diff --git a/SolidState/ElectronBands.ipynb b/SolidState/ElectronBands.ipynb index f92a37dfe6b4e1aec4518e62be4c9a87c9fb83fb..36182deb7cb9d9d6ddacb18fe77c4201aa8d34e0 100644 --- a/SolidState/ElectronBands.ipynb +++ b/SolidState/ElectronBands.ipynb @@ -163,146 +163,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 2. Tight Binding\n", - "\n", - "En este modelo, consideramos que las funciones de onda de los electrones en la red son una superposición de funciones de onda atómicas, cuya base es de la forma:\n", - "\n", - "\\begin{equation*}\n", - "\\chi_{\\mathbf{k} l i} = \\sum_{\\mathbf{R}} e^{i \\mathbf{k} \\cdot \\mathbf{R}} \\phi_l (\\mathbf{r} - \\mathbf{t}_i - \\mathbf{R}),\n", - "\\end{equation*}\n", - "\n", - "donde $l$ es el orbital atómico, $i$ es el átomo en la celda primitiva y $\\phi_l$ es la función de onda atómica del átomo $l$ en la posición $\\mathbf{t}_i$. La expansión de la función de onda en esta base es entonces:\n", - "\n", - "\\begin{equation*}\n", - "\\psi_{\\mathbf{k}} (\\mathbf{r}) = \\sum_{l i} c_{\\mathbf{k} l i} \\chi_{\\mathbf{k} l i} (\\mathbf{r}),\n", - "\\end{equation*}\n", - "\n", - "entonces, solo queda encontrar los valores propios del Hamiltoniano de la red, que se puede escribir como:\n", - "\n", - "\\begin{equation*}\n", - "\\left<\\chi_{\\mathbf{k} m j} | \\hat{H} | \\chi_{\\mathbf{k} l i}\\right> = \\hat{H}_{mjli} = \\sum_{\\mathbf{R}} e^{i \\mathbf{k} \\cdot \\mathbf{R}} \\left<\\phi_m (\\mathbf{r} - \\mathbf{t}_j) | \\hat{H} | \\phi_l(\\mathbf{r} - \\mathbf{t}_i- \\mathbf{R})\\right>.\n", - "\\end{equation*}\n", - "\n", - "\n", - "\n", - "Para nuestro caso, consideramos únicamente el orbital $s$ de los átomos, de modo que podemos omitir el Ãndice $l$ y, además, los valores esperados para los orbitales atómicos del hamiltoniano no serán calculados, y serán tomados como constantes de la forma:\n", - "\n", - "\\begin{equation*}\n", - "t_{ij} = -\\left<\\phi (\\mathbf{r} - \\mathbf{t}_j) | \\hat{H} | \\phi(\\mathbf{r} - \\mathbf{t}_i)\\right>,\n", - "\\end{equation*}\n", - "\n", - "siendo $t_{ii}$ la energÃa de los electrones en el orbital $s$ del átomo $i$ (\"autointeracción\"), y $t_{ij}$ con $i \\neq j$ la energÃa de interacción (términos de hopping) entre los orbitales $s$ de los átomos $i$ y $j$. Además, tomaremos únicamente los primeros vecinos de los átomos A (12 átomos O) y B (6 átomos O), y los segundos vecinos de los átomos O (2 átomos B y 4 átomos A).\n", - "\n", - "Con estas consideraciones, las ecuaciones para cada $i=$\\{A, B, $O_{xz}$, $O_{xy}$, $O_{yz}$\\} son, con $H_{i}=\\sum_{j} H_{ij}$:\n", - "\n", - "\\begin{align*}\n", - "H_A &= -t_{AA} - t_{AO}[3 + 2(e^{-ia\\mathbf{k}\\cdot \\hat{x}}+e^{-ia\\mathbf{k}\\cdot \\hat{y}}+e^{-ia\\mathbf{k}\\cdot \\hat{z}}) + (e^{-ia\\mathbf{k}\\cdot (\\hat{x}+\\hat{y})}+e^{-ia\\mathbf{k}\\cdot (\\hat{x}+\\hat{z})}+e^{-ia\\mathbf{k}\\cdot (\\hat{y}+\\hat{z})})], \\\\\n", - "H_B &= -t_{BB} - t_{BO}(3 + e^{-ia\\mathbf{k}\\cdot \\hat{x}}+e^{-ia\\mathbf{k}\\cdot \\hat{y}}+e^{-ia\\mathbf{k}\\cdot \\hat{z}}), \\\\\n", - "H_{O_{xz}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{y}}), \\\\\n", - "H_{O_{xy}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{z}}), \\\\\n", - "H_{O_{yz}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{x}}).\n", - "\\end{align*}\n", - "\n", - "De modo que la matriz se puede escribir de la forma:\n", - "\n", - "$$\n", - "H = \\begin{pmatrix}\n", - "-t_{AA} & 0 & H_{02} & H_{03} & H_{04} \\\\\n", - "0 & -t_{BB} & H_{12} & H_{13} & H_{14} \\\\\n", - "H_{20} & H_{21} & -t_{OO} & 0 & 0 \\\\\n", - "H_{30} & H_{31} & 0 & -t_{OO} & 0 \\\\\n", - "H_{40} & H_{41} & 0 & 0 & -t_{OO}\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "Donde:\n", - "\n", - "- $H_{02} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}} + e^{-i a \\vec{k} \\cdot \\vec{z}} + e^{-i a \\vec{k} \\cdot (\\vec{x} + \\vec{z})}\\right) = H_{20}^*$\n", - "- $H_{03} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}} + e^{-i a \\vec{k} \\cdot \\vec{y}} + e^{-i a \\vec{k} \\cdot (\\vec{x} + \\vec{y})}\\right) = H_{30}^*$\n", - "- $H_{04} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{z}} + e^{-i a \\vec{k} \\cdot \\vec{y}} + e^{-i a \\vec{k} \\cdot (\\vec{z} + \\vec{y})}\\right) = H_{40}^*$\n", - "- $H_{12} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{y}}\\right) = H_{21}^*$\n", - "- $H_{13} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{z}}\\right) = H_{31}^*$\n", - "- $H_{14} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}}\\right) = H_{41}^*$\n", - "\n", - "Al ser una matriz hermÃtica $5 \\times 5$, obtendremos valores 5 valores propios reales para cada $\\vec{k}$, que serán las bandas de energÃa de los electrones en la red. Ahora, procedemos a calcular estas bandas de energÃa con la implementación numérica." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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jubkZ69ats/ucMWPG4JxzzrH72L///W8ArXmhN9xwg83jSqUSM2fOtPva9oqPj8ewYcMAAD/++KPHyxk3bpyUzyg3evRo6e/p06fbrU8sPqe0tFQqowW07mtieagHH3wQKpX9wkBXXXUVEhMTcfz4cYt8dXG7zs7OlnI75aKiovDUU0+58vHc5up6HT9+PHr16mVzf1paGgYPHgwA+O233zxqgy/3S18R94WhQ4fioosusnk8JiYGDz/8sEvL8mR/94Xjx49bnOfEnGuDwYCTJ0+isrKyXct3dGwQP+e+ffvQ2Ngo3X/y5Enpu3744Yel0nRyo0ePlrY/T2VnZ0vHZWtXXnklANtt+7///S90Oh0A4Mknn7T72gcffDDoyuf5AgPgCCC09vRL//R6PbZv344pU6Zg5cqVGDp0qMMRsvX19XjxxRcxbNgwpKenIzo62mJCDZGzAU6DBg2ye39WVpb0d01NjfT3gQMHpNsjRoxwuFxnj7Wn7ZdffjkAYMqUKXjwwQexfv16i4ObJ7Zu3dpmm509Jp7g582bh8zMTIf/vv32WwCtA0xcJS7bbDbjjDPOcLjsMWPGAGgdSHbixAm7y3L3u66vr5cO0E899ZTTz/bHH384/WxDhgxx+BnFgT1Dhw51OOvTkCFDHAaArli5ciUmTpyIbt26IS4uzmJwz5IlSwC0Dq701HnnnWf3fnk92HPPPbfN55w8eVL6u6SkRPo+pk6d6nDdd+rUSRq0I1//4nZdWFjocL0OHTo0oOvV0TYJnN4u5dukO3y5X/qKuC+IPx7scXX2MXf3d185cOCAxTnOYDBg9+7dePjhh7FhwwZcdtll+Oc//+nRslNSUuz+8AQsP6d8MNwvv/wiDUBrzzmsLeeee67dHyDytlmvf/H7z8nJcVjPPCEhAQMGDGhX20IB6wBHoJiYGPTr1w/z589HTU0N/vOf/2Dq1KkoLy9HYmKi9Ly9e/fi4osvtji5xMbGokOHDtJOJ/Yey3uVrDnq1ZOfFOWjpKurq6W/HfWqAK09K460p+0vvPAC9u3bh3Xr1mHu3LmYO3cuoqKi0K9fP1x22WWYPn2603bZI34mTz6P0WiURrvX1dWhrq6uzfdzJ2AXe0daWlpcvhrgaPnuftdVVVXSicLVE6Wj97Z3pUB07NgxAJYnLGsajQapqalt1le1ZjabceONN2Lx4sXSfSqVCsnJyYiOjgbQ+r01NTU53U/a4sq6dXf9y3vGxHXUFvn6d2W7jomJQceOHd2+0uSt9eponYjLA+BRlQZf75e+4sq+4Orxzd3tzV+io6PRq1cvPP/88zCZTJg7dy7+7//+D6NHj0Z+fr5by3Jl+wG8fw7zVtus178r3z/g+jYQytgDHOFuu+02AK0H8K+//trisZtvvhkVFRXIy8vDv//9b5w4cQINDQ2orq5GVVWVRc+p4KSkWHt4Okd7e9reoUMHfPfdd/jhhx/wyCOPSD2D27ZtQ3FxMXr06GFxUvbW53H0mDzdQCwH1tY/d6ZDFZffq1cvl5YtCILXZsaSf7bNmze79N6OSiWJM0HZI37HbW1PnmzH7733HhYvXoyoqCjMmjULf/75JwwGA2pqalBVVYWqqiopXcdX+4mn5Ou/qqrKpfVvryySp/upM8G+Xn29X/qaL76zYHTrrbcCAEwmk5T+Ecl8eSwMNQyAI1xubq70t7yW6KFDh7Bx40YAwOLFizF+/HikpKRYvNbdnjJXyXvynF3adJR24a22X3jhhXj++efx448/4uTJk1i+fDnOOuss6PV6TJs2za0eLfEzOfs8jh6LiYmRirn//vvvLr+nqzIzMwEA+/fvb1cPpSfkl+Z98dlE4vp3lgtoMBgcpnY4I+bB3nrrrZg9eza6d+9uc1nSV/tKe4nfPeDZ+ndluw7X9err/dJX0tLSADjfF9qq2R1KHJ3jfEl+DnO2LgOxnl05FrryeDhgABzh5CeuuLg46e9Dhw5JfzsaWCTmtXlb165dpYDV0YAnAPjuu+/s3u+LtsfExODKK6/EsmXLALROGuDOgKaBAwcC8OzzAKfzW//97387LW7uCXHZzc3N+M9//uPVZbclOTkZBQUFAE4HPL4gTl+8fv16h8/56aefYDKZ3F62uL052tZOnTqFn3/+2e3l+kOfPn2ktCdP1r+4Xa9fv95hj9GGDRtCcr2KPWTOesJ8uV/6irgvOJvgoq3JL9pD/BHjrx5GR+c4X+rfv7/0OT095vuK+P2XlZVZTBIkd+rUKbcmZwpVDIAj3KJFi6S/xZMZAKlnA2itEmCtvr4ec+bM8UmbFAoFJkyYAAB455137M72VFJSgs8//9zu69vTdpPJ5PREJh/N6+ySu7WJEycCaB00Y+/kotfr8eKLLzp8/fTp0wG05jY7ex7QmtPc3NzsctsGDhwoBRlPPvlkm7mg3h7UIn62tWvXthmEefre4qXygwcPWmzzIkEQ8Pe//92jZYvbm71tDQCeeeYZ1NfXe7RsX1OpVJg2bRoAYOHChW3+qLNe/+J2XV5ejoULF9o832w2e3ycCPR6FX8YyAcNWvPlfukr4r6wYcMG/PTTTzaPGwwGvPTSSz57f1fWqzc5Osf5UocOHTBq1CgAwEsvvYSmpiab53z77bfSlUp/GjVqlPQdODrmvfLKK0GRr+5rDIAjVFVVFWbOnCmdtM4//3yLkiwFBQXIyckBAEybNs3i1+CmTZtQWFjY5hSQ7fH4448jISEBx48fx8iRI6XR5oIgYPXq1bjkkksclmlpT9srKirQo0cPzJkzB9u3b7foufrtt99w4403AmjtSRg6dKjLn2fcuHHSL+9x48Zh6dKlUg7h7t27cckll1gMnLA2duxYXH311QCAxx57DHfeeSf27t0rPd7c3Iyff/4Zjz76KHJzc50uy5pCocA777wDjUaD8vJyDBo0CJ9//rnFAfDw4cP4+OOPMXLkSDz66KMuL9sVd9xxhzSafPLkyZg5c6ZFL35jYyO+//573HPPPW4PYBFddNFFGDlyJIDWvPcFCxbAYDAAaP3Ob7jhBvzwww8elf4Rq2P861//wrx586Qgp6qqCg888ABeeOEFu6XJgsVTTz2F/Px8mEwmjBkzBnPnzrX4EVRXV4dVq1ZhypQpNmWzBg0aJJVbuvPOO/Gvf/1LWq/l5eWYOHEiNm3aFJLrtU+fPgCATz75xGEw4Mv90lcmTpyI3r17QxAEXHPNNVi+fLl0LPrjjz9w+eWX+zS1RFyvOp1OquLhC7W1tXj11VelIC8vLw/XXHONz97P2jPPPIOoqCjs2bMHl112mVTFxmQyYcmSJZgwYYJUctOf4uLipGP4v/71LzzyyCPSD9v6+no8//zzKCoqQnJyst/b5nftqiJMQcvRRBgZGRk2U5yeddZZwuHDh22WsWLFCoupLWNjY6UZnWJjY4Vvv/3WpWLpzjh6vSC0FpmXT4WckJAgTVLR1lTInrb9wIEDFusmKipKSElJsZhSNjo6Wvj3v//t0vcgV1paKmRnZ0vL0Wg00nfhylTIDQ0NwnXXXWfRvri4OIspLMV/joryO7N69WqhY8eOFp+9Y8eO0noT/1kXVvfGd33s2DFhxIgRFu+TmJhoM/WtSqWyea