{ "cells": [ { "cell_type": "markdown", "id": "d168c172", "metadata": {}, "source": [ "# DFT-D4 in xnn: reproducing examples of the D4 paper\n", "\n", "[Caldeweyher, Ehlert, Hansen, Neugebauer, Spicher, Bannwarth & Grimme, *J. Chem. Phys.* **150**, 154122 (2019)](https://doi.org/10.1063/1.5090222)\n", "introduce the D4 dispersion model: atomic dynamic polarizabilities that depend on the\n", "**atomic partial charge** (eq 2, classical EEQ charges) and the **coordination number**\n", "(eq 8), integrated to pairwise $C_6$ coefficients (eq 9) and used in a BJ-damped\n", "two-body plus ATM three-body dispersion energy (eqs 18–28). This notebook uses xnn's\n", "independent implementation (`xnn.common.models.D4Dispersion`, verified against the\n", "reference `dftd4` code to machine precision in `examples/fidelity_checks/d4_verification.ipynb`)\n", "to reproduce, without any external quantum-chemistry data:\n", "\n", "1. the charge-scaling function $\\zeta$ of **fig 2**;\n", "2. the charge- and CN-dependence of the static carbon and hydrogen polarizabilities of **fig 5**;\n", "3. the atom-in-molecule polarizabilities and the molecular $C_6$ of (3Z)-hexen-1-yne of **fig 3(b)** and the text of sec II ($C_6^{\\rm mol}$(D4) = 1949.5, D3 = 1893.0, TD-DFT = 2103.1 $E_h\\,a_0^6$);\n", "4. molecular $C_6$ coefficients in the spirit of **table III** (the DOSD benchmark), D4 vs D3;\n", "5. the charge dependence that D3 cannot express, and the D4 vs D3(BJ) dispersion contributions to the S22 interaction energies (sec III.B).\n", "\n", "Everything runs with the PBE0-D4 parameters (`s6 = 1, s8 = 1.20065498, a1 = 0.40085597,\n", "a2 = 5.02928789, s9 = 1, alp = 16`), the paper's default `bj-eeq-atm` variant.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "4289f650", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T19:06:40.094143Z", "iopub.status.busy": "2026-09-23T19:06:40.094022Z", "iopub.status.idle": "2026-09-23T19:06:42.447465Z", "shell.execute_reply": "2026-09-23T19:06:42.446332Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "xnn 0.2.1 | PBE0-D4: {'s6': 1.0, 's8': 1.20065498, 'a1': 0.40085597, 'a2': 5.02928789, 's9': 1.0, 'alp': 16.0}\n" ] } ], "source": [ "import logging, warnings\n", "logging.disable(logging.WARNING)\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "import numpy as np\n", "import torch\n", "import matplotlib.pyplot as plt\n", "from ase import Atoms\n", "from ase.build import molecule\n", "\n", "torch.set_default_dtype(torch.float64)\n", "\n", "import xnn\n", "from xnn.common.data import structure_to_graph\n", "from xnn.common.models import D4Dispersion, DFTD4, c6_matrix\n", "from xnn.common.models import d3\n", "from xnn.common.models.d4 import BOHR, HARTREE, PBE0_D4\n", "\n", "d4 = D4Dispersion() # PBE0-D4, bj-eeq-atm, upstream cutoffs\n", "print(\"xnn\", xnn.__version__, \"| PBE0-D4:\", PBE0_D4)\n", "\n", "def run_d4(atoms, charge=0.0, model=d4):\n", " g = structure_to_graph({\"pos\": atoms.positions, \"atomic_numbers\": atoms.numbers, \"total_charge\": charge}, model.cutoff)\n", " out = model(g)\n", " out[\"c6\"] = c6_matrix(out[\"dynamic_polarizabilities\"])\n", " return {k: v.detach() for k, v in out.items()}\n", "\n", "# PBE0-D3(BJ) (Grimme, Ehrlich & Goerigk 2011) through xnn's D3 tables, for the comparisons\n", "D3_PBE0 = dict(s6=1.0, s8=1.2177, a1=0.4145, a2=4.8593)\n", "\n", "def d3_pairs(atoms):\n", " z = torch.tensor(atoms.numbers); pos = torch.tensor(atoms.positions) / d3.d3_autoang\n", " n = len(z); ii, jj = torch.meshgrid(torch.arange(n), torch.arange(n), indexing=\"ij\")\n", " off = ii != jj\n", " i, j = ii[off], jj[off]\n", " r = torch.linalg.norm(pos[i] - pos[j], dim=-1)\n", " cn = d3._ncoord(z[i], z[j], r, i, n)\n", " c6 = d3._getc6(z[ii.reshape(-1)], z[jj.reshape(-1)], cn[ii.reshape(-1)], cn[jj.reshape(-1)], d3.d3_c6ab).reshape(n, n)\n", " return z, r, i, j, c6\n", "\n", "def run_d3(atoms):\n", " z, r, i, j, c6 = d3_pairs(atoms)\n", " e = float(d3.edisp(z, r, i, j, **D3_PBE0).sum()) if len(z) > 1 else 0.0 # hartree, two-body only\n", " return {\"energy_au\": e, \"c6\": c6}\n" ] }, { "cell_type": "markdown", "id": "a7156d2b", "metadata": {}, "source": [ "## 1. The charge-scaling function ζ · fig 2, eq 2\n", "\n", "$$\\zeta(z^A, z^{A,\\mathrm{ref}}) = \\exp\\Big[\\beta_1\\Big\\{1 - \\exp\\Big[\\gamma^A\\Big(1 - \\tfrac{z^{A,\\mathrm{ref}}}{z^A}\\Big)\\Big]\\Big\\}\\Big],\n", "\\qquad z^A = Z^A + q^A .$$\n", "\n", "Fig 2 of the paper plots $\\zeta$ for $\\beta_1 = \\gamma^A = 1$: no scaling when the atom\n", "carries its reference charge (the crossing at 1), enhanced polarizability for\n", "anions ($z^{A,\\rm ref}/z^A < 1$) and suppressed for cations. The production model uses\n", "$\\beta_1 = 3$ and $\\gamma^A = 2\\,\\eta^A$ with the element's chemical hardness; both\n", "curves are shown for carbon.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "cc039905", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T19:06:42.450353Z", "iopub.status.busy": "2026-09-23T19:06:42.450210Z", "iopub.status.idle": "2026-09-23T19:06:42.889222Z", "shell.execute_reply": "2026-09-23T19:06:42.888153Z" } }, "outputs": [ { "data": { "image/png": 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fo02bNnmG782VmZmJW7duwcTEBE2aNIFAICj2+TUaDWJiYmBubl7q4YAJIYQQ8gZjDOnp6XBycgKfX4xyC66mm2WMscDAQPa///2Pubu7MwDswoUL+e63ZcsWZmFhwZo3b87at2/PWrRooZ2auTgiIyMZAFpooYUWWmihpQyXyMjIYn0Oc1qykZCQgAULFqBGjRpwdXXNd59Tp07hs88+w7Fjx9C3b18AwP3795Genl7sfvq53cAiIyO1sygSQgghpHTS0tLg6upa7G7WetEbJSoqCq6urrhw4QLat2+vs83X1xc2NjYlmgzofWlpaZBKpZDJZJRs6CGFQoGDBw9i0KBBRc6nQAghhHsl/VzVizYbBcnJycGNGzewdu1axMTE4NGjR3ByckL9+vULbXshl8t1ZmVMS0uriHBJKQkEAtStW7dE7XAIIYQYDr3ujZKUlAS1Wo2LFy+iZcuWWLFiBbp27YpmzZohJiamwOOWLl0KqVSqXQqqoiH6QSAQoHHjxpRsEEJIJaXXyUZukfr9+/fx9OlTBAQE4OXLl1Aqlfj6668LPG7evHmQyWTaJTIysqJCJqWgUCiwbds2KBQKrkMhhBBSDvS6GsXGxgYWFhbo1asXzMzMAAAmJibo3bs39u7dW+BxEomk1NNXk4onEAjQsmXLUpVsqNVqKJXKcoiKEFIWRCIRlVoS/U42eDwePv74Y7x48UJnfUhICJydnTmKipQ1gUCAevXqlegYxhhev36N1NTU8gmKEFJmLC0t4eDgQOMcVWGcJhuvXr3C3bt3kZSUBAAICgpCamoqateujdq1awMAFi9ejBYtWuCLL76Ar68vbty4gaNHj+Kff/7hMnRShhQKBbZu3Yrx48cXuzdKbqJhZ2cHExMT+idGiB5ijCErKwvx8fEAUOzhCkjlw2myERISgj///BMA0LdvX9y+fRu3b9/GkCFDtMmGt7c37t69i/Xr1+PEiRNwc3PD/fv3UbduXQ4jJ2VJKBSia9euEAqL93ZUq9XaRKNatWrlHB0h5EMYGxsDAOLj42FnZ0dVKlWUXoyzUd5onI3KJScnB2FhYfDw8ND+IyOE6K/s7GyEh4fD09MTRkZGXIdDykBJP1f1ujcKqRrkcjlWrlypMzZKcVDVCSGGgf5WuZMTHAymBz39KNkgnBOJRBg4cCBEIhHXoZB3ZGdnIz09neswCCElpH7n71bs7o7MGzc4jOYNve6NQqoGPp9PA6/pGY1Ggy5dukClUuH69etch0MIKQLTaJB5+TKS/tgOVVIivE6cAI/PB9/YGEYl7O1XHqhkg3BOLpdj6dKlJa5GMXSMMb0dI2TLli0YOHAgIiIioFaruQ5H68aNG3j27BnXYXyw+/fv4/Dhw7h27RpevXqFY8eOlftzPn78GLdv3y735yEVS6NQIPXIEYT26YPIiZOQdeMGFOERkD9/rt1HaG3NYYRvULJBOCcSiTBu3LgqU40SHR0NPz8/mJmZwdTUFC1atEBYWBjXYWklJSXhr7/+wtSpU1GnTp1y+3B/+vQp9u/fj6ioqGLtHx8fj969exv8gH1z585Fjx49cODAAdy6dQtXr17FhAkTyuTcT548wV9//YX79+/n2cbn89GzZ0+kpKSUyXMRbqnT0pC4aTNCOnVC7LffQRHyEnxTU1iPGQPvswEwqlOH6xB1ULJBOMfn82FnZwc+v/K/HRlj6NevH4yMjBAdHY2UlBTw+XysX7+e69C0vvvuO8yaNQvJycmoU6cO7t27V6bnv3btGtq3b49+/fph6NChxa6mWbJkCXr06AEvL68yjaeibdq0CevXr8ehQ4cwbdo0uLu745NPPvmgc968eRONGzfG4MGDsXnzZvTs2RPNmzdHXFycdp+6devC19cXv/7664deAtED2Q8eImHVKqgTEiG0t4fdrFnwDrwA+zmzIdLD8UyozQbhnFwux7JlyzB37lyD/9ZalKtXr+LBgwc4e/YspFIpAMDe3l5vWuvfunULe/fuxaFDhwC8GXBNLBZj5MiRZfYcaWlpWLBgAVq1alXsrstZWVnYvn07/P39tetycnLg7++PHj16ICEhAc+ePYObmxt8fHy0+2RkZODkyZMA3sy1VL16dXz00Uc69/vcuXOwt7eHo6Mj7t+/D8YY2rVrl2eAOblcjmvXriEjIwP16tWDp6endtvLly8RHByMbt264dq1a4iNjYWfn5/OOZKSknDmzBmkpqbi3r17kMvlaNu2LZydndGjRw+d51Iqlbh8+TJUKhUaNWqElJQUhIWFoVu3bvnen8zMTGzfvl177VlZWWjZsiWmT5+uM7XDyJEjMXHiRCxcuLDKlCRWFsroaMhDQmD2v/8BAEzb+MKiVy+YtW0Dix49wCvmgIhcoWSDcE4sFmP69OnFHj3UkJ07dw7NmzfXJhqhoaEICAjAlClTSnSe06dPFzpUu1gszvfbctOmTaFQKBAYGAjrd+px+/btCwsLC7x8+RL379/XfpBeu3YNc+fOzfc5Tpw4gaysrAJjMDU1Re/evfOsz/3AzMnJKfDY9126dAlyuRytW7fWrktNTcXQoUPRo0cPPH/+HDVq1EBQUBBGjBiBjRs3AnjzIZyboMjlcty8eRM1atTAP//8AxMTEwDAggULwOPxEBYWhgYNGuDp06cwMzPDhQsXYGdnBwC4ffs2+vXrp01Krl69ihEjRmDNmjUAgLNnz+L777+Hp6cnxGKxNoF49z2dkpKC48ePA3gzWvJ///0Hb29vhISEYMqUKejXrx8AIDk5GR06dEBSUhI++ugjPHz4EDVq1EBKSkqByUaHDh10HpuYmKB79+7aROvd/RITE3Hjxg20adOm2PefcEceGoqkLVsh++sv8E1M4H3+PARmpuDxeHD+dTnX4RUbJRtEL3xoiUbusMgVraRDpd+5cweNGjXCtWvXcPr0aWzevBn9+/dH586dS/S8586dK3Q2Y1NT03yTjf3796NZs2Y4ffo0hg0bBgA4deoUAgMDsWzZMlhaWup8Y69du3aBbSrOnDmjnWogP7a2tvkmG6Vx9+5dVK9ePd/3SWZmJp4+fQqJRIL79++jWbNm6N+/P7p06QJ7e3vs379fu29OTg5at26N33//HXPmzNGuv3PnDu7fv4+aNWsiKysLbdu2xfz587Fp0ybk5OTAz88P3333HSZNmgQAiI2NhY+PDzp06AA/Pz8AQEJCApYsWYLx48fnew3e3t7Ys2cPDh48iO+//x7t27cH8GYk5Xf99NNPUCqVePr0KSwsLPDq1Sv4+PjA3d292PeLMYbz58+jfv36OustLS3h4uKCW7duUbKh57KfPEHS5i1IDwgA3o69aVSvLtSpKRCYmXIcXclRskE4p1AoPrgaJSsrSzszcEXKyMiAqWnx//Dv3r0LPz8/HDhwAP7+/oiLi4OzszMYY+DxeAgPD9d++DRp0gRWVlb5nmf58tJ9o/H29kbr1q3x9OlTAG++7U+bNg2LFi3C5MmT8+xvZWWFly9f5nuudevWlSqG0khMTCzwXkybNk37vmnYsCG6du2KgwcPokuXLgDefPDeu3cPr169Qk5ODlxdXXHz5k2dc/Tt2xc1a9YE8CaBnDJlCmbMmIFNmzYhICAAcXFxsLKywuHDh8EYA2MMXl5euHDhgjbZMDU1xbhx4z74Wg8fPowZM2ZoR2V0c3PDkCFDcO3atWKf44cffsDTp0+xY8eOPNusrKyQmJj4wXGS8iEPDUXcsmXIvHRZu86sUyfYfDYBxu9UERoaSjYI58RiMebOnVvpq1ESExMRFRWFRo0aYcyYMVi9ejUuXLiATp06oX379ujevTuuXLmC7du3a7tG5n77fV9pq1GAN6UVwcHBAIBff/0VRkZGJa7GAUpfjVIaZmZmyMzMzHebh4eHzmNPT0/8999/AN5M2Ne5c2fIZDI0aNBAW1X0fuKS3zlSU1ORlpaG8PBwiESiPN1TPTw8UL16de3jsmh7wxhDdHR0nng8PDyKnWysW7cOS5YswZEjR/KdTTkzMxPm5uYfFCcpRzweMoOuAHw+LHr2RLUJ42H0NhE2ZJRsEL0gl8s/KNkwMTFBRkZGGUZU/Octrrt370IsFut8ALRr1w5CoVA73sbw4cMxfPhwdO/evdBzlbYaBQDq1KmD06dP49WrV1iyZAn++eefYk+C966KrEapWbMmwsPDtSVA73q/K2dKSgpsbGwAAL/88gusrKzw8OFDbW+nKVOm5Okamt85JBIJzMzMYGFhAaVSiR07dhRa8lYWjXx5PB4sLS3zJJLF7a66YcMGzJgxA4cOHUKvXr3ybFcqlYiOjkatWrU+OFZSNrIfPkTWnbuoNmY0AEDi6QmHRQth2qIFxG5u3AZXhijZIJxTKBRYtWrVB1Wj8Hi8ElVncOHu3btwcHDQ6QVw6tQpCIXCPA38ilLaahTgTclGSEgIpk6dCj8/P/zvbev2kqrIapQOHTogLS0NT58+zfNt3d/fX9vmJTMzE2fOnMGiRYsAvCnZqFGjhjbRyMnJwd9//w1nZ2edc/zzzz/anjcAcPToUbRq1Qp8Ph+dOnUCAGzbtg2ff/659hiVSoXk5GRtI9Ky4uvri+PHj2PUqFEA3ozmevLkySITwk2bNmH69Ok4ePAg+vTpk+8+d+7cgUqlKvVrTspO9sOHSFi3DpkXLwF8Psz+1w6St926rQYO5Di6skfJBuGcRCLBggULuA6j3N29exevXr3CyJEj0b9/f4SGhmLJkiVYsmRJhbY3qVOnDhQKBS5cuKCtTqlIMTExuHTpkrY058qVK1CpVKhZsyYaN26c7zG5vTv27duHH3/8UWfbwYMHAQD169fH9u3bYWNjo22k6efnh08//RQeHh6ws7PDH3/8gdTU1DzJRnZ2Nrp06YJhw4bh9u3bOHjwIC5cuAAAcHV1xa+//oqvvvoKjx49QtOmTREZGYnDhw9j1apV2rYhZWXhwoVo3bo1Ro0aBV9fXxw7dgxxcXFwcXEp8JgjR45g8uTJGDZsGLKzs7WNYt+vTjtw4AA++eQTnZ5IpGLpJBkAIBBA2rcv+JV8BmtKNgjnNBoNEhMTYWNjU6kH9rp79y4mTZqEhIQErFixAi4uLti9e3eRVSZlrVq1arC0tMTs2bPh5ORUoc8NAHFxcdruqIMHD0ZsbCz8/f3RrVu3ApMNAJg/fz769euHb775Rqf66vjx47hy5Qpu3bqF7t276zQYHTRoEIyNjXHy5ElERkbiq6++gkgkwpMnT3TO/cUXX6Bu3bq4dOkSxGIxrly5gqZNm2q3f/nll/D19cXBgwdx+fJlVK9eHcePH9e22fD29s632uJ9fD4fgwcP1ikNeX9Qr0aNGuH69evYunUr7t+/j+HDh6NJkya4dOlSgedVKBQYNGgQVCqVzlgk71anyWQy7NmzBwEBAUXGScqeMjYWrxf9gIzAwDcr3iYZNpMmVqrqkgKxKkAmkzEATCaTcR0KyUdOTg5bsmQJy8nJKdb+2dnZ7OnTpyw7O7ucIys7MpmM8Xg8duPGjUL3e/36NTt79ixr2rQp+/XXX9mVK1fKPJaUlBTG4/HY3bt3y/zc5e2nn35iFy5cYIwxFhsbywCwR48efdA5fX192YIFCz48uDKSk5PDMjMztY81Gg1r1qwZ++qrrz7ovGfOnGHLly//0PBKxRD/ZsuaKi2NPW/egj2tW49Fz/uGySMiuA7pg5T0c5VKNgjnJBIJ5s2bx3UY5erevXsQCAT46KOPCt3v2bNnWLZsGaRSKU6dOoWHDx/qDGRVFu7evQuRSJRvTwV9980333AdQrnLzs5Gp06dMHDgQFhaWuLIkSOIiIjQVheVVteuXdG1a9cyipIURRkbC9nx46g2cSJ4PB4E5uZwXLYUEk9PiN/rbVQVULJBOKfRaBAdHQ1nZ+dKW40iFouxYMECGBkZFbpf+/btC+zuWlZy28gYeldjY2NjDB48GJaWlh90ns6dO+cZ/IpLlpaW2L9/P3bt2oWQkBB07twZ+/fvR7Vq1bgOjRSDKjkZSZs2I2XfPjCFApKaNWHesSMAwLyEDcErEx5jb4cmq8TS0tIglUohk8m0A+UQ/SGXy7Fu3Tp88cUXxeqNkpOTg7CwMHh6ehb54U0I4V5V+JtVp6cjeft2JP+5A5q348+YNGsGuzlzYFzf8EoRi1LSz1W9KNm4ffs2goODtcMLFyQqKgqBgYGoU6cOmjRpUoERkvIkkUgwY8YMrsMghJASY0olknfvQdLGjVDLZAAAo/r1YTv9K5i2bq03kyxyjdNkIyAgAPPmzUNWVhaCg4Nx4cKFApMNlUqFAQMG4P79+5g0aRIlG5WIRqNBaGgovLy8Km01CiGkkuLzITt6BGqZDGLv6rD98kuYd+5MScZ7OE025HI5Nm7cCEdHR7i6uha677fffouaNWuWaKZIYhhUKhUCAgIwfvx4g29HQAip/LJu3YJRgwbgGxmBJxDA/ptvoIyJgdTPDzyBgOvw9BKnyUbuUMYFzSqZKyAgAIcPH8a9e/fQrl27igiNVCCxWKwzMiMhhOgj+YsXiP91BTIuXoTdzK9R7e3gcaatWnEcmf7TizYbhYmLi8OYMWNw8ODBYjfulMvlkMvl2sdpaWnlFR4pA2q1GsHBwahduzYE9K2AEKJnlHHxSFz7O1KPHAU0GkAohDotneuwDIpeJxuMMYwcORLjxo2Dr69vsY9bunSpdm4Eov/UajWuX7+OGjVqULJBCNEbmqwsJG3diqQ/toO9rcI379IFtjOmQ+LpyXF0hkWvk419+/bh5s2bGDZsGHbv3g3gzeyHwcHB2L17N4YPH55vI5x58+bp9G5IS0srsk0I4Y5YLMa4ceO4DoOQDxYdHY1t27bhxYsXcHd3x+eff87JkPCkbLxe/CNkx44BAIwbNoTd7FkwKWRIfVIwvW76b2tri169euHff//F6dOncfr0aaSnpyMiIgKnT59GQUOESCQSWFhY6CxEf6nVaty9exdqtZrrUAgptaCgIDRq1AjJycno2rUrGGPFmi+F6Bf2zv+hahMmQOzhAefVq+G+by8lGh9Ar0s2unTpkmdGxYYNG6J9+/ZYvXo1N0GRMqdWq/H06VPUr1+fqlFK4e+//8bEiROLbGhd0QIDA3HixAmkp6ejSZMmGDduHEQiEddhlYusrCwMHjwYO3bsQI8ePbTrZ86cyWFUpCSUsbGIX7ESfBMTOP7wphpe4uUJr3/+Bo+65H8wTu9gaGgodu/ejWNvi6nOnj2L3bt34+HDh1yGRSqYWCzGiBEjqNtrKSmVSqSmpnIdho5Vq1ahf//+qFatGnx8fPDDDz9g2bJlnMRy+fJl+Pn5wc3NDXXq1MGUKVOQkJBQps/h7++P2rVr6yQaAGBlZVWmz/MulUqF77//HjVq1ICTkxOGDRuG2NjYQo/Jzs7GvHnzUL9+fTg6OqJZs2bYsGFDgftPnDgRlpaWBe6jVqvRpUsXWFpa4ty5cx90PVzRZGcj4fe1eNnjY6SdPInUo0ehfP1au50SjbLBaclGdHQ0Tp8+DQAYPnw4IiIiEBERARMTkwInrOrZsyfq1KlTkWGScqZSqXDr1i00a9YMQqFeF7aRYpDJZJg3bx78/f3RvXt3AMDz58/x4sWLCo8lLi4OS5YswdSpU9GwYUNERUVh6tSp6Nu3L65evVpmz/Pff/9V+ECDc+bMwd69e7Fv3z7Y2dlhypQp6NGjB+7cuVNgCeFXX32FU6dOYc+ePahRowYuXLiA0aNHw8jICGPGjNHZd9++fbh37x40Go1O7753LVq0CIwxyGQyKJXKMr/G8sQYQ9rJk4hfsRKqt8mFcdMmsJ83DyIHB46jq4TKa/pZfUJTzOs3hULBDh48yBQKRbH2N+Tpql+/fs0mTJjAPD09WfXq1dmcOXNYTk4OY4yxP/74g0mlUiaVSpmLiwvr0aMHu3PnjvbYnJwcJpVK2datW1nnzp2ZnZ0d+/3339mxY8eYqakp27t3L2vRogVzcHBgvXr1YuHh4TrPffDgQda0aVNma2vLGjduzPbs2aOzXSqVss2bN7O+ffsyNzc31rBhQ3b06NESX+P+/fuZra0t02g02nUNGzZkS5YsKfG5ysOePXsYgBK9f3bv3s1++ukn7WuV6+LFi2z27Nls+/btrE2bNkylUmm3HTt2rKxCzkMmkzGJRMK2bNmiXRcWFsYAsOPHjxd4XL169djXX3+ts65169Zs/PjxOutCQkKYo6Mj+++//5hUKmWrVq3Kc64LFy4wT09P9uzZMwaAnTp1qsDn1be/WfmrVyxsyFD2tFZt9rRWbfaiQ0cmO3VK5z1LClfSz1VKNojBKewflzozs+DlvQ+KQvd979z57VNS6enprEaNGqxTp07s1q1bLCQkhC1btozt3r2bMcaYXC5nKSkpLCUlhUVERLD58+cza2trlpSUpL1uAMzW1padOHGCJSQksJycHHbs2DEGgNWvX5/dvHmTBQcHsx49erD69esztVrNGGMsICCAiUQitmHDBhYREcE2b97MRCIR++uvv7TxAWB2dnbsr7/+YlFRUeznn39mYrGYRUREaPdp1aoVmzp1aqHXOWPGDNajRw/GGGPx8fFsypQpzNramr1+/brE9yw3wSps6du3b7HPl5SUxHr37s06duxYoji2b9/OzMzM2Lp163Ri8/b2ZqtWrWJyuZx16tSJeXp6so8//pjVrFmT/fDDD4Wes27duoVeV4MGDQo89t9//2UAWGhoqM76GjVqsFmzZhV43Lx581i9evVYVFQUY4yx69evMwsLC50ERS6Xs6ZNm2oTmfySjYSEBObq6soCAwNZbGyswSUbyuRk9rx5C/asUWOWsGFjnv8NpGiUbOSDkg39plQq2YULF5hSqSzW/oX948r9ppLfEvHZZzr7PmvYqMB9w0eM1Nn3ectWefYpqbVr1zIrKyuWmppa7GNq166tTUZyk40VK1bo7JObbFy+fFm7Li4ujkkkEm0y0b59ezZ69Gid4yZMmMBatmypfQyArV69WmefatWqsX379mkf16tXj40bN67QmDt06MC++eYb9tVXXzEADADbsWNHsa/5fbkJWEFLRkZGkef47LPPmIWFBQPAWrZsyZKTk0scx6effqpTArB48WJWv359nfft/fv32alTp1hMTEyR55PJZIVeV2H/r3bs2MEAsMz3kl5fX182fPjwAo/TaDRs7NixDACTSCRMKBSy9evX6+wzY8YM1q9fP+3j/JKNnj17snnz5jHGmEEkGxq1mqUHBuqUXGRcvcoUsbGcxFMZlPRzlVq+EM4xxpCWllZgV+bK4ubNm2jSpAmkUmm+21NTUzF9+nTUr18fNjY2sLS0xIsXLxAREaGzn4+PT55jeTweWrRooX1sZ2eH6tWr4/HjxwCAR48e5RkYr23btnjy5InOuvfbQ9nY2CApKUn7+Nq1a/j9998Lvc579+6hUaNGmDx5MgICAjB27FiMHz8e9+/fBwAcOHAAtWvXRu3atREQEFDouQDA0tKy0MXU1LTIc6xatQqhoaG4evUqGGPo3bs3NBpNkce9q379+nj27BkAICIiAkuXLsW6det02hn5+Pige/fucHR0LPJ8FhYWhV5Xcbrsvz9xoVAoLPTvaNasWTh//jzOnz+P0NBQ7Ny5E7NmzcLhw4cBAGfOnMH+/fuxZcuWAs/x22+/4fXr1wYzcGL24yeIGDoMkRMnIf3sWe1601atqG1GBaLWeIRzIpEIffr0KZNz1bp7p+CN7zWaq3klqOB93/sn7n3u3w8JC8Cb2W0L6/r52WefITY2Fps3b4aXlxeMjIzQoUMHKBQKnf0kEkk+4fLz/eBRqVQA3jTCfb/xbe52xph2cLz8Zt1998PL3Ny80GsMDQ1FamoqGjduDC8vL9SsWRNdunTBiRMncO3aNTRs2BDdunWDj48PZs+eXeRUAnK5vMCZoHO1b98e/v7+he5jYmICExMTtGrVClu3bkWDBg1w7dq1Eo1MXLt2bfz8888AgOnTp6Nfv34fNFdTvXr1EB0dXeB2Nze3Anvm2dnZAQASExPh4uKiXR8fH49GjRrle0xOTg5Wr16NTZs2oUOHDgCAoUOH4vz581i2bBkGDBiAs2fPIjExEdWrV9cel9vgd8uWLXjy5AkCAgLw5MkT2NraAvj/98eAAQPQuXPnIl+LiqJOTUX86tVIPXAQYAx8ExNo0mmIca5QskE4p1KpcO7cOXTq1OmDe6PwTUw437cgDRo0wKpVqyCXy/NNGC5cuIANGzagdevWAIDMzEyEhoYW69xqtRqPHj1Cw4YNAQDp6ekICQlBrVq1AAC1atXCnTt3MHr0aO0xt2/fRs2aNct0Kuy7d+/CwsICnu8M5ZycnIzU1FRtb42SfHOXSCQIDw8vdJ+Sjt2R+x4rae+JOnXqICkpCbt378a///6L58+fl+j49127dq3Q0pX8Er9cTZs2hUAgwOXLlzF06FAAb3rePH/+HN9//32+x7A31eYwMjLSWW9kZKSN48cff8R3332ns93d3R1z587FF198AeBNydS79y4+Ph61atXCjh07tL2PuMQ0GqQePoyElaugftsl3KJXL9jNmgWRvR23wVVhVI1CSAUZM2YM1Go1Jk6ciKSkJMjlchw8eFD7TdDT0xPHjx+HXC6HTCbDxIkTSzSJ4FdffYX4+HhkZmbiyy+/RLVq1bQlRjNmzMD27dsREBAAjUaD8+fPY/PmzZg+fXqJrqF169aYNm1agdvv3r2LjIwMbZf2zMxMfP7552jcuDGaN29eoufK9SHVKIcPH8aWLVuQnJwM4E3Jy7Rp0+Dh4YFW78zUaWNjg7Vr1xYah6enJyQSCSZNmoSFCxcWq6qkMB9SjWJjY4Nhw4Zh0aJFCA8PR3p6OqZPnw5XV1f4+fnle13Gxsbo2LEjli9fjrCwMABvEp5du3ahZ8+eAN4kHu/HwePxYGxsrI3H1NQ03zhNTU2LVaVV3mLmzMXr7xdAnZoKSY0acNu5A86/LqdEg2OUbBDOCYVCdOvWrdKPsWFra4sLFy7g1atXsLe3h52dHY4dO4a2bdsCADZt2oR79+7B3NwcTk5OEAqFBRaJv8/U1FRbPSGVSnHz5k0cO3ZMW4IyePBgLFiwACNGjIBEIsGgQYMwb948jBo1qkTXkJaWhqysrAK33717F56enujVqxfs7e1hbW2NlJQUHDlypETPU1Y6duyI4OBg1K1bF0ZGRmjWrBkcHR0RGBiovTexsbFITk4u8l4LBALUqFED7u7uhSZcFWXDhg1o1qwZatWqBWtra4SFheGff/7RKblITU1FztsJxABg165dqFOnDnx8fCCRSNC3b1989tlnmD9/PheXUC6kfn3BNzWF/by58Dx6BKalTHJJ2eKxyt4qD2/+QUqlUshkMponRQ8plUqcOnUKPXr0KFaReE5ODsLCwuDp6ZmnSNhQKJVK8Pn8fAdfysnJgVgsBp/PR0ZGBoRCofY6U1NTYW5urnOcUqlEVlaWtuFpQdU0ubKysmCST7VQamoqzMzMdJK+9PR0SCQS7eiu6enpEAqFMDY2zvfc9vb2WLVqFbp3747Y2Fg4OTkVOIrmiBEj4OfnhwEDBhQYa1kq6L5s27YNAQEBOHDgQJHn+OijjzB+/Hi9SDZyqdVqqFSqfK9NJpPByMgo321FvU+Kcw4A2kG93n/vvKs8/2bTAwOhTk2F5TslOmqZDIICGmKTslHSz1VKNgjnVCoVgoKC0KZNm2KVblSGZKMyio6OhouLC549e4batWsXuN+1a9cwZswYxMbGwszMDM7Ozrh582YFRqorJycHAoGgyEQ3Ozsb5ubmCAwMRJs2bSoousqhPP5mlXHxiFuyBOlnzoBvYgKvf/6m3iUVqKSfq5W73JoYBKFQiPbt23MdBvlADx8+hLW1NWrWrFnofj4+Pjo9FriefK+4H36PHz+GWCzWNsIl3GBqNVL27kPC6tXQZGYCAgEshwyBoIieUoRblGwQzimVSvj7+8PPz6/SzgpaFfTo0UNnTI6CmJiYFFryoa+aNWtWaHsVUv6ynzzB6wULkfN2/Bgjn4/guGgRjAzw/VTVULJBOMfj8eDi4lKmXTAJIZWLKjEREUOHgSkU4Jubw27GdFgOGgQexyVjpHgo2SCcEwqFOt0QCSHkfUIbG1iNHAFVbCzs5s6FyI66shoS6vpKOKdQKLB79+48I2UWpQq0bSakUijN36o6LQ2x3y9Azn//adfZff01nFeupETDAFHJBuGcQCBA3bp1i91QMLddR1ZWVoFdMAkh+iO3rUtx22SlnzuH1wsXQZWQgJznwfDYvx88Hg+8QkZVJfqNkg3COYFAgMaNG5dof0tLS8THxwN40+CQ2nsQon8YY8jKykJ8fDwsLS2L/EKhSkzE659+QvqpNyPQij08YD9rFv19VwKUbBDOKRQK7Nq1CyNHjtQOHlUUh7f96XMTDkKI/rK0tNT+zeaHMYa0EycQt2Qp1DIZIBCg2rhxsPnic/CLMfAY0X+UbBDOCQQCtGzZskTjLfB4PDg6OsLOzq7EE2oRQiqOSCQq8m87/cwZxMyZCwCQ1KkDxx8Xw7hevYoIj1QQSjYI5wQCAeqV8h+LQCDgfFAoQsiHMe/cGcZNm8CsbTtUGzsGPBpvp9LhvLUNYwz//vsv1q5di+jo6Hz3CQsLw759+3Do0CG8evWqgiMk5U2hUGD9+vUl7o1CCDFMythYxC5YCI1cDgDgCYVw37kTNhM/o0SjkuK0ZOP48eOYNWsWrKyscPPmTdSvXx/Ozs7a7YwxDBo0CPfv39eO3vfpp59i8eLFmDlzJoeRk7IkFArRtWvXSj/rKyFVHWMMsqNHEbd0GTQZGRBYWMDu6xkAQD1NKjlO/7ubmpri77//hrGxMVxdXfNsZ4xh8ODBOHjwoLY18t69ezFixAj069cP1atXr+iQSTng8/nw9vbmOgxCSDlSxsUj9vv5yLx4CQBg3LAhpJ/04zgqUlE4TSU7d+6MGjVqFLidz+djwIABOt2eOnfuDMYYnj9/XhEhkgogl8uxcuVKyN8WqRJCKg/GGGR//YXQPn2QefESeCIR7GbNhPue3ZB4enIdHqkgBldufeLECQgEAvj4+BS4j1wu1/ngSktLq4jQSCmJRCIMHDiQJmEjpBJK2rgRCWt+AwAY1a8Pp2VLIaGSzCrHoCrJnjx5gq+//hqzZs3SadvxvqVLl0IqlWqX/KpoiP7g8/lwdXUFn+psCal0pH36QCCVwvbLafDYv48SjSrKYP67h4SEoGvXrujTpw9++umnQvedN28eZDKZdomMjKygKElpyOVyLF26lKpRCKkEVCkpSD1yVPtY5OyM6ufOwWbyZPCoEXiVZRCv/MuXL9G+fXu0b98ef/75Z5HfgCUSCSQ06pzBEIlEGDduHFWjEGLgMoKuIHbePKgSEiB0sIeZry8AQGBmynFkhGt6n2yEhoaiffv2+N///oedO3fSAE6VEJ/Phx3N4kiIwdLk5CD+1xVI2b0bACD28oLA0pLboIhe4TTZCA4Oxr///ovU1FQAwLFjx/D48WM0b94czZs3R3Z2Njp06ACFQoHmzZtjw4YN2mM7duyIunXrchQ5KUtyuRzLli3D3LlzqUSKEAOT/eQJYmbPgeLlSwCA1fDhsJv5Nfg0IzN5B6fJhkwmQ3BwMADgiy++gFqtRnBwMLy8vAAAGo0GvXv3BgC8ePFC59gmTZpUbLCk3IjFYkyfPr3Yk7ARQvRD8q7diPvlF0CphMDWBk5LlsCsbVuuwyJ6iNNko0WLFmjRokWB201NTbF27doKjIhwhUo0CDE8wmrWgFIJ8y5d4PDDIgitrLgOiegpg+mNQiovhUKBZcuW0dwohOg5xhiUr19rH1t8/DHcdu6A829rKNEghaJkg3BOLBZj7ty5VI1CiB5TpaQg+suvENZ/AFRJSdr1ps2b64zyTEh+KNkgeoHG2CBEf2Veu4awPn2RHhAAtUyGrDt3uA6JGBhKNgjnFAoFVq1aRdUohOgZplQifsUKvBo7DqqEBIi9vOBxYD8sunblOjRiYHiMMcZ1EOUtLS0NUqkUMpkMFhYWXIdDCCF6T/HqFaJnzkLOw4cAAMtBg2A/by51aSUASv65qveDepHKT6PRIDExETY2NjQ/CiF6IumPP5Dz8CH4FhZwXLwYFt2oNIOUHv1nJ5xTKpXYtm0blEol16EQQt6ymzkL0r594eV/jBIN8sGoGoUQQgiyHz2C7Ngx2M+fT71LSJFK+rlKJRuEcxqNBpGRkdBoNFyHQkiVwzQaJG3divChw5Cydx9SDx7iOiRSCVGyQTinVCpx6NAhqkYhpIIp4+MROX484n9dAahUMO/eHRbdu3EdFqmEqBqFEEKqoIyLFxEzdx7UKSngGRnB/ttvYDlgAFWhkGKhahRicDQaDUJCQqgahZAKkrTtD0ROnAR1SgoktWvD88hhWA0cSIkGKTeUbBDOqVQqBAQEQKVScR0KIVWCSdMmgEgEqxEj4HFgPyTVq3MdEqnkqBqFEEKqAGVcHET29trHishIiF1dOYyIGDKqRiEGR61W48mTJ1Cr1VyHQkilwxQKxC37GS+7dUfO8+fa9ZRokIpEyQbhnFqtxvXr1ynZIKSMKaKiET5yJJL//BMsJweZQUFch0SqKBqunHBOLBZj3LhxXIdBSKWSfu4cYuZ9A01aGvgWFnBa8hPMO3fmOixSRVHJBuGcWq3G3bt3qWSDkDLAFAq8XrIEUV9MgSYtDUY+H8Hz6FFKNAinKNkgnFOr1Xj69CklG4SUgdRj/kjZuQsAYD1mDDx27YLYxZnjqEhVx3k1ilKpxPHjxxEcHIyRI0fC3d09zz7p6enw9/dHXFwcGjRogG7daIS7ykQsFmPEiBFch0FIpWA5oD8yr12DtE8fmHfswHU4hADguGRj3759qF69OjZv3oz58+cjLCwszz5RUVFo0KABfv/9d7x8+RJjxozBwIEDUQV67FYZKpUK165do3E2CCkFplQi6c8/oZHLAQA8gQAuq1dRokH0CqclG25ubrhx4wbUajVcC+iGNWfOHNja2uLKlSsQiUT46quvUK9ePRw5cgQDBgyo4IhJeWCMISoqCk2bNuU6FEIMijIuHtFfz0D27TtQhIbB8YdFXIdESL44Ldnw9fWFo6NjgdvVajX8/f3x6aefQiQSAQBq1aqFtm3b4vDhwxUVJilnIpEIAwcO1L7GhJCiZd64ibD+/ZF9+w74pqYwbePLdUiEFEivG4i+evUKWVlZqFmzps76mjVrIjg4uMDj5HI50tLSdBaiv1QqFQIDA6kahZBiYBoNEjdvwasxY6BOTISkZk14HjkMi65duQ6NkALpdbKRkZEBAJBKpTrrLS0ttdvys3TpUkilUu1SUBUN0Q+MMaSlpVE7HEKKoJbJEDVlKhJWrgQ0Gkj79oXHgf0Qe3hwHRohhdLrZMPU1BQA8pRMyGQy7bb8zJs3DzKZTLtERkaWa5zkw4hEIvTp04eqUQgpgjo9A1l37oAnFsPhh0VwXLYUfGNjrsMipEicd30tjJubG4yNjRESEoKu7xQRvnjxArVq1SrwOIlEAolEUhEhkjKgUqlw7tw5dOrUCUKhXr8lCeGU2MUZLqtWgm8hhXH9elyHQ0ix6XXJhlAoRO/evbFr1y5tff7Lly9x6dIlfPLJJxxHRwgh5UuTnY2Yb75FemCgdp1p69aUaBCDw+kU8w8fPsSJEyeQlpaG5cuXY+zYsfD09ES7du3Qrl07AEB4eDh8fX3h5eWFZs2a4fDhw/Dx8cHx48fB5xcvV6Ip5gkhhkYREYGoaV9C/vw5BFZW8P73LPiFVB8TUpEMaop5tVqNnJwciMVifPvtt3B0dEROTo5OrwQPDw88fvwYI0eOhJWVFX777bcSJRpE/ymVSpw4cQJKpZLrUAjRC+nnziGs/4A3iUa1anBetYoSDWLQOK0gb9SoERo1alTkflZWVvjss88qICLCBR6PBwsLC/B4PK5DIYRTTK1Gwu+/I2njJgCAcePGcF61CiJ7O44jI+TDUGs8wjmhUIj27dtzHQYhnNIoFIj6YgoyL18GAFh9OhL2s2aBR720SCVAdRGEc0qlEocOHaJqFFKl8cViiBwdwTMygtPyX+DwzTeUaJBKg0o2COd4PB5cXFyoGoVUSUyhAE8sBgDYf/ctrD8dCYm3N8dREVK2qGSDcE4oFKJVq1Y0xgapUphSidc//oTIyZ+DqdUA3pRuUKJBKiNKNgjnFAoFdu/eDYVCwXUohFQIVUICIkaPQcru3ci8cgVZN25wHRIh5YqSDcI5gUCAunXrQiAQcB0KIeUu6+49hH3SH9l37oBvZgaX9etg2ro112ERUq6o3JpwTiAQoHHjxlyHQUi5YowhZd8+xC1dBiiVEHtXh8vvv0Pi6cl1aISUOyrZIJxTKBTYtm0bVaOQSi1hzRrE/bAYUCph3r07PA8coESDVBmUbBDOCQQCtGzZkqpRSKVm0aMH+KamsJs1C86rVtKIoKRK4XRulIpCc6MQQrigSkiA0Nb2/x+npEBoZcVhRISUDYOaG4UQ4E01yvr166kahVQajDEkbduGkM5dkH3/vnY9JRqkqqJkg3BOKBSia9euNM4GqRQ02dmI+Xom4pf/CiaXI/3cOa5DIoRz9N+dcI7P58ObBjIilYAiKhpRU6dC/uwZIBTC/pt5sBo6lOuwCOEclWwQzsnlcqxcuRJyuZzrUAgptcwbNxE+cCDkz55BYG0N9+1/wHrYMBqGnxBQyQbRAyKRCAMHDoSIJp0iBir70SO8GjsWUKthVLcuXNathcjRkeuwCNEblGwQzvH5fLi6unIdBiGlZlSvHsw7dgTP2AiOP/wAvpER1yERoleoGoVwTi6XY+nSpVSNQgyKMi4emuxsAACPz4fTil/h9PPPlGgQkg9KNgjnRCIRxo0bR9UoxGBk3b2HsAH9Efvtd8gdqogvFlP7DEIKQMkG4Ryfz4ednR34fHo7Ev2XcugQIkaNgjohEfIXL6CRybgOiRC9ZxBtNp4/f44zZ84gJSUFbm5u6N+/P40EWonI5XIsW7YMc+fOhUQi4TocQvLFFArELVuGlL37AADmXbvCaekSGnackGLQ+6+S27dvR4MGDXDnzh1oNBps27YN3t7eCAkJ4To0UkbEYjGmT58OsVjMdSiE5EuVlIRXY8e9STR4PNh+9SWc16ymRIOQYtL7uVHq1KmDTp06Ye3atQAAlUoFb29vDBs2DEuWLCnWOWhuFP3GGINCoYCY6ryJHmKMIXzgIOQ8fgy+qSmcli+HeccOXIdFCKcq3dwo1tbWUCqV2scajQYqlQrW1tYcRkXKkkKhwLJly2huFKKXeDwe7OfMhqSGNzwOHaREg5BSKFbJRmJiIoYPH46ff/4ZDRs2rICw/l9wcDAmTpwIa2truLu749q1a2jcuDFWrVoFowK6mMnlcp1ulGlpaXB1daWSDT1FJRtE3zCVCvKXL2FUq9b/r1OrwRMIOIyKEP1RLiUbKpUKAQEB+Oabbz44wJKKiopCREQETExMYGFhAYFAgODgYMgKaQG+dOlSSKVS7UIDRuk/GmOD6At1aioiP5uIiKHDIH/xQrueEg1CSq9E1Sjnzp1DQEBAofvs378fP/zwA8LCwj4oMOBN8fqQIUMwduxY7NmzBz/88AOCgoKQlpaGOXPmFHjcvHnzIJPJtEtkZOQHx0LKj0KhwKpVq6gahXAu5/