJycHObMmcOcOXPIycnBbrdz2223MWLECH7xi19Qm5UF//oXuN3wyiswZYpW6RQREZF2\np3nGpctwu927/WwYBtdeey1nn302LpcLjjsOXnvNrB3/05/gsMPgjjssilZERES6AvWMS5c3aNCg\nXT+MGgXPP29+f+ed8MIL1gQlIiIiXYKScZE9XXYZPPqo+f0118A771gbj4iIiHRaSsZFWhCYNAlu\nu41QMIj/4ovxz59PKBSyOiwRERHpZJSMi+whEokwdepUHs3M5NI+fRhfVcX4Cy8k97zzKCkpsTo8\nERER6USUjIvswTAM7r33XmY++SRLHQ4SunfHFQwS+OAD8nJymDt3rtUhioiISCehZFykBZWVlWRk\nZBAKh1mbnEwoNRWjro7gV19R8Mc/Ul5ebnWIIiIi0gkoGRfZB5vNxoABA3AlJrIqKYlIcjJUVcHi\nxbBzp9XhiYiISCegZFykBVlZWXi9XgD69OlD/4EDYfhwHImJ+HbuxH3llVBTY3GUIiIiEu+UjIu0\nwG63U1hYiNPpBCAxMRFncjKzFi0ix+uF9983p0AMBi2OVEREROKZknGRffB4PPh8PhwOBw6HA5/P\nR+bJJ5vzjqenw+uvw3XXQThsdagiIiISpxxWByASy3JycsjOzgbA7XabO489Fv75Tz4fNQrns8/y\ngx494A9/AMOwLlARERGJS+oZFzkAt9u9KxFvdPrp2P/wB+4zDF5+9FEiDz5oTXAiIiIS15SMixyi\nE266iScLClgETP31r6n84x+tDklERETijJJxkTbIvP56/vTEE6QDvltuYd2MGYRCIfx+P36/n1Ao\nZHWIIiIiEsNUMy7SRs4bbmDKjh28c889bLjlFn758ssURyIAeL1eCgsL8Xg8FkcpIiIisUg94yLR\ncNddjJ4yhcfDYQIff4yrpgaXy0UgECAvL4+5c+daHaGIiIjEICXjItFgGBRNmUKxx4MRicDXX0NF\nBYZhEAwGKSgooLa21uooRUREJMYoGReJFsOAI46AXr3MxYCWLoXKSioqKog0lK2IiIiINKdkXCRK\nsrKy8GZlERkyxFwUqL6e8JdfsmX9elwul3rGRUREZC9KxkWixG63U1hYiNPlguHDweMhIRzm023b\nuLpfP+bPn89rr71GWCt2ioiISAMl4yJR5PF48Pl8OBIScAwfju/CC8kKh7m0oICxaWkseO89br31\nVkpLS60OVURERGJAPExteClwBXAC0AvYAMwFHgQqLIxLpEU5OTlkZ2cD5uqdFBbCjTeS9tln/Ckz\nk3kXXURCQoLFUYqIiEgsiIee8VuBeuBXwHlAAeAD3gUMC+MS2Se3220m4gDXXw9vvQUJCdhmzyZn\n5kzcdXV7HaPFgkRERLqeeOgZ/wmwrdnPHwAB4DlgJPC+BTGJHJzzzoMdO2D5cvjoIzjtNJg/H448\nEoDS0lLy8/MpLi4GtFiQiIhIVxEPPePbWtj3RcPX3h0ZiEibeL3w6adw/PGwejWceir8v/9HKBTi\nuuuu4+uvv8YwDC0WJCIi0oXEQzLekrMbvq6wNAqRg3XYYfDBB/DjH0MgAKNHU1RQQHFxMU6nk+++\n+47S0tLdFgsqLy+3OmoRERFpJ/GYjB8GTMOsGf/K4lhEDl5KCsybBzfeCHV18POfY2zaRGZmJkcc\ncQQ7duxg5cqVVFRofLKIiEhnF2/JeArwOlAHXG1xLCKHzuGAGTPgscfIArwbNxJZsYKkxEQGDRpE\nRkYGGzduZOzYsbsGgoqIiEinE0+zkSQB84FjMctUlrfwnP2uOT5p0iSuuuqq6Ecm0grr1q2jf//+\nez/w7bdUzpnD3GCQcGIiZGRgczi44IILcLvdGEY8/TeVeLTPtikSA9Q+xSrPPvsszz333IGe1uY/\n0vHyV94JzAPOAMYAn+3jeZFIZL/5uIhlFi5cyMiRI1t+