2zaXbljhw5YlHgXz4VslKpFObNmyfk5OQIAITFixe73P7a2lqL5YpTkortvv3229s1ragrn8/ZuhUEy+3a3rSx+/fvF/r27Wux/jt06CAVzBf/2Sv4f/z4cYvXWk8x/dZbb3k0FXJ716sr683Z68UJI8TP1LlzZyE3N1cYMmSIxfN8vV/KeWsq5N27dwuZmZl2j0UajUZYsWKF9Jg4q6DIG/u7ONumeFzPzc0VcnNzhVdeeaXNzyVyNhFGSkqKxXEjJydH2Llzp80yXJ0K2ZG29qt3333Xoh1JSUnSOc1bUyG3tX7sLdtoNArjx4+32LeSk5OlSbImT54s3HTTTdJ+Fq7YAxwB5AXCjx49isbGRmRmZmL06NH417/+ha1bt9otiXL55ZdLNRQ7dOgAk8mE1NRU3Hzzzfjll1/sTujgTZdddhl++eUXXHfddUhPT0dzczMyMjJwzz33YPv27Q5rGLan7Z07d8aXX36JBx54AOeff75U/1SlUqGgoAB33303du7c6dEkHN26dcOOHTswY8YMdO3aFYIgICYmBuPHj8fGjRulnjRHYmNjsXjxYqxbtw6TJ09Gt27dYDabcerUKaSnp2PEiBF44YUX8Oeff3pUwmbkyJHYt28fnnvuOVx44YVISkrCyZMnoVQqUVBQgFtuuQVffvkl3njjDbeX3ZbU1FR8++23WL58OcaPH4/s7GwYDAbo9Xp07twZl1xyCd58802HOWuuyMzMxJYtWzBz5kz07NkTSqUSKpUKl156Kb777jvcdtttUikrd3pmOnTogI0bN+L+++9HXl4eoqKioFKpUFhYiMWLF+Odd97xuM3+0rVrV2zduhUffvghLr/8cnTq1Em6ZN+1a1dcffXVeP/997Fp0yab13bs2BEbN27E7Nmz0atXL2m9jhkzBmvWrMFdd93lUZsCvV5vvPFGfPTRR7jwwgsRGxuLI0eOoKyszGbAn6/3S1/o1asXfvvtN9x3333Iy8uTjkUTJkzA5s2bLWpq+6KX8vPPP8cDDzyAnj17wmg0oqysDGVlZR6nRVhPhKHT6dCxY0cUFhZi7ty52LVrF3r37u3dD+GC6dOn46effsIVV1yBlJQUGAwG5Obm4vHHH8f//ve/gPWyqlQqLFmyBPPnz8d5550HrVYLk8mEgQMHYv78+fjwww+l7yIQvdT+ohCECKh1QUTUhj///BM9e/YE0Hr5Pjs7O8AtIgqMNWvWYNSoUdBoNKivr4darQ50k8iPBEFATk4OKioq8OGHH2Ly5MmBbpJPsAeYiAjAc889B6A1h5zBL0UqQRDw/PPPAwAuvvhiBr8R6KOPPkJFRQVUKpXPr/QGEgNgIooIe/bswa233ooNGzZYVA/Ys2cPbr75ZnzwwQcAWgczEYWzdevW4f7778fWrVuh1+sBtAa+27ZtwxVXXIG1a9dCoVDgkUceCXBLyVeuv/56fP755xZVlo4ePYp//OMf0gRZN910U5szxoUypkAQUUTYsWOHRU3ZpKQkGI1GixH+9913H1577bVANI/Ib7744gupegXQWo9br9dL5boUCgVeeuklzJgxI1BNJB/r0KGDNOYhNjYWarXaYjrviy66CCtXrpRKpoUjBsBEFBHq6+sxb948fPvtt/jjjz9QXV0Nk8mE9PR0DB48GNOnTw/ry31EoqqqKsyfPx9r167F/v37cezYMQiCgKysLFx00UW45557/FYzlwLjww8/xDfffIPt27ejuroap06dQocOHdCvXz9cd911mDx5ctinvzAAJiIiIqKIwhxgIiIiIoooqkA3IBSYzWZUVlYiISFBmh+eiIiIiIKHIAior69HVlYWlErnfbwMgF1QWVnJskhEREREIeDQoUPo0qWL0+cwAHZBQkICgNYV6o8RkUajEatXr8aoUaPCPgmdvIfbDbmL2wy5i9sMucuf24xOp0N2drYUtzkT8gHwhg0b8OKLL2Lbtm04cuQI/vOf/+Cqq66SHhcEAbNnz8a8efNQW1uLQYMG4a233nJrWkQx7SExMdFvAXBsbCwSExN5gCGXcbshd3GbIXdxmyF3BWKbcSVdNeQHwTU0NKBv375488037T7+wgsvYO7cuXjzzTexZcsWZGZmYuTIkRaF8ImIiIgocoR8D/All1yCSy65xO5jgiDg1VdfxZNPPolrrrkGALBw4UJkZGRg0aJFuP322/3ZVCIiIiIKAiHfA+zMgQMHUFVVhVGjRkn3aTQaDBs2DBs3bgxgy4iIiIgoUEK+B9iZqqoqAEBGRobF/RkZGSgrK3P4OoPBAIPBIN3W6XQAWvNYjEajD1pqSXwPf7wXhQ9uN+QubjPkLm4z5C5/bjPuvEdYB8Ai62RoQRCcJkg/99xzmD17ts39q1evRmxsrNfb58iaNWv89l4UPrjdkLu4zZC7uM2Qu/yxzTQ2Nrr83LAOgDMzMwG09gR36tRJur+6utqmV1ju8ccfx4wZM6TbYlmNUaNG+a0KxJo1azBy5EiOsiWXcbshd3GbIXdxmyF3+XObEa/YuyKsA+CuXbsiMzMTa9aswTnnnAMAaG5uxvr16/H88887fJ1Go4FGo7G5X61W+3WH9/f7UXjgdkPu4jZD7uI2Q+7yxzbjzvJDPgA+deoU9u3bJ90+cOAAduzYgZSUFOTk5OD+++/H3//+d/To0QM9evTA3//+d8TGxmLSpEkBbDURERERBUrIB8Bbt27F8OHDpdti6sKUKVOwYMECPPLII9Dr9bjrrrukiTBWr17t0iwhRERERBR+Qj4ALiwshCAIDh9XKBQoKipCUVGR/xpFREREREErrOsAExERERFZYwBMRERERBGFATARERERRRQGwEREREQUURgAExEREVFEYQBMRERERBEl5MughSNTkxnGw2o0nTThWHkTFACSu2mhO2xASr4WKi1/txARke+Z9GZUlzRI56Fje0+huSza4vyUVhDH8xKFHAbAQcakN2P55L3QHcrA4gUlQEvr/QoVIJiA2HQVCmd1RWqvWNTs1zM4JiKidjPpzagp1SOxswY1+/VoMZgBAD8+V476yubWJ0Xhr3NSOhZ/fPr8FJeuxtj3e6HxhJHnIQoZDICDTE2pHrpDfx1sWk7fL5ha/2+sNuHre/6UHYjsB8cMiImIyBkx6I3tqMbyW/ag4agRiihAaHHwghb7fzdUG7F47O8QWoC4DDXGvsdgmIIfA+Agk5KvRWJ2dGsQLAtyLf4GnAbHYkDMAxEREdnTVGvC0htKbIJeh8Ev4PScJL6u4ejpYFjslMnsF8/zDwUdBsBBRqVVYuxHPfHVR2sx+trhqC83QQEgIUuDL6btRmP1X9GuswPRX0+RH4gYDBMRRTZ5j++ym0rQVNN64rAIepUAzKdvJmRF48LHc6DSKP/KAa7H5p83Y8z1hTj5ZzM2PFOGhmr7QbTYKZOQFY3CojzmClNQYQAchFQxSqg7GxHTQYWENK10/3XLzrIYjCDmADsLjvmrnIiIHPX4ApBuix0lukoDWgxmqDRKm6A1s388oquaEdNBhewLtJi4rE+baRT1lc1YMX0v4jLUGPdJAWKSGXpQ4HErDCEqrRJZAxKk2/K/5cFxQpbG7oGIv8qJiCKLWMVh3cwDaKg2ArAMTmNSonDNhwUWVwfjO0W7vHyVVon0PnEAgIlLTwfDFp0yf2k4asTnk3bh4jndeN6hgGMAHCasg2P5gciVX+VMjyAiCi/yXl85eY+v2CPrTtDriDwYFjtlWgxmKU0CaO2AWTF9L5JyNBi3qIDnGwoYBsBhyt1f5fJcYV6iIiIKbU21JiyZsFPK8xX5q8ND3ikzblGBTSBeV25AdUmDRccNkT/xp1cEEIPh+E7RuG7ZWbh8Xk9c8kZ3xKWrpefIc4WXTNiJplqTg6UREVGwMunNqNxWj6WTSiyC39h0Fa6Y1xMTl/ZBfKdopPfxXwpCTLIKE5f2weXzeiIh63RP87qZB3iuoYBhABxhxF/l2RckYdyiAsRltAbBiqjTz2mqacHnk3bh0MY6HNlWD5Pe7GBpREQULJpqTfhs3E6snL5XSjkAWvN8xy/qjU4DEgKWciCeewqL8qT7Gqpbc4J5nqFA4HXuCCb+KrdXFqex2oRv7t0HABwsR0QUxOwNdBMFW1pbWkEc4jLUUjoEc4IpULilRTh5esSEJX2kHmE5cbDcZ+OYGkFEFExMejOWTiqx6fWVpzwES/ALtJ5zxn1SYHOuEXOCifyFATBJHOVpiZgfTEQUXI6VNKCu3GBxX1yGOuApD844OtesLzrIdAjym+DbMyigxDyta5f0tjtYTswP5kGKiChwxMFu3xcdlO5LyIoOyl5fe+zlBItXG5dOKuH5hXyOATDZZT1YLibl9Cg5MWeLKRFERP4nH+xWX9ks3T+sKC9oe30dSSuIQ1KOxuI+pkOQP4TOXkIBE5OsspsfLM7qw95gIiL/MOnNdie3SMrRIL0gLkCt8pxKq8S4RQVMhyC/YwBMLpHnbMlTItgbTETkP8dKGiyCX3GwWyhXUGA6BAVCaO4tFBDiQUpeP1jE3mAiIt+xl/Mblx7cg93cxXQI8qfQ32PI79gbTETkP/JSZ/Kc3+Fzugb9YDd3OEqH2FBcxo4V8joGwOSRtnqDWS6NiMg77JU6C9Wc37bYS4fQVbAXmLyPATC1i6PeYJZLIyJqH2elzkI559cVaQVxSOzCXmDynfDde8hv5L3B9sqlcRADEZF7HKU9hGKpM0+otEoMm5Un3dZVGFC6uobnEvKa8N6DyK8clUvjIAYiIvdEUtqDI/JBcUoVsL64jB0q5DUMgMmrOMUlEVH7mPRmrC8+KN2OlLQHa+KguGGzcmH+a0gJO1TIWyJnTyK/cVbTkRUiiIicO1bSAF1F5KU92KPSKpE/KoX5wOR1kbc3kd/Yq+nIChFERI5Z9/4mdomstAd7mA9MvsAAmHxGXtORFSKIiJwz6c0oXV1j0fs7dFZuRPb8WmM+MHkb9yryKVaIICJqW1OtCZ+N24n1xWVQ/jW3RaQNenOG+cDkbQyAyS9YIYKIyD6T3oylN5Sg4agRAGA2AcNm5UbcoLe2MB+YvIl7FvkNK0QQEVkS0x7E4BcA4jLUyB+VwuDXDnv5wDWl+sA1iEIW9y7yK1aIICJqJU52IU97iMtQY9wn7Pl1Rp4PHJehRmJnTRuvILLFPYwCwlGFiKU3MCeYiCKDfLILMe1h4tI+iElWBbhlwU2lVWLs+70Ql6FGw1Ejlk/bw/MGuY0BMAWEowoRDUeNzAkmorBnr9wZ0x5cpztskNJG6spZFo3cxz2NAkZeISI2/XSPB3OCiSjcWU92wXJn7knJ17IsGrUL9zYKuJhkFS6e0026zZxgIgpnnOyi/VgWjdqLATAFBeYEE1Ek4GQX3sOyaNQe3OMoKDjLCWZuFxGFA3tVHzjZRfuwLBp5igEwBQ15TrA4YYaY28V0CCIKdfaqPnCyi/aTX0FM7BKNFoOZnSbUJu51FHTECTPkuV0NR434fNIuDo4jopDEqg++I7+CCCiwYvpeDoijNnHPo6Ak5nbJp05urDbxwEZEIYd5v76n0iqh0iihq2jtYeeAOGoL9z4KWiqtEuM+KbAIggEe2IgodDDv139S8rUcEEcuYwBMQU1Mh7h8Xk8kZJ0+sK2beYA5wUQU9Jj36z8cEEfu4B5IQU8cHFdYlCfd11DNEmlEFNyY9+t/HBBHruJeSCEjrSDOIh2CJdKIKJjVlOqZ9+tnHBBHruKeSCHDOieYJdKIKFiZ9GaYDGYkdmntjWTer//YGxDHVAiyxgCYQgpLpBFRsBMHvq2cvheAgCvm9WTer5+l5GulVIi4DDUSO2vaeAVFGu6NFHJYIo2Igpl84JuuohlRGiWDXz9TaZUY+34vxGWo0XDUiOXT9vDcQBa4R1JIYok0IgpG9ga+peRrA9egCKY7bEDDUSMAnhvIFgNgClkskUZEweZYSQMHvgUJ1gUmZ7hXUkhjiTQiChb2en858C1wWBeYnGEATGGBJdKIKJA43XFwYl1gcoR7JoUFlkgjokDhdMfBi3WByZGICICLioqgUCgs/mVmZga6WeRljkqkMR2CiHypplTP6Y6DGOsCkz0Rs3f27t0bR44ckf79/vvvgW4S+YC9EmlMhyAiX0rsrJGOOUk5nO44GLEuMFmLmD1UpVIhMzNT+peWlhboJpGPMB2CiPzFpDdj+bQ9aDhqRFyGGmPf78XgNwixLjBZi5i99M8//0RWVha6du2K6667Dvv37w90k8iHmA5BRL4mDnwT0x8ajhqhO2wIcKvIEeu6wEyDiGyqQDfAHwYNGoQPP/wQPXv2xNGjRzFnzhxccMEF2LVrFzp27GjzfIPBAIPh9EFMp9MBAIxGI4xGo8/bK76HP94rrKmAnBEJiHtHhYbq1ii44agRf3xzDN1GdoAqJrx+/3G7IXdxm/GcqcmM5ZP3QneoGQoVIJiAxOxoJOSqwnp9hvI2k5CrQmJ2NHSHmpHQWQ1DYzP09aqwOxcEG39uM+68h0IQBMGHbQlKDQ0NyM/PxyOPPIIZM2bYPF5UVITZs2fb3L9o0SLExsb6o4nkReZGJU7MS4dZpwKUAmBWQJloQsfp1VDGsjeYiNxnPKxGzXsZ0u3EK08gpncTFOqIO6WGFMGogLFSBd2XKWipVSMqxYiOt1fzewsTjY2NmDRpEurq6pCYmOj0uREZAAPAyJEj0b17d7z99ts2j9nrAc7Ozsbx48fbXKHeYDQasWbNGowcORJqtbrtF1CbTE1m7F9zEj89WyHdF5ehxjWfnRE2v/653ZC7uM14rumkCV9O+RMNR41IzI7G2I96hs2xxJlw2GaO7WrEylv2Sbcvf6870nqzc8tX/LnN6HQ6pKamuhQAR0QKhDWDwYDdu3fjoosusvu4RqOBRmM7QlStVvt1h/f3+4UztRo445I07Jh/VMoBazhqRO3eZmQNSAhw67yL2w25i9uMe0x6M76e/oc08O2qD85ETEJknU5DeZtJPyMBSTka1JUbEJehRkpuHNTqyPr+AsEf24w7yw//n6sAHnroIaxfvx4HDhzAzz//jPHjx0On02HKlCmBbhr5kVgdIjb99IFufdFBHNlWz4FxROSyYyUNHPgWwlgRgoAICYArKipw/fXX44wzzsA111yD6OhobN68Gbm5uYFuGvlZTLIKF8/pJt2ur2zGiul7WSKNiFxi0puxvvigdDuxiwYp+drANYg8wooQFBF9/p9++mmgm0BBRJwbXuzBAU6XSJu4tA9reBKRXWLZM11Fs3Tf0Fm5PGaEIHFiDDENghNjRB7utRRx5HPDx6VzxjgiaptJb8bSSSVYX1wG5V9dR0k5GqQXxAW2YeQRpkEQA2CKSCqtElkDEjBuEWeMI6K21ZTqpatGZhMwbFYuxi0qYO9vCGMaRGTjnksRjTPGEZErEjtrpB/LSTka5I9KYfAb4sQ0CABI7BKNFoOZx/0Iwr2XIp5Kq0T+qBTp5Aa0BsHVJQ0BbBURBQuT3ozl0/ZIZc/Gvt+LwW8YkKfDAQqsmL4XSyex8yNScA8mAkukEZF94sA3lj0LTyqtEiqNErqK1u+UqRCRgwEw0V9YIo2I5BwNfGPZs/AiT4VgRYjIwQCYSEYskSbHnGCiyMSBb5GBFSEiE/diIhmWSCMiEQe+RQ5WhIg83JOJrLBEGhFx4FtkYUWIyMO9mcgBRyXSlkxgEEwUzjjwLfKwIkTkYQBM5IS9EmlNNS34fNIuVoggCkMc+Ba5WBEisjAAJmqDWCItJiVKuq+x2sQeAqIwxIFvkY0VISIH92giF8QkqzBhSR+LnmCgtYeAE2YQhQ8OfItsrAgRObhXE7lIzAm+fF5PJGRFS/dzwgyi8MCBbwSwIkSk4J5N5AaxQkRhUZ50HyfMIAoP8vQHDnyLXEyDiAwMgIk84GjCDA6OIwpd1ukPHPgWmZgGERkYABN5wNGEGeLgOPYGE4UWpj+QHNMgwh/3biIP2ZswQ8R6wUShg3V/yRonxgh/DICJ2kk+OE7eG8x6wUTBj3V/yR5OjBH+GAATeYG8N9hevWCmRBAFJ9b9JUc4MUZ44x5O5EWO6gVzgBxRcGLdX3KGFSHCF/dyIi9zlBLB3mCi4MKBb9QWVoQIX9zTiXzAlQFyp440o3pnAw+mRAHCur/kClaECE8MgIl8yNkAucVjf8cXU/awR5goAEx6M0wGMxK7tF7S5sA3ckSeBsHtJHyoAt0AonAn7w1eMmEnmmpaAABC639SfvCwp/Kg0iiRVhDHy7BEPiRWfqgrNyCxSzSumNeT+x05JFaEqCnVI7GzBjWleqTka7m9hDgGwER+Ig6QW3pDCRqOGqGIOh0EN1ab8M29+wAAcemtuYiNJ4w8yBL5wLGSBin1QVfRjCiNkvsZOaXSKpGSr5V+OCXlaFgtJMQxACbyIzEloqZUj9iOaiy/ZY+UWyZqqDZi8djfIbS0jjoe+x6DYSJvMenNWF98ULqd2IWXtMk18pxxMRc4vU9cgFtFnmIATORnKq1SOmhOXNoH1SUNWF90EPWVzdJz5OkR1sGwrtKAFoMZKo0Syd20qNmvhwJAfI4KzWVqHP5ZB402GsndtNAdNjBwJpKpKdVDV3F6Xxs6K5f7B7lEzAWuKzewJFoYYABMFEBifvC1S3rjyPZ6bHimDA3VlukR8mB40ZW/A/KiEVEAWuR/Z2D1woMAAIUKEEyOA2cGxxSJxLq/DUeNSMrRIL2APXjkGrEkmpjGtnzaHqZBhDAGwERBQKVVIvuCJExcZpseIQ+GYV0xrcXB32gNfgH7gbO94FgBMDCmsMa6v9Re9kqiMQ0iNDEAJgoi1ukRToNhwE4PsIPHrAJnR8GxGBjHpqtQOKsrMvvFM0CgsGGv7m9MMk+D5Dp5GkRil2i0GMww6c08ToYg7vlEQcpeMJzYWYOa/XqHOcCrFq/Duf0HQaONRkKWxrXAWRYci4FxY7UJX9/zJxKyonHh4zksz0YhT173V1dhYD1X8ohYEq26pAEbisuwYvpeVoQIUQyAiUKAPBjOGpBg8Zh422g0IjrXiM6DEqFWt0664ShwdhgcW/Ui11c2S+XZGAxTqGLdX/ImlVYJlUYJXQUrQoQyBsBEYcxZ4GwdHCsAJGRp8MW03Wistp2ZTh4Ms1YxhRLW/SVvY0WI0McAmChCOQqOr1t2FqpLGtBiMOPH58otyrOJWKuYQgXr/pIvsCJE6GMATEQWxNJsAHDtkt4Og2FHtYrHfVLAgUUUNFj3l3yFFSFCG48CROSQGAxnX5CEa5f0xiVvdEdcemt+sSLq9PPkwfCSCTtx6kgzqnc2wKS3rttG5D/ygW8AWPeXvEpMgwDANIgQxG4aInKJq7WKm2pa2CNMAceBb+RrTIMIbfyWiMgtYu5wfKdoTFzaB1ct7IXrl5+FmJTTXcLyHuHPJ+3CkW317A0mv5LX/OXAN/IVe2kQFBp4NCAij8mD4QlL+iAuwzY9orHahBXT9+KzcUyNIP8RpzwGwJq/5DPyNAhuZ6GF1yWJyCtiklV2Z68TcbAc+QunPCZ/ESfGkEpKlupZDSdE8BsiIq+xTo+4fF5PadAcYDtYrqnWtt4wUXvJ6/6KUx4T+YpKq0RKvhbLp+3BF1P2YOmkEl7lCgEMgInIJ8QKEuMWFdhNjWiqaWF+MHkd6/5SIMhzzpkLHBp4/ZGIfMo6NWLZTSVoqmntChbzg5kSQd7Cur8UCJwZLvTwqEBEPudosJyI1SLIG1j3lwJFLIkWl6GWSqLxWBbc2N1CRH4l9ghXlzRg3cwDaKhuHSjH3mBqD9b9pUDjzHChhUcGIvI7e/nBIg6QI0+w7i8FmrwkWmKXaLQYzOwFDmI8OhBRwIi9wdbVIjhAjtzFur8UaGJJtMvn9QSgwIrpe1kRIogxACaigJL3Bstnk5NPoMHeYHKGdX8pWKi0Sqg0SugqWBEi2PEIQURBISZZxQFy5BF5+gPr/lKgyVMhWBEieDEAJqKg4Sglgr3B5Ii9yg9Mf6BAYkWI0MAAmIiCSlsD5NgbTCKx8sPK6XsBCLhiXk+MW1TA9AcKOHsVISi48ChBREGJvcHUFvmUx6z8QMGEaRDBj0cKIgpaLJdGjnDKYwpmTIMIfgyAiSjoOSuXtvQGlhmKRJzymIId0yCCG48WRBQSHJVLazhqROnqGgbBEYRTHlMokKdBcHBm8OFco0QUUsRyaUtvKEHDUSOUKmB9cRm2vlvJKZQjAKc8plAhToxRU6pHYmcNakr1SMnXclsNEvwWiCjkiCkRw2blwvxXCjArREQGTnlMoUSlVSIlX4vl0/bgiyl7ODNcEOFRg4hCkkqrRP6oFIvBcawQEf445TGFGvmPNuYCB4+ICYD/+c9/omvXroiJicGAAQPwww8/BLpJRNROKq0S4z6xXyGCg+PCD6c8plDEkmjBKSKOHJ999hnuv/9+PPnkk9i+fTsuuugiXHLJJSgvLw9004ionRxViGg4akR1SUMAW0beximPKRSxJFpwiogAeO7cubjllltw66234swzz8Srr76K7OxsvP3224FuGhF5gbxCRGz66UFw64sOMic4jDD9gUIVS6IFn7APgJubm7Ft2zaMGjXK4v5Ro0Zh48aNAWoVEflCTLIKF8/pJt2ur2xmTnCYYPoDhTJ5GkRil2i0GMz8YR5gYV8v6Pjx42hpaUFGRobF/RkZGaiqqrL7GoPBAIPh9KU1nU4HADAajTAajb5r7F/E9/DHe1H44HbTqkPPaCRmR0N36PQkCWKFiGGzc5B6ZixUMQycgNDZZkxNZuxfc9Ii/aGmrAFp8bEBblnkCZVtJuiogCs/7IHjJY348e8VWDF9LxKzozH2o55hfzzy5zbjznuEfQAsUigUFrcFQbC5T/Tcc89h9uzZNvevXr0asbH+O+CuWbPGb+9F4YPbDRBzowJRlSrULesIc33rYa6x2oRv7tyPqBQjOt5eDYVaCHArg0cwbzOCUYET76ajpUYNKAXArEBUihH/27ceijJ+h4ESzNtMMDMeVqO+orVDTneoGV99tBbqzpHxY8If20xjY6PLzw37ADg1NRVRUVE2vb3V1dU2vcKixx9/HDNmzJBu63Q6ZGdnY9SoUUhMTPRpe4HWXzBr1qzByJEjoVar234BEbjd2NN0vQlfTvlTyr0DgJYaNQZkX4TM/vEBbFlwCIVt5tiuRqys2dd6w6zAkCe7oNvIDmHfaxasQmGbCWamJjOWr94L3aFmxKWrMPra4YjpEN6hmD+3GfGKvSvCe60DiI6OxoABA7BmzRpcffXV0v1r1qzB2LFj7b5Go9FAo7EtU6JWq/26w/v7/Sg8cLs5TZ2mxsSlfVBd0oD1RQdRX9maFrGh6FDrlMqcNQ5AcG8zKblx0uj5pBwNzrgkjbm/QSCYt5lgplYDV31wpjST5dfTSzFuUUFEbNP+2GbcWX74r3EAM2bMwPz58/H+++9j9+7deOCBB1BeXo477rgj0E0jIh8TK0QUFuVJ9zVUs05wKODANwpHrAgRHCKi+2PixIk4ceIEiouLceTIEfTp0wdff/01cnNzA900IvKTtILTPYlA60Cq0tU1yB+VwqAqSNmr+8teewp1YkWIunIDJ8YIoIg56t911104ePAgDAYDtm3bhqFDhwa6SUTkR9azxilVwPriMpZIC1ImvRkmgxmJXVqDA9b9pXDBiTGCQ8QEwERE4qxxw2blwvxXzCuWSOOEGcHDpDdj6aQSrJy+F4CAK+b1jJg8SYoMTIMIPB5NiCiiqLRK5I9KkXqCgdYSaSum78XSScwLDgbHShqk1AddRTOiNEoGvxRWODFG4PGIQkQRxzodQlRXbkB1SUOAWkVAa+/v+uKD0u3ELkx9oPCj0ioxblEBLp/XE4CCP8ADgAEwEUUkMR3i8nk9kZAVLd2/vugg0yECqKZUD13F6Vn8hs7KZe8vhSWVVgmVRgldRevVDqZC+BePKkQUseyVSKuvbGZvTAAldtZIPfNJORqkF8QFuEVEviNPhWBFCP9iAExEES+tIE46CYmYDuF/rPtLkYYVIQKHRxYiinjyfDx5OsS6mQdYIs2P7NX9JQp3rAgRGAyAiYjAGeMCjXV/KVKxIkRgMAAmIpIRZ4wTiTPG8YTkO6z7S5GMFSECg0cXIiIZzhjnf/LUB9b9pUjEihD+xyMMEZEVRzPGMR3CN6wrPzD1gSIRK0L4FwNgIiI77M0Yx3QI72PlB6JWrAjhXzzKEBE5wHQI3zLpzShdXcPKD0R/YUUI/2EATETkBNMhfEMc+La+uAxKVet9TH+gSMeKEP7DAJiIqA2O0iE4UYbn5APfzCZg2KxcVn6giMeKEP7DIw0RkQvEdIjYdJV03/qigziyrZ4nJw9YD3zLH5XC4JcIrAjhLzzaEBG5KCZZhYvndJNu11c2s4fGAxz4RuQcK0L4Ho84RERuSCuIk05MorpyA9Mh3MApj4mcY0UI32MATETkBnmOXkJWtHT/huIynqBcxLq/RG1jRQjfYgBMROQmlVaJrAEJKCzKk+7TVRhYI9gFTH8gcg3TIHyLRx0iIg/J0yFYI7htrPtL5DqmQfiWqu2n2CotLcV3332HjRs3oqKiAsePH0dsbCzS0tJw1llnYdiwYRg6dCiio6PbXhgRUYgS0yFKV9dgfXEZgNM1gicu7cOeTRmx7m9duQFKVWvpM6Y/EDlnnQZRurqGFVO8xOUAWBAELF68GO+88w5++ukn6T5rX375Jf7+978jOTkZU6dOxd13342uXbt6r8VEREFErBG89d1K6UQl1gjOGpAQ4NYFD3t1f3kiJ3JOTIMQfziuLy7DjgVVrJntBS6tvVWrVuHss8/GjTfeiD/++AO33nor3nvvPfz666+oqqpCc3Mz6urqcODAAaxatQpFRUU488wz8corr+DMM8/EjBkzUFtb6+vPQkQUEKwR3DbW/SVyn3iVST4TJQfEeYdLPcCXXnophg0bhhUrVmDMmDGIioqyeU5CQgISEhKQm5uLUaNG4amnnkJ5eTnmz5+PN954Ax06dMCsWbO8/gGIiIKBWCN4xfS9AE7XCE7K0UR8bw0HvhF5TrzKtGNBFerKDRwQ5yUuHYG+++47rFu3Dpdddpnd4NeRnJwcFBcX4+DBgxg7dqzHjSQiCgWsEWyLA9+I2o8D4rzPpQC4sLCwXW+SlJSEvn37tmsZRETBjjWCLYkD39YXl0H51/VGDnwj8gzrAnuXy9eg7r//fuzcudOXbSEiCnmsEXyavYFvkZ4OQuQpeV3gxC7RaDGYI+6Y4k0uH4Vef/119O3bF4MGDcK8efOg0+l82S4iopDGGsEc+EbkTfIrTIACK6bvxdJJJQyCPeTykei1117D2WefjS1btuDOO+9EVlYWpk6dih9++MGX7SMiCkn2Rm+LNYIj4YTFgW9E3qfSKqHSKKGraL2yEuljDNrD5aPRvffei+3bt2P79u246667EBMTgw8//BCFhYXo2bMn/vGPf+DIkSO+bCsRUUgRR2+LvaBAaxAcCekQ8vQHDnwj8p6UfC0Su3CMQXu5/XO8b9++eOONN3DkyBF8+umnGDlyJPbv348nnngCubm5uPLKK7F8+XK0tLT4or1ERCFFrBEsBsFiOkQ4X7o06c0wGcxI7NKaAsKBb0Teo9IqMWxWnnRbV8EBcZ7w+HqUWq3GhAkTsGrVKpSVlaG4uBg5OTlYuXIlrrnmGnTu3BmPPPKIN9tKRBSSYpJVmLi0j00x+3C8dClWflg5fS8AAVfM68mBb0ReJh9jwLrAnvHKEalz586YOXMm9u3bh++//x4XXHABqqur8fLLL3tj8UREIU9Mh5Bfulw380DYDYo7VtIgpT7oKpoRpVEy+CXyMtYFbj+vHZVOnTqF9957D0888QQ2btwIAIiLi/PW4omIQp71pcuG6vAaFGfSm7G++KB0O7ELUx+IfMW6LnAkjC3wpnYHwOvXr8fUqVPRqVMnTJ8+HRs3bsSgQYPwr3/9C5WVld5oIxFR2EgriAvbQXE1pXroKpql20Nn5bL3l8hH5HWBI2Fsgbd5dGSqqKjAnDlz0L17d4wYMQIffvghYmNj8cADD2DXrl3YuHEjbrnlFsTHx3u7vUREIS2cB8VZ1/1NL+BVQCJfsVdqMVzHFviCywFwc3MzPvvsM4wePRpdu3bFrFmzUFZWhjFjxuDzzz/H4cOH8dJLL+HMM8/0ZXuJiEJeOA6KY91fIv+zN7aAZdFco3L1iZ06dcLJkychCALy8/Nx8803Y+rUqcjKyvJl+4hCkklvRk2pHomdNajZr4cCQHI3LWr269FiMEOlUUq3XX2srefF56jQXKbG4Z910GijvbZ83WEDUvK1DGa8TDxxbX//iJQ2sL7oIAqL8pBWEBdS69ukN6N0dY1N3d+YZJdPMUTkIXFswYrpewGcnnqdMy865/LRSa/XY9KkSbjllltQWFjowyYRBSeT3ozqkgaHQaP497HdDdjwTBkaqo1QRAGCWBI7CoC8PLb8tquPtfm8DKxeeNBry1eoAMHUWmZn7Hu9oKs0uB3Ah1ow50/WJ676ymasmL4XSTmakCkdJpY9qys3QKkCzCbW/SXyN7Esmrgfri8uw44FVSFzHAkElwPgI0eOICkpyZdtIQooMcC1F8QlZGnwxbTdaKz+63q1iwGkIA86reeG8eQxbyzDjeULsil8F135OyC/quZigJ2QFY0LH8+xWKeOguhI7G2Wn7hEYjpE1oCEALbMNfIZ38wmYNisXPY8EfmZmA9curoG64vLALQeR2pK9Ujvw1x8e1wOgO0Fv1VVVVi2bBn27NmDxsZGzJ8/HwBw7NgxHDhwAGeddRa0WvYCUHCx15PbYjDjx+fKUV95egS70wDP1QBVidNBo196gH24fOuUMhcD7PrKZnxz7742ly/2Nsemq1A4qytSe8U6TdMIl95l8cRVXdKA9UUHpW1wQ3EZxn8a/L034sC3hqNGJOVoGPwSBYiYVrVjQRXqyg2cIKMNHido/fOf/8SDDz4Ig6H1l79CoZAC4OrqagwePBjvvPMObrvtNu+0lMhD8oDXaU+uNWcBngsBZFx660AgXaXBbznAqxavw7n9B3ktBzghS4Plt7QObLJI53C2DpytVyeBstjb3Fhtwtf3/OmVdRwqAbJKq0TWgAQUFlnm8QV7LzAHvhEFF3GCjKU3lEgTZDANwj6PAuAVK1bgnnvuwcCBAzFr1ix88803eOedd6THe/fujbPPPhtffPEFA2DyK+vBZzY9u856cq15qXcyvtPp0bnWwYz8tquPOXqe0WhEdK4RnQclQq1We235E5f2sVmnrgbwba7/dvayN1RbpWZYLcPV9ItgCZTTCuKQ2CU6JAbFceAbUXCyniAj2H9IB4pHR6oXX3wROTk5WLduHeLi4rBt2zab55x11ln44Ycf2t1AImfkAa/DwWdyTnpyxWAJgEv5qa4GkKFOpVVKOWSeBPDXLultN+XEW3nWFqkZVt+vq+kXbQXK/spNDpVBcRz4RhS8UvK1Fj+kQyWdyt88CoB37NiByZMnO53quHPnzjh69KjHDSOyxzqdwdHlebvBL5z35NrrZZMHdezZ8ox4eV/kLIi+btlZ3q20IedhnrI7lTC8ESiHwqC4YyUNHPhGFKRYFs01Hp3RzWazdInVkWPHjkGjYfI1tY+r+bs2Aa9s8Jl1756znlwKLGfBsvzv7AuSMHFZH6e1lgG4nn4h52ElDG8N4nM0KC5Y0iFMejPWFx+Ubid28e7AN2fVWFhFhMg19sqibX23EuM+KWBnzl88WgtnnHEGfvzxR4ePm0wmrF+/HmeddZbHDaPIJT8Bupy/Kwt4rQdGWQcM3PnDg6PUDPnfrqRfuJWn7KQShi8G8Q1+MBurHywFcDodIjZNhcKnWwNsfwV88h+iLc2CdGkVAIbOypXe35Xg1a3vwsm6s77tac3qQP+gIPIFe2XRGo4asfSGEkxc2ofbPDwMgG+44QY89NBDmDNnDmbOnGnxWEtLCx566CHs378fjz76qFcaSeFNftIEYHsCFFn1zNk74TkafEaRydX0C2eBsseVMLwwiM/eZPWNx1oDbEfbvzvVRsTZA6u2n0JajwTXe9L/EpumRmKWBpXb6t0LXl3tjXe2Hq1ue1qz2ln+N4NjCmViWbSt71ZKg+IajhqZDvEXhSAIgrsvMhqNGDVqFDZs2IDu3btDo9Fg165dGDduHLZu3YqDBw9i1KhR+Oabb6BQKHzRbr/S6XRISkpCXV0dEhMTff5+RqMRX3/9NS699NI2U01ClcNeXifsXWLmJc/TImG7CRR71UW8NojPG3xdb9oZX3weR8t357O1971gPzgOpqohgcDjTOhpqjVJZdHkg1b9NbDWn9uMO/GaRz3AarUa//3vfzF79my88847qK2tBQB8/vnnSExMxKOPPorZs2eHRfBL3uNJ0NtW/i7TGcgfXK2E4fVBfPLbCgDy7gr5bSeVMLwy46AzLpYSdHfmQMB+NRZnP0A86ql38lkcDY6010b+GKdgFZOswsSlfWxmiQumgbWB4FEPsJwgCPjjjz9QU1ODxMREnHnmmYiKimr7hSGEPcCecTqAzQl50BvJPS3uCpftJlJY9yq7EuD95+YS6I+1RmGx6VEwGxVoqjW5HkR72AOckBWNCx7KRtWv9fh1YbXlB3EzeG3rc7Znn3elp96tgZIuaisdK5zwOBO6THozPr9ul5TDn5AV7ZeBtWHVAyynUCjQq1ev9i6GwoTLA9hkrE+a4XjSILLmyiA+69t/ezZfKm3UWN26Q7U3B3jV4nU4//zBDnOAxWUsn7bHou6vJ6UEXf2cnvKkZrWj/G/A9eDYUf5xWwNyifwpVOqM+wuvH1O7ib0usR3Vjnt5rU4c7OUlcp+9GsENR43QVRo8mvVPnD0w85x4qNUqh887sq3ead3fUL6M6mygpKPg2OlgP1k6ivUgx7ZSuoh8LRTqjPuLSwHw2WefjaKiIlxzzTVuv0FlZSX+/ve/Izs7m1UhwoSrk1HIWQ9gy+wXz4M+kZsCUSPY13V/g5mj4FgMjF2qFCILiOU5xRzUS4Hg6BiybuYBjFsUWTWCXfqkOTk5GD9+PLp27YrJkydj/Pjx6NOnj8Pnnzx5Et9++y0+/vhjrFq1CklJSfj444+91mjyP1dSG6yDX/Z2EHmfGJQVFtleyozLUHu10L1Jb0bp6hqHdX8jlXVgDAATl/Zxa1p267rR1nnEjSeMPF6ST9g7hjRUG/H5pF24eE63iLkq69JRcuXKlfjuu+/w1FNPobi4GM888wzi4+PRt29fZGRkIDk5GXq9HjU1Nfjzzz9RWtpauD0pKQkPPvggHnvsMSQkRFbXeqhzeQCb7MAuHugd9fJG0i9LIl9zlA7hrUL3Jr0ZSyeVWOT9JuVokF4Q196mhyV5/rG9mQrbGhchzyNePPZ3i2Mpe4fJF9IK4hCXoZZqBDdWm3zyQzpYufzpRowYgREjRuD333/HggUL8N1332Hjxo0wmy2nRurYsSPGjh2Lq666ChMmTEBMTIzXG02+4ckANvZaEAWG/FLmupkH0FDt3UL3x0oanOb9knP2BuTJc4pdmdrdUe8wB9WRN6i0Soz7pECqESxqOBoZvcFuh/dnnXUWXn75ZQBAQ0MDKisrceLECWi1WqSlpSErK8vrjSTf8KSXF3Ce2sDZ14j8R7yUOW5RgUWh+/XFZdj6bqXHvThNtSasnblfuh1Jeb++ZJ06Ia8b7SyPmFUmyFfEGsHWP6QjoTe4XZ8oLi4OPXr0QI8ePbzVHq/Ly8tDWVmZxX2PPvoo/vGPfwSoRYHjdMphF3p5mdpAFJzsFbpvOGrEkgk7MWFJH7f2UZPejKU3lFj8GGber29YB8RiHrFNRR1WmSAfsvdDWuTpcSQUhNencaC4uBi33XabdDs+Pj6ArfE9ec+u09I9chzARhTSVFol8kelYOu7ldIJrKmmxa1LmeKgN/kJMC5DzbxfP5GnTbjaO+xOlQlO5UzOOOoNFo8jw57KC6vSpRERACckJCAzMzPQzfAqR0Eu4NnMRuzlJQp9Yk7fkgk70VTTuuPLL2U6y9NvqjVZpFGY/8o5HfdJ5BXIDwaOeoc9rTLh6ox94RLckGfkvcHWxxHxx1W4TAUeEVHN888/j2eeeQbZ2dm49tpr8fDDDyM6OnhzVZtOmqDfocXJ3k04suUEFIIC2YOTUL75JEyNLVCqlChZcgynqv7qpVHCohfAgpPgNz5TjYIJaYhSK5E9OAmHt+kQl6pGVLQCpib7Aban05u297FgWUYwLz8+R4XmMjUO/6yDRhsdcu0PlzYGw/KHPpmLDc+Uo+nk6TSGhqNGLL7ydwhmIDpJiXOmZiLrgng0/KzF77XVKFl8HI3HW59vNgFnT0lH5tnxqN2vD8l1EMzLb88yACBKo8SQR7PReNyIrAGJKN98EuZmwfl5QXYukPcUWz9XPC+YTWaotSrp3COehw7+dAINJbHS+cnU2GL3eeL5ypPHgmUZkb78guvS8PuH1TCesgwwrLcf8UdYdHwU/vZiNxz8vhYQgO5jOmLff0/AbDajJSsKwUYhCIIQ6Eb40iuvvIL+/fsjOTkZ//vf//D4449j7NixmD9/vsPXGAwGGAynSwvpdDpkZ2fj+PHjbc4t3V5NJ0349PIS6de7T8kPkNY9xfLbrj7mjWX4evmh0EZPl299wgu19odTG4Np+d4Q6usgGJfvizY66wwhCigBV/27O5KzfZtOpdPpkJqairq6ujbjtZAMgIuKijB79mynz9myZQsGDhxoc//SpUsxfvx4HD9+HB07dnRr+YsWLUJsbKxnjXaRfocWui/tt4uIiIgoFMVdVIf44fU+fY/GxkZMmjQpfAPg48eP4/jx406fk5eXZ7cG8eHDh9GlSxds3rwZgwYNsvvakOsBVgCQf4uOenZDoVfE18sPhTZ6unz2AHP5bT3PVeG8DoJl+cF0rLA+hxB5XfD1AIdkDnBqaipSU1M9eu327dsBAJ06dXL4HI1GA41GY3O/Wq2GWq326H1dpU5T47qVBfjqnz/g4hsG48iWBru5Ol2HJ0u1H8MlLy6Y8+5CYfnxOSqsWrwO5/YfxBxgLt/h847tbsCJPxsRpVYi87xYrHl/E3r37oP8EaluHVNCeR0EevnB3MaELA32f1/jMC/04E8nUFJSgpHTzseRLQ1Bm/8aDDm0kbT8Az/UQH+sBd3+lox9/z1hkwN8PGsXkrP7+j6GcmP57e4BPnToECorKy16TOWGDh3ansW3y6ZNm7B582YMHz4cSUlJ2LJlCx544AEMHDgQy5cvd3k5Op0OSUlJLv2i8Aaj0Yivv/4al156qc83Fgof3G7IXdxmyF3cZshd/txm3InXPO4BXrFiBR5++GH8+eefTp/X0uLutTfv0Wg0+OyzzzB79mwYDAbk5ubitttuwyOPPBKwNhERERFRYHkUAH///fe4+uqrkZmZiXvuuQdvvPEGhg0bhl69euHHH3/Erl27cPnll2PAgAHebq9b+vfvj82bNwe0DUREREQUXDyqWPyPf/wD8fHx2LZtG1577TUAwPDhw/H222/jt99+w7PPPou1a9di7NixXm0sEREREVF7eRQAb9myBVdddRUyMjKk+8zm1iGlCoUCjz/+OM455xzMmjXLO60kIiIiIvISjwLgxsZGdO7cWbqt0Wig0+ksnnP++efjp59+al/riIiIiIi8zKMAODMzE8eOHZNud+7cGbt27bJ4zokTJwI6AI6IiIiIyB6PAuC+ffti586d0u3hw4dj3bp1+PTTT9HQ0ID//ve/+Oyzz3D22Wd7raFERERERN7gUQB85ZVXYseOHSgrKwMAPPHEE4iPj8cNN9yAxMREXHrppWhpacGcOXO82lgiIiIiovbyqAzatGnTMG3aNOl2165dsWXLFsydOxf79+9Hbm4u7rjjDvTr189b7SQiIiIi8oo2A+Dff/8dffr0gUKhcPq8/Px8vPXWW15rGBERERGRL7SZArFs2TKMGzfO4VTHREREREShpM0e4BEjRuD111/HxRdfjBUrViA5ORkbNmxw+Q2GDh3argYSEREREXlTmwHwRRddhG3btuHaa6/FkCFDUFJSgsLCwjZTIkQshUZEREREwcSlQXB5eXn46aef8MADDwAAZs2a5XIATEREREQUTFyuAhEdHS0NcisqKvJVe4iIiIiIfMqjOsBERERERKGKATARERERRRSPJsLo1q1bm89RKpVITEzEGWecgauvvhoTJkzw5K2IiIiIiLzKowDYbDbDZDKhsrKydSEqFVJTU3H8+HGYTCYAQFZWFqqrq7Fjxw4sWbIE8+fPx8qVKxEdHe291hMRERERucmjFIgdO3agU6dO+Nvf/oZNmzbBYDCgsrISBoMBGzduxMUXX4ysrCyUl5dj7969uPTSS7F27Vq8/PLL3m4/EREREZFbPAqAH330URgMBqxatQqDBg2SSqIpFAqcf/75WLVqFZqamvDYY4+he/fu+Pe//43c3Fx8+umnXm08EREREZG7PAqAly9fjksvvRRKpf2XR0VF4dJLL8Xy5csBADExMRgxYgT27dvneUuJiIiIiLzAoxxgnU4HnU7n9Dl1dXWoq6uTbqempnryVkRE5CUmvRnVJQ1oMZih0igRn6NCc5kaVdtPodNZSVBpWRiIiOwz6c2oKdUjsbMGNfv10nEkuZsWNfv1UAB2/25pMUEwBt/kaR4FwAUFBfjss8/w6KOPIjc31+bxgwcP4rPPPkNBQYF0X3l5OdLS0jxvKREReUQMfNcXHUR9ZfPpB6IAtGTgm4X7kZAVjcKiPKQVxDEQJiLpuKEAkJClwfJb9qDhqBGKKEBokT0xCkCL87+jktNhGm2GWu2nxrvAowD4iSeewPjx49G3b1/cdtttGDx4MNLS0nDs2DFs3LgR8+fPR319PZ544gkAQHNzM1avXo1Ro0Z5tfFERORcU60JS28oQcNRo+2DspNYfWUzVkzfi7gMNcZ9UoCYZI9OD0QUwsRe3tiOanwxbTcaq1sre8mDWYvgF7A4jjj6u6VWjdrSJmj7abzfaA95dIS75pprMH/+fNx///14+eWXpUFwACAIAuLj4/Huu+/immuuAQA0NjbivffeQ+/evb3TaiIickrsvVk38wAaqu0Ev4Blb81fGo4a8fmkXbh4Tjf2BhNFAHnQ67CXV/63EoBZdtulHmAjkvNjfNJ+T3n8E3/atGkYN24cli9fjl9//RU6nQ6JiYno27cvxo4di6SkJOm5HTp0wNixY73SYCIics5Rr29sugrDnsoDACkHeNXidTi3/yD89OxhKVBurDZhxfS9SMrRYNyiAgbBRGFKfqyQB73WvbwKFSCYgLgMNca+1wu6SoNbOcDbyn+AKia4jiMeBcDFxcXo1q0bbrzxRtx0003ebhMREXmoqdaEJRN2oqnG8gxmL7XBaDQiOteIzoMSMW5Rkk3QXFduQHVJA7IGJPit/UTkW/Ie32U3lUjHCnnQKwbDsekqFM7qitResdAdNiAlXwuVVon4TpaTmsmPEdZ/G41GKI4Ivv1QHvAoAJ4zZw4eeOABb7eFiIg8JE95kAe/sekql9IZYpJVmLi0j81guQ3FZRj/KXuBicKBox5f4HTQK/byNp4wSgEvgLAbF+DRp8nNzUVNTY2320JERB4w6c1YOqkEdeUGi/tjUqIwflFvl09cKq0SWQMSUFiUhxXT9wIAdBXsBSYKZfLyhxueKZNSneTBb0xKFK75sMAi6LXu5Q03HgXA119/PRYsWIC6ujqLXF8iIvK/YyUNNsFve6o5pBXEIbFLNHQV7AUmCkXyoPfH58otyx/+Rd7jKx4rwj3olfMoAJ45cyZ++eUXjBgxAsXFxTj33HORnp7u7bYREZET8vq+Im/U81VplRg2y7IXuHR1DfJHpTAIJgpC1jV7LUqY2eEozSGSeBQAa7VaAK0lz6688kqHz1MoFDCZHH8BRETkGUdpD8OK8tDJC+kKaQVxSMrRoK7cAKUKWF9chh0LqlgVgiiA7M3GBsCyl9dOeUOR9Q/kSOrxteZRAHzRRRdZ1P4lIiL/spf2kJSjQXpBnFeWr9IqMW5RAUpX12B9cRkAVoUg8jV5T65URuyvcmNOZ2OTs7o/ISsaFz6eA5VGydreMh4FwN9//72Xm0FERK7wVdqDPSqtEvmjUrD9/SPMByayIs+zdVQP153HbPJ1rXtync3GJiPW7BVLmGX2i+f+akd41bQIE6YmM4yH1Wg6acKx8ia7Owx/xRFFHl+nPdjDfODI0lZQd2zvKTSXRUvnJ28Ffw4nUQjgMtp6zGZwmaMZ0dx5TM7ZlMNWs7HJe3mTu2ktavaSfe0KgJubm/Htt99iz549aGhowFNPPQUAaGpqgk6nQ2pqKpRKrnx3mPRmLJ+8F7pDGVi8oMThDmO9sTM4Jgp/vk57cIT5wOHBXv6o0x5IwEHglo7FH5d4FuC5+liwLKOtx+QcTR3szmNyVu/lbDY26/O+P2r2Wm9PzmaCE4zBlzbr8Rr68ssvMX36dBw7dgyCIEChUEgB8G+//YbBgwfjo48+wqRJk7zW2EhQU6qH7tBfBx8nO0x9ZTO+uXdf6w0XgmMFwMCYKIQ11ZqwduZ+6bav0h7scZQPXFOqR3of3wbf5DnrygAO80c9Ceo8DfBcfSxYltHWY3JeCLCddW5Z9+z6cwCbdW7ysd0NUk1hi+3JweeMSk6HabQZarXfmtwmjwLgn376CePHj0enTp3w2muvYfPmzVi8eLH0+HnnnYfu3btj6dKlDIDdlJKvRWJ2dGsQ7MmvTjgOjsUdCwB7iolCiElvxtIbSizKGvky7cEeMR94x4Iq1JUbEJehRmJnjd/en9rmtBSWs/xRT4I6X/euBssynDxmfU71RoqF9XnZesCpv2Zjk6fCAM6rTFhsTw7+bqlVo7a0Cdp+wXPM8Hgq5A4dOmDr1q1IS0vDiRMnbJ4zYMAA/O9//2t3AyONSqvE2I964quP1mL0tcNRX26y2WEA10ueyO+3CIzBnCGiUGDSm1G6ugYNR43SfXEZap+nPdij0iox9v1e0lSqy6ftYRpEgNhLZ3B6XnCSP+pOUHdsbz02/7wZY64vRH25KWJzgB1dVZUHrNbBq6uPBYork2cAsI035NuTwx5gI5LzY7zd5HbxKADevHkzxo8fj7S0NIfPyc7OxpdffulxwyKZKkYJdWcjYjqokJCmle6X7yDXLultt1QK4HpwLA+IOWqUKPjIB70pVYDZdHrWpkDtn7rDBikYZ1k0/5EHvA4vP8tZ3ecsf9SdoC6zfzyiq5ptzk/Wz/M0+AvGZbT1WKiTV5ZxGPTKyeKKuHQ1xr7fuj05ywHeVv4DVDHBFVN4FAAbDIY2p0Cuq6vjADgfUmmVDndIR8Gxs190wl9XyRqrTfj6nj/ZO0wUBOSD3swmYNis3IBXX0jJ13KaZD9wNX/XUTks606N1F6xTvNHwy2oo7aZ9GYc2V4v/Zhypq2xRfLtyTo2MRqNUBwRfPUxPOZRANytWzds3brV6XM2bdqEXr16edQoah9HwbEYGLvSU8zeYaLAsVfrN7GLJuDBL8CyaL7icf6u7PJzWx0X/sofpeDmSo9vW2OGwuEHk0d7w7hx4zBnzhx8+OGHuOmmm2wef+mll7Bz50688MIL7W4geY91YCzvKXY2dzh7h4n8x1Gt36GzcoNmH2NZNO9wmHPpYv6u9eXnQJTCotDSVGuScvitxaarMOypvIgZJO/R3vHwww9j6dKluPnmm/Hxxx+jqakJAPDII49g06ZN2LhxI/r164d77rnHq40l77IOiK9bdpZLB2N7vcNiXlnjCSODYaJ2CFStX3dwmmTPOO3llXMhf9fR5Wcie8Rtb93MA3bTHeLS1Ri3qCCifjR59Enj4+Pxww8/4J577sGSJUvQ0tK6t7700ktQKBSYMGEC/vnPf0KjCZ5yF9Q2eUDsbu9ww1EjFo/9HUILUyWIPBXIWr/u4jTJzrldpUHG3fxdImccXVWKtB5fax6H+snJyfjkk0/w+uuvY8uWLaipqUFiYiLOPfdcZGRkeLONFACe9A6LuWlMlSByXzDU+nUX84FPa2+VBubvkq/Yu6okVpOJ5O2q3Z+8Y8eOGDNmjDfaQkHMWe+wo9HJHEhH5JpgqvXrrkjMB5bn7qo0Sq9UabA+JkZyYELeYW8wbTBfVfI37mHkNuve4YlL+6CmVI/YjmqPBtJxR6RIFoy1ft0RzvnA1tO/Oiwp6aUqDUTe4ijtIdivKvmTxwFwSUkJ3nzzTWzZsgUnT56U8oDlFAoFSktL29VACn4qrRLpfVp7qjwZSMcpmimSBWOtX3fZywdeN/OA0woFwcJRkAt4NuMmqzRQMAiFwbSB5tHet379eowZMwYGgwEqlQoZGRlQqWwXJQjBV/iYfMuTgXTOpmgO1pMmUXu5WuvX3mAqb03/Gp+jQnOZGlXbTyGtR4LLy7DXc2mdD9xQbcSiK3932PtpvXxv9oZapyg4WgeAh0GuFVZpoGASSoNpA8mjAPixxx6DyWTC/PnzMWXKFERFRXm7XRQGXB5IZ8Ve7zAvGVKosx4ktb64DI3HLMsRDZ7RxeXcUotgzdHfLj2WgW8W7nd5GfYqFMiDy7gM9elcZvPpRVj80LVavqvT9Loa3DtLUfA0yJW/zvqqlfWxiQEvBUooDqYNFI8C4F9//RXXXXcdpk2b5u32UBiz1zvsTjDMgXQUjFzpoXUayMr896FSi6DRaW6po4kSXH2eh8uwzue3DgyHPJKNn54/5FYFBHk5RXmvMQDPg3tH7+dikAu0Pf2rHNMZKNBCeTBtIHi0xyYkJCA9Pd3bbaEI4igYBuAwIOaMdORP1oGtvR5IT3poHQW/ACwDP8AyWFPCtcDQ7R7gdi7DKrd/9YP7EZuuwqVv9pB6h9usgSu/7WwduBPcyzlpv7PUjHCc/pXCU6gPpg0EjwLgyy67DD/88IO320IRytEUzZ7MSOeocDyRNXuDn8S/HdZxdRK4udxDqwDgaHhEO1MDPMkBXrV4Hc4/f7DLOcA2+fx2el4bq01Y/8xBTFzax+6YAG/8kHD2mL0UBUefjUEuhYNwGEzrbx4FwC+88AKGDBmC++67D//4xz8QGxvr7XZRBGvPjHRi73Bbg1IofDkLbF0a/GQVZAmu9kA66aEVt8eY5Cgo1UBjdesDsWkqXPXBmdL22dbgMOvcUnmw5uhvZ48ZjUZE5xqReU481GqVy8sQ8/mt2yz+aABa0xnkpdCsf+haL18sp+jKYL+2fgTY28+dvTdRKDPpzVhffFC6bW8wLdnyKACeMGEC4uLi8NZbb2HBggXo0aMHkpKSbJ6nUCiwdu3adjeSIpcnM9IBjnMK2xq8QsHL1Vxbh72TnuaIygNbD3to5T2cciOe7Yb4TtEWga11cBaMuaWOgtlxiwrw+aRd0vp3Z2pkeTlFVwP4th4jCndi3q9YfhAAhs7K5fnMBR4dWb///nvp71OnTmH79u12n6dQKDxqFJEjLvcOO8gptC655iyAYW+xf7R7EJmL+ame5Iha13H1tIf2yLZ6m+A3HGtyxiSrcPGcbpwamcgP7OX9huNxxVc8CoDNZutRCkT+56h32J1R985Gn/uzbmm4cDZwzGeDyJwFuW4OfnJ0Kb09PbTWlyfDvSZnJE6NTBQIzPttn+C7tkbkIUdTNMt7Fp3WB7X6Xedu3VJ3ByAFSwDkaCYsd/MvXRo45o1BZC7k2jqqUevq4CdvXUq3d3ky3GtyhvPUyETBgnm/7ccAmMKWvZxCeYWJNnsg5VytW+pG+ai2epjdHeEvzup1+GcdNNpol17nVnkqNx5zOHCsnYPIXKmGYN0zH6gc0aZaE5beUIKGo8aIuzxpb2pkd/KBici5mlI9837byeUAuH///rjjjjswffp06b7//ve/+O9//4u5c+faPH/27Nl45plnYDLZjtj3pmeffRZfffUVduzYgejoaJw8edLmOeXl5bj77rvx3XffQavVYtKkSXjppZcQHc3ZeiKNdS8xYL+nGGhjilRHPcduXJ531sPseX3WDKxeeNC91zlqbxvt92jgWDvKfLlaDSEYBo2JszGJeb+ReHnSempkXYUBNaV66UcpEXkusbNGmnUxUn5Ye5vLZ4odO3agqqrK4r7NmzfjtddesxsAA4AgOCp26T3Nzc249tprMXjwYLz33ns2j7e0tOCyyy5DWloafvzxR5w4cQJTpkyBIAh44403fN4+Cn6ORp97VLfUGzNVWd/2NAh19TE5L/QAOxo41t4yX8EQ2LrC0WxMkRT8iuT5wIldotFiMMOkN0fceiDyJpPejOXTWs8/cRmtx1vuU+4LjTOKE7NnzwYALFiwwO7jq1evRklJCQ4dOoSsrCwAwMsvv4ypU6fi2WefRWJior+aSiHG3bql7uTQAm70MHt7li+r2+6mYrhag9XRwLFQKPPlKc7GZEnMB64uacCG4jKsmL4XSTkaDogj8pD4A1sc/NZw1AjdYUNYHUf9JezX2KZNm9CnTx8p+AWA0aNHw2AwYNu2bRg+fHgAW0ehzFHPsat1Sp31MHuaA7xq8Tqc23+QyznA9iYNYA1Wz3FUti2VVgmVRgldRet64YA4Is84KnuWkq8NdNNCUtgHwFVVVcjIyLC4Lzk5GdHR0TYpHSKDwQCDwSDd1ul0AFpnTTIajXZf403ie/jjvSiAVEDa2TF/3RBkf1vfdvS35W1xVq/0/lqo1WqXXyegBUajsyK55Iqmkyasnblfup3QJRo5IxIgqIJ3/frrWJOQq0JCZzXqD7e+z/rig7jq455QxUTuD4NQxfNT4Bz7o9HiB/aQJ7ug28gOQX2MAfy7zbjzHkEZABcVFUmpDY5s2bIFAwcOdGl59ibkEATB4UQdzz33nN33X716tV+nfV6zZo3f3ovCB7cb/xOMChx/KwNm3elDquriQ1j93X4nrwoe/thmVH+LBhamAwDqK5rx1Udroe7MICpU8Tjjf+ZGJZSJ6TDrVIhKMeJP88/Y953vx1p5iz+2mcbGRpefG5QB8D333IPrrrvO6XPy8vJcWlZmZiZ+/vlni/tqa2thNBpteoZFjz/+OGbMmCHd1ul0yM7OxqhRo/ySM2w0GrFmzRqMHDnyr548orZxuwkMU5MZ+9ecRLWuQrovLkONy2++OOh7OP25zZiazFj+3V7oDjUjobMagwYORuqZsUG/jsgSjzOBYWoyY/nkvTDrmhGXrsKVHxYgpkNQhnA2/LnNiFfsXeHW2vv444+xefNm6fa+fa0lnC699FKb54qPeSI1NRWpqakev15u8ODBePbZZ3HkyBF06tQJQGtPrkajwYABA+y+RqPRQKPR2NyvVqv9usP7+/0oPHC78Z+mWhOW3fCHRa1fcdBbTEJonJwA/2wzajUwfnFvaUDcN3fu54C4EMbjjP+Y9GaUf1cH3aHWQdMN1Sboj5qRkBZa698/xxnXl+/WEXrfvn12A9tVq1bZfb6jFANvKi8vR01NDcrLy9HS0oIdO3YAALp37474+HiMGjUKBQUFmDx5Ml588UXU1NTgoYcewm233cYKEETkMdb6dZ+9AXGsDUzkGAe++Y7LAfCBAwd82Q6PzZo1CwsXLpRun3POOQCAdevWobCwEFFRUfjqq69w1113YciQIRYTYRAReYK1fj2Xkq+VagPHZaiR2Nn2ahsRtaop1bOyjI+4HADn5ub6sh0eW7BggcMawKKcnBysXLnSPw0iorBmb4rjSK716y6VVomx7/eS1uHyaXuYBkHkgPWMbwx+vSd0ktSIiAKMaQ/eoTtskNYh6wIT2ccZ33yLa5KIyEXHShqY9uAFKflaJHY5PVPghuIymPTmALaIKPjIJ9YRZ3wj7+FRm4jIBSa9GeuLD0q349KZ9uAplVaJYbPypNu6itbBcETUyvp4k9iFA9+8jUduIqI2iIPedBXN0n3D53RFTDKzyDyVVhCHpJzWAXCJXaLRYjCzF5joLzWleovjzdBZufyx7WVcm0RETjTVmvDZuJ1YX1wG5V/xblKOBukFLN3VHiqtEuMWFeDyeT0BKLBi+l4snVTCIJginklvhslgRmKX1h+IPN74BrsviIgc4KA332JdYCJL8rq/iV2iccW8nkgriOPxxge4RomI7GCtX/8Q6wIDYF1ginjyur+6imZEaZQ83vgI1yoRkRV7aQ+s9esbYl1gsdbp8ml7mAZBEUus+wtwxjdf45GciEimqdaEJRN22qQ9TFzah4PefMS6LnDp6hoGwRRxWPfXv7hmiYj+Iub8NtW0SPcx7cH35GkQShWwvriMA+Io4sjTH1j31/d4RCcigv2c35iUKKY9+IFYEWLYrFyYTa33iQPiiCKBvcoPTH/wLV7PI6KI11Rrkqo9KFWtaQ9izi/THvxDpVUif1QKdiyoQl25gQPiKGKw8kNgcO0SUURzVOqMOb/+xwFxFIlY+SEwuIaJKGKx1FnwsR4QxzQICnes/BAY7N4goojkLO2BwW/giAPimAZBkYCVHwKHa5mIIg7THoIX0yAokrDyQ+AwACaiiMK0h+DHusAUCVj5IbDY1UFEEYNpD6FBngYh1gXesaAK4xbxe6LwwMoPgcc1TUQRgTO8hQ7WBaZwx8oPgce1TURhjzO8hR6xLrA4QxwHxFE4YeWHwOORn4jCGmd4C10cEEfhiJUfggOv+xFR2OIMb6HPXl3g9D5xAW4VkefsVX7g8cj/uMaJKOyY9GZUlzRg3cwDaKi2zPll2kNokQ+IS+wSjRaDGSa9md8hhSwx/aHhqJHpDwHEAJiIwoq811eOOb+hSRwQV13SgA3FZVgxfS+ScjSsCEEhiekPwYNrnYjChvUEFyKWOgttKq0SKo0SuorWy8asCEGhihNfBA/2ABNR2DhW0mAR/Mamq3DxnG6srxkGOEUyhTr5xBe6CgPTHwKMZwQiCnkmvRmV2+rxfdFB6b64dDXGL+qNTgMSGPyGAVaEoFAmTnyxcvpeAAKumNeTaTwBxh5gIgppjnJ+h8/pypHVYca6IkR1SQOyBiQEuFVEbePEF8GHa5+IQpLY67t0km3wm5SjQXoBS2WFm5R8LRK7REu3NxSXsReYQgInvgg+7B4hopDjqNeXOb/hTaVVYtisPKyYvhcAoKtgXWAKfqz8EJz4DRBRSHFW6YE5v+EvrSBOmh5ZXheYKFix8kNw4lmCiEKKvUoPV8zriYlL+zDnNwKIdYEvn9cTgAIrpu/F0kklDIIpKMkrPwBMfwgmPFsQUUgQZ3dbb1XpYdwiTmscaRzVBWYqBAUTsfKDOIvhFfN6Mj0riPCsQURBj5UeyBrrAlOwY+WH4MZvgoiCFis9kCOsC0zBjpUfghu7TogoKLHSA7XFui5w6eoa5I9K4XZBAcfKD8GP3wYRBRVnvb6s9EByYhoEAChVwPriMg6Io6DAyg/Bjz3ARBQ02OtL7hArQpSursH64jIAHBBHwUFMf2g4amT6Q5DimYSIgkJTrQlLJuxkry+5RaVVIn9UitQTzAFxFGhMfwgN/EaIKKDkKQ9NNS3S/azvS67igDgKJkx/CA08qxCR35n0ZtSU6hHbUY3lt+yx6fWNSYnC+EW9GfiSy6wHxDENggJBPvGFrsLA9IcgxrMLEfmVPM9XEQUILZaPx2WoMe4TTm5B7pHXBZZPkcxLz+QvnPgitPAMQ0R+I+b5iqkO8uCXA92oPcQBcdUlDdhQXIYV0/ciKUeDcYsKuD2RX3Dii9DCb4aIfM5Rnq8iqvV/DnQjb3A0RTKRP8jL8jH1IfixB5iIfMpRabOYlChc82EBGk8YkZKvZeBLXsEpkimQLpqZCwXAK1khgN8OEXmd2ON7aGOdwwktJizpg/hO0UjvwxMFeQ8rQlAgiPm/K6fvxYY5ZYFuDrmAPcBE5DUmvRnVJQ1YX3QQ9ZXNNo8zz5f8wboiRHVJA7IGJAS4VRTO5Pm/rEISGngGIqJ2M+nNOLSxDp9dsxMrp++1G/wyz5f8JSVfi8Qu0dLtDcVl7AUmn5GXPgOY/xsq2ANMRB4Re3tbDGb8+Fy53aAXABKyolFYlMdeX/IblVaJYbPysGL6XgCAroI9cuQbLH0WuhgAE5Fb2kpzAFpTHYY9lQeVRsmTAQVEWkEc6wKTz7H0WehiAExELjHpzTiyvR4bnilDQ7XR4fPi0tUYt4gTWVBgsS4w+UNiZ4004JKpD6GFZygisiFOVZzYWYOa/XqX0hwufDyHPb4UVBzVBWYqBHmDSW/G8mmtU7nHZagx9v1ePPaFEAbARCSx7uW1N1WxiGkOFApYF5h8RZ7+0HDUCN1hA698hRB+U0QRSMzjVQBI7qZ12MvrKPhlmgOFCrEusDgZy/Jpe5gGQV7B9IfQxrMXUQiyTlFQAIjPUaG5TI3DP+ug0UZLga11kAvAMtCNAuAg0IUSwF/Vo5jmQKHKui5w6eoa5I9K4TZMHmP6Q+hjAEwU5Kx7a4/tbrCfohAFoCUDqxcelN2G7d/WnPTyjn2/F3SVBk7tSSFNngahVAHri8uwY0EVe4LJY0x/CH38toiCkMMau1aBrEWKgnUg6+wxOdky7fXyxneKdvJiouAnVoQoXV2D9cWt09RyQBx5Sj7xha7CwPSHEMUAmChIuDSxhHUgK0tRsOnlddIDLA905akS7OWlcKXSKpE/KgU7FlRxQBx5jBNfhA8GwERBoKnWhM8n7UJjtcn5E2WBrHWKQnyOCqsWr8O5/Qc5zQG2l8ObNSDBVx+NKGhwQBy1Fye+CB8MgIkCRN7ju+GZMofBb1u9tWKKgtFoRHSuEZ0HJUKtVgOwDGwZ5BLZDohjGgS5g5UfwkfIB8DPPvssvvrqK+zYsQPR0dE4efKkzXMUCoXNfW+//TbuuOMOP7SQyJIrUwk7q7jAQJbIc6wLTJ5i5YfwEvIBcHNzM6699loMHjwY7733nsPnffDBBxgzZox0OykpyR/NI7LQVGuSLr/aE5uuQuGsrsjsF88DK5EPMA2CPMXKD+El5L+52bNnAwAWLFjg9HkdOnRAZmamH1pEZF9TrQlLJuxEU41tSYaErGgUFuVxMAWRH7AuMHlCfvWA6Q+hL+QDYFfdc889uPXWW9G1a1fccsstmD59OpRK+wc7g8EAg8Eg3dbpdABacyyNRvs9d94kvoc/3ot8z9RkxvGSRqwvKrcIfmPTVbjwyS6IilYi9cxYqGKUENACo9FZzTLHuN2QuyJ1m0nIVSExOxq6Q81Q/FUXePsHRzD2o55QxTAIdiZStxlTkxm1pU24dF4+6g83Izk/BoLK8+N1JPHnNuPOe0REAPzMM8/g4osvhlarxdq1a/Hggw/i+PHjmDlzpt3nP/fcc1LPstzq1asRGxvr6+ZK1qxZ47f3It8wNypxYl46zDrLXU0RZ0LcTZX49cTB1juOeO89ud2QuyJxm4m5UQHsioHuy44AAN2hZnz10VqoO0dWYOepSNpmBKMCJ95NR0uNGlEpRnS8vRqKMiHQzQo5/thmGhsbXX6uQhCEoPsWi4qK7Aagclu2bMHAgQOl2wsWLMD9999vdxCctZdffhnFxcWoq6uz+7i9HuDs7GwcP34ciYmJrn2IdjAajVizZg1Gjhwpjean0CLv9bWu7hCXrsKVH/ZETAfv/v7kdkPuivRtxtRkxvLJe6E71Oyz/TLcROI2c2xXI1besk+6ffl73ZHW23+dYaHOn9uMTqdDamoq6urq2ozXgnJPv+eee3Ddddc5fU5eXp7Hyz///POh0+lw9OhRZGRk2Dyu0Wig0diODFar1X7d4f39fuQdTbUmLLvhD5uBbrHpKlw8p5vP83y53ZC7InWbUauBqz44UxoQ9/X0Ug6Ic1EkbTMpuXEWpc/Sz0iASs1txF3+2GbcWX5QBsCpqalITU312fK3b9+OmJgYdOjQwWfvQZHJ0UC3uAw1xn1SwBHDREGGdYHJGZY+C18hfzYuLy9HTU0NysvL0dLSgh07dgAAunfvjvj4eKxYsQJVVVUYPHgwtFot1q1bhyeffBLTp0+328tL5Amxtu+6mQdsBrr5o9eXiDwjH9mf2CUaLQYzTHoz91cCwNJn4Szkv8VZs2Zh4cKF0u1zzjkHALBu3ToUFhZCrVbjn//8J2bMmAGz2Yxu3bqhuLgYd999d6CaTGHGUW3fmJQojF/UmwdLoiCm0ioxblEBqksasKG4DCum70VSjoapEAST3gyTwYzELhroKlj6LNyE/Jl5wYIFTmsAjxkzxmICDCJvkff6NlRbBr9MeSAKHSqtEiqNErqK1p6+unIDqksaOOtiBDPpzVg6qUS6MnDFvJ68khdmeHYm8oD84CjHlAei0JSSr0Vil2joKlqnJ99QXIbxn7IXOFLJUx90Fc2I0ii5LYQZfptEHjhW0mAT/MZlqDF+UW90GpDAAyVRiFFplRg2K0+6ratoHRBHkSmxswZxGa0VBZj6EJ7YA0zkBjHtYX3RQek+TmNMFB7SCuKkAXFxGWokduZA6UjEyg+Rgd8okYuaak34bNxOrJy+F/WVzdL9w4ry2OtLFAZUWiXGvt9Lqvm6fNoemPTmQDeL/Mxe5QcKPzxjE7lArO9rXekhKUeD9ALWDCUKF9Z1gUtX1zAIjjBMf4gMDICJ2mDSm7H0hhKb+r5XzOvJUklEYUasCwwAShWwvrgMSyeVMAiOEEx/iBz8VomcMOnNKF1dY9HzK9b3ZdoDUfgR6wIPm5ULs6n1PnGGOAp/TH+IHDx7Ezkg5vyuLy6D8q/honEZakxY0of1fYnCmEqrRP6oFKknmAPiIoN84guA6Q/hjgEwkRWT3ozKbfVYOun07G5mEzBsVi4mLmXwSxQJOCAusoi13VdO3wtAYIpbBOCZnEjG0QQXcRlq5I9K4cGQKIJYD4irKdUjvQ8HvYYjTnwRefjtEsk4muBi3CfsCSCKNPIBcYldotFiMLMXOEyx8kPkYQ8w0V+aak1YO3O/dJsTXBBFNnFAXHVJAzYUl2HF9L1IytHw0niYYeWHyMRvmAinS501Vpuk+zjBBRGptEqoNEroKlqvDNWVG1Bd0hDgVpE3sfJDZOKZnSKevVJncRlqTnBBRABaUyESu0RLtzcUlzEVIkyw8kPkYgoERbSmWhOW3tBa7UGpaq32wJxfIpJTaZUYNisPK6bvBQDoKlpniOPA2NAmH/Sc2CUaV8zryZS3CMJvmSKWmPbAUmdE1Ja0gjjOEBdmWPkhsvGbpojkKO2BPTpEZA9niAs/rPwQ2djNRRGHaQ9E5AlxhrgdC6pQV27gDHEhjJUfiN82RZSmWhOWTNjJtAci8ghniAsPrPxADIApYog5v001LdJ9THsgIndZzxDHsmihh+kPxLM+RQR7Ob8xKVFMeyAit7EsWmhj+gMBDIApAjTVmvDZuJ1YX1wG5V9ZDnEZakxYwrQHInKfWBZNpKvgYLhQwvQHAhgAU5hjqTMi8gV5WbTELtFoMZjZCxwCOPEFiRgBUNhiqTMi8hWxLFp1SQM2FJdhxfS9SMrRYNwiplUFK058QXIMgCkssdQZEfmaSquESqOErqL1Ero4IC5rQEKAW0b2cOILkuM3T2GHaQ9E5C8cEBc6WPmB5BgAU1hh2gMR+ZO9AXGlq2sYBAcZVn4ga/z2KWw4qvbAtAci8iX5gDilClhfXIalk0oYBAcJsWOElR9IjteDKSw4Sntgzy8R+Zo4IK50dQ3WF5cBaM0HrinVI71PXIBbF9nkA9/E8SBMfyCAPcAUJo6VNDDtgYgCRqVVIn9UitQTHJehRmJnTYBbRfKBb2LHCCt1EMAAmEKcSW9G5bZ6fF90ULovLp1pD0TkfyqtEmPf74W4DDUajhqxfNoepkEEmPXAN3aMkIgpEBSy5Je25IbP6cpqD0QUELrDBulqFMuiBRYHvpEz3BIoZB0rabAJfpNyNEgvYM4dEQUGy6IFD055TM4wAKaQYy/tISGrdVYf5nYRUSCxLFrwYN1fcobXiSmkyGd4kxtWlIdOvMxIREFALIsmVh5YX1yGHQuq+APdj5j+QG3h1kAhw7rUmYhpD0QUTMSyaMNm5cJsar1PzAcm32PdX3IFA2AKGdalzmLTVUx7IKKgJJZFYz6wf4mDo+UTIjH9gexh1EBBz1Gps/GLeqPTgAQGv