l/CBs4CJlXr74pcYuK4jokQiqFEiUbc+fOxcSJE5GWlpbv9vv37+PTTz9FYGAgmjdvjtevX39QcHFxcUhKSkLLli3/P2A+H82bN8fjx48LPE4ikcDCwkJnIfpLIpFgwYIF1O2VcCrtTADChw6FMjISImdneOzbC/MO1D6DkLJQomRj4MCBaNy4MYYMGZLvt9C7d++iTZs2OH/+PEaPHo2TJ09+UHDOzs6wsLDAhQsXtOtUKhWCgoJQp06dDzo30R8ajQbx8fHQaDRch0KqIKbRIH7NGkR/+SVYVhZMWrWEx+FDMKpdm+vQCKk0StwbZdeuXUhNTUWPHj0QExOjsy0wMBAuLi4AgOXLl2P8+PEfFhyfj3Xr1mH16tXo1asXpk2bhkaNGkEmk+GHH374oHMT/aFUKrFt2zadXkeEVJTUw4eRtGEjAMB61Ci4bdkCoZUVx1ERUrkUqzeKRqPBzZs3UbduXVhYWEAmk+Hzzz/HsWPH0K9fP9SoUQP//fcf9u/fD39/f/Tp06dMg4yKikJgYCCSkpLg7u6O7t27F9gTJT80zgYhpCBMqUTklCmQfvwxpH37ch0OIQahpJ+rHzSo16VLl7Bnzx7cunULYrEYo0aNwuTJk0t7unJDyYZ+02g0iI6OhrOzM82PQipE1p07MP7oI/DeTv7HGKNu14SUQEk/Vz9obpR27dqhXbt2H3IKQqBUKnHo0CF88cUX1EiUlCvGGJK2bEXCqlWwGjYMDvO/AwBKNAgpZwYxERup3CQSCWbMmMF1GKSS02RnI/bbb5H2zykAbwbuYhoNeFSaRki5o2SDcE6j0SA0NBReXl5UjULKhTI6GpFTpkL+7BkgFMLhu29hNWQI12ERUmXQf3bCudwRalUqFdehkEoo8+ZNhA0YCPmzZxBYW8P9z+2UaBBSwfR+1teyQA1ECama1BmZeNmpE9QyGYzq1oXL2t8hcnLiOixCDF6lm/WVVH5qtRpPnjyBWq3mOhRSyQjMTOG4dCks+vSG+57dlGgQwhFKNgjn1Go1rl+/TskGKRPK+HhkP3yofWzesQOcf/kFfGNjDqMipGqjZINwTiwWY9y4cRCLxVyHQgxc9sOHCB8wEJETJ0EZHc11OISQtyjZIJxTq9W4e/culWyQD5Lq74+IESOhio+HwNoajBocE6I3KNkgnFOr1Xj69CklG6RUmEqFuKXLEDt3HphCAbMOHeBxYD/E7u5ch0YIeYvG2SCcE4vFGDFiBNdhEAOkTk1F9IwZyLx6DQBg8/lk2EyZQgN1EaJn6C+ScE6lUuHatWs0zgYpscRNm5F59Rp4JiZwXrMGttOmUaJBiB6iv0rCOcYYoqKiUAWGfCFlzHbaVJh37QqPfftg0a0r1+EQQgpAg3oRQgwG02iQ9s8pWHzcg0owCOEQDepFDI5KpUJgYCBVo5BCqTMyETV1GmJmzkTi+g1ch0MIKQFqIEo4xxhDWloaVaOQAikiIhD5xRdQhLwETyyGyNmZ65AIISVAyQbhnEgkQp8+fbgOg+ipjMtBiP76a2jS0iC0s4PL2t9h/NFHXIdFCCkBqkYhnFOpVDhz5gxVoxAdjDEkbfsDkRMnQpOWBmMfH3gcPkSJBiEGiJINQoheUkZEIGH1akCjgXRAf7jt2gmRnR3XYRFCSsFgeqMEBATg/PnzMDExwfDhw1G9evViH0u9UQgxTKlHjkKTnQ2r4cPA4/G4DocQ8lal642iVqsxcOBAjB49GhKJBBKJBAMHDsSTJ0+4Do2UEaVSiRMnTkCpVHIdCuFYxpUryH7nb9uy/yewHjGcEg1CDJzeNxBdvXo1zpw5g0ePHsH97VwH06ZNQ2ZmJseRkbLC4/FgYWFBHyhVGGMMydu2IX7lKggd7OF55AiEVlZch0UIKSN6n2xs2LABw4cP1yYaAGBsbAxjY2MOoyJlSSgUon379lyHQTiiycxEzHffIf3UaQCAaatW4JuYcBwVIaQs6XWbDZlMBktLS+zcuRM8Hg937tyBk5MTBg0apJN8vE8ul0Mul2sfp6WlwdXVldps6CmlUgl/f3/4+flBJBJxHQ6pQIqICERNmQr5ixeASASHb7+B5eDBVMpFiJ6rVG020tPTAQA//fQTjh07BldXV9y+fRt16tTB5cuXCzxu6dKlkEql2sXV1bWiQialwOPx4OLiQh8wVUzGxYsIGzgI8hcvILC1gfuOP2E1ZAi9DwiphPS6ZCM3c+rSpQsCAgK06/v06YO0tDQEBgbmexyVbBCi3xhjiJo0GRkXL8K4YUM4r1kDkT11ayXEUFSqkg0LCwu4urqiYcOGOut9fHwQERFR4HESiQQWFhY6C9FfCoUCu3fvhkKh4DoUUkF4PB6cfvkZNp9PhvvOHZRoEFLJ6XWyAQDDhw/Hv//+q+0WqVarcfbsWTRp0oTjyEhZEQgEqFu3LgQCAdehkHIkDw1Dwtp12jlwBFIpbKdNA08s5jgyQkh50/veKN9++y2uXLmCBg0aoHnz5rh9+zY0Gg0OHjzIdWikjAgEAjRu3JjrMEg5Sj9/HjGzZkOTmQmRgz0sBwzgOiRCSAXS+2TDzMwMgYGBuHjxIiIiIjB69Gi0bduWei1UIgqFArt27cLIkSMhpm+5lQrTaJC4dh0S168HABg3bQIz6uZMSJWj98kGAPD5fHTo0IHrMEg5EQgEaNmyJVWjVDLq1FREz5mDzIuXAABWI0fCfvYs8OiLAiFVjkEkG6RyEwgEqFevHtdhkDKU/eQJoqd9CWV0NHgSCRwWLYSlnx/XYRFCOKL3DURJ5adQKLB+/XrqjVKJaGQyKGNjIXJ1hcf+fZRoEFLFUckG4ZxQKETXrl0hFNLbsbIwbd0azitXwrRVSwikUq7DIYRwjEo2COf4fD68vb3B59Pb0VApoqIQMWo0FOHh2nUW3btRokEIAUDJBtEDcrkcK1eu1Bn1lRiO9MBAhH3SH1k3biB24SKuwyGE6CEqtyacE4lEGDhwIHVnNjBMrUbiunVIXL8BAGDk8xGcli7hOCpCiD6iZINwjs/n02R5BkaVkoKYr2ci8+pVAIDV8OGwnzObRgMlhOSLqlEI5+RyOZYuXUrVKAZC8eoVwj7pj8yrV8EzNobT8l/gMP87SjQIIQWikg3COZFIhHHjxlE1ioEQOThAZGcHvkQC59/WwKhmTa5DIoToOUo2COf4fD7s7GjWT32mTk8H38gIPJEIPLEYzr//Br6JCQRmZlyHRggxAFSNQjgnl8uxaNEiqkbRU9mPnyDsk/5IWLNGu05kZ0eJBiGk2CjZIJwTi8WYPn06TcKmZxhjSN6zBxFDh0IZGYm0U6ehzsjkOixCiAGiahSiFyQSCdchkHeo09MR+918pJ85AwAw69QJTkt+gsDMlOPICCGGiEo2COcUCgWWLVtGc6Poiewnb6pN0s+cAYRC2M2dA5e1v9NooISQUuMxxhjXQZS3tLQ0SKVSyGQyWFhYcB0OeQ9jDAqFAmKxGDwej+twqjRNVhZCOnaCOjUVQidHuKxaBWMfH67DIoTomZJ+rlLJBtEL1DhUP/BNTGD/3Xcw69gRXkePUqJBCCkTlGwQzikUCqxatYqqUTiS/egxsm7f1j6W9uoJl3VrIbC05C4oQkilQtUohFRRTKNB8vbtiF+9BkJLS3ge94fQ2prrsAghBqCkn6vUG4VwTqPRIDExETY2NjTNfAVRxscjdu487dwmxo0agScQcBwVIaSyMqj/7GfPnsWQIUOwc+dOrkMhZUipVGLbtm1QKpVch1IlZFy8iDC/fm/mNjEygsMPi+C8ZjX1NiGElBuDKdmIjY3FuHHjkJOTAwcHB3z66adch0TKiEQiwbx587gOo9JjajXif/kFyTveJOuSWrXgvOJXSLy9OY6MEFLZGUTJhkajwfDhwzF79mw4OTlxHQ4pYxqNBpGRkdBoNFyHUrnx+VAlJQMArEaOhMfBA5RoEEIqhEEkGz/99BOMjIwwZcoUrkMh5UCpVOLQoUNUjVIOGGPQvO1WzOPx4LBwAVy3bIbDt9+AT6O2EkIqiN5Xo1y5cgUbNmzAvXv3in2MXC7XGbchLS2tPEIjZUQikWDGjBlch1HpqFNTEbtwEZhCAZd1a8Hj8SAwM4NZ27Zch0YIqWL0umQjJSUFw4YNw6ZNm2Bvb1/s45YuXQqpVKpdXF1dyzFK8qE0Gg1CQkKoGqUMZVwOQmjvPkg/fRoZly5B/uwZ1yERQqowvU429u3bB5lMhj179mDIkCEYMmQIIiIicOrUKQwZMqTAD6d58+ZBJpNpl8jIyAqOnJSESqVCQEAAVCoV16EYPE12Nl4v/hGREyZAlZAAsacnPPbtg1HdulyHRgipwvS6GqVLly6wfm+QoevXr6N69erw8/MrcB4NiURCs4gaELFYjM8//5zrMAxe9qPHiJk9G4qwMACA1YgRsPt6BvjGxhxHRgip6gxuBNGGDRuiffv2WL16dbGPoRFE9ZtarUZwcDBq164NAQ0sVSpMrUZor95QhIVBaGcHxyVLYNbGl+uwCCGVFE3ERgyOWq3G9evXoVaruQ7FYPEEAjj+9CMsPv4YXieOU6JBCNErBleycebMGdjZ2aFRo0bFPoZKNkhlwzQapOzfD55QCKtBg7gOhxBSxVT6uVG6devGdQikjKnVajx48AA+Pj5UjVIMiqgoxH7zLbJu3gRPIoFpq1YQU48rQogeo2oUwjm1Wo2nT59SNUoRmEaD5D17ENqn75tEw9gYdrNmQeTszHVohBBSKIMr2SCVj1gsxogRI7gOQ68pIiMR++13yLp5EwBg0qwZHH/6EWI3N44jI4SQolGyQTinUqlw69YtNGvWDEIhvSXfp05PR1j/AdCkpb0pzfj6a1gNGwoenwomCSGGgf5bEc4xxhAVFQUDa6tcYQTm5rD+9FOYNGsGr+P+sB4xnBINQohBMbjeKKVBvVGIIWEqFZJ37IRJixYwrl9Puw58PiUZhBC9QONsEIOjUqkQGBhIw5UDyH78BGGDBiF++XLEfj//TZIBgCcUUqJBCDFYVEFOOMcYQ1paWpWuRtFkZSHht9+RvHMnoNGAL5XCevhwgLoCE0IqAUo2COdEIhH69OnDdRicybh0Ca8XLoIyJgYAYPHxx7D/Zh6ENjYcR0YIIWWDymUJ51QqFc6cOVMlq1Eygq4g8rOJUMbEQOTkBNdNG+G8cgUlGoSQSoVKNgjhkGnrVjBu2gTG9RvAduoU8E1NuQ6JEELKHPVGIaQCZT96hMSNm+D8y8/axIKpVODR+CKEEANCvVGIwVEqlThx4gSUSiXXoZQbVUoKYhcsRPigwcg4dw6Jm7dot1GiQQip7Oi/HOEcj8eDhYUFeDwe16GUOabRIPXIESSsWAl1aioAwKJ3b1gNH8ZtYIQQUoEo2SCcEwqFaN++PddhlLnsR4/xevFi5Dx8CACQ1PCG/fz5MG3enOPICCGkYlGyQTinVCrh7+8PPz8/iEQirsMpM8k7diDn4UPwTU1hM3UKrIcPB68SXR8h5M04QUqlEnK5HAqFAgqFAkqlMs/v7/8s7roP2Za7qFQq7N69m9MvdZRsEM7xeDy4uLgYfDWKJicHmuxsCK2sAAB2M6aDJxTCdvp0iOztOI6OkMqFMYacnBxkZ2frLHK5HDk5OZDL5dqlqMelOebdx4YgIyOD0+en3iiEfCDGGNL+/gfxK1bApFFDOK9cyXVIhHBCpVIhMzNTu+QmAFlZWXmSgoKWkuyrj3g8HsRiMUQiEcRisc7v+a0rantp1727CIVCVK9eHVKptMyus6Sfq1SyQTinUChw8OBBDBo0CGKxmOtwSiT7/n3ELV2G7AcP3jzm8aBOS4OAklqip95PCN5fMjIySr2dq2/5AoEAxsbGMDY2hpGRESQSCSQSic7v+T0u7rriHieRSCCgKQbyRckG4ZxAIEDdunUN6o9UER6O+DVrkH7qNACAZ2ICm88mwHr0aPCNjDiOjlQ2crkc6enpSEtLQ3p6us7v+a0r7PecnJxyj5fP58PU1BQmJibaJKCgpTj7FLVfZWrrVVnpfbKRlZWFXbt24erVqxAKhWjTpg0+/fRTg/pgIoUTCARo3Lgx12EUW8bly4icNBlQqwEeD1I/P9h+9RW1yyB5MMaQnZ2N1NRUpKamQiaTaX8v6HF+iUJ5jEGTmxC8u5iZmeVZV9zt726TSCQG3waLlC29TjY0Gg3q1auH7t27o1OnTsjKysKiRYtw6NAhnDx5EnyacrtSUCgU2LVrF0aOHKm31SiMMe0/T5MmTSCwtoJR3bqwmzEDRrVqcRwdKU9yuRwpKSlISkpCcnJykcnC+4/LMlEwMTGBubk5zM3NYWFhkef3/Na9/7uZmRnMzMwoISAVSq+TDR6Phxs3bsDO7v+/MTZu3BgtWrTA7du30ZzGK6gUBAIBWrZsqZelVZqcHKTs2YuMy5fh9sc28Ph88E1M4HX8OITW1lyHR0pALpcjOTlZZ8lNIN7//d3HmZmZH/zcfD4flpaWkEqlsLS01C7vPpZKpZBKpXkSh9yfZmZmENJos8RA6fU7l8fj6SQaAODg4ADgTUtYUjkIBALUq1eP6zB0aORypB46jKTNm6GKjwcApJ87B4suXQCAEg2OKRQKJCQkIDExEQkJCTpLYmIiEhMT8yQQH5I08Pl8WFlZwcrKCtbW1kUmDe9vMzMzo1IEUqXpdbKRn5UrV8La2hotWrQocJ/3+z5TYqLfFAoFtm7divHjx3NejZJfkiF0dITt1Kkw79iR09gqK8YYMjIy8k0eCnpc2r9pPp8Pa2trnaVatWqFPs5NLqjalpDSM6hkY9euXVi7di0OHz4Mc3PzAvdbunQpFi1aVIGRkQ8hFArRtWtXzouIlbGxCB885P+TDAcH2Ez8DNL+/cHX07Yk+ooxBplMhri4OMTFxeH169f5/oyLi0N8fHypukwKBALY2NjA1tZWu+Q+trGx0SYN7yYPFhYWlDQQwgGDGdTr0KFDGD58ODZt2oQxY8YUum9+JRuurq40qBfJg2k04L398GGMIXzQYKgSEijJyAdjDOnp6QUmDe+vK2kCYWRkpJM4vJs85Lfe0tKSEgdCOFIpB/U6cuQIRowYgY0bNxaZaADQDq5CDINcLse6devwxRdfVNjrpk5NRcq+fUj194fn4cMQmJuDx+PBedUqCO1sq1ySkZGRgZiYmCKXko7aaG5uDgcHB9jb22t/vv+7nZ0dbG1tYWpqSu0aCKmk9D7ZOHbsGIYNG4YNGzZg7NixXIdDyoFIJMLAgQMrZGAeZWwskv/cgZRDh8CysgAAsmP+sP50JABA7OJc7jFUpOzsbMTGxhaZRKSnpxf7nGZmZjoJQ35JRO5PY2Pjcrw6Qoih0OtqlLS0NNjY2EAqleZpEDpt2jR07dq12OehuVGqNvmLF0jaug2yv/8GVCoAgKR2bVQbNw4WPbqDZ4BdCtPT0xEZGYmoqCidn5GRkYiOjkZMTAxSUlKKfT5zc3M4OTkVuDg6OsLBwQGmpqbleFWEEENQqapRjI2NcfTo0Xy31alTp4KjIeVFLpdj5cqVmDFjRrlUo6iSkxHa7xNtkmHSogWqjR8P0za+eltsn5mZqU0c8ksmoqKiIJPJinUuIyMjODs7F5lIFNbomhBCPoRel2yUFSrZ0G8ajQaJiYmwsbEpkwZ/6oxMZF67qh0TAwBi5syBJkeOauPHwbhBgw9+jg+Rk5ODV69e5ZtA5P6empparHNZWlrCxcUFrq6u2p+urq5wdnbWJhhSqVRvkypCiGGqVCUbpGrg8/l5Bm8rDXlYGFL27IXs2DFoMjMh+ecfSLw8AQCOS5dqe52UN4VCgcjISISFhSE8PFz7M/f32NjYYp3H3Nxcmzy8n0y4uLjAxcWFSiMIIQaBkg3COblcjmXLlmHu3LklrkZhSiUyLl1Cyv4DyLx8Wbte7OUFdVIi8DbZKMtEQ6VSISoqSieRePdndHQ0iiowNDU1LTCJyP2dSuEIIZUFJRuEc2KxGNOnTy/x6KE5z5/j1fjxUCckvlnB48GsfXtYjRgO09atS111oFarERMTk2+pRHh4OCIjI6FWqws9h5GRETw8PODp6anzM/f3atWqUdUGIaTKoGSD6IXilGhocnKgjIqCxNsbACD28ABTKCGwsYGlX19YDhoEsZtb0efRaBAXF1dgNcerV6+KnKlTLBbD3d09TxKR+9POzo6SCUIIeYuSDcI5hUJRYDUKYwzZ9+4j7eRfkJ38GwIrS1Q/fRo8Hg98iQTuO3dC4uUJ3jtjdDDGkJCQkG81R+5S1OiWQqEQbm5uBZZOODo60uiVhBBSTJRsEM6JxWLMnTtXpxpFHhIC2V8nkXbyJJTR0dr1AjMzKGNjkS6R/H9pxF8n8iQUWW8H7CoIn8+Hq6trvqUSHh4ecHJy4nyuFkIIqSzovynRC3K5XJtsJPz2OxLXr9duU4lEeGlrgyA+H2fj4hBWu3aRI17yeDw4OTkV2GbCxcWlQkYsJYQQUsWSjdx6eNXbwZ2EQiGUSiV4PF6e3xUKBQQCAQQCQZ7fhUIh+Hw+5HI5RCJRvr/nfnAqFAqd3yUSCTQaDZRKZb6/q1QqiMViqNVqqNXqPL+rVCowxiASifL8bkjXJJPJ3nQDvX8fmZeD8MTNFY8ePUJ4eDiso2Pwq4UFLuVk45+0NFyQyaASCMAYg1qthkgkgkAggK2tLapXr66t7nB3d4eHhwe8vLy0I13S60TXRNdE10TXVPbXpFAoSvT5W6Uqnc+ePQsAOHfuHM6dOwcAOHXqFIKCggAA/v7+uHXrFgDg4MGDePDgAYA3U9sHBwcDALZu3YrQ0FAAwLp16xD9toh/5cqVSEx80yti2bJlSE9P17ZFUCgUSE9Px7JlywAAiYmJWLlyJQAgOjoa69atAwCEhoZi69atAIDg4GDs2rULAPDgwQMcPHgQAHDr1i34+/sDAIKCgnDq1Cm9vKa1a9fi2bNnOHDgAH755RfMnj0bn332GWbPmoXmDg74oXdvnFu/Hh7LfoYwMRHqkBAcOXIE5ubmMG7eDO1CXuBc48aw7dMHfQYOxNy5c7F06VKcOnUKGzZswPnz5xEbG4tJkyZh5syZWLJkCYRCIVxcXFCjRg3s2rWLXie6Jromuia6pnK6pv3796MkqtQIoomJiahWrZrBZI76nA0zxhAREYGXL18iKipK24vj5cuXiIiIQHJyMhQKBfh8PoRCIXhKJaba2eF/FlJU5/Oh5vPBeDzw1GqEmpshvG498Jo20SmdMDIyoteJromuia6JrkkPryklJQW2trbFHkG0SiUbNFx58cnlckRGRur04Hi3e2hMTEyhxzsIhahjaYlkZ+c3bSXc3TEq6AqMMjPBhEIYtWwB6x4fw6xjB6hNTMp1bhRCCCFlq6Sfq5RsVFG583O8m0RERERof4+NjS1yFEwTExN4enrC09MTNVxc0FAigVdGJqzCwsCPjobA0hI1rgSBJxAAAFKPHAXf2Aim7f4HgRnNHEoIIYaK5kYhAIDs7Gyd5OHd38PDw/H69esiz2FiYqLT8PL9Xh02NjZIPXQIqUeOIOfSZeDdUTX5fIg9PaFOTobQ1hYAYNn/k3yfR6PRIDo6Gs7OzjR2BSGEVEKUbBggjUaDhIQE7QyhkZGR2llEc5OJ+Pj4Is9jZmaWJ5l497GNjY12FExVUhKy799H9v0HqNatGwRvM1llTAxyHjwEAIhcXWHSvBnMfH1h2ro1BJaWxboepVKJQ4cO4YsvvqBqFEIIqYQo2dAzjDHIZDJt8vD+8urVK0RFRRWr25G5ubm2JCK/hMLa2jrfIbWZUomc5/8h5UzAmwTjwQMoIyO1240bNYJ5xw4AAIuPP4bY3QOmzZtB5OxcqmuWSCSYMWNGqY4lhBCi/yjZqECMMSQlJSEmJka7REVF5UksMjIyijwXj8eDo6OjdoZQNzc3nREx3d3dYWlpWeT8HJqcHMj/+w9Ce3uI7O0BALK/TiL2m2/ef0JIvKvDyMcHwmrW2tVGNWvCqGbNkt+Md2PQaBAaGgovLy+qRiGEkEqIko0ywBhDWlqaNoGIjo7WSShyl9jY2GIPhFKtWjVtAvHukrvOycmpRCNgMo0GypgYyENCoHgZipznwZA/ewZ5aBigVsNu7hxUGz0aAGDc0Ad8qRTGPh/B2McHxg0bwvijjyAwNy/N7SmSSqVCQEAAxo8fX+KZXwkhhOg/SjZKISEhAdOmTdNJJIqai+Ndtra2cHZ2hpOTE5ycnHSSCFdXV7i4uMDExKRUsWkUCiijoiB/+RIiB0cYN6gPAMh58hThAwfme4zA2hp427cbAMSenqh57Sp4FVTKIBaL8fnnn1fIcxFCCKl4lGyUgkQiyXf0NCsrK20CUdDi4OBQZt/e1WlpSNm7D4qoSChfRUIRFQlV7GvgbZdVy6FDtMmGxMsTPLEYYg8PSLyrQ+ztDaM6dWBUty6E702HzuPxgAqcHl2tViM4OBi1a9eG4G03WUIIIZWHQSQbV69exbp16xAXF4cGDRpg7ty5sH/bvoAL5ubmWL16NRwcHODk5ARnZ2c4OjrC2Nj4g8/NVCrI//sPyrg4qOLioHz9Gqq4eKjiXkP5Og5mbdvCft7cNzvzeEhYvTrPOXgmJpB4ekLk4Khdxzc1Ra17d7VjXugTtVqN69evo0aNGpRsEEJIJaT3g3pdunQJnTt3xowZM9CqVSusXbsWYWFhuH//PszMzIp1Dq4H9WIqFXKePYMqKQnqpGSoU5KhSkqGOjkJquQUGDdqCNu31QjqjEz817Rpgecy+9//4Lppo/Zx7IKFENrZQuzqCpGrK8SurhBUq1Zkw1BCCCGktCrdCKJt27aFo6OjdvKazMxMODo6YuHChcXuLlkeyYYmJwdJW7ZCnZ4GTVo61Onp0KSlaX+atmsLx4UL3+ybnY3njRoXeC6z9u3hunGD9nFI124QmJlB6OAAkYM9hHb2EDrYQ+TgAJGLK8Qupetiqq/UajUePHgAHx8fKtkghBADUKlGEM3KysLVq1exY8cO7TpTU1N07twZZ8+e5XZsBh4PiW9nw8uPKu7/B9XiGxtD7OUFvrExBNbWEFpbv/lZzRoCK2uIPT10jvUOOFNeUesltVqNp0+fon79+pRsEEJIJaTXyUZkZCQ0Gg2c3xssytnZGefPny/wOLlcDrlcrn2clpZW5rHxJRJYDRsGvqkp+BbmEJhbQGBhDv7bn7lDdOeq/s/fZR5DZSEWizFixAiuwyCEEFJO9DrZUCqVAKCdajyXsbFxoeNVLF26FIsWLSrX2ADA4fv55f4cVYFKpcKtW7fQrFkzCIV6/ZYkhBBSCno9XKO19ZuRKpOSknTWJyUlabflZ968eZDJZNol8p2hton+YYwhKiqqyFlmCSGEGCa9TjacnJxgb2+PO3fu6Ky/efMmGjVqVOBxEokEFhYWOgvRXyKRCAMHDizRiKiEEEIMh14nGwAwZswYbN26FbGxsQAAf39/PH78GGPGjOE4MlJWVCoVAgMDoXpnFFNCCCGVh95XkC9YsADPnz+Ht7c33N3dER4ejjVr1qBFixZch0bKSO7cMlSNQgghlZPej7OR69WrV4iLi0PNmjUhlUpLdCzXg3oRQgghlUlJP1f1vholl5ubG5o1a1biRIPoP5VKhTNnzlA1CiGEVFIGk2wQQgghxDDpfZsNUvkJhUJ069aN6zAIIYSUkyqRbOQ2SymPkUTJh1MqlTh79iy6dOlC3V8JIcQA5H6eFrfZZ5VINtLT0wEArq6uHEdCCCGEVB7p6enFaktpML1RPoRGo0FMTAzMzc0NZur1tLQ0uLq6IjIystL3oKFrrbyq0vXStVZeVel6i3utjDGkp6fDyckJfH7RzT+rRMkGn8+Hi4sL12GUSlUaAZWutfKqStdL11p5VaXrLc61lqR3KPVGIYQQQki5omSDEEIIIeWKkg09JZFIsGDBAkgkEq5DKXd0rZVXVbpeutbKqypdb3lda5VoIEoIIYQQ7lDJBiGEEELKFSUbhBBCCClXlGwQQgghpFxViXE29NV///2HjIwM1KtXr8jGOI8ePYJMJtNZZ2tri1q1apVniGVGJpPh8ePH8PLygqOjY7GOSUhIQHh4ONzd3WFnZ1fOEZYdxhju3LkDiUSCBg0aFLqvSqXC9evX86yvXbs2bGxsyivEMqNQKPD8+XOYm5vDzc2tWIP7AEBISAhkMhnq1q0LY2Pjco6y7ISHhyMjIwPVq1cvMu64uDi8ePEiz3pfX1+DGFwwOzsbz58/h6WlJdzd3YsVs1KpxOPHj2FkZIQ6depUQJRlQ6PR4MWLF1Cr1fDy8oKRkVGh+z958gQpKSk666ytrVG3bt3yDLNMaTQaXLt2Debm5vjoo4+K3D8pKQmhoaFwdXWFg4NDyZ+QkQoXGxvLmjdvziwtLZmXlxeztrZmJ0+eLPQYX19f5urqynx9fbXLggULKibgDxAWFsYmTJjAHBwcmEAgYL///nuxjps5cyaTSCSsbt26TCKRsKlTpzKNRlPO0X4YlUrFfv75Z1a9enUmlUqZr69vkcckJCQwAKxhw4Y6r+2///5bARGXXmZmJpsxYwaztrZmDRo0YA4ODqxOnTrsxo0bhR6XkJDAWrduzaRSKfP29mZSqZQdPXq0gqIuvb1797IaNWowd3d3Vq9ePWZubs5WrlxZ6DFbtmxhEolE53X19fVlcrm8gqIunbS0NPb5558za2tr1rhxY2ZjY8Pq1avH7t27V+hx58+fZ/b29szDw4NVq1aNffTRRyw8PLxigv4AW7duZW5ubqxu3brM29ubWVpasvXr1xd6TLdu3Zizs7PO6zp79uwKirhsLFq0iPH5fNaiRYsi9/3+++91/h+PGzeOqdXqEj0fJRsc6NWrF2vRogXLyspijDG2ePFiZmZmxuLi4go8xlCSi/edPn2abdq0iaWnpzOpVFqsZGP37t3M2NiY3blzhzHG2IMHD5iJiQnbtm1beYf7QdLT09msWbNYSEgImzhxYomSjaL+keubV69esRUrVrDMzEzGGGNKpZKNGjWKOTo6MpVKVeBxAwYMYI0bN2YZGRmMMcaWL1/OjI2NWVRUVIXEXVo///wzCwkJ0T4+fvw44/F4hSaFW7ZsYe7u7hUQXdl6+fIl27FjB1MqlYwxxhQKBevbty/z8fEp8BiZTMaqVaum/cBVKBSsQ4cOrG3bthUR8gdZtWoVS0hI0D7etm0bA8D++++/Ao/p1q0b+/rrrysivHJx6dIl5uXlxYYMGVJksuHv789EIhG7cuUKY4yx4OBgJpVK2Zo1a0r0nJRsVLDXr18zHo/HDh8+rF2XlZXFTE1NC/0g9vX1ZdOnT2c3b95kkZGRFRFqmStustGxY0c2YMAAnXVDhgwp1oe3vihpsnHixAl2584dlpqaWgHRlY+goCAGgD1//jzf7cnJyUwgELDdu3dr18nlciaVStny5csrKswy4+LiwhYtWlTg9i1btjBXV1f26NEj9uTJE70v0SjML7/8wmxsbArcvnPnTiYSiVhKSop23enTpxkA9uLFiwqIsOyEhoYyACwwMLDAfbp168YmTpzIbt26xSIiIvS+1PVdSUlJzN3dnV28eJFNnDixyGSjT58+rHv37jrrxo8fX2jymR9qIFrBHjx4AMYYmjRpol1nbGyMevXq4d69e4Ueu3HjRkyYMAH16tWDj48P7t+/X87RcuPevXs69wcAmjdvXuT9MWTjx4/HqFGjYGtrixEjRminbzYkt27dglgsLnB25UePHkGtVuu8tmKxGD4+Pgb32kZFReH169fw9vYucr8BAwagZ8+eqFatGn777bcKivDDPX78GJcuXcLWrVuxZs0aLF68uMB97927By8vL1haWmrXNW/eXLtN371+/RpBQUHw9/fH2LFj8fHHH6NNmzaFHvPnn39i/Pjx8PHxQb169XDjxo0KivbDjB07FsOGDUO7du2KtX9B/48fP34MpVJZ7OelZKOCJScnAwCqVaums75atWrabfmZNGkSEhMTcf/+fcTExKB69erw8/NDRkZGucZb0RhjSE1Nzff+ZGVlQS6XcxRZ+RCLxdi3bx/i4uLw6NEjPH78GBcvXsT06dO5Dq1Enj9/joULF2LmzJkFNpws7Xtf36hUKowePRo1a9ZE//79C9yvVq1aePLkCYKDgxEWFoZNmzbhq6++wl9//VWB0Zbetm3bMGvWLMyZMwd16tRBt27dCtw3OTk5z+tqaWkJPp9vEK/tjRs3MHfuXMyYMQMvXrzApEmTIBAICtx/1KhRSEhIwP379xEbG4vGjRvDz88vT6NRffP7778jOjoaixYtKvYx+b221apVg1qtLtGXIko2KphIJAIA5OTk6KzPzs6GWCwu8LgRI0bAxMQEAGBqaoqVK1ciIiIC165dK79gOcDj8SAUCvO9P8D/37/KwsLCAkOGDNE+rlmzJr7++mscOHAAzEAG93316hW6deuGzp0744cffihwv9K+9/WJRqPB6NGj8ezZM5w4caLQXmRt27bV6ZGR+21y//79FRHqB1u1ahVu3LiBmJgY2NnZoXPnzgV+kxWJRHleV4VCAY1GYxCvbd++fREUFITQ0FAsX74cffv2LfR/69ChQ2Fubg4AMDIywurVq/H69WsEBgZWUMQlFxkZidmzZ2Py5Mm4ceMGgoKC8Pr1a6SnpyMoKKjAxCG/1zb3/3FJXltKNiqYu7s7ACA6OlpnfXR0NNzc3Ip9Hnt7+3zPUxm4ubnle39cXFyK3bXSkNnb2yMzMzNPV2d99OrVK7Rv3x6NGjXCvn37Cv02WFbvfa5oNBqMGTMG58+fx4ULF1C9evUSn8Pe3t7g/mYlEgmmTZuG0NBQPH/+PN993N3d831dARjEa/uuoUOHwtnZGWfOnCn2MdbW1hCJRHr92mZlZaFJkyb4448/MHfuXMydOxc3btxAZGQk5s6di4iIiHyPK+i1tbS01CZcxVH5/3PrmYYNG8LGxgYnTpzQrnv27BlevHiBLl26aNc9fPhQ+4ednZ0NjUajc56AgAAAQP369Ssg6vIVExODoKAg7eMuXbrg5MmT2m/2jDGcOHFC5/4YKqVSiaCgICQmJgIAMjMz8+wTEBAAFxcXnfpvfRQVFYUOHTrAx8cHBw8ezLfU6dGjR3j27BkAoG7dunByctJ574eGhuLRo0d6/9pqNBqMHTsWZ8+exYULF1CzZs08++TW++e+b99/bbOysnD16lW9/5vN7z0ZEhIC4P+rwNRqNYKCghAfHw/gzd9sXFwcbt68qT3m+PHjMDMzQ6tWrSog6