8PPPmTtmDAVlZZCYiO8XvyDnoYdAibh0\ngP22TRGLqX1KrGroLGvzH+p4KFOxAX/HnMbwIvadiIvEr5NOImfJEuYccwxzamrI+f3v4Zxz4Msv\n93rqwoUL+e6775p+1vzkIiIi8SsekvEnMFfhfBSoBk5tth1mYVwi0dW/P+4lS3DPmAE9e8KiRTBi\nBEycCBs3Nj2tvr6eu+66i4cffpjVq1eTm5vL+PHjGT9+PLm5uZSUlFj4JkRERORgxEMyfh5mLfg9\nwH/32K61MC6R6HM64aabzHnIb7sNEhLghRdg8GD4zW9g507GjBnD888/T7du3TjzzDP59ttvSUhI\n0PzkIiIicSgekvEBgB0z1j23aRbGJdJ+0tPh4YdhxQrIzYWaGrj/fnPFzqeeIjkxkQsvvJDevXtT\nWVnJxoaec81PLiIiEl/iIRkX6boGDoRXXoGPPjJX7NyyBfLz4Qc/gEWLcLlcDBw4kD59+lgdqYiI\niBwCJeMi8eD00+G//4WXX4Z+/WDZMrKuuALvmjVEKiqw2cz/ypFIBIfDgc/n0/zkIiIicUDJuEi8\nMAyYMAG+/RamT8fudlO4dSvOL76AlSuhqgqn08msWbPIyclh+/bt/OxnP2PhwoWEw2GroxcREZEW\nKBkXiTeJiXDHHbB6NZ4bb8RnGDiKinB89hm+FSvIfOwx+Phj0t1urr76ambPns3kyZNZtGhRU1Ku\n6RBFRERiQ2dbUUSL/kjMareFK1asoHzaNHj7bdw7duzan5kJ48YRueACPnO7efbll6mrq+Oaa67h\nkUceobi4GACv10thYSEejyf6sUlc0KIqEsvUPiVWdaVFf0Rkf4YMwf3SS7i3boX//Aduvhn69zcH\nez79NMYFF3DK+efzZHEx12Zlcf9vf0sgEMDlcmk6RBEREYspGRfpLJxOc9XOxx+HtWth6VKYNg1O\nPBGqqjDmzePwBx6g7D//wViyxFxIqKpK0yGKiIhYyGF1ACLSDgwDhg83t9/8xky833gDZs+GDz+E\nsjJzW7MGHA5qkpPZ4XBQ+vLLuMeNg6wsq9+BiIhIl6CecZGuoG9fuPFGst5/H+9PfkJkyBDIyACn\nk0gwSEJZGWds28Yt11/PtN69WZaZSeSii+DBB+Hdd2H7dqvfgYiISKeknnGRLsRut1P4zDPk5eUR\nzMwEwBkMMmvSJDJXraLyk0/492ef8dDWraS8/jq3vv46RzYePGgQoRNPpGjwYBgxgqxzz8Xucln2\nXkRERDoDJeMiXYzH48Hn81FQUACA7+c/JzMnB4BkICcc5qJvv+XTl1+mR1ERLFsGS5ZQuno1+atX\nU9xwHq/dTuE55+AZOxZGjTJLYmz6sE1ERORgaGpDkQ4Sa9NzNQ7WbM1KnaGaGnJ//GMCGzdiVFTA\njh1EqqtxAj4gB6BHD3MA6ahR5nbUUWbtusS8WGubIs2pfUqsitbUhuoZF+miWpOENyoqLaW4uhrX\nYYdRUVHBZsOgx+GH0z0SoWDnTrLtdtx+P8yZY24AXu+uxHzUKBgwoJ3eiYiISPzSZ8oiclCSk5Px\ner1U1NayvLSUNYmJfPbMM4RWroS//AUuu8wcHFpcDC++CJMnw8CBZjJ+222wfLnVb0FERCRmKBkX\nkQPKysrC6/USiUQwDAO3202/fv0YPnw4EyZMYN7rr/P2qlVw3XXw0ktmIr5sGfzpT3DRRYTS0vCv\nW4f/kUcIDRsGJ58MTz6pWVpERKTLU5mKiByQ3W6nsLDQnIUlGATA6XQya9YsMhtmZdltvIZhwNCh\nMHQopZdfTv5111G8ahWUlOANBCj8/HM8n38OU6bARRfB1VfDmDFgt1vx9kRERCyjnnERaZXGWVgc\nDgcOhwOfz9eUiEPTQJbd1NTUcPbZZ/P9unUk9OqF65hjCJx2GnnDhjF3+HCor4dXXoGxY+Hww+Gu\nu2Dlyo58WyIiIpZSz7iItFpOTg7Z2dlA6waAFhUVEQ6HKSkpwe/3k5aWRnp6Oik9e1LgdJK9bBnu\n116DZ5+F1avhoYfM7bTT4KqrYMIESEtr3zclIiJiIfWMi8hBcbvdrZ6Jxel00r17d4488kiOPPJI\nXC4XRUVFrF+/3nxCnz5wzz3w3Xfw4Ydw7bWQkgIff0zo+uvxZ2biz8kh9Omn7fiORERErKNkXETa\nTfOBny6Xi4yMDI488kgGDhyIz+fbldQbBpxxBjz9NBQXU/rEE+T26sX42lrGv/YauaeeSsnpp8Nb\nb0E4bO2bEhERiSKVqYhIu2nNwM/mHnvsMUpKSli0aBG2o4/GFQzCpk0ENm0i7+OP8Y0bR87RR8Ot\nt8IVV0BiYke/JRERkahSz7iItKsDDfxsbvLkyQwdOpT169fzzTffsGbTJkrT0oiceirBI46gwOWi\n/NtvzSkU+/WD+++Hbds6+B2JiIhEj3rGRaTdtXbgZ2pqKmeffTaHH344TqeT8vJyysrK6N69O/Tt\naybgeXnwxBOweDH85jfw4INwzTXmNIlHHEEoFKKoqAgwy2Tsmi5RRERimJJxEekQrR302VhnHggE\nSE9PJz09nUgk0tSr7s7JgWuuoeadd3j9V7/ipCVLGPDEExhPPknpj39M/s6dFNfVAeD1eiksLMTj\n8bTnWxMRETlkKlMRkZjSWGfudDqb9jXWmefk5Jg7DIPqk09m88SJ/Pr88xnfvz8PGQY5b71FyaJF\nuJYvx1VeTmDbNvLy8pg7d65F70ZERGT/lIyLSMxpTZ159+7dmTJlCn9/6y0e+/BDek6fzpqUFDbb\nbFBeDsuXY3zyCcHVqyl4/HHKy8v3+5qhUAi/34/f7ycUCrXn2xMREWmiMhURiUmtrTM3DIM+ffow\n9rLL+NvcubgcDigqgk2boLoa1q2Ddev4JieH4IUXcuyVV5KWnr7bOUpLS8nPz6e4uBhQeYuIiHQc\n9YyLSMw6mAWGmuY0t9nMxYROOYXI8OE4PB58hkFowQLe+MUv+Gnfvlx92mk8+uCDLFiwgEAgQH5+\nPoFAAJfLhcvlIhAIqLxFREQ6hHrGRaRTaHFO84wMZr3zDpn19fDUU/zwL38hVFzMmk8+4X9LlrBo\n6FCCkydTXFyMy+VqOpdhGASDQQoKCsjOzt7nDYFmbhERkbZSz7iIdBr7rDXv0wfuvRc2bMD+yisM\nPvtsLq2pYdqXXzLU54Nly2DrVohEms61ceNG/H4/H3zwAZs3bybS7DEwS1tyc3MZP34848ePJzc3\nl5KSko5+yyIiEucMqwOIssiefzBFYsXChQsZOXKk1WF0CY2DNfdb4rJ8ORQUEHruOXIrKggAhtMJ\nHg+R7t2pSUzk1DPOIDU1lZUrV1JXV8fgwYOZOnUqLpeL3NxcAoEAhmFeRiORCE6nE5/Pt2vWl32I\ntR51tU2JZWqfEqsarv9tzqVVpiIinU6r6syHDoWZM7H/7ncUFhSQN20awcpK2LwZ5+bNzDYMMhMS\n4Ec/gptvpvSII/hu7VqSkpLYtGnTXqUtO3fuJDEx8YClLRosKiIizSkZF5GuLTUVzx134DviCAqm\nT4dt2/AlJJC5ejV8/LG53Xsvvdxueo0aZSbnw4btdopQKERJSQnV1dUA3HnnnQwZMoQhQ4YwZsyY\n3Z7XfLAo0DRYtDU96iIi0vkoGRcRAXIuuYTshsTZ7XbDzp2wcCG88465ffcdzJsH8+aRBXiT6Hb4\nNgAAGk9JREFUkgikpWH07Ik9PZ2BAwfidDq58sorGTZsGGvWrGHLli27vUZRURHFxcU4nU7q6upw\nuVytHiwKsVfeIiIibadkXESkwW6JcGoqjBtnbgDr18O778K772J/7z0KAwHyqqsJNpSbOO12ZvXr\nR+bf/ga9e3NC797QuzfMnm1+7d0bwmEAqqurWb9+PfX19SQmJuJyuejWrRtLlizhrLPOajG2Qy1v\nUQIvIhLblIyLiLRGv34webK5hUJ4Fi/G99hjFMyfD+Xl+EIhMteuhbVr93mKLMDrcBBwOjkmMZGw\nzUZ1VRXBqipOB8puuw08HnNWl8YtHGZjdTWTli2jNhzGZTMnwQp88w15gwfj69OHnH0k5KV1deSv\nXElxXR0A3rQ0CseNwzNwIGRmgtdrbpWV5o2CTRNsiYh0NM2mItJBNCNA51ReXg6RCG6AzZsPuJXU\n1ZEHBBuOdwCzgMz9vMabQH7DMWHABSQAPYCewBxgz+KWEJAL5iwxDfsigBPwAc2r0xeOHMnIDz+E\njIymBD3k8VCUkgL9+pE1ciT2446DZgNWRTqKrp0SqzSbiohIDNittCUtDYYM2feTIxE8gQC+55+n\n4PnnIRTCN3YsmaedZvZKG8buW8O+40tLGfDAA7gSEgiFw9TW11NXX4/T6YRu3WDqVEhObnqZd774\ngkVLl/L1okUkJybicjpJsNtxhEIE6+ooqK8n++STcW/bBlu2QGIihEJQVARFRZRiJv/FDefzAoUO\nB55jj4UTTti1DR9uvn4zKosRETk4SsZFRDqKYUDPnuRMmUL2tdcCrZuGMSsUwjtnDoFAALth0A1I\najavubuxrr3BkQMGsDkjg/Ann1AWClFbVUVdXR1ZWVn08nrB4YBnnoGG1y5/4w02zpiBJxLBuW0b\n+VOmmDO+1NVBVRWBnTvJq67Gt3gxOYsXw1//ar6QzWbefDQk56UDB5L/1FMUb9sGaNpGEZHWUJmK\nSAfRR63SFiUlJeTl5REMmgUuDoeDWbNmmSuMtiAUCrV6YaI//vGPfP75500riC5evJhu3bqRkZFB\ncmOPeyiEo7qaObm5uL/5Br76Cr75xuxRZ4+ymKQkcLuJuN04e/bEd9tt5FxyyT7fm3rTZX907ZRY\npTIVEZEuxOPx4PP5KCgoAMDn8+0zEQew2+0UFhbulsA7nc4WE/jjjju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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rp = np.linspace(0, rmax, 50)\n", "for umax in [1, 5, 10, 15]:\n", " popt, pcov = curve_fit(pw_vector, r, smooth_3s(r), p0=np.ones(umax))\n", " ek = e_kinet_pw(umax, box=BOXLENGTH)\n", " valrms = rms(smooth_3s(r), pw_vector(r, *popt))\n", " print(\"{:3d} plane waves, ENCUT = {:8.2f} eV r^2 = {:8.4f}\".format(umax, ek, valrms))\n", " plt.plot(rp, pw_vector(rp, *popt), \"r-\", label=\"{} plane waves\".format(umax), lw=2)\n", "\n", " plt.plot(rp, OA3s(rp), \"ko--\", label=\"AO 3s\", alpha=.75)\n", " plt.legend()\n", " plt.title(\"Fit a smooth 3s AO with plane waves\")\n", " plt.xlabel(\"r / $\\AA$\")\n", " plt.ylabel(\"wavefunction\")\n", " plt.savefig(\"fit_smooth3s_{}.pdf\".format(umax))\n", " plt.clf()\n", "\n", "plt.plot(rp, pw_vector(rp, *popt), \"r-\", label=\"{} plane waves\".format(umax), lw=2)\n", "plt.plot(rp, smooth_3s(rp), \"ko--\", label=\"AO 