0QUlJgP7H+s+0uu4hZBQU38Nb9y+l7UVzZL97PUGRGFAk6T7F+s+0uu4lZBQY2lzogolDEf2H848I3cwS2DghJLnRFRuGA+sO9x4Bu5i9eQKeiw1BkRhRsxH3jF9L0ATucD8xJ9+8lnBVWqWnN/OfCN2sK9joIKS50RUbhiPrBvcOAbeYJbBwUN8RIWS50RUThiPrBvcOAbeYJbCAWFploTPhu306J2Y1wGS50RUXhhPrB3ceAbeYpbCQVcU60JSybslHp+xUtYE5f2YakzIgo79uoDsxfYfRz4Ru3BAJgCSsz5bappke6Ly1DzEhYRhbW0gjj2ArcDZ3yj9mKEQQFjL+c3JiUK4z5hvi8RhTfOEtc+8hrxHPhGnuCWQgHhKOd3whKmPRBRZGBVCM+Y9GasLz4o3U7swoFv5D5uLeRX4gQXSyeVMOeXiCIaq0J45lhJA3QVzdLtobNyGfyS27jFkN+Ivb4rp+9FQ/XptAfm/BJRpGJVCPfY6/1ljXjyBCMO8gtHE1zEZaiZ80tEEY35wK4Rx42w95e8gdebyS+OlTTYTHBx8ZxuSCuI48GLiCKemA8sTue7vrgMW9+txLhPCpgaBsfTHbP3lzzFyIN8Ssz5/b7ooHRfXDonuCAikrOXD9xw1IilN3BQHMDpjsn7uOWQz8hzfusrT1+yGj6nK3s0iIisiPnA4rS+QGsQzEFxnO6YvI9bD3mdvUoPIl6yIiJyTKVVYtwnBYhNP91JEMmD4sTzyRdTOd0xeRe74cirmmpNdge7MeeXiMg1Mcmtx8sV0/cCOD0oLtJ6PeV5vyJxumNeRaT2ipw9iXyuqdaEJRN22q30wJxfIiLX2Zsk47NxO9FUawpwy/xHPtubiNMdk7cwGqF2k6c8NNW0SPfHpqtwxbyenOCCiMhNkT4ozrreb0JWNK6Y15MD38hrQnorOnjwIG655RZ07doVWq0W+fn5ePrpp9Hc3GzxvPLyclxxxRWIi4tDamoq7rvvPpvnkGccTW4RkxLFXl8ionZwNCguEmoEW8/2Nqwoj+cT8qqQ3pL27NkDs9mMd999F7t27cIrr7yCd955B0888YT0nJaWFlx22WVoaGjAjz/+iE8//RRLly7Fgw8+GMCWhz5nA93iMtSYsIS9vkRE7SUOihOD4EhIh+Bsb+QPIR2hjBkzBmPGjJFud+vWDX/88QfefvttvPTSSwCA1atXo6SkBIcOHUJWVhYA4OWXX8bUqVPx7LPPIjExMSBtD2Uc6EZE5D8xySpMXNoHpatrsL64DEBrT/CSCTvDrrOBs72Rv4TPXvOXuro6pKSkSLc3bdqEPn36SMEvAIwePRoGgwHbtm3D8OHDbZZhMBhgMJxOvNfpdAAAo9EIo9Fo83xvE9/DH+/lDlOTGcdLGrG+qByN1ZY9D3HpKlz5YU/EdFBBQAuMxhYHSyFfCdbthoIXt5kQogJyRiQg7h0VGv46/jbVtGDpDSW45rMzoIrxT4Doy22m6aQJX075Ew1HjVCoAMEEJGZHI7lnNLfREObP44w776EQBEHwYVv8qrS0FP3798fLL7+MW2+9FQAwffp0HDx4EKtXr7Z4rkajwYIFC3D99dfbLKeoqAizZ8+2uX/RokWIjY31TeODnLlRiRPz0mHWWf5mUiSY0OGaGqizjFCow2ZTIiIKSuZGJY6/nQ6h4fSxOPHKE4jp3RTSx2DBqMDxtzIszjHh8LnIvxobGzFp0iTU1dW1eYU/KHuAHQWgclu2bMHAgQOl25WVlRgzZgyuvfZaKfgVKRQKm9cLgmD3fgB4/PHHMWPGDOm2TqdDdnY2Ro0a5ZeUCaPRiDVr1mDkyJFQq9Vtv8DHmk6a8J9Jf8Css+zVbe31LUBMh6DcjCJOsG03FPy4zYSmpr9Z9pTqvuyIls2nr8L5ki+2GVOTGfvXnES1rkK6Ly5DjbEzhvmtZ5t8x5/HGfGKvSuCMnK55557cN111zl9Tl5envR3ZWUlhg8fjsGDB2PevHkWz8vMzMTPP/9scV9tbS2MRiMyMjLsLluj0UCj0djcr1ar/XqS8Pf7WTPpzaguacC6mQdsypsx1zd4BXq7odDDbSa0qNPUtjnB1SYsv2mv347N3tpmmmpNWHbDH2g4aoRSBZhNrcHvuE8KEJMQlCEKecgfxxl3lh+UW1dqaipSU1Ndeu7hw4cxfPhwDBgwAB988AGUSsudfvDgwXj22Wdx5MgRdOrUCUDrwDiNRoMBAwZ4ve3hwtFAN7G8WTgNuiAiCjViibSt71ZKx+nGahNWTN97OoAM8uO0SW+2OM+YTcCwWbkRN+MdBUZIb2GVlZUoLCxEdnY2XnrpJRw7dgxVVVWoqqqSnjNq1CgUFBRg8uTJ2L59O9auXYuHHnoIt912GytAWBFLmx3aWMfyZkREQc66RJqo4agRn0/ahSPb6oO2XrBY7UF+nonLUDP4Jb8J6Uhm9erV2LdvH/bt24cuXbpYPCaO7YuKisJXX32Fu+66C0OGDIFWq8WkSZOkMmnUqqnWhM8n7bKp7gAw5YGIKFiJJdLEdDVxQqJg7g2WX2G0TnvgOYb8JXj2CA9MnToVU6dObfN5OTk5WLlype8bFGLEHN8WgxkbnimzG/wG48GTiIhOU2mVyBqQgHGLCmxS14KtXnBTrQlLJuyUxpUw7YECJfB7A/mdGPiuLzqI+kr7U0InZEWjsCiPvb5ERCHCUW9wU00LPp+0K6BX8hwNqmbaAwUKA+AIYtKbcWR7PTY8UyYdGK3FpqtQOKsrMvvF84BERBRi5L3B8p7WQKZEOBtUzbQHChQGwGFOnubw43Pl7PElIooAMckqTFjSx25KxOeTdmHYU3lQaZQ+PebLe32tO12YXkeBxi0vjJj0ZtSU6pHYWYOa/fo2g97YdJVfDoJEROR/zgbIfXPvPgBAXLoaY9/vhcYTRqTka71yHnB2tZGDqilYMAAOYfKA99juBulgo4gChBbnr41LV2PcIv76JiIKZ84GyAFAQ7URi8f+DqHlr9nX3vMsGHblaiN7fSmYcCsMQqYmM4yH1Wg6acKx8iYoACR300q9uiqNEglZGiy/ZU/rVJhWAa+j4DchKxoXPp7DHl8ioggj7w22HgAtnjMajp4OhsXxIKm9YlGzXy+dh47tPYXmsmjp/NRiaK0z3NbVRvb6UrBhABxkTHozlk/eC92hDCxeUAKIwWwUTv9tddsm4FUC+Kv2OYNeIiICTvcGX7ukt0WKgrwTRfy/sdqEr+/50/LcI/2djsUfl1iekxzg1UYKVtwig0xNqR66Q3/9ipYfXKwPNPLbsoBXzOfSVRqgABj0EhGRBZVWiewLkjBxWR/UlOoR21Ht8Iqiw/OQk+CXHS8UChgAB5mUfC0Ss6Nbg2C7v7xbKVSAYDqds2Ud8MZ3ivZ/44mIKGSotEqk94kDAExcejoY/mLa7tMTIzk6D1mdkxj0UqhhABxkVFolxn7UE199tBajrx2O+nKT3Rzg5G5a6A4bpIEKDHiJiMhT8mD4umVnobqkweLcczoHuB6bf96MMdcXor7cJJ2TGPRSqGEAHIRUMUqoOxsR00GFhDStdH/WgASL5zGnioiIvE3MFRbJ/87sH4/oqmab8xNRqOHPNSIiIiKKKAyAiYiIiCiiMAAmIiIioojCAJiIiIiIIgoDYCIiIiKKKAyAiYiIiCiiMAAmIiIioojCAJiIiIiIIgoDYCIiIiKKKAyAiYiIiCiiMAAmIiIioojCAJiIiIiIIgoDYCIiIiKKKAyAiYiIiCiiMAAmIiIioojCAJiIiIiIIooq0A0IBYIgAAB0Op1f3s9oNKKxsRE6nQ5qtdov70mhj9sNuYvbDLmL2wy5y5/bjBiniXGbMwyAXVBfXw8AyM7ODnBLiIiIiMiZ+vp6JCUlOX2OQnAlTI5wZrMZlZWVSEhIgEKh8Pn76XQ6ZGdn49ChQ0hMTPT5+1F44HZD7uI2Q+7iNkPu8uc2IwgC6uvrkZWVBaXSeZYve4BdoFQq0aVLF7+/b2JiIg8w5DZuN+QubjPkLm4z5C5/bTNt9fyKOAiOiIiIiCIKA2AiIiIiiigMgIOQRqPB008/DY1GE+imUAjhdkPu4jZD7uI2Q+4K1m2Gg+CIiIiIKKKwB5iIiIiIIgoDYCIiIiKKKAyAiYiIiCiiMAAmIiIioojCADjITJ06FQqFwubf1KlTA900CjItLS244IILMG7cOIv76+rqkJ2djZkzZwaoZRSsxOPLHXfcYfPYXXfdxWMNOcRzE7lLvs2oVCrk5OTgzjvvRG1tbaCbBoAzwQWlMWPG4IMPPrC4T6vVBqg1FKyioqKwcOFC9OvXD5988gluuOEGAMC9996LlJQUzJo1K8AtpGCUnZ2NTz/9FK+88op0XGlqasLixYuRk5MT4NZRMOO5idwlbjMmkwklJSWYNm0aTp48icWLFwe6aQyAg5FGo0FmZmagm0EhoEePHnjuuedw7733Yvjw4diyZQs+/fRT/O9//0N0dHSgm0dBqH///ti/fz+WLVsm/WhatmwZsrOz0a1btwC3joIZz03kLvk206VLF0ycOBELFiwIbKP+whQIohB37733om/fvrjpppswffp0zJo1C/369Qt0syiI3XzzzRY9ee+//z6mTZsWwBYRUbjbv38/Vq1aBbVaHeimAGAATBTyFAoF3n77baxduxYZGRl47LHHAt0kCnKTJ0/Gjz/+iIMHD6KsrAw//fQTbrzxxkA3i4jCzMqVKxEfHw+tVov8/HyUlJTg0UcfDXSzADAFgigsvP/++4iNjcWBAwdQUVGBvLy8QDeJglhqaiouu+wyLFy4EIIg4LLLLkNqamqgm0VEYWb48OF4++230djYiPnz52Pv3r249957A90sAOwBJgp5mzZtwiuvvILly5dj8ODBuOWWW8AZzqkt06ZNw4IFC7Bw4UKmPxCRT8TFxaF79+44++yz8frrr8NgMGD27NmBbhYABsBEIU2v12PKlCm4/fbb8be//Q3z58/Hli1b8O677wa6aRTkxowZg+bmZjQ3N2P06NGBbg4RRYCnn34aL730EiorKwPdFAbARKHsscceg9lsxvPPPw8AyMnJwcsvv4yHH34YBw8eDGzjKKhFRUVh9+7d2L17N6KiogLdHCKKAIWFhejduzf+/ve/B7opDICJQtX69evx1ltvYcGCBYiLi5Puv+2223DBBRcwFYLalJiYiMTExEA3g4giyIwZM/Cvf/0Lhw4dCmg7FALPkEREREQUQdgDTEREREQRhQEwEREREUUUBsBEREREFFEYABMRERFRRGEATEREREQRhQEwEREREUUUBsBEREREFFEYABMREQXAl19+iaKiIpSVlQW6KUQRhwEwEXlVYWEhFApFoJsRcoqKiqBQKPD9998HuilBI5y3pf/973+49tprcfz4ceTm5ga6OUQRhwEwUYjYtm0bbrnlFvTo0QNxcXHQarXIz8/H5MmTsWbNmkA3j4hcVFNTgwkTJuCyyy7D66+/HujmEEUkVaAbQETOmc1mPPTQQ3jllVegUqkwYsQIXHnllVCr1di/fz+++uorfPzxxyguLsZTTz0V6Obiww8/RGNjY6CbQWEgHLclQRBw0003oXPnzli0aBGUSvZDEQUCA2CiIDdz5ky88sor6NevHz7//HPk5+dbPK7X6/Hmm2/ixIkTAWqhpZycnEA3gcJEOG5LCoUCK1euDHQziCIef3oSBbF9+/bhhRdeQMeOHbFq1Sqb4BcAtFotHn74YcyePVu6b+/evXjkkUfQv39/dOzYETExMejZsycee+wxnDp1ymYZYq6lwWDAE088gZycHGi1WgwYMADffvstAKC+vh733XcfOnfujJiYGAwePBhbt251uCy5BQsWQKFQYMGCBVi7di0uvPBCxMXFoWPHjpgyZYrD4H3lypUYPnw4kpKSoNVq0a9fP7z66qtoaWlxaz0eOHAAt956K3JycqDRaNCpUydMnTrV7uAjhUKBwsJCHDt2DNOmTUN6ejq0Wi3OP/98t/Nzm5ubMXfuXPTv3x9xcXFISEjARRddhC+//NKt5Xjjc/3yyy8YP3689NyMjAwMHjwY//jHPyyel5eXh7y8PNTW1uK2225DRkYGtFotzjvvPLvtrqysxNNPP43zzz8f6enp0Gg0yMvLw1133YXq6mqH6+W1117Deeedh4SEBMTHx6OgoAAzZsxAbW2t9DxHOcAmkwmvvPIK+vbtC61Wi6SkJAwfPhxfffWVy+vu+++/h0KhQFFRETZt2oTRo0ejQ4cOFu8nCALef/99DBkyBImJiYiNjcXAgQPx/vvv212mIAhYuHAhhg4dig4dOiA2NhY9evTAHXfcgfLycul5U6dOhUKhwMGDB+22Z8OGDRg2bBji4+ORkpKCSZMmoaKiwub9xO/q5MmTuO+++5CdnQ2VSoUFCxZIz3F3H/rtt99w4403okuXLtI2NWbMGKxYscLied74DogCSiCioPXkk08KAIQnnnjCrdc999xzQkpKijBu3DjhgQceEP7v//5PGDRokABAOP/884Xm5maL5w8bNkwAIIwdO1bo1q2bcPfddwvTpk0TNBqNoNFohG3btgkDBw4U+vTpI9x3333C9ddfLyiVSiElJUWoq6uzuyy5Dz74QAAgXHPNNUJ0dLQwbtw44cEHHxTOPfdcAYAwZMgQm8/w6quvCgCElJQU4Y477hAefPBBoWfPntJyzGazS+ti8+bNQlJSkqBSqYSrr75aePjhh4Vrr71WUKlUQnp6ulBaWmrxfABC3759hR49eggDBgwQ7r//fmHSpElCVFSUEB0dLfz+++8uvW9TU5NQWFgoABDOOecc4d577xXuuOMOITs7WwAgvPHGGxbPf/rppwUAwrp167z+ubZv3y5oNBohNjZWuP7664XHHntMuOOOO4SLLrpI6Natm8Vyc3NzhU6dOgn9+/cXzjzzTOHhhx8WbrvtNiEhIUFQKBTCxx9/bPH8xYsXC3FxccKVV14p3HfffcKDDz4ojBgxQgAgdOvWTTh58qTF8/V6vTB06FABgNCjRw/h3nvvFR566CFh7NixglarFbZv3y491962ZDabhWuuuUYAIPTs2VN48MEHhTvuuENISUkRAAivvfaaS+tv3bp1AgBh5MiRglqtFkaNGiU8/PDDwsSJE6X3mTRpkvQ+t99+u3DvvfcKvXr1EgAIDz74oE27Jk6cKAAQOnfuLNxxxx3CI488IkyYMEHo0KGD8J///Ed67pQpUwQAwoEDB2zaM3r0aCE6Olq4+uqrhccff1wYPXq0AEDIzs4WqqqqbL6rzMxM4ZxzzhG6d+8u3HnnncL//d//CV9//bUgCO7vQ8uWLRM0Go2gVquFa665Rnj88ceFW265RejTp48wduxYr38HRIHEAJgoiIkB1LfffuvW6yoqKgSDwWBz/+zZswUANkGMGGgMGTJEOHXqlHT/p59+KgAQOnToIFx77bWC0WiUHnv++ecFAMLcuXPtLktODIBVKpXw448/SvebTCbpM27atEm6v7S0VArkysvLpfsNBoO0/I8++qjN9dDc3Czk5eUJCQkJwo4dOywe++GHH4SoqCjh8ssvt7gfgABAuOuuu4SWlhbp/vnz5wsAhNtvv73N9xUEQXjiiScEAEJRUZFFoKHT6YSBAwcK0dHRwuHDh6X73QmA3f1cM2bMEAAIy5cvt1nW8ePHLW7n5uYKAIQRI0ZY/FDavXu3oNVqhQ4dOgg6nU66/+jRo0J9fb3NchcuXCgAEObMmWNx/8MPPywAECZPniyYTCaLx06ePGmxLHvb0ocffigAEIYNG2axjR86dEhIT08X1Gq1sH//fpv2WBMDTgDCe++9Z/P4vHnzBADCLbfcYrHdGwwG4YorrhAACFu3bpXuf+uttwQAwsUXXyw0NjZaLKuxsVE4ceKEdNtZAAxAmD9/vsXrxf122rRpFveL39WoUaNs3tPdfejo0aNCfHy8EBcXJ/zyyy826+PQoUPS3976DogCiQEwURATe5v27NnjleWdOHFCACBMnTrV4n7xhPj9999b3G8ymQS1Wi0AEMrKyiweKy8vFwAIU6ZMsbssOTEAvummm2zaJD72+uuvS/cVFxcLAITnn3/e5vmbNm2SAo22LFu2TAAgPPPMM3Yfv+aaawSlUmnRiw1AiIuLswnqjEajoFKphP79+7f5vi0tLUJycrLQvXt3uz3VX375pU0vsDsBsLufSwyAV69e3eayxaDqp59+snns7rvvdvnHh9lsFhITE4XCwkLpPpPJJCQmJgpJSUlCTU1Nm8uwty2Jvcs///yzzfOfe+45p+tFTgw4zznnHLuPn3322UJcXJyg1+ttHvvtt99seoELCgqEqKgoYe/evW2+t7MA+IwzzrDZZhobG4W0tDRBq9VaBJzid/Xrr7/avIe7+9ALL7wgABBmzZrVZvu99R0QBRIHwRGFIUEQ8MEHH2DBggXYuXMn6urqYDabpccrKyvtvu6cc86xuB0VFYX09HQ0NDTYDEjq1KkTAODw4cMut6t///