tKRy+VQq9U661JTU5GYmKhTdfD48WM8ffpUe4xKpdI55sKFC1AqlXr92taqVQtBQUE6S9++fVG3bl0EBQVpxwSKi4tDUFCQ9jOnS5cu+Oeff3Tu0/Hjx0v+N1ui5qSkTGzatIlJJBK2evVqdujQIVavXj3WsWNHnX1atGjBBg8ezBhj7MmTJ6xZs2Zs48aN7MyZM+zXX39lVlZWbOjQoVyEXyLp6ens8uXL7PLly8zMzIxNnz6dXb58mT179ky7z6pVq9i7b8WwsDBmZWXFhg8fzk6cOMFGjRrFLCwsDKJV++3bt9nly5dZ3759WYMGDbTXnis2NpYBYPv27WOMvelSOXz4cLZ371528uRJNnHiRCYUCtnevXu5uoRiSUxMZN7e3qx27drs/Pnz2uu8fPmyTo+a//3vf6xv377axzt27GAikYj9+uuv7MiRI6xhw4asTZs2Je6zX9EmT57MxGIx27Ztm861vtsddsOGDQwAy87OZoy96bHw3Xffsb/++ovt37+ftWzZkjk4OLCIiAiuLqNYVqxYwYYNG8b27NnDzpw5w37++WdmZWXFJk6cqN0nJSWFAWDbt2/XruvXrx/z9vZm+/fvZ+vXr2empqbsl19+4eAKii8kJIQ1bdqUrV+/ngUEBLCdO3eyJk2asOrVq+v0rOnUqRPr2bMnY+zN/6dGjRqxdevWsTNnzrDVq1czGxsb1qdPH46uovTy642yZcsWBoClp6czxhiLiYlhdnZ2bMCAAezEiRNs4sSJzMTEhD169KhEz0UjiHLgs88+g42NDXbt2oWMjAwMGjQIX3/9tc4+Pj4+2pE269atiz///BMbNmzA0aNH4ejoiM2bN2PAgAFchF8i0dHRmDt3LoA313Tz5k3cvHkTHTp00LZud3Z2hq+vr/YYDw8PXL9+HcuXL8eqVavg6emJ69evF9nyXx8sX74cUVFRAN60x8i99osXL0IgEEAsFsPX1xe2trYAgNmzZ+PYsWM4evQoEhMT4e3tjXv37un1NyTgzbef3Kq8+fPn62z7/fff0ahRIwBAgwYNdIpaP/30U1haWmLHjh04ffo0evfujVmzZul99VhCQgKaNWuGP/74Q2e9n58fZs6cCQBwdHSEr6+v9lqOHDmCDRs2YPPmzRAKhfj4448xbdo0SKXSCo+/JGbMmIETJ07gyJEjeP36NVxcXLBr1y707NlTu49QKISvr6/2PQAA+/btw+rVq/HHH39AIpFg06ZNGD58OBeXUGzVq1fH3r17sX79evj7+8PKygojR47E+PHjYWpqqt2vQYMG2vYJHh4eOHDgANavX4/jx4/D3t4ea9aswdChQ7m6jFLz9vbO0zbMwcEBvr6+2ipRR0dHXL9+Hb/88gtWrVoFNze3UpXQ0RTzhBBCCClX+v11ghBCCCEGj5INQgghhJQrSjYIIYQQUq4o2SCEEEJIuaJkgxBCCCHlipINQgghhJQrSjYIIYQQUq4o2SCE6LXJkyfD2toaBw4c4DoUQkgpUbJBCClTM2bMgKenZ5mc68WLF7h58yZCQkIKnc69ouMihJQMJRuEkDLz4MEDxMbGwsLCQjts+4eIiopC7dq1YW1tDaGw9LMrlHVchJCSoWSDEFImGGOYP38+Vq1ahaZNm+LevXsF7rt+/Xp8+eWXaN++PXr06IHMzExMnDgRrq6uqFWrFnbv3o1Xr17h448/xsGDB2FmZoaYmBid57p+/ToUCkWZxkUIKR+UbBBCysTOnTvRr18/ODg4oGnTprh7926B+yoUCly4cAEbN27E0aNH8cMPP8DMzAy3b9+Gv78/fv75ZwgEAhw6dAj9+/fH69evtRMTAsDNmzfRs2dP7WRRZRUXIaR80KyvhJBiSU1NRXBwcJ71VlZWcHBwwJw5c5CRkYGpU6dCrVaja9euhZ5vwIABqF27NgDgxo0buHnzJjZt2gQAkMvlePbsGYyMjCAUCmFmZqZz7MmTJ9G9e3cIBALIZDI8e/aszOIihJQ9SjYIIcVy6dIlLFmyRPtYrVbj9u3bmDx5MgQCAVauXIk+ffoAABITE9GuXbtCz5c7ZTcA1KtXDx06dMC0adMgEokAAMbGxrhw4UK+x548eRKzZ88GAAQFBWHx4sXabRqNBrdu3cKECRMgkUhKHBchpOxRNQohpFj69OmD69ev4/r167hy5Qpq1aoFT09P9OnTB1euXMHQoUNhZmYGMzMzeHh4IDMzE4mJiQgODkbDhg0LPfePP/6Ihw8fwtXVFQ4ODnBwcEBGRka++0ZHR+Px48fo3r07AKBnz57auK5evYo6derA3d0dfn5+hcZFCKk4PMYY4zoIQojh0Gg0+PTTT3H16lUEBgbC0dERjDGdkgoAyMrKgpGREbZt2waVSoXJkydrtymVSgDQlmLkYowhKysLjDGYmZlBrVZDpVJBIpFo99m0aRP27t2Lixcv5olr7NixCAwMRGBgIJydnQuNi8+n71qEVBRKNgghxabRaDBq1ChcuXIFgYGBcHNzK/IYhUIBkUgEHo9XJjH07t0b7dq1w6xZs3TiGjduHC5cuIDAwEB4eHiUyXMRQsoGJRuEkGLRaDQYPXo0Ll++jMDAQLi7u1d4DDk5OahWrRpu376NOnXqaOMaN24czp8/j8DAQBq4ixA9ROWIhJAi6UOiAQDnzp2Dg4ODTqIxfvx4SjQI0XPUG4UQUqTp06fjyJEj+OOPPxAbG4vY2FgAgLu7u874F+Xt5MmT6NWrl/bxrFmzsH//fmzbtg1xcXGIi4sDALi5ucHJyanC4iKEFI6qUQghRerfvz+io6PzrF+0aBG6detWYXG4ublh27Zt6NKlCwBg0KBBePXqVZ795s+fj549e1ZYXISQwlGyQQgxCA8ePEDbtm2RmJiYp4cJIUS/UZsNQohBePr0KSZMmECJBiEGiEo2CCGEEFKuqGSDEEIIIeWKkg1CCCGElCtKNgghhBBSrijZIIQQQki5omSDEEIIIeWKkg1CCCGElCtKNgghhBBSrijZIIQQQki5omSDEEIIIeWKkg1CCCGElCtKNgghhBBSrv4PLtp3yYJ+rPsAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def zeta(a, c, ratio):\n", " return np.exp(a * (1 - np.exp(c * (1 - ratio))))\n", "\n", "ratio = np.linspace(0.3, 3.9, 400)\n", "eta_c = float(d4.d4.hardness[6])\n", "plt.figure(figsize=(5.5, 3.6))\n", "plt.plot(ratio, zeta(1.0, 1.0, ratio), \"k\", label=r\"$\\beta_1 = \\gamma^A = 1$ (paper fig 2)\")\n", "plt.plot(ratio, zeta(d4.d4.ga, d4.d4.gc * eta_c, ratio), \"C3--\", label=rf\"carbon: $\\beta_1$ = {d4.d4.ga:.0f}, $\\gamma^C$ = {d4.d4.gc * eta_c:.3f}\")\n", "plt.axhline(1, color=\"gray\", ls=\":\", lw=0.8); plt.axvline(1, color=\"gray\", ls=\":\", lw=0.8)\n", "plt.xlabel(r\"$z^{A,\\mathrm{ref}} / z^A$\"); plt.ylabel(r\"$\\zeta$\"); plt.legend(); plt.title(\"charge-scaling function (eq 2)\")\n", "plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "ac9b8fe5", "metadata": {}, "source": [ "## 2. α(0) of carbon and hydrogen vs charge and coordination number · fig 5\n", "\n", "Fig 5 maps the static atom-in-molecule polarizability $\\alpha^A(0)$ (bohr³) over the\n", "two model coordinates, the effective nuclear charge $z = Z + q$ (cationic below,\n", "anionic above $Z$) and the coordination number. The reference systems (white circles)\n", "sit at their own $(\\mathrm{CN}^{A,\\rm ref}, z^{A,\\rm ref})$ and are reproduced exactly at those\n", "points; everywhere else the Gaussian weighting of eq 8 and the charge scaling of eq 2\n", "interpolate. Both maps are generated directly from xnn's `DFTD4` building blocks.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "2c849d56", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T19:06:42.891939Z", "iopub.status.busy": "2026-09-23T19:06:42.891813Z", "iopub.status.idle": "2026-09-23T19:06:43.331274Z", "shell.execute_reply": "2026-09-23T19:06:43.330592Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "core = d4.d4\n", "\n", "def alpha_map(Z, cn_range, z_range, n=161):\n", " cn = torch.linspace(*cn_range, n); z = torch.linspace(*z_range, n)\n", " CN, ZZ = torch.meshgrid(cn, z, indexing=\"xy\")\n", " zs = torch.full(CN.shape, Z, dtype=torch.long).reshape(-1)\n", " q = (ZZ - core.zeff[Z]).reshape(-1) # partial charge behind z = Z_eff + q\n", " w = core.reference_weights(zs, CN.reshape(-1), q)\n", " alpha = core.dynamic_polarizabilities(zs, w)[:, 0].reshape(CN.shape)\n", " nref = int(core.nref[Z])\n", " refs = (core.refcn[:nref, Z].numpy(), (core.refq[:nref, Z] + core.zeff[Z]).numpy())\n", " return CN.numpy(), ZZ.numpy(), alpha.numpy(), refs\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(11, 4.2))\n", "for a, (Z, name, cnr, zr, vmax) in zip(ax, [(6, \"carbon\", (0.0, 4.8), (5.5, 6.5), 16), (1, \"hydrogen\", (0.0, 0.95), (0.5, 1.4), 35)]):\n", " CN, ZZ, A, (rcn, rz) = alpha_map(Z, cnr, zr)\n", " im = a.pcolormesh(CN, ZZ, A, cmap=\"Greys\", vmin=0, vmax=vmax, shading=\"auto\")\n", " a.scatter(rcn, rz, s=40, facecolor=\"white\", edgecolor=\"k\", zorder=3, label=\"reference systems\")\n", " a.axhline(Z, color=\"w\", lw=0.6, ls=\":\")\n", " a.set_xlabel(\"CN\"); a.set_ylabel(\"z = Z + q (cationic below, anionic above)\"); a.set_title(rf\"(paper fig 5) $\\alpha^{{{name[0].upper()}}}(0)$ for {name}\")\n", " plt.colorbar(im, ax=a, label=\"bohr³\"); a.legend(loc=\"lower right\", fontsize=8)\n", "plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "ef91514b", "metadata": {}, "source": [ "## 3. (3Z)-hexen-1-yne · fig 3(b) and the molecular $C_6$ of sec II\n", "\n", "The paper illustrates the partitioning with (3Z)-hex-3-en-1-yne (HC≡C–CH=CH–CH₂–CH₃),\n", "a molecule with sp, sp² and sp³ carbons: fig 3(b) shows the atom-in-molecule $\\alpha(0)$\n", "from D4 (black) and D3 (red), and the text gives the molecular dispersion coefficient\n", "$C_6^{\\rm mol} = \\sum_{p,q} C_6^{pq}$: **1949.5** (D4), 1893.0 (D3) and 2103.1 (TD-PBE38/daug-def2-QZVP)\n", "$E_h\\,a_0^6$. The paper's geometry is not available here; we build the molecule with\n", "RDKit (MMFF94 optimized), so the coordination numbers -- and with them the individual\n", "atomic polarizabilities -- differ slightly from the published ones. The observable of\n", "interest, $C_6^{\\rm mol}$, is much less sensitive to the geometry and to the partitioning.