IntroductionPotentialFitting.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "f2adfe85-18c8-4430-b370-1b4d6f1b05b3",
   "metadata": {},
   "source": [
    "# Interatomic potentials\n",
    "\n",
    "In general interatomic potentials can be written as a sum of functional terms depending on the positions of the atoms in a structure. Then the energy $U$ of the system is\n",
    "\n",
    "$U = \\sum_{i=1}^N U_1(\\vec{r_i}) + \\sum_{i,j=1}^N U_2(\\vec{r_i}, \\vec{r_j}) + \\sum_{i,j,k=1}^N U_2(\\vec{r_i}, \\vec{r_j}, \\vec{r_k}) +...$\n",
    "\n",
    "The one body term only matter when the system is within an external field. Most classic interatomic potentials don't use 4th and higher order body terms, pair potentials only use the 2 body term. As a general rule potentials that include higher order body terms can be more accurate but are slower.\n",
    "\n",
    "There are many different forms for $U_i$, which cover a wide range of different run time and accuracy necessities.\n",
    "\n",
    "Simple pair potentials (f.e Lennard-Jones, Morse, Buckingham) only contain very few parameters, typically less than 10. In many body potentials (f.e. EAM, MEAM, Tersoff) the typical number of parameters is 10-50 and for machine learning potentials the number of parameters can reach several thousands.\n",
    "\n",
    "# Fitting\n",
    "\n",
    "In the fit process the parameters of the chosen functions for $U_i$ are optimized. For this purpose an objective or cost function is defined and minimized. In general the objective function is defined as\n",
    "\n",
    "$\\chi^2 = \\sum_i w_i r_i$\n",
    "\n",
    "where $w_i$ is a weight and $r_i$ is a residual that describes the difference to target values. This residual can be defined in different ways, so it is not possible to simply compare the residual for different fitting processes or codes. A more in depth explanation and some examples can be found on https://atomicrex.org/overview.html#objective-function.\n",
    "\n",
    "The minimization can be done with local or global optimization algorithms.\n",
    "Generally local optimization algorithms should all be able to find the local minimum coming from some initial parameter set, so the \"best\" local algorithm is the one finding the minimum in the shortest time. Typically used local algorithms are f.e. (L)BFGS or Nelder-Mead.\n",
    "Examples for global algorithms are evolutionary algorithms or simulated annealing. For most problems it is impossible to tell a priori which global algorithm will give the best results, so using global algorithms typically involves testing many of them.\n",
    "\n",
    "# EAM potentials\n",
    "\n",
    "EAM potentials are pair functionals. \n",
    "In a generalised form they are equal to Finnis-Sinclair, effective medium theory or glue potentials. Their total energy can be written as\n",
    "\n",
    "$E = \\frac{1}{2}\\sum_{ij}V(r_{ij}) + \\sum_i F(\\rho_i)$\n",
    "\n",
    "with\n",
    "\n",
    "$\\rho_i = \\sum_j \\rho(r_{ij})$\n",
    "\n",
    "The original functions for V, $\\rho$ and F were derived from different theories, but they can be chosen freely.\n",
    "\n",
    "# Fitting code\n",
    "\n",
    "Fitting is done using the pyiron interface to the atomicrex code https://atomicrex.org. It can be used to fit different types of classic interatomic potentials:\n",
    "- pair potentials\n",
    "- EAM\n",
    "- MEAM\n",
    "- Tersoff\n",
    "- ABOP\n",
    "- ADP (in development)\n",
    "\n",
    "It allows to fit different properties (energies, forces, lattice constants, elastic properties, etc.) and implements the LBFGS minimizer. Additionally it offers an interface to the nlopt library which implements several global and local optimization algorithms and the ability to apply arbitrary constraints to parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f4075857-362a-400f-b043-2fc5ad54a407",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyiron import Project, ase_to_pyiron\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d70cf5ae-8e25-444c-b24f-2d676ef8d2f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "pr = Project(\".\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d83afb5-b99d-4081-9883-ce67c3557f5d",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Get the training data\n",
    "Load a job that contains structures with energies and forces from DFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "71b278fc-7886-4863-87f2-50c31e9d3787",
   "metadata": {},
   "outputs": [],
   "source": [
    "tc = pr['../../introduction/training/Al_basic_atomicrex']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57cc1f71-1255-4d15-9c31-e598098fe1e4",
   "metadata": {},
   "source": [
    "### Have a look at the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "25b99c5a-e8a2-42de-aaf0-2794d675385b",
   "metadata": {},
   "outputs": [
    {
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       "             V         E  space_group crystal_system\n",
       "0    16.484415 -3.753374          225          cubic\n",
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       "3    15.495350 -3.737149          225          cubic\n",
       "4    15.825038 -3.746438          225          cubic\n",
       "..         ...       ...          ...            ...\n",
       "303  28.793489 -3.016706            1      triclinic\n",
       "304  29.358067 -2.979471            1      triclinic\n",
       "305  29.922645 -2.942740            1      triclinic\n",
       "306  30.487223 -2.906539            1      triclinic\n",
       "307  31.051801 -2.870883            1      triclinic\n",
       "\n",
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tc.plot.energy_volume(crystal_systems=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f039bd7e-e62e-43d6-9c22-6a4bb1c68c73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "      <th>alpha</th>\n",
       "      <th>beta</th>\n",
       "      <th>gamma</th>\n",
       "      <th>V</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.039967</td>\n",
       "      <td>4.039967</td>\n",
       "      <td>4.039967</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>65.937658</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.900545</td>\n",
       "      <td>3.900545</td>\n",
       "      <td>3.900545</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>59.343892</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.929227</td>\n",
       "      <td>3.929227</td>\n",
       "      <td>3.929227</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>60.662645</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.957496</td>\n",
       "      <td>3.957496</td>\n",
       "      <td>3.957496</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>61.981399</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.985366</td>\n",
       "      <td>3.985366</td>\n",
       "      <td>3.985366</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>90.000000</td>\n",
       "      <td>63.300152</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>303</th>\n",
       "      <td>7.008729</td>\n",
       "      <td>7.232998</td>\n",
       "      <td>10.690023</td>\n",
       "      <td>121.764941</td>\n",
       "      <td>89.204727</td>\n",
       "      <td>90.106498</td>\n",
       "      <td>460.695818</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>304</th>\n",
       "      <td>7.054241</td>\n",
       "      <td>7.279967</td>\n",
       "      <td>10.759441</td>\n",
       "      <td>121.764941</td>\n",
       "      <td>89.204727</td>\n",
       "      <td>90.106498</td>\n",
       "      <td>469.729069</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>305</th>\n",
       "      <td>7.099174</td>\n",
       "      <td>7.326338</td>\n",
       "      <td>10.827974</td>\n",
       "      <td>121.764941</td>\n",
       "      <td>89.204727</td>\n",
       "      <td>90.106498</td>\n",
       "      <td>478.762321</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>306</th>\n",
       "      <td>7.143545</td>\n",
       "      <td>7.372128</td>\n",
       "      <td>10.895651</td>\n",
       "      <td>121.764941</td>\n",
       "      <td>89.204727</td>\n",
       "      <td>90.106498</td>\n",
       "      <td>487.795572</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>307</th>\n",
       "      <td>7.187372</td>\n",
       "      <td>7.417357</td>\n",
       "      <td>10.962497</td>\n",
       "      <td>121.764941</td>\n",
       "      <td>89.204727</td>\n",
       "      <td>90.106498</td>\n",
       "      <td>496.828823</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>308 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            a         b          c       alpha       beta      gamma  \\\n",
       "0    4.039967  4.039967   4.039967   90.000000  90.000000  90.000000   \n",
       "1    3.900545  3.900545   3.900545   90.000000  90.000000  90.000000   \n",
       "2    3.929227  3.929227   3.929227   90.000000  90.000000  90.000000   \n",
       "3    3.957496  3.957496   3.957496   90.000000  90.000000  90.000000   \n",
       "4    3.985366  3.985366   3.985366   90.000000  90.000000  90.000000   \n",
       "..        ...       ...        ...         ...        ...        ...   \n",
       "303  7.008729  7.232998  10.690023  121.764941  89.204727  90.106498   \n",
       "304  7.054241  7.279967  10.759441  121.764941  89.204727  90.106498   \n",
       "305  7.099174  7.326338  10.827974  121.764941  89.204727  90.106498   \n",
       "306  7.143545  7.372128  10.895651  121.764941  89.204727  90.106498   \n",
       "307  7.187372  7.417357  10.962497  121.764941  89.204727  90.106498   \n",
       "\n",
       "              V   N  \n",
       "0     65.937658   4  \n",
       "1     59.343892   4  \n",
       "2     60.662645   4  \n",
       "3     61.981399   4  \n",
       "4     63.300152   4  \n",
       "..          ...  ..  \n",
       "303  460.695818  16  \n",
       "304  469.729069  16  \n",
       "305  478.762321  16  \n",
       "306  487.795572  16  \n",
       "307  496.828823  16  \n",
       "\n",
       "[308 rows x 8 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,7))\n",
    "tc.plot.cell()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cb440b6-aa79-4369-80d6-141dcfc37696",
   "metadata": {},
   "source": [
    "### Create an atomicrex job"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "56951cee-038f-44e7-bb11-b20841036f81",
   "metadata": {},
   "outputs": [],
   "source": [
    "job = pr.create.job.Atomicrex(\"FitAl\", delete_existing_job=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9807a140-dc20-4c4a-b22c-dcc89c789425",
   "metadata": {},
   "source": [
    "### Training Data\n",
    "Set the training data. This can also be done structure by structure to set other fit properties and weights, but here we simply load the TrainingContainer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "adbcf0a6-1ef8-4697-93d5-bd9346aad1ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "job.add_training_data(tc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d275454-0b14-4862-b4f0-8b7166852f96",
   "metadata": {},
   "source": [
    "Set the potential type. In this case an EAM potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e90476e0-54cf-4a6e-9424-bf282517a4b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "job.potential = job.factories.potentials.eam_potential()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cd689cb-0d35-4b5c-93e6-e0112a5382b2",
   "metadata": {},
   "source": [
    "### Functions\n",
    "Reminder: $E = \\sum_{ij}V(r_{ij}) + \\sum_i F(\\rho_i)$ with $\\rho_i = \\sum_j \\rho(r_{ij})$\n",
    "\n",
    "It is necessary to define a pair potential, an electronic density function and an embedding function.\n",
    "For all of those it is possible to choose between different functional forms.\n",
    "Classic pair potentials are physically motivated and have a very limited number of paramaters that can often be derived from an experimentally measurable quantity.\n",
    "Splines or polynomials offer more flexibility, but can lead to unphysical oscillations or overfitting. Compared with the machine learning potentials shown later the number of parameters is very low no matter which functions you choose.\n",
    "\n",
    "In this case a generalized morse function is used for the pair interaction. It has the form\n",
    "\n",
    "$(\\frac{D_0}{S-1}exp(-\\beta \\sqrt{2S}(r-r_0))-\\frac{D_0S}{S-1}exp(-\\beta\\sqrt{2/S}(r-r_0)))+\\delta $\n",
    "\n",
    "The parameters in the morse potential can be derived from phyiscal quantities, here they are just educated guesses. For example $r_0$ is the equilibrium distance of a dimer. The nearest neighbor distance in fcc Cu is about 2.8 $\\mathring A$ so it is taken as initial value.\n",
    "In the case of analytic functions the initial parameter choices should not matter too much, since the functional form is constrained.\n",
    "\n",
    "The electronic density will be a cubic spline. The embedding function will be $-A*sqrt(\\rho)+B*rho$, which can be defined as a user function.\n",
    "\n",
    "The pair function and the electron denity and their first derivatives are required to smoothly approach 0 at the cutoff distance $r_{c}$\n",
    "For this purpose the pair function is screened by multiplying with the function:\n",
    "\n",
    "$\\Psi(\\frac{r-rc}{h})$ where $\\Psi(x) = \\frac{x^4}{1+x^4}$ if $x<0$ else $\\Psi(x)=0$\n",
    "\n",
    "For the spline it is necessary to set a node point with y value 0 at the cutoff "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "96a1900f-f4d2-43b6-87dd-cf5570517836",