4293Xp0gUAcPLkSem+7du3A2jNAbV2/vnnQ6vVYseOHW2+3+bNmwEAe/bsQVFRkc3jVVVVMJvN2Lt3LwYOHCjd36NHD8THx1s8V6VSISMjw6Kdjvzxxx+ora1FVlaWRW626NixY1K7POHu5xo/fjxeffVVXHXVVZgwYQJGjhyJCy+80OEgM7VajfPPP9/m/osuughvvfUWduzYgRtvvFG6f9myZXj33Xfxyy+/oLa21iK/VL6t7dmzBzqdDn/729+QnJzs0Wffvn27lJNsTdxeXNk2RPaW09jYiN9//x1ZWVk2OdIAYDQaAZz+/hoaGlBSUoLu3bujR48eLr+3PUOGDLHJexbz8VetWoW9e/eiT58+0mMxMTE466yzbJbj7j70v//9DwAwatSoNtvo7e+AKBAYABMFsczMTOzZsweHDx/GGWec4fLr7rvvPrz55pvIzs7GlVdeiU6dOkGj0QAAZs+eDYPBYPd1iYmJNvepVCokJSXZvR84HQy4wtly5EGTTqcDAGRkZNhdTnp6ukuBd01NDQDgk08+cfq8hoaGNtspttWVAXji++7atQu7du1y+X1d5e7nGjx4ML777js899xzWLx4sTRIasCAAXjxxRcxfPhwi9d17NjRbnku8fuoq6uT7nv55Zfx0EMPIS0tDaNGjUKXLl2g1WoBAK+++qrFtib+eOjcubMbn9aSTqdDdna23ccyMzNt2tcWe9tYbW0tBEHA4cOH7f6AEYnr1xufS5Senu60ndafLT093e5AQXf3IXc+g7e/A6JAYABMFMSGDBmC77//HmvXrsWIESNcek11dTXeeustnH322di0aRNiY2Olx6qqqpye0IOFGIgfPXrU7ixZ1dXVdoN1R8tZsWIFLr/8cu820oX3HTduHD7//HOfLd+dzzVs2DAMGzYMer0eP//8M1asWIF//vOfuOyyy/D7779bVBg5ceIEzGazTRB89OhRAKd/IJhMJjzzzDPIysrCjh07kJaWJj1XEAS88MILFq/v0KEDAPeuGlhLTEyU2mFNvN+VbUNkL3gUXz9gwAC7lU6sieujPZ9L5KhyhvW6FzmaKc/dfUj+3eTl5Tlto7e/A6JAYBk0oiA2depUREVFYd68edJlc0fEnrb9+/dDEAT87W9/swh+AeCHH37wWVu9SUzFsFd27H//+x/0ej369evX5nIGDRoEANi0aZM3m9emM888E4mJidi6datbPeSuas/n0mq1KCwsxMsvv4wnnngCer1eKnUnMhqNUpqFnLj9iOv++PHjqKurw/nnn28R/ALA1q1bodfrLe4744wzkJiYiC1btliUO3PHOeecA71eL12yl1u/fr1F+zyVkJCAM888E7t373Yp5UUs43bgwAH8+eef7Xrvn376CYIgWNyn1+uxbds2aLVa9OzZ06XluLsPiekMq1evdmnZvv4OiHyNATBREOvevTseeeQRHD9+HJdccgkOHDhg85ympibMnTtXygUVe3s2btxokfdbUVGBxx57zC/tbq9JkyZBpVJh7ty5FjmkRqNR+gxTp05tczljx45FTk4O5s6diw0bNtg8bjQa8eOPP3qt3SKVSoU777wTZWVleOihh+wGwTt37nTY29cWdz/XDz/8IF0SlxN768SUBbmnnnrKot179uzB+++/j6SkJIwdOxYApBrJv/zyi8WMbbW1tbj33nttlqlSqXD77bejrq4O//d//2eTTlJXV2e3TrXclClTAACPP/64RfsOHz6MuXPnQqVS4YYbbnC6DFfcd999aGxsxG233WY3VeXAgQMWdXzvvvtutLS04K677rIJ/JuamqS0lbb88ccfNnWGX3zxRRw7dgzXX389oqOjXVqOu/vQlClTEB8fj5dfftlu/q68d9tf3wGRLzEFgijIzZkzB01NTXjllVdwxhlnYMSIEejTpw/UajUOHDiAb7/9FidOnMCcOXMAtA5OGzduHJYuXYqBAwfi4osvxtGjR7Fy5UqMGDEC+/fvD/Analt+fj6ef/55PPjggzj77LMxYcIExMXFYeXKldizZw/Gjh1rMQjLEY1Gg88//xyXXHIJhg0bhosvvlgaQFReXo4ffvgBHTt29HgwmjOzZ8/GL7/8gtdffx1fffUVhg0bhrS0NBw+fBi///47fv31V2zatMlhzqcz7n6ul19+GWvWrMHw4cPRrVs3xMTE4JdffsHatWvRvXt3XH311RbL79SpE06ePIl+/frhsssuQ11dHRYvXoympib861//QkJCAgBAqVTirrvuwssvv4y+ffviiiuugE6nwzfffIPc3FxkZWXZtL24uBibN2/GRx99hM2bN+OSSy6BRqPB/v37sWrVKvz4449Oew8nT578/+3dPUjrUBgG4O8O5dBqgi4VFZsihqpQcRARRKpQREGKk9TFQQr+LIJdhQ6iUzOLoIgOgh3EgoIdBDsIFkFXZ3ERLQ5FkCq+d2qxWrWF+zPkfdacJCcnJ/CRHN7I/v6+JJNJ6erqkrGxMXl6epJEIiHZbFYsy5LW1taqx/SjmZkZOT8/l+3tbTk7O5NgMChNTU1yd3cn19fXkslkZHd3t7hcYG5uTtLptCQSCTFNU0KhkOi6Ljc3N5JKpWRzc1PGx8d/PO/w8LDMz8/L0dGRtLe3y+XlpaRSKWlpaZHV1dWK+1/tM+R2u2VnZ0fC4bD09vZKKBQSn88nDw8PkslkxOv1ysHBgYj8u3tA9Ff91wwKIqrYxcUFpqen0dbWBqfTCaUUvF4vJicnP8Vb5XI5RKNReL1eKKVgmiaWl5eRz+eL+Z3vlYubKjAMA4ZhlN1W6bEKUWdbW1ufjlGIf4rFYp+2JZNJBAIBaJoGpRT8fj8syyrJZa3E7e0tFhYWYJomlFLQdR0dHR2IRCI4OTn58ZoKvhuLcl5fX7G+vo7+/n7oug6lFDweD0ZGRrC2tlaSuVztjzCqua7j42NMTU3B5/NB0zTU1tais7MTS0tLZXOADcNANptFJBKB2+2GUgo9PT1lc4Tz+TxWVlaKffB4PFhcXEQul/tyvJ6fnxGPx9Hd3Q2n01nsTzQaxePjY7HdV/Py5eUF8Xgcfr8fSilomoZAIFC2f1/5bt69t7e3h2AwiPr6ejgcDjQ3N2NwcBCWZeH+/r6k7dvbGzY2NtDX14eamhq4XC6YponZ2dmSLN7vYtBisRjS6TQGBgbgcrlQV1eHcDhcsn9BJfOx2mfo6uoKExMTaGhogMPhQGNjI0ZHR3F4eFjS7k/cA6L/6RfwYbERERHZVuGN5vvP+/T3nZ6eytDQkMRisbLRdkT0Z3ENMBERERHZCgtgIiIiIrIVFsBEREREZCtcA0xEREREtsI3wERERERkKyyAiYiIiMhWWAATERERka2wACYiIiIiW2EBTERERES2wgKYiIiIiGyFBTARERER2QoLYCIiIiKyFRbARERERGQrvwEOxfeQsQd5kQAAAABJRU5ErkJggg==", - "text/plain": [ - "<Figure size 800x600 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Definimos las constantes de hopping\n", - "tAA = 7 # eV\n", - "tBB = 8 # eV\n", - "tOO = 5 # eV\n", - "tAO = 2.1 # eV\n", - "tBO = 1.0 # eV\n", - "\n", - "# Definimos la base cartesiana\n", - "x = np.array([1,0,0])\n", - "y = np.array([0,1,0])\n", - "z = np.array([0,0,1])\n", - "\n", - "\n", - "# Definimos las componentes de la matriz hamiltoniana como función de k\n", - "def HamiltonianoTB(k):\n", - " # El orden de los Ãndices 5x5 es: A, B, Oxz, Oxy, Oyz\n", - " H = np.zeros((5,5),dtype=complex)\n", - " H[0,0] = -tAA\n", - " H[1,1] = -tBB\n", - " H[2,2] = -tOO\n", - " H[3,3] = -tOO\n", - " H[4,4] = -tOO\n", - " H[0,2] = -tAO*(1+np.exp(-1j*a*np.dot(k, x))+np.exp(-1j*a*np.dot(k, z)) + np.exp(-1j*a*np.dot(k, x+z)))\n", - " H[0,3] = -tAO*(1+np.exp(-1j*a*np.dot(k, x))+np.exp(-1j*a*np.dot(k, y)) + np.exp(-1j*a*np.dot(k, x+y)))\n", - " H[0,4] = -tAO*(1+np.exp(-1j*a*np.dot(k, z))+np.exp(-1j*a*np.dot(k, y)) + np.exp(-1j*a*np.dot(k, z+y)))\n", - " H[1,2] = -tBO*(1+np.exp(-1j*a*np.dot(k, y)))\n", - " H[1,3] = -tBO*(1+np.exp(-1j*a*np.dot(k, z)))\n", - " H[1,4] = -tBO*(1+np.exp(-1j*a*np.dot(k, x)))\n", - " H[2,0] = -tAO*(1+np.exp(1j*a*np.dot(k, x))+np.exp(1j*a*np.dot(k, z)) + np.exp(1j*a*np.dot(k, x+z)))\n", - " H[3,0] = -tAO*(1+np.exp(1j*a*np.dot(k, x))+np.exp(1j*a*np.dot(k, y)) + np.exp(1j*a*np.dot(k, x+y)))\n", - " H[4,0] = -tAO*(1+np.exp(1j*a*np.dot(k, z))+np.exp(1j*a*np.dot(k, y)) + np.exp(1j*a*np.dot(k, z+y)))\n", - " H[2,1] = -tBO*(1+np.exp(1j*a*np.dot(k, y)))\n", - " H[3,1] = -tBO*(1+np.exp(1j*a*np.dot(k, z)))\n", - " H[4,1] = -tBO*(1+np.exp(1j*a*np.dot(k, x)))\n", - " return H\n", - "\n", - "# Obtenemos las bandas de energÃa\n", - "bands_TB = np.array([np.linalg.eigvalsh(HamiltonianoTB(k)) for k in k_path]).T\n", - "\n", - "# Graficamos las bandas de energÃa\n", - "color = 'darkorchid'\n", - "n_graf = len(bands_TB) # número de bandas a graficar\n", - "for i in range(n_graf):\n", - " plt.plot(np.arange(400), bands_TB[i], '.', markersize=3, color = color)\n", - "plt.xticks([0,100,200,300,400],['$\\\\Gamma$','X','M','$\\\\Gamma$','R'])\n", - "plt.xlabel('Camino en el espacio recÃproco')\n", - "plt.ylabel('EnergÃa (eV)')\n", - "# plt.ylim(0,400)\n", - "plt.title('Bandas de energÃa mediante Tight Binding')\n", - "plt.grid()\n", - "plt.show()\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 3. Modelo Kronig-Penney\n", + "## 2. Modelo Kronig-Penney\n", "\n", "La extensión a tres dimensiones del modelo presentado en Kittel representa una gran dificultad al tratar de considerar deltas de dirac como potenciales, pues para representar cada sitio, la forma del potencial deberÃa ser como $V(x,y,z) = \\delta (x-x_0) \\delta (y-y_0) \\delta (z-z_0)$, de modo que la ecuación de Schrödinger\n", "\n", @@ -367,7 +228,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -460,14 +321,82 @@ "plt.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Tight Binding\n", + "\n", + "En este modelo, consideramos que las funciones de onda de los electrones en la red son una superposición de funciones de onda atómicas, cuya base es de la forma:\n", + "\n", + "\\begin{equation*}\n", + "\\chi_{\\mathbf{k} l i} = \\sum_{\\mathbf{R}} e^{i \\mathbf{k} \\cdot \\mathbf{R}} \\phi_l (\\mathbf{r} - \\mathbf{t}_i - \\mathbf{R}),\n", + "\\end{equation*}\n", + "\n", + "donde $l$ es el orbital atómico, $i$ es el átomo en la celda primitiva y $\\phi_l$ es la función de onda atómica del átomo $l$ en la posición $\\mathbf{t}_i$. La expansión de la función de onda en esta base es entonces:\n", + "\n", + "\\begin{equation*}\n", + "\\psi_{\\mathbf{k}} (\\mathbf{r}) = \\sum_{l i} c_{\\mathbf{k} l i} \\chi_{\\mathbf{k} l i} (\\mathbf{r}),\n", + "\\end{equation*}\n", + "\n", + "entonces, solo queda encontrar los valores propios del Hamiltoniano de la red, que se puede escribir como:\n", + "\n", + "\\begin{equation*}\n", + "\\left<\\chi_{\\mathbf{k} m j} | \\hat{H} | \\chi_{\\mathbf{k} l i}\\right> = \\hat{H}_{mjli} = \\sum_{\\mathbf{R}} e^{i \\mathbf{k} \\cdot \\mathbf{R}} \\left<\\phi_m (\\mathbf{r} - \\mathbf{t}_j) | \\hat{H} | \\phi_l(\\mathbf{r} - \\mathbf{t}_i- \\mathbf{R})\\right>.\n", + "\\end{equation*}\n", + "\n", + "\n", + "\n", + "Para nuestro caso, consideramos únicamente el orbital $s$ de los átomos, de modo que podemos omitir el Ãndice $l$ y, además, los valores esperados para los orbitales atómicos del hamiltoniano no serán calculados, y serán tomados como constantes de la forma:\n", + "\n", + "\\begin{equation*}\n", + "t_{ij} = -\\left<\\phi (\\mathbf{r} - \\mathbf{t}_j) | \\hat{H} | \\phi(\\mathbf{r} - \\mathbf{t}_i)\\right>,\n", + "\\end{equation*}\n", + "\n", + "siendo $t_{ii}$ la energÃa de los electrones en el orbital $s$ del átomo $i$ (\"autointeracción\"), y $t_{ij}$ con $i \\neq j$ la energÃa de interacción (términos de hopping) entre los orbitales $s$ de los átomos $i$ y $j$. Además, tomaremos únicamente los primeros vecinos de los átomos A (12 átomos O) y B (6 átomos O), y los segundos vecinos de los átomos O (2 átomos B y 4 átomos A).