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "5b49fef4", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T19:06:43.334120Z", "iopub.status.busy": "2026-09-23T19:06:43.333995Z", "iopub.status.idle": "2026-09-23T19:06:44.920975Z", "shell.execute_reply": "2026-09-23T19:06:44.920274Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C6,mol D4: 1951.0 (paper D4: 1949.5)\n", "C6,mol D3: 1894.0 (paper D3: 1893.0) TD-DFT reference: 2103.1 [Eh bohr^6]\n", "\n", "atom CN q_EEQ alpha(0) xnn D4\n", "C1 (≡CH) 1.91 -0.181 9.81\n", "C2 (≡C-) 1.97 -0.072 9.35\n", "C3 (=CH) 2.89 -0.093 9.24\n", "C4 (=CH) 2.89 -0.133 9.40\n", "C5 (CH2) 3.80 -0.145 7.36\n", "C6 (CH3) 3.75 -0.222 7.63\n", "H1 0.93 +0.124 1.97\n", "H2 0.92 +0.111 2.03\n", "H3 0.92 +0.103 2.07\n", "H4 0.92 +0.097 2.10\n", "H5 0.92 +0.097 2.10\n", "H6 0.92 +0.111 2.03\n", "H7 0.92 +0.111 2.03\n", "H8 0.92 +0.089 2.15\n", "paper fig 3(b), D4 carbons : [9.39, 9.17, 8.84, 8.95, 6.57, 6.76] sum 49.68\n", "xnn (MMFF geometry) carbons : [9.81, 9.35, 9.24, 9.4, 7.36, 7.63] sum 52.78\n", "paper fig 3(b), D4 hydrogens: [2.3, 2.44, 2.48, 2.45, 2.41, 2.46] mean 2.42\n", "xnn (MMFF geometry) hydrogens: [1.97, 2.03, 2.07, 2.1, 2.1, 2.03, 2.03, 2.15] mean 2.06\n" ] } ], "source": [ "from rdkit import Chem\n", "from rdkit.Chem import AllChem\n", "\n", "mol = Chem.AddHs(Chem.MolFromSmiles(\"C#C/C=C\\\\CC\")) # (3Z)-hex-3-en-1-yne\n", "AllChem.EmbedMolecule(mol, randomSeed=7); AllChem.MMFFOptimizeMolecule(mol, maxIters=5000)\n", "hexenyne = Atoms(numbers=[a.GetAtomicNum() for a in mol.GetAtoms()], positions=mol.GetConformer().GetPositions())\n", "\n", "out4 = run_d4(hexenyne); out3 = run_d3(hexenyne)\n", "c6mol_d4, c6mol_d3 = float(out4[\"c6\"].sum()), float(out3[\"c6\"].sum())\n", "print(f\"C6,mol D4: {c6mol_d4:8.1f} (paper D4: 1949.5)\")\n", "print(f\"C6,mol D3: {c6mol_d3:8.1f} (paper D3: 1893.0) TD-DFT reference: 2103.1 [Eh bohr^6]\")\n", "\n", "# per-atom static polarizabilities: xnn D4 (our geometry) vs the values printed in fig 3(b)\n", "paper_fig3b = {\"C\": [9.39, 9.17, 8.84, 8.95, 6.57, 6.76], \"H\": [2.30, 2.44, 2.48, 2.45, 2.41, 2.46]}\n", "alpha = out4[\"polarizabilities\"].numpy(); cn = out4[\"coordination_numbers\"].numpy(); q = out4[\"eeq_charges\"].numpy()\n", "labels = [\"C1 (≡CH)\", \"C2 (≡C-)\", \"C3 (=CH)\", \"C4 (=CH)\", \"C5 (CH2)\", \"C6 (CH3)\"] + [f\"H{i}\" for i in range(1, 9)]\n", "print(f\"\\n{'atom':10s} {'CN':>6s} {'q_EEQ':>7s} {'alpha(0) xnn D4':>16s}\")\n", "for lab, c, qq, a in zip(labels, cn, q, alpha):\n", " print(f\"{lab:10s} {c:6.2f} {qq:+7.3f} {a:16.2f}\")\n", "print(\"paper fig 3(b), D4 carbons :\", paper_fig3b['C'], \" sum\", sum(paper_fig3b['C']))\n", "print(\"xnn (MMFF geometry) carbons :\", np.round(alpha[:6], 2).tolist(), \" sum\", round(float(alpha[:6].sum()), 2))\n", "print(\"paper fig 3(b), D4 hydrogens:\", paper_fig3b['H'], \" mean\", round(np.mean(paper_fig3b['H']), 2))\n", "print(\"xnn (MMFF geometry) hydrogens:\", np.round(alpha[6:], 2).tolist(), \" mean\", round(float(alpha[6:].mean()), 2))\n" ] }, { "cell_type": "markdown", "id": "cc5e1916", "metadata": {}, "source": [ "The molecular coefficient lands within 0.1% of the paper's D4 value (and the D3 value\n", "from xnn's D3 tables within a few tenths of a percent of the paper's 1893.0), while the\n", "individual carbon polarizabilities come out a few percent higher and the hydrogens a\n", "few percent lower than the fig 3(b) labels. That redistribution between carbon and its\n", "attached hydrogens is what the paper itself points out for atomic partitioning (\"the\n", "individual atom-in-molecule polarizabilities from D3 and D4 also differ (by about 10%).\n", "However, the physical observable, i.e., the total molecular dispersion coefficient, is\n", "similar\"): the partitioning depends on the EEQ charges, which shift with the geometry\n", "(our MMFF structure vs the paper's DFT one), whereas $C_6^{\\rm mol}$ does not.\n" ] }, { "cell_type": "markdown", "id": "6d4377fb", "metadata": {}, "source": [ "## 4. Molecular $C_6$ coefficients · in the spirit of table III\n", "\n", "Table III of the paper benchmarks molecular $C_6$ coefficients against the experimental\n", "dipole-oscillator-strength-distribution (DOSD) values of Meath and co-workers for 1225\n", "molecule pairs (D4: MAD 3.8%, D3: 4.7%). The full DOSD set is not bundled here; the cell\n", "below evaluates D4 and D3 on the small molecules of ASE's G2 collection for which the\n", "homomolecular DOSD $C_6$ is widely tabulated. **Caveat:** the reference column was\n", "transcribed from the literature (Kumar & Meath's DOSD compilations) without access to the\n", "original tables at the time of writing and should be checked against them before being\n", "quoted; the statistics are indicative only. The trend matches the paper: D4 lowers the\n", "mean deviation, most visibly for the heteroatom-rich molecules.\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "a897d202", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T19:06:44.922728Z", "iopub.status.busy": "2026-09-23T19:06:44.922645Z", "iopub.status.idle": "2026-09-23T19:06:45.226947Z", "shell.execute_reply": "2026-09-23T19:06:45.226114Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "molecule DOSD D4 D3 dev D4 % dev D3 %\n", "H2 12.1 12.2 12.5 +1.2 +3.7\n", "N2 73.4 82.4 88.5 +12.3 +20.6\n", "O2 62.0 60.1 51.3 -3.0 -17.3\n", "CO 81.4 96.1 100.8 +18.1 +23.9\n", "CO2 158.7 175.4 156.4 +10.5 -1.4\n", "N2O 184.9 170.8 161.0 -7.6 -12.9\n", "NH3 89.1 84.1 84.7 -5.6 -5.0\n", "H2O 45.4 44.5 44.5 -2.1 -1.9\n", "CH4 129.7 123.8 127.7 -4.5 -1.6\n", "C2H2 204.1 206.1 206.7 +1.0 +1.3\n", "C2H4 300.2 294.2 294.5 -2.0 -1.9\n", "C2H6 381.9 362.1 364.0 -5.2 -4.7\n", "C3H8 768.1 726.7 721.1 -5.4 -6.1\n", "C6H6 1723.0 1764.8 1659.7 +2.4 -3.7\n", "HF 19.0 19.0 18.9 -0.1 -0.5\n", "HCl 130.4 127.1 126.9 -2.5 -2.7\n", "Cl2 389.2 389.1 361.7 -0.0 -7.1\n", "SO2 294.0 379.5 331.2 +29.1 +12.7\n", "CS2 871.1 850.3 800.5 -2.4 -8.1\n", "OCS 402.2 446.3 413.4 +11.0 +2.8\n", "NO 69.8 71.3 68.3 +2.2 -2.1\n", "CH3OH 222.0 212.9 208.7 -4.1 -6.0\n", "SiH4 343.9 368.1 372.3 +7.0 +8.3\n", "PH3 307.5 308.2 309.2 +0.2 +0.5\n", "\n", "MAD (%) 5.8 6.5\n", "MD (%) +2.1 -0.4\n", "AMAX (%) 29.1 23.9\n", "(paper table III, 1225 DOSD pairs: MAD 3.8 % (D4) vs 4.7 % (D3), MD -0.1 vs 2.4, AMAX 29.1 vs 23.9)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dosd = { # C6(A-A) in Eh bohr^6, experimental DOSD values (transcribed, see caveat)\n", " \"H2\": 12.1, \"N2\": 73.4, \"O2\": 62.0, \"CO\": 81.4, \"CO2\": 158.7, \"N2O\": 184.9, \"NH3\": 89.1,\n", " \"H2O\": 45.4, \"CH4\": 129.7, \"C2H2\": 204.1, \"C2H4\": 300.2, \"C2H6\": 381.9, \"C3H8\": 768.1,\n", " \"C6H6\": 1723.0, \"HF\": 19.0, \"HCl\": 130.4, \"Cl2\": 389.2, \"SO2\": 294.0, \"CS2\": 871.1,\n", " \"OCS\": 402.2, \"NO\": 69.8, \"CH3OH\": 222.0, \"SiH4\": 343.9, \"PH3\": 307.5}\n", "rows = []\n", "for name, ref in dosd.items():\n", " atoms = molecule(name)\n", " c4 = float(run_d4(atoms)[\"c6\"].sum()); c3 = float(run_d3(atoms)[\"c6\"].sum())\n", " rows.append((name, ref, c4, c3))\n", "dev4 = np.array([(r[2] / r[1] - 1) * 100 for r in rows]); dev3 = np.array([(r[3] / r[1] - 1) * 100 for r in rows])\n", "print(f\"{'molecule':9s} {'DOSD':>8s} {'D4':>8s} {'D3':>8s} {'dev D4 %':>9s} {'dev D3 %':>9s}\")\n", "for (name, ref, c4, c3), e4, e3 in zip(rows, dev4, dev3):\n", " print(f\"{name:9s} {ref:8.1f} {c4:8.1f} {c3:8.1f} {e4:+9.1f} {e3:+9.1f}\")\n", "print(f\"\\n{'MAD (%)':9s} {'':8s} {'':8s} {'':8s} {np.abs(dev4).mean():9.1f} {np.abs(dev3).mean():9.1f}\")\n", "print(f\"{'MD (%)':9s} {'':8s} {'':8s} {'':8s} {dev4.mean():+9.1f} {dev3.mean():+9.1f}\")\n", "print(f\"{'AMAX (%)':9s} {'':8s} {'':8s} {'':8s} {np.abs(dev4).max():9.1f} {np.abs(dev3).max():9.1f}\")\n", "print(\"(paper table III, 1225 DOSD pairs: MAD 3.8 % (D4) vs 4.7 % (D3), MD -0.1 vs 2.4, AMAX 29.1 vs 23.9)\")\n", "\n", "plt.figure(figsize=(4.6, 4.2))\n", "ref = np.array([r[1] for r in rows])\n", "plt.loglog(ref, [r[2] for r in rows], \"o\", label=f\"D4, MAD {np.abs(dev4).mean():.1f} %\")\n", "plt.loglog(ref, [r[3] for r in rows], \"r+\", ms=9, label=f\"D3, MAD {np.abs(dev3).mean():.1f} %\")\n", "lim = [8, 2500]; plt.plot(lim, lim, \"k:\", lw=0.8); plt.xlabel(\"C6 (DOSD, transcribed) [Eh bohr⁶]\"); plt.ylabel(\"C6 (calc.)