3s\", alpha=.75)\n", "plt.legend()\n", "plt.title(\"Fit a smooth 3s AO with plane waves\")\n", "plt.xlabel(\"r / $\\AA$\")\n", "plt.ylabel(\"wavefunction\")\n", "smooth_popt = popt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Slater type atomic orbital" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1 plane waves, ENCUT = 6.02 eV r^2 = 1.0939\n", " 5 plane waves, ENCUT = 150.41 eV r^2 = 0.7347\n", " 10 plane waves, ENCUT = 601.65 eV r^2 = 0.1954\n", " 15 plane waves, ENCUT = 1353.71 eV r^2 = 0.0695\n", " 20 plane waves, ENCUT = 2406.59 eV r^2 = 0.0293\n" ] }, { "data": { "text/plain": [ "(-1, 5)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MTIwVGRlpJSUlWb/++muZ2/CMppKWlmbdeeedVmxsrBUZGWlddtllVkZGRql4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rp = np.linspace(0, rmax, 50)\n", "for umax in [1, 5, 10, 15, 20]:\n", " popt, pcov = curve_fit(pw_vector, r, slater_ns(r, z=11, n=3), p0=np.ones(umax))\n", " ek = e_kinet_pw(umax, box=BOXLENGTH)\n", " valrms = rms(slater_ns(r, z=11, n=3), pw_vector(r, *popt)) \n", " print(\"{:3d} plane waves, ENCUT = {:8.2f} eV r^2 = {:8.4f}\".format(umax, ek, valrms))\n", " plt.plot(rp, pw_vector(rp, *popt), \"r-\", label=\"{} plane waves\".format(umax), lw=2)\n", "\n", " plt.plot(rp, slater_ns(rp, z=11, n=3), \"ko--\", label=\"AO 3s\", alpha=.75)\n", " plt.legend()\n", " plt.title(\"Fit a slater type 3s AO with plane waves\")\n", " plt.xlabel(\"r / $\\AA$\")\n", " plt.ylabel(\"wavefunction\")\n", " plt.ylim(-1, 5)\n", " plt.savefig(\"fit_slater3s_{}.pdf\".format(umax))\n", " plt.clf()\n", "\n", "plt.plot(rp, pw_vector(rp, *popt), \"r-\", label=\"{} plane waves\".format(umax), lw=2)\n", "plt.plot(rp, slater_ns(rp, z=11, n=3), \"ko--\", label=\"AO 3s\", alpha=.75)\n", "plt.legend()\n", "plt.title(\"Fit a slater type 3s AO with plane waves\")\n", "plt.xlabel(\"r / $\\AA$\")\n", "plt.ylabel(\"wavefunction\")\n", "plt.ylim(-1, 5)" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }