{
 "cells": [
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   "cell_type": "code",
   "execution_count": 9,
   "id": "3200850a-b8fb-4f50-9815-16ae8da0f942",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import os\n",
    "from pathlib import Path\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from ase import Atom, Atoms\n",
    "from ase.data import chemical_symbols, covalent_radii, vdw_alvarez\n",
    "from ase.io import read, write\n",
    "from pymatgen.core import Element\n",
    "from scipy import stats\n",
    "from scipy.interpolate import splrep, BSpline, CubicSpline, UnivariateSpline\n",
    "from tqdm.auto import tqdm\n",
    "\n",
    "from mlip_arena.models import MLIPEnum, REGISTRY\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02ff9cf9-49a2-4cec-80d3-56c6661a513b",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Compute MLIP homonuclear diatomics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "90887faa-1601-4c4c-9c44-d16731471d7f",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== ORBv2 ==========\n",
      "Selected GPU cuda:0 with 40339.31 MB free memory from 1 GPUs\n",
      "Downloading ORB model from https://storage.googleapis.com/orbitalmaterials-public-models/forcefields/orb-v2-20241011.ckpt to /global/homes/c/cyrusyc/.cache/orb/orb-v2-20241011.ckpt...\n",
      "Download completed.\n",
      "GPU tensorfloat matmuls precision set to 'high'. This can achieve up to 2x speedup on Nvidia A100 and H100 devices.\n"
     ]
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     "text": [
      "Atoms(symbols='H2', pbc=True, cell=[7.4399999999999995, 7.441, 7.441999999999999])\n"
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     "output_type": "stream",
     "text": [
      "Atoms(symbols='He2', pbc=True, cell=[8.866, 8.866999999999999, 8.868])\n"
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     "text": [
      "Atoms(symbols='Li2', pbc=True, cell=[13.144000000000002, 13.145000000000001, 13.146000000000003])\n"
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     "text": [
      "Atoms(symbols='Be2', pbc=True, cell=[12.276, 12.277, 12.278])\n"
     ]
    },
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     "text": [
      "Atoms(symbols='B2', pbc=True, cell=[11.842, 11.843, 11.844000000000001])\n"
     ]
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     "text": [
      "Atoms(symbols='C2', pbc=True, cell=[10.974, 10.975, 10.976])\n"
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     "text": [
      "Atoms(symbols='N2', pbc=True, cell=[10.292, 10.293, 10.294])\n"
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      "Atoms(symbols='O2', pbc=True, cell=[9.3, 9.301, 9.302000000000001])\n"
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      "Atoms(symbols='F2', pbc=True, cell=[9.052, 9.052999999999999, 9.054])\n"
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      "Atoms(symbols='Ne2', pbc=True, cell=[9.796000000000001, 9.797, 9.798000000000002])\n"
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     "text": [
      "Atoms(symbols='Na2', pbc=True, cell=[15.5, 15.501, 15.502])\n"
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     "text": [
      "Atoms(symbols='Mg2', pbc=True, cell=[15.562, 15.562999999999999, 15.564])\n"
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      "Atoms(symbols='Al2', pbc=True, cell=[13.950000000000001, 13.951, 13.952000000000002])\n"
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      "Atoms(symbols='Si2', pbc=True, cell=[13.578, 13.578999999999999, 13.58])\n"
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     "text": [
      "Atoms(symbols='S2', pbc=True, cell=[11.718, 11.719, 11.72])\n"
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     "text": [
      "Atoms(symbols='Cl2', pbc=True, cell=[11.284, 11.285, 11.286000000000001])\n"
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     "text": [
      "Atoms(symbols='Ar2', pbc=True, cell=[11.346, 11.347, 11.348])\n"
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      "Atoms(symbols='K2', pbc=True, cell=[16.926000000000002, 16.927000000000003, 16.928])\n"
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      "Atoms(symbols='Sc2', pbc=True, cell=[15.996, 15.997, 15.998000000000001])\n"
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      "Atoms(symbols='Ti2', pbc=True, cell=[15.252, 15.253, 15.254000000000001])\n"
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      "Atoms(symbols='V2', pbc=True, cell=[15.004, 15.004999999999999, 15.006])\n"
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      "Atoms(symbols='Cr2', pbc=True, cell=[15.190000000000001, 15.191, 15.192000000000002])\n"
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      "Atoms(symbols='Fe2', pbc=True, cell=[15.128, 15.129, 15.13])\n"
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      "Atoms(symbols='Cu2', pbc=True, cell=[14.756, 14.757, 14.758000000000001])\n"
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     "text": [
      "Atoms(symbols='Lu2', pbc=True, cell=[16.988000000000003, 16.989000000000004, 16.990000000000002])\n"
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     "text": [
      "Atoms(symbols='Hf2', pbc=True, cell=[16.306, 16.307000000000002, 16.308])\n"
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     "name": "stderr",
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     "text": [
      "IOPub message rate exceeded.\n",
      "The Jupyter server will temporarily stop sending output\n",
      "to the client in order to avoid crashing it.\n",
      "To change this limit, set the config variable\n",
      "`--ServerApp.iopub_msg_rate_limit`.\n",
      "\n",
      "Current values:\n",
      "ServerApp.iopub_msg_rate_limit=1000.0 (msgs/sec)\n",
      "ServerApp.rate_limit_window=3.0 (secs)\n",
      "\n"
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      "Atoms(symbols='Md2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
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      },
      "text/plain": [
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atoms(symbols='No2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f92f7ecf653e4e8794856a16f3f96f2d",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atoms(symbols='Lr2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "37812fa907744861a1540588da19cb3a",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atoms(symbols='Rf2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8afb278d247b439883d0c46fa4a0144b",
       "version_major": 2,
       "version_minor": 0
      },
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atoms(symbols='Db2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "30c5d695a8334d938b2bc90aafc45848",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atoms(symbols='Sg2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "79cd1e8a0a1d42c19fbcb67cdba0bd42",
       "version_major": 2,
       "version_minor": 0
      },
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atoms(symbols='Bh2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b60db221da2b4e6e87b6d25c5c6bb6f9",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atoms(symbols='Hs2', pbc=True, cell=[12.0, 12.001, 12.002])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fb6ff68f1b3c4cf593c625d3b280275f",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "IOPub message rate exceeded.\n",
      "The Jupyter server will temporarily stop sending output\n",
      "to the client in order to avoid crashing it.\n",
      "To change this limit, set the config variable\n",
      "`--ServerApp.iopub_msg_rate_limit`.\n",
      "\n",
      "Current values:\n",
      "ServerApp.iopub_msg_rate_limit=1000.0 (msgs/sec)\n",
      "ServerApp.rate_limit_window=3.0 (secs)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for model in MLIPEnum:\n",
    "    \n",
    "    model_name = model.name\n",
    "    \n",
    "    if model_name != 'ORBv2':\n",
    "        continue\n",
    "    \n",
    "    print(f\"========== {model_name} ==========\")\n",
    "\n",
    "    calc = MLIPEnum[model_name].value()\n",
    "\n",
    "    for symbol in tqdm(chemical_symbols[1:]):\n",
    "\n",
    "        s = set([symbol])\n",
    "\n",
    "        if \"X\" in s:\n",
    "            continue\n",
    "\n",
    "        try:\n",
    "            atom = Atom(symbol)\n",
    "            rmin = 0.9 * covalent_radii[atom.number]\n",
    "            rvdw = vdw_alvarez.vdw_radii[atom.number] if atom.number < len(vdw_alvarez.vdw_radii) else np.nan\n",
    "            rmax = 3.1 * rvdw if not np.isnan(rvdw) else 6\n",
    "            rstep = 0.01\n",
    "\n",
    "            a = 2 * rmax\n",
    "\n",
    "            npts = int((rmax - rmin)/rstep)\n",
    "\n",
    "            rs = np.linspace(rmin, rmax, npts)\n",
    "            es = np.zeros_like(rs)\n",
    "\n",
    "            da = symbol + symbol\n",
    "\n",
    "            out_dir = Path(REGISTRY[model_name][\"family\"]) / str(da)\n",
    "            os.makedirs(out_dir, exist_ok=True)\n",
    "\n",
    "            skip = 0\n",
    "\n",
    "            element = Element(symbol)\n",
    "\n",
    "            try:\n",
    "                m = element.valence[1]\n",
    "                if element.valence == (0, 2):\n",
    "                    m = 0\n",
    "            except:\n",
    "                m = 0\n",
    "\n",
    "\n",
    "            r = rs[0]\n",
    "\n",
    "            positions = [\n",
    "                [a/2-r/2, a/2, a/2],\n",
    "                [a/2+r/2, a/2, a/2],\n",
    "            ]\n",
    "\n",
    "            traj_fpath = out_dir / f\"{model_name}.extxyz\"\n",
    "\n",
    "            if traj_fpath.exists():\n",
    "                traj = read(traj_fpath, index=\":\")\n",
    "                skip = len(traj)\n",
    "                atoms = traj[-1]\n",
    "            else:\n",
    "                # Create the unit cell with two atoms\n",
    "                atoms = Atoms(\n",
    "                    da,\n",
    "                    positions=positions,\n",
    "                    # magmoms=magmoms,\n",
    "                    cell=[a, a+0.001, a+0.002],\n",
    "                    pbc=True\n",
    "                )\n",
    "\n",
    "            print(atoms)\n",
    "\n",
    "            atoms.calc = calc\n",
    "\n",
    "            for i, r in enumerate(tqdm(rs)):\n",
    "\n",
    "                if i < skip:\n",
    "                    continue\n",
    "\n",
    "                positions = [\n",
    "                    [a/2-r/2, a/2, a/2],\n",
    "                    [a/2+r/2, a/2, a/2],\n",
    "                ]\n",
    "\n",
    "                # atoms.set_initial_magnetic_moments(magmoms)\n",
    "\n",
    "                atoms.set_positions(positions)\n",
    "\n",
    "                es[i] = atoms.get_potential_energy()\n",
    "\n",
    "                write(traj_fpath, atoms, append=\"a\")\n",
    "        except Exception as e:\n",
    "            print(e)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1bbfae1-790d-4586-9d7d-79c1ba658dcb",
   "metadata": {},
   "source": [
    "# Analysis and output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a0ac2c09-370b-4fdd-bf74-ea5c4ade0215",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== MACE-MP(M) ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c76d9da0324b41ea82a7f3c1c6bbbd02",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n",
      "/tmp/ipykernel_252771/4211250337.py:197: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  \"tortuosity\": etv / (abs(es[0] - es.min()) + (es[-1] - es.min())),\n",
      "/tmp/ipykernel_252771/4211250337.py:199: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-descending-force\": stats.spearmanr(rs[iminf:], fs[iminf:]).statistic,\n",
      "/tmp/ipykernel_252771/4211250337.py:201: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-repulsion-energy\": stats.spearmanr(rs[imine:], es[imine:]).statistic,\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== CHGNet ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3480954042c54cfaa14639051e927a2e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== M3GNet ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0cab810ea1b149da864700de1aa2a8a6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n",
      "/tmp/ipykernel_252771/4211250337.py:200: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-ascending-force\": stats.spearmanr(rs[:iminf], fs[:iminf]).statistic,\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== ORB ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5746ba4b3e184c219ec3b21f7a08db5c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== SevenNet ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "067c399a9bb84555b40030b9ee9b1078",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n",
      "/tmp/ipykernel_252771/4211250337.py:202: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-attraction-energy\": stats.spearmanr(rs[:imine], es[:imine]).statistic,\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== eqV2(OMat) ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5ace0e7a29a84f6eb87611ac4301a634",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== EquiformerV2(OC22) ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1f5c9bf8e5734c9fafaaf88a9627525d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n",
      "/tmp/ipykernel_252771/4211250337.py:197: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  \"tortuosity\": etv / (abs(es[0] - es.min()) + (es[-1] - es.min())),\n",
      "/tmp/ipykernel_252771/4211250337.py:201: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-repulsion-energy\": stats.spearmanr(rs[imine:], es[imine:]).statistic,\n",
      "/tmp/ipykernel_252771/4211250337.py:202: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-attraction-energy\": stats.spearmanr(rs[:imine], es[:imine]).statistic,\n",
      "/tmp/ipykernel_252771/4211250337.py:197: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  \"tortuosity\": etv / (abs(es[0] - es.min()) + (es[-1] - es.min())),\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== EquiformerV2(OC20) ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1848f508ae534cd8a46e96d12a1f8d4c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== eSCN(OC20) ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fb9dfedf4d2944f1b420187d25ebe5ff",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== MACE-OFF(M) ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "864a1e4b6cd048d78864977aaf3bc34a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== ALIGNN ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "57d521c2b1ee45f0b8cb70b351f57f57",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/118 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n",
      "/tmp/ipykernel_252771/4211250337.py:202: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-attraction-energy\": stats.spearmanr(rs[:imine], es[:imine]).statistic,\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "========== ORBv2 ==========\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eb7e69ba02b14c4c90c0e665c091e9e2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_252771/4211250337.py:207: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n",
      "/tmp/ipykernel_252771/4211250337.py:200: ConstantInputWarning: An input array is constant; the correlation coefficient is not defined.\n",
      "  \"spearman-ascending-force\": stats.spearmanr(rs[:iminf], fs[:iminf]).statistic,\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "for model in MLIPEnum:\n",
    "    \n",
    "    model_name = model.name\n",
    "    \n",
    "    # json_fpath = Path(REGISTRY[model_name][\"family\"]) / \"homonuclear-diatomics.json\"\n",
    "    \n",
    "    # if json_fpath.exists():\n",
    "    #     continue\n",
    "\n",
    "    # if model_name != \"ORBv2\":\n",
    "    #     continue\n",
    "\n",
    "    print(f\"========== {model_name} ==========\")\n",
    "    \n",
    "    df = pd.DataFrame(columns=[\n",
    "        \"name\", \n",
    "        \"method\", \n",
    "        \"R\", \"E\", \"F\", \"S^2\",\n",
    "        \"force-flip-times\",\n",
    "        \"force-total-variation\",\n",
    "        \"force-jump\",\n",
    "        \"energy-diff-flip-times\",\n",
    "        \"energy-grad-norm-max\",\n",
    "        \"energy-jump\",\n",
    "        \"energy-total-variation\",\n",
    "        \"tortuosity\",\n",
    "        \"conservation-deviation\",\n",
    "        \"spearman-descending-force\",\n",
    "        \"spearman-ascending-force\",\n",
    "        \"spearman-repulsion-energy\",\n",
    "        \"spearman-attraction-energy\",\n",
    "        \"pbe-energy-mae\",\n",
    "        \"pbe-force-mae\"\n",
    "    ])\n",
    "    \n",
    "\n",
    "    for symbol in tqdm(chemical_symbols[1:]):\n",
    "\n",
    "        da = symbol + symbol\n",
    "\n",
    "        out_dir = Path(REGISTRY[model_name][\"family\"]) / da\n",
    "\n",
    "        traj_fpath = out_dir / f\"{model_name}.extxyz\"\n",
    "\n",
    "\n",
    "        if traj_fpath.exists():\n",
    "            traj = read(traj_fpath, index=\":\")\n",
    "        else:\n",
    "            continue\n",
    "\n",
    "        Rs, Es, Fs, S2s = [], [], [], []\n",
    "        for atoms in traj:\n",
    "\n",
    "            vec = atoms.positions[1] - atoms.positions[0]\n",
    "            r = np.linalg.norm(vec)\n",
    "            e = atoms.get_potential_energy()\n",
    "            f = np.inner(vec/r, atoms.get_forces()[1])\n",
    "            # s2 = np.mean(np.power(atoms.get_magnetic_moments(), 2))\n",
    "\n",
    "            Rs.append(r)\n",
    "            Es.append(e)\n",
    "            Fs.append(f)\n",
    "            # S2s.append(s2)\n",
    "\n",
    "        rs = np.array(Rs)\n",
    "        es = np.array(Es)\n",
    "        fs = np.array(Fs)\n",
    "\n",
    "        # sort interatomic distances and align to zero at far field\n",
    "        indices = np.argsort(rs)[::-1]\n",
    "        rs = rs[indices]\n",
    "        es = es[indices]\n",
    "        eshift = es[0]\n",
    "        es -= eshift\n",
    "        fs = fs[indices]\n",
    "\n",
    "        iminf = np.argmin(fs)\n",
    "        imine = np.argmin(es)\n",
    "\n",
    "        de_dr = np.gradient(es, rs)\n",
    "        d2e_dr2 = np.gradient(de_dr, rs)\n",
    "\n",
    "        # avoid numerical sensitity close to zero\n",
    "        rounded_fs = np.copy(fs)\n",
    "        rounded_fs[np.abs(rounded_fs) < 1e-2] = 0 # 10meV/A\n",
    "        fs_sign = np.sign(rounded_fs)\n",
    "        mask = fs_sign != 0\n",
    "        rounded_fs = rounded_fs[mask]\n",
    "        fs_sign = fs_sign[mask]\n",
    "        f_flip = np.diff(fs_sign) != 0\n",
    "        \n",
    "        fdiff = np.diff(fs)\n",
    "        fdiff_sign = np.sign(fdiff)\n",
    "        mask = fdiff_sign != 0\n",
    "        fdiff = fdiff[mask]\n",
    "        fdiff_sign = fdiff_sign[mask]\n",
    "        fdiff_flip = np.diff(fdiff_sign) != 0\n",
    "        fjump = np.abs(fdiff[:-1][fdiff_flip]).sum() + np.abs(fdiff[1:][fdiff_flip]).sum()\n",
    "        \n",
    "\n",
    "        ediff = np.diff(es)\n",
    "        ediff[np.abs(ediff) < 1e-3] = 0 # 1meV\n",
    "        ediff_sign = np.sign(ediff)\n",
    "        mask = ediff_sign != 0\n",
    "        ediff = ediff[mask]\n",
    "        ediff_sign = ediff_sign[mask]\n",
    "        ediff_flip = np.diff(ediff_sign) != 0\n",
    "        ejump = np.abs(ediff[:-1][ediff_flip]).sum() + np.abs(ediff[1:][ediff_flip]).sum()\n",
    "        \n",
    "        try:\n",
    "            pbe_traj = read(f'./vasp/{da}_FM/PBE.extxyz', index=\":\")\n",
    "\n",
    "            pbe_rs, pbe_es, pbe_fs = [], [], []\n",
    "\n",
    "            for atoms in pbe_traj:\n",
    "                vec = atoms.positions[1] - atoms.positions[0]\n",
    "                r = np.linalg.norm(vec)\n",
    "                pbe_rs.append(r)\n",
    "                pbe_es.append(atoms.get_potential_energy())\n",
    "                pbe_fs.append(np.inner(vec/r, atoms.get_forces()[1]))\n",
    "\n",
    "            pbe_rs = np.array(pbe_rs)\n",
    "            pbe_es = np.array(pbe_es)\n",
    "            pbe_fs = np.array(pbe_fs)\n",
    "\n",
    "            indices = np.argsort(pbe_rs)\n",
    "            pbe_rs = pbe_rs[indices]\n",
    "            pbe_es = pbe_es[indices]\n",
    "            pbe_fs = pbe_fs[indices]\n",
    "\n",
    "            pbe_es -= pbe_es[-1]\n",
    "\n",
    "            xs = np.linspace(pbe_rs.min(), pbe_rs.max(), int(1e3))\n",
    "\n",
    "            cs = UnivariateSpline(pbe_rs, pbe_es, s=0)\n",
    "            pbe_energy_mae = np.mean(np.abs(es - cs(rs)))\n",
    "\n",
    "            cs = UnivariateSpline(pbe_rs, pbe_fs, s=0)\n",
    "            pbe_force_mae = np.mean(np.abs(fs - cs(rs)))\n",
    "        except:\n",
    "            pbe_energy_mae = None\n",
    "            pbe_force_mae = None\n",
    "        \n",
    "        \n",
    "#         edged_es = np.convolve(es, [1, -2, 1], mode='valid')\n",
    "#         # edged_es[np.abs(edged_es) < 0.1] = 0\n",
    "#         prob = np.exp(-es[1:-1]) / np.sum(np.exp(-es[1:-1]))\n",
    "#         edged_es *= prob\n",
    "#         # edged_es /= np.abs(es[1:-1])\n",
    "#         ejump = np.linalg.norm(edged_es)\n",
    "#         ejump = np.abs(edged_es).sum() / 2.0\n",
    "        \n",
    "#         edged_fs = np.convolve(fs, [1, -2, 1], mode='valid')\n",
    "#         # edged_fs[np.abs(edged_fs) < 0.1] = 0\n",
    "#         edged_fs *= prob\n",
    "#         fjump = np.linalg.norm(edged_fs)\n",
    "        # fjump = np.abs(edged_fs).sum() / 2.0\n",
    "        \n",
    "#         fig, axes = plt.subplot_mosaic(\n",
    "#             \"\"\"\n",
    "#             ac\n",
    "#             bd\n",
    "#             \"\"\",\n",
    "#             constrained_layout=True\n",
    "#         )\n",
    "        \n",
    "\n",
    "#         axes['a'].plot(rs, es)\n",
    "#         axes['b'].plot(rs[1:-1], edged_es)\n",
    "#         # axes['b'].plot(0.5*(rs[1:] + rs[:-1]), np.diff(es))\n",
    "#         axes['b'].text(0.7, 0.7, f\"{ejump:.3e}\", transform=axes['b'].transAxes)\n",
    "        \n",
    "#         axes['c'].plot(rs, fs)\n",
    "#         axes['d'].plot(rs[1:-1], edged_fs)\n",
    "#         axes['d'].text(0.7, 0.7, f\"{fjump:.3e}\", transform=axes['d'].transAxes)\n",
    "        \n",
    "\n",
    "        conservation_deviation = np.mean(np.abs(fs + de_dr))\n",
    "        \n",
    "        etv = np.sum(np.abs(np.diff(es)))\n",
    "\n",
    "        data = {\n",
    "            \"name\": da,\n",
    "            \"method\": model_name,\n",
    "            \"R\": rs,\n",
    "            \"E\": es + eshift,\n",
    "            \"F\": fs,\n",
    "            \"S^2\": S2s,\n",
    "            \"force-flip-times\": np.sum(f_flip),\n",
    "            \"force-total-variation\": np.sum(np.abs(np.diff(fs))),\n",
    "            \"force-jump\": fjump,\n",
    "            \"energy-diff-flip-times\": np.sum(ediff_flip),\n",
    "            \"energy-grad-norm-max\": np.max(np.abs(de_dr)),\n",
    "            \"energy-jump\": ejump,\n",
    "            # \"energy-grad-norm-mean\": np.mean(de_dr_abs),\n",
    "            \"energy-total-variation\": etv,\n",
    "            \"tortuosity\": etv / (abs(es[0] - es.min()) + (es[-1] - es.min())),\n",
    "            \"conservation-deviation\": conservation_deviation,\n",
    "            \"spearman-descending-force\": stats.spearmanr(rs[iminf:], fs[iminf:]).statistic,\n",
    "            \"spearman-ascending-force\": stats.spearmanr(rs[:iminf], fs[:iminf]).statistic,\n",
    "            \"spearman-repulsion-energy\": stats.spearmanr(rs[imine:], es[imine:]).statistic,\n",
    "            \"spearman-attraction-energy\": stats.spearmanr(rs[:imine], es[:imine]).statistic,\n",
    "            \"pbe-energy-mae\": pbe_energy_mae,\n",
    "            \"pbe-force-mae\": pbe_force_mae\n",
    "        }\n",
    "\n",
    "        df = pd.concat([df, pd.DataFrame([data])], ignore_index=True)\n",
    "\n",
    "    json_fpath = Path(REGISTRY[model_name][\"family\"]) / \"homonuclear-diatomics.json\"\n",
    "\n",
    "    if json_fpath.exists():\n",
    "        df0 = pd.read_json(json_fpath)\n",
    "        df = pd.concat([df0, df], ignore_index=True)\n",
    "        df.drop_duplicates(inplace=True, subset=[\"name\", \"method\"], keep='last')\n",
    "\n",
    "    df.to_json(json_fpath, orient=\"records\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "15ad3492-f40c-432d-bbbc-1aaae3652311",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.9, 0.9, 'MAE:  52.528')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "fig, axes = plt.subplots(2)\n",
    "axes[0].plot(rs, fs)\n",
    "axes[0].plot(rs, cs(rs))\n",
    "\n",
    "axes[1].plot(rs, fs - cs(rs))\n",
    "\n",
    "axes[1].text(0.9, 0.9, f\"MAE: { np.abs(fs - cs(rs)).mean(): .3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e0dd4367-3dca-440f-a7a9-7fdd84183f2c",
   "metadata": {
    "tags": []
   },
   "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>name</th>\n",
       "      <th>method</th>\n",
       "      <th>R</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>S^2</th>\n",
       "      <th>force-flip-times</th>\n",
       "      <th>force-total-variation</th>\n",
       "      <th>energy-diff-flip-times</th>\n",
       "      <th>energy-grad-norm-max</th>\n",
       "      <th>...</th>\n",
       "      <th>energy-total-variation</th>\n",
       "      <th>conservation-deviation</th>\n",
       "      <th>spearman-descending-force</th>\n",
       "      <th>spearman-ascending-force</th>\n",
       "      <th>spearman-repulsion-energy</th>\n",
       "      <th>spearman-attraction-energy</th>\n",
       "      <th>tortuosity</th>\n",
       "      <th>force-jump</th>\n",
       "      <th>pbe-energy-mae</th>\n",
       "      <th>pbe-force-mae</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>HH</td>\n",
       "      <td>ORB</td>\n",
       "      <td>[3.7199999999999998, 3.70996794, 3.69993586, 3...</td>\n",
       "      <td>[-2.253027916, -2.2530450821, -2.2531223297, -...</td>\n",
       "      <td>[0.00029414, 0.00030291, 0.00033964, 0.0003847...</td>\n",
       "      <td>[]</td>\n",
       "      <td>4</td>\n",
       "      <td>133.563746</td>\n",
       "      <td>3</td>\n",
       "      <td>102.248369</td>\n",
       "      <td>...</td>\n",
       "      <td>13.361551</td>\n",
       "      <td>3.256510</td>\n",
       "      <td>-0.995613</td>\n",
       "      <td>0.578188</td>\n",
       "      <td>-0.974646</td>\n",
       "      <td>0.503110</td>\n",
       "      <td>1.294458</td>\n",
       "      <td>33.598923</td>\n",
       "      <td>1.380663</td>\n",
       "      <td>2.621806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>HeHe</td>\n",
       "      <td>ORB</td>\n",
       "      <td>[4.433, 4.42297362, 4.41294724, 4.40292086, 4....</td>\n",
       "      <td>[-0.0489044189, -0.0488109589, -0.0487890244, ...</td>\n",