   "metadata": {},
   "outputs": [],
   "source": [
    "morseB = job.factories.functions.morse_B(\"V\", D0=0.15, r0=3.05, beta=1.1, S=4.1, delta=-0.01)\n",
    "morseB.screening = job.factories.functions.x_pow_n_cutoff(identifier=\"V_screen\", cutoff=7.6)\n",
    "morseB.parameters.D0.min_val = 0.05\n",
    "morseB.parameters.D0.max_val = 1.55\n",
    "\n",
    "morseB.parameters.r0.min_val = 2.6\n",
    "morseB.parameters.r0.max_val = 3.1\n",
    "\n",
    "morseB.parameters.S.min_val = 1.5\n",
    "morseB.parameters.S.max_val = 4.5\n",
    "morseB.parameters.delta.max_val = 0.005"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "252c78d0-9230-4e23-83a1-20304f1630b5",
   "metadata": {},
   "source": [
    "It is also possible to plot most of the functions. This can help to judge if the initial parameters are reasonable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1c380b21-78e8-404c-a9ae-a5b6d6ea85fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 720x504 with 1 Axes>,\n",
       " <AxesSubplot:xlabel='r [$\\\\AA$]', ylabel='func(r)'>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "morseB.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b93e8548-cdcf-4d51-bbc0-ae7e5646cd02",
   "metadata": {},
   "outputs": [],
   "source": [
    "rho = job.factories.functions.spline(identifier=\"rho_AlAl\", cutoff=7.6, derivative_left=-0.2, derivative_right=0)\n",
    "## the spline requires node points and initial values\n",
    "init_func = lambda r: np.exp(-r)\n",
    "nodes = np.array([1.0, 2.2, 2.7, 3.2, 4.0, 5.0])\n",
    "init_vals = init_func(nodes)\n",
    "rho.parameters.create_from_arrays(x=nodes, y=init_vals, min_vals=np.zeros(len(nodes)), max_vals=np.ones(len(nodes)))\n",
    "# set node point at cutoff\n",
    "rho.parameters.add_node(x=7.6, start_val=0, enabled=False)\n",
    "rho.derivative_left.max_val = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "56710703-5e6e-485e-a9d9-bc2c4bedac5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# User function for embedding term\n",
    "F = job.factories.functions.user_function(identifier=\"F\", input_variable=\"r\")\n",
    "F.expression = \"-A*sqrt(r)+B*r\"\n",
    "F.derivative = \"-A/(2*sqrt(r))+B\"\n",
    "F.parameters.add_parameter(\"A\", start_val=3.3, min_val=0.0)\n",
    "F.parameters.add_parameter(\"B\", start_val=1.8, min_val=0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "865bca67-41c4-4bb1-b357-ba2c4d37ce8b",
   "metadata": {},
   "source": [
    "Assign functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ce82c058-99b1-4044-89e4-d5b9fc6191d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "job.potential.pair_interactions[morseB.identifier] = morseB\n",
    "job.potential.electron_densities[rho.identifier] = rho\n",
    "job.potential.embedding_energies[F.identifier] = F"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fa3875d-c6ac-4a93-8917-0219be6bd90e",
   "metadata": {},
   "source": [
    "Set a fit algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d0c70020-3999-482a-9fc3-037d6b4e5be9",
   "metadata": {},
   "outputs": [],
   "source": [
    "job.input.fit_algorithm = job.factories.algorithms.ar_lbfgs(max_iter=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6e161ce8-8d33-4eea-8d41-889287ccb7c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The job FitAl was saved and received the ID: 8397\n"
     ]
    }
   ],
   "source": [
    "job.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd20a5b9-74f8-4609-96f8-d8c84f7a6976",
   "metadata": {},
   "source": [
    "Have a look at some of the outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8a895b83-d90e-489f-8382-393a520ae0a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "499.7455700028165"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(job.output.iterations, job.output.residual)\n",
    "job.output.residual[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "74465658-bc69-486c-a327-4cd7a5790ec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "electron_densities": {
        "rho_AlAl": {
         "cutoff": "7.6",
         "derivative_left": {
          "enabled": "True",
          "final_value": "-0.06831674064258404",
          "fitable": "True",
          "max_val": "0.0",
          "min_val": "None",
          "param": "'derivative-left'",
          "reset": "False",
          "start_val": "-0.2",
          "tag": "None"
         },
         "derivative_right": {
          "enabled": "False",
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