\"); plt.legend(); plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "baec3c68", "metadata": {}, "source": [ "## 5. What the charge dependence buys · sec III.B\n", "\n", "D3 knows only the geometry; D4 also knows the charge state. The paper's dirhodium\n", "example (fig 7b) shows a *dication* with **more** D4 dispersion than D3 because the\n", "charge redistributes over the ligands and populates new reference systems. The\n", "mechanism is visible on a benzene dimer: with D3 the dispersion energy is independent of\n", "the total charge, with D4 the cation and anion differ from the neutral dimer (the\n", "$\\alpha(0)$ maps of sec 2 explain the direction: anions are more polarizable).\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "b7456ac7", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T19:06:45.228742Z", "iopub.status.busy": "2026-09-23T19:06:45.228668Z", "iopub.status.idle": "2026-09-23T19:06:45.255586Z", "shell.execute_reply": "2026-09-23T19:06:45.254860Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "benzene dimer (PD): PBE0-D3(BJ) dispersion -704.28 meV, charge independent\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " PBE0-D4 q_tot = -1: -740.85 meV (2-body -745.28, ATM +4.42); sum alpha(0) = 141.2 bohr³\n", " PBE0-D4 q_tot = +0: -689.64 meV (2-body -694.06, ATM +4.42); sum alpha(0) = 136.3 bohr³\n", " PBE0-D4 q_tot = +1: -645.17 meV (2-body -649.59, ATM +4.42); sum alpha(0) = 131.8 bohr³\n" ] } ], "source": [ "from ase.data.s22 import create_s22_system, get_number_of_dimer_atoms, get_interaction_energy_cc, s22\n", "\n", "dimer = create_s22_system(\"Benzene_dimer_parallel_displaced\")\n", "e_d3 = run_d3(dimer)[\"energy_au\"] * HARTREE * 1e3\n", "print(f\"benzene dimer (PD): PBE0-D3(BJ) dispersion {e_d3:9.2f} meV, charge independent\")\n", "for q in (-1.0, 0.0, +1.0):\n", " out = run_d4(dimer, charge=q)\n", " print(f\" PBE0-D4 q_tot = {q:+.0f}: {float(out['energy']) * 1e3:9.2f} meV \"\n", " f\"(2-body {float(out['energy_2body']) * 1e3:8.2f}, ATM {float(out['energy_3body']) * 1e3:+6.2f}); sum alpha(0) = {float(out['polarizabilities'].sum()):7.1f} bohr³\")\n" ] }, { "cell_type": "markdown", "id": "bca0b09d", "metadata": {}, "source": [ "### Dispersion contributions to the S22 interaction energies\n", "\n", "The BJ parameters of PBE0-D4 were fitted to S66x8, S22x5 and NCIBLIND10 (sec II.F); on\n", "S22 the paper reports D4 slightly ahead of D3(BJ)-ATM for hybrid functionals (fig 7a).\n", "Without the DFT part we cannot recompute interaction energies, but we can isolate the\n", "**dispersion contribution** $E_{\\rm disp}(AB) - E_{\\rm disp}(A) - E_{\\rm disp}(B)$ of the\n", "two corrections at the same PBE0 parametrization and compare it with the CCSD(T)/CBS\n", "reference interaction energies: for the dispersion-bound complexes dispersion is the whole\n", "story, for the hydrogen-bonded ones a fraction of it. D4 and D3(BJ) agree closely for\n", "these neutral organic dimers, as the paper finds -- the differences appear for\n", "heteroatoms and for charged or metal-containing systems.\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "1185ab3a", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T19:06:45.256991Z", "iopub.status.busy": "2026-09-23T19:06:45.256914Z", "iopub.status.idle": "2026-09-23T19:06:46.134916Z", "shell.execute_reply": "2026-09-23T19:06:46.134130Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "S22 complex CCSD(T) Eint D4 disp. D3(BJ) disp. [kcal/mol]\n", "Ammonia_dimer -5.96 -0.96 -0.98\n", "Water_dimer -9.44 -0.62 -0.67\n", "Formic_acid_dimer -35.35 -2.61 -2.59\n", "Formamide_dimer -30.31 -2.93 -2.84\n", "Uracil_dimer_h-bonded -38.91 -4.27 -3.99\n", "2-pyridoxine_2-aminopyridine_complex -31.97 -5.06 -4.81\n", "Adenine-thymine_Watson-Crick_complex -31.48 -5.56 -5.18\n", "Methane_dimer -1.00 -0.98 -1.08\n", "Ethene_dimer -2.82 -2.14 -2.33\n", "Benzene-methane_complex -2.73 -2.65 -2.73\n", "Benzene_dimer_parallel_displaced -4.93 -8.67 -8.43\n", "Pyrazine_dimer -7.90 -8.64 -8.28\n", "Uracil_dimer_stack -18.32 -11.82 -11.23\n", "Indole-benzene_complex_stack -8.63 -12.37 -11.79\n", "Adenine-thymine_complex_stack -21.92 -16.80 -15.69\n", "Ethene-ethyne_complex -2.84 -1.11 -1.25\n", "Benzene-water_complex -6.19 -2.18 -2.52\n", "Benzene-ammonia_complex -4.36 -2.53 -2.71\n", "Benzene-HCN_complex -8.56 -2.73 -3.28\n", "Benzene_dimer_T-shaped -5.10 -4.65 -4.74\n", "Indole-benzene_T-shape_complex -10.57 -6.36 -6.31\n", "Phenol_dimer -13.33 -5.04 -5.03\n", "\n", "D4 vs D3(BJ) dispersion contribution: mean |diff| 0.26 kcal/mol, max 1.11\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "names = s22\n", "d4_int, d3_int, cc = [], [], []\n", "for name in names:\n", " dimer = create_s22_system(name); n_a, n_b = get_number_of_dimer_atoms(name)\n", " mono_a, mono_b = dimer[:n_a], dimer[n_a:n_a + n_b]\n", " e4 = [float(run_d4(a)[\"energy\"]) for a in (dimer, mono_a, mono_b)]\n", " e3 = [run_d3(a)[\"energy_au\"] * HARTREE for a in (dimer, mono_a, mono_b)]\n", " d4_int.append((e4[0] - e4[1] - e4[2]) * 1e3); d3_int.append((e3[0] - e3[1] - e3[2]) * 1e3)\n", " cc.append(get_interaction_energy_cc(name) * 1e3)\n", "d4_int, d3_int, cc = map(np.array, (d4_int, d3_int, cc))\n", "kcal = 1e3 / 43.3641 # meV -> kcal/mol\n", "print(f\"{'S22 complex':32s} {'CCSD(T) Eint':>13s} {'D4 disp.':>10s} {'D3(BJ) disp.':>13s} [kcal/mol]\")\n", "for n, c, a, b in zip(names, cc, d4_int, d3_int):\n", " print(f\"{n:32s} {c / kcal:13.2f} {a / kcal:10.2f} {b / kcal:13.2f}\")\n", "print(f\"\\nD4 vs D3(BJ) dispersion contribution: mean |diff| {np.abs(d4_int - d3_int).mean() / kcal:.2f} kcal/mol, max {np.abs(d4_int - d3_int).max() / kcal:.2f}\")\n", "\n", "fig, ax = plt.subplots(figsize=(11, 3.8))\n", "x = np.arange(len(names)); w = 0.28\n", "ax.bar(x - w, cc / kcal, w, color=\"0.6\", label=\"CCSD(T)/CBS interaction energy\")\n", "ax.bar(x, d4_int / kcal, w, color=\"C0\", label=\"PBE0-D4 dispersion contribution (2-body + ATM)\")\n", "ax.bar(x + w, d3_int / kcal, w, color=\"C3\", label=\"PBE0-D3(BJ) dispersion contribution (2-body)\")\n", "ax.set_xticks(x); ax.set_xticklabels([n.replace(\"_\", \" \") for n in names], rotation=75, fontsize=7); ax.set_ylabel(\"kcal/mol\"); ax.legend(fontsize=8)\n", "ax.axhline(0, color=\"k\", lw=0.6); ax.set_title(\"S22: dispersion contributions of D4 and D3(BJ) at the PBE0 parametrization\"); plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "cc0cb1c1", "metadata": {}, "source": [ "## Summary\n", "\n", "* Fig 2 and fig 5 follow directly from the two model ingredients, the charge-scaling\n", " function ζ and the Gaussian CN weighting over the (charge-scaled) reference systems.\n", "* The (3Z)-hexen-1-yne molecular $C_6$ reproduces the paper's D4 value (1949.5 $E_h a_0^6$)\n", " to 0.1% from an MMFF geometry, with the D3 value from the same tables the paper used.\n", "* Molecular $C_6$ coefficients against (transcribed) DOSD data show the improvement of\n", " D4 over D3 that table III quantifies.\n", "* D4 responds to the total charge where D3 cannot, and reproduces D3(BJ)'s dispersion\n", " contributions for the neutral organic S22 complexes.\n", "\n", "Every number here comes from the same `DFTD4` module that trains and deploys with xnn's\n", "short-range models; `d4_benchmark.ipynb` compares it with the reference `dftd4` code on\n", "accuracy and speed.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.12" } }, "nbformat": 4, "nbformat_minor": 5 }