\n", + "\n", + "Con estas consideraciones, las ecuaciones para cada $i=$\\{A, B, $O_{xz}$, $O_{xy}$, $O_{yz}$\\} son, con $H_{i}=\\sum_{j} H_{ij}$:\n", + "\n", + "\\begin{align*}\n", + "H_A &= -t_{AA} - t_{AO}[3 + 2(e^{-ia\\mathbf{k}\\cdot \\hat{x}}+e^{-ia\\mathbf{k}\\cdot \\hat{y}}+e^{-ia\\mathbf{k}\\cdot \\hat{z}}) + (e^{-ia\\mathbf{k}\\cdot (\\hat{x}+\\hat{y})}+e^{-ia\\mathbf{k}\\cdot (\\hat{x}+\\hat{z})}+e^{-ia\\mathbf{k}\\cdot (\\hat{y}+\\hat{z})})], \\\\\n", + "H_B &= -t_{BB} - t_{BO}(3 + e^{-ia\\mathbf{k}\\cdot \\hat{x}}+e^{-ia\\mathbf{k}\\cdot \\hat{y}}+e^{-ia\\mathbf{k}\\cdot \\hat{z}}), \\\\\n", + "H_{O_{xz}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{y}}), \\\\\n", + "H_{O_{xy}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{z}}), \\\\\n", + "H_{O_{yz}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{x}}).\n", + "\\end{align*}\n", + "\n", + "De modo que la matriz se puede escribir de la forma:\n", + "\n", + "$$\n", + "H = \\begin{pmatrix}\n", + "-t_{AA} & 0 & H_{02} & H_{03} & H_{04} \\\\\n", + "0 & -t_{BB} & H_{12} & H_{13} & H_{14} \\\\\n", + "H_{20} & H_{21} & -t_{OO} & 0 & 0 \\\\\n", + "H_{30} & H_{31} & 0 & -t_{OO} & 0 \\\\\n", + "H_{40} & H_{41} & 0 & 0 & -t_{OO}\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "Donde:\n", + "\n", + "- $H_{02} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}} + e^{-i a \\vec{k} \\cdot \\vec{z}} + e^{-i a \\vec{k} \\cdot (\\vec{x} + \\vec{z})}\\right) = H_{20}^*$\n", + "- $H_{03} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}} + e^{-i a \\vec{k} \\cdot \\vec{y}} + e^{-i a \\vec{k} \\cdot (\\vec{x} + \\vec{y})}\\right) = H_{30}^*$\n", + "- $H_{04} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{z}} + e^{-i a \\vec{k} \\cdot \\vec{y}} + e^{-i a \\vec{k} \\cdot (\\vec{z} + \\vec{y})}\\right) = H_{40}^*$\n", + "- $H_{12} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{y}}\\right) = H_{21}^*$\n", + "- $H_{13} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{z}}\\right) = H_{31}^*$\n", + "- $H_{14} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}}\\right) = H_{41}^*$\n", + "\n", + "Al ser una matriz hermÃtica $5 \\times 5$, obtendremos valores 5 valores propios reales para cada $\\vec{k}$, que serán las bandas de energÃa de los electrones en la red. Ahora, procedemos a calcular estas bandas de energÃa con la implementación numérica." + ] + }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 75, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", "text/plain": [ "<Figure size 800x600 with 1 Axes>" ] @@ -477,15 +406,58 @@ } ], "source": [ - "#Ploteamos SitioOxy para todos los valores de alpha con un k fijo\n", - "k = X\n", - "alpha = np.logspace(0,10,100)\n", - "plt.semilogx(alpha, [SitioA(a,k) for a in alpha])\n", - "plt.xlabel('alpha')\n", - "plt.ylabel('Sitio Oxy')\n", - "plt.title('Sitio Oxy')\n", + "# Definimos las constantes de hopping\n", + "tAA = 5 # eV\n", + "tBB = 12 # eV\n", + "tOO = 6 # eV\n", + "tAO = 1.1 # eV\n", + "tBO = 1.0 # eV\n", + "\n", + "# Definimos la base cartesiana\n", + "x = np.array([1,0,0])\n", + "y = np.array([0,1,0])\n", + "z = np.array([0,0,1])\n", + "\n", + "\n", + "# Definimos las componentes de la matriz hamiltoniana como función de k\n", + "def HamiltonianoTB(k):\n", + " # El orden de los Ãndices 5x5 es: A, B, Oxz, Oxy, Oyz\n", + " H = np.zeros((5,5),dtype=complex)\n", + " H[0,0] = -tAA\n", + " H[1,1] = -tBB\n", + " H[2,2] = -tOO\n", + " H[3,3] = -tOO\n", + " H[4,4] = -tOO\n", + " H[0,2] = -tAO*(1+np.exp(-1j*a*np.dot(k, x))+np.exp(-1j*a*np.dot(k, z)) + np.exp(-1j*a*np.dot(k, x+z)))\n", + " H[0,3] = -tAO*(1+np.exp(-1j*a*np.dot(k, x))+np.exp(-1j*a*np.dot(k, y)) + np.exp(-1j*a*np.dot(k, x+y)))\n", + " H[0,4] = -tAO*(1+np.exp(-1j*a*np.dot(k, z))+np.exp(-1j*a*np.dot(k, y)) + np.exp(-1j*a*np.dot(k, z+y)))\n", + " H[1,2] = -tBO*(1+np.exp(-1j*a*np.dot(k, y)))\n", + " H[1,3] = -tBO*(1+np.exp(-1j*a*np.dot(k, z)))\n", + " H[1,4] = -tBO*(1+np.exp(-1j*a*np.dot(k, x)))\n", + " H[2,0] = -tAO*(1+np.exp(1j*a*np.dot(k, x))+np.exp(1j*a*np.dot(k, z)) + np.exp(1j*a*np.dot(k, x+z)))\n", + " H[3,0] = -tAO*(1+np.exp(1j*a*np.dot(k, x))+np.exp(1j*a*np.dot(k, y)) + np.exp(1j*a*np.dot(k, x+y)))\n", + " H[4,0] = -tAO*(1+np.exp(1j*a*np.dot(k, z))+np.exp(1j*a*np.dot(k, y)) + np.exp(1j*a*np.dot(k, z+y)))\n", + " H[2,1] = -tBO*(1+np.exp(1j*a*np.dot(k, y)))\n", + " H[3,1] = -tBO*(1+np.exp(1j*a*np.dot(k, z)))\n", + " H[4,1] = -tBO*(1+np.exp(1j*a*np.dot(k, x)))\n", + " return H\n", + "\n", + "# Obtenemos las bandas de energÃa\n", + "bands_TB = np.array([np.linalg.eigvalsh(HamiltonianoTB(k)) for k in k_path]).T\n", + "\n", + "# Graficamos las bandas de energÃa\n", + "color = 'darkorchid'\n", + "n_graf = len(bands_TB) # número de bandas a graficar\n", + "for i in range(n_graf):\n", + " plt.plot(np.arange(400), bands_TB[i], '.', markersize=3, color = color)\n", + "plt.xticks([0,100,200,300,400],['$\\\\Gamma$','X','M','$\\\\Gamma$','R'])\n", + "plt.xlabel('Camino en el espacio recÃproco')\n", + "plt.ylabel('EnergÃa (eV)')\n", + "# plt.ylim(0,400)\n", + "plt.title('Bandas de energÃa mediante Tight Binding')\n", "plt.grid()\n", - "plt.show()\n" + "plt.show()\n", + "\n" ] }, { @@ -493,7 +465,16 @@ "metadata": {}, "source": [ "## 4. Análisis\n", - "\n" + "\n", + "Los modelos presentan diferentes comportamientos para las bandas de energÃa de los electrones en la red, dado que todos se fundamentan de manera diferente.\n", + "\n", + "En el modelo Empty Lattice, el más simplificado de todos donde no hay nada más que la red, se observa una dispersión cuadrática de la energÃa con respecto al vector de onda $\\vec{k}$ como es de esperarse para este modelo, dada su forma simple. Cabe notar que este mismo resultado sirve para cualquier cristal cuya red sea cúbica simple, como es nuestro caso. Esta aproximación permite hacerse a una idea de la forma de las bandas, al menos en sus niveles de menor energÃa.\n", + "\n", + "En el modelo generalizado de Kronig-Penney, se observa un comportamiento muy distinto. Primero, todas las bandas son decrecientes en el camino $\\Gamma - X$, lo cual no sucedÃa en Empty Lattice. Además, debido al método numérico empleado, valores de energÃa negativos no son permitidos, por lo que hay errores en algunas secciones de los caminos. Es importante resaltar la falta de literatura sobre este modelo en 3D, dificultando la obtención de resultados más correctos. En este modelo se consideran potenciales que se hacen tender a $\\delta$ de Dirac en cada punto en donde hay un átomo, mejorando la aproximación de Empty Lattice, pero aún con mayor margen de mejora.\n", + "\n", + "Por último, el model de Tight Binding es el más realista de los tres, pues considera la interacción entre los electrones en la red, a primeros (y segundos para el oxigeno) vecinos. Se observa que las bandas de energÃa son más complejas que en los otros modelos, con una mayor cantidad de mÃnimos y máximos locales. Si bien la forma de las bandas depende fuertemente de la elección de las constantes de hopping y de energÃa atómica (que no se calcularon en este trabajo), se puede observar que la dispersión de los electrones en la banda de menor energÃa tiene una forma muy similar a la del modelo Emppty Lattice. De estas bandas podemos identificar que la de menor energÃa esta asociada al átomo B, pues es mÃnima en $\\Gamma$ y máxima en R (cuando está más cerca y más lejos del átomo, respectivamente), mientras que la banda de mayor energÃa está asociada al átomo A, pues es máxima en $\\Gamma$ y mÃnima en R (cuando está más lejos y más cerca del átomo, respectivamente). Las demás bandas en medio corresponden a los átomos O. Es de notar que una de estas bandas es constante a lo largo de todo el camino, lo cual no parece ser correcto, pues recorremos un camino tridimensional en el espacio recÃproco. Esto puede deberse a errores en la implementación de los vecinos considerados, o una elección erronea de las constantes tomadas.\n", + "\n", + "En general, los diferentes modelos se aproximan de diferentes maneras y con diferentes rigores al problema de las bandas electrónicas. Estos modelos sirven para comprender las propiedades de conducción de los materiales, asà como otras propiedades térmicas y eléctricas. En particular, el modelo de Tight Binding es el más utilizado en la literatura para describir las bandas de energÃa de los electrones en los materiales, pues es el más realista de los tres, siempre y cuando se realice el calculo correcto de las constantes de hopping y de energÃa atómica." ] } ],