       "      <td>[0.00020237, 0.00022884, 0.00022473, 0.0002023...</td>\n",
       "      <td>[]</td>\n",
       "      <td>2</td>\n",
       "      <td>125.775458</td>\n",
       "      <td>3</td>\n",
       "      <td>133.955726</td>\n",
       "      <td>...</td>\n",
       "      <td>13.115419</td>\n",
       "      <td>2.880469</td>\n",
       "      <td>-0.995071</td>\n",
       "      <td>-0.047308</td>\n",
       "      <td>-0.971360</td>\n",
       "      <td>0.339413</td>\n",
       "      <td>1.462191</td>\n",
       "      <td>31.778227</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>119</th>\n",
       "      <td>LiLi</td>\n",
       "      <td>ORB</td>\n",
       "      <td>[6.572, 6.56198152, 6.55196304, 6.54194454, 6....</td>\n",
       "      <td>[-0.6005258560000001, -0.600976944, -0.6010656...</td>\n",
       "      <td>[-5.638e-05, -9.191e-05, -0.000119780000000000...</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>21.673787</td>\n",
       "      <td>4</td>\n",
       "      <td>11.264810</td>\n",
       "      <td>...</td>\n",
       "      <td>6.484533</td>\n",
       "      <td>0.676364</td>\n",
       "      <td>-0.993505</td>\n",
       "      <td>0.999677</td>\n",
       "      <td>-0.999719</td>\n",
       "      <td>0.948915</td>\n",
       "      <td>1.048659</td>\n",
       "      <td>0.069108</td>\n",
       "      <td>0.304063</td>\n",
       "      <td>0.650049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>120</th>\n",
       "      <td>BeBe</td>\n",
       "      <td>ORB</td>\n",
       "      <td>[6.138, 6.12797338, 6.11794676, 6.10792016, 6....</td>\n",
       "      <td>[0.1439437866, 0.1446228027, 0.1446933746, 0.1...</td>\n",
       "      <td>[0.00024622, 0.00020539, 0.00021473, 0.0002307...</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>74.423075</td>\n",
       "      <td>5</td>\n",
       "      <td>17.538560</td>\n",
       "      <td>...</td>\n",
       "      <td>11.756050</td>\n",
       "      <td>3.683254</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.970939</td>\n",
       "      <td>-0.980368</td>\n",
       "      <td>0.695956</td>\n",
       "      <td>1.058202</td>\n",
       "      <td>0.021102</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>121</th>\n",
       "      <td>BB</td>\n",
       "      <td>ORB</td>\n",
       "      <td>[5.921, 5.91097088, 5.90094174, 5.89091262, 5....</td>\n",
       "      <td>[-1.7345266341999999, -1.7349262238, -1.735033...</td>\n",
       "      <td>[-5.236e-05, -9.37e-06, 1.198e-05, 1.637e-05, ...</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>149.497415</td>\n",
       "      <td>8</td>\n",
       "      <td>33.563880</td>\n",
       "      <td>...</td>\n",
       "      <td>16.196704</td>\n",
       "      <td>5.626231</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.923103</td>\n",
       "      <td>-0.987539</td>\n",
       "      <td>0.815314</td>\n",
       "      <td>1.190810</td>\n",
       "      <td>0.672005</td>\n",
       "      <td>1.081229</td>\n",
       "      <td>1.333676</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",
       "      <td>...</td>\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",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>346</th>\n",
       "      <td>NhNh</td>\n",
       "      <td>ORBv2</td>\n",
       "      <td>[6.0, 5.989982779999999, 5.979965579999999, 5....</td>\n",
       "      <td>[-1.2127504348754883, -1.2130546569824219, -1....</td>\n",
       "      <td>[0.0, 7.4e-07, 0.0, 7e-08, 9.54e-06, 4.87e-06,...</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>418.177464</td>\n",
       "      <td>10</td>\n",
       "      <td>66.461493</td>\n",
       "      <td>...</td>\n",
       "      <td>23.668904</td>\n",
       "      <td>38.121299</td>\n",
       "      <td>-0.939579</td>\n",
       "      <td>0.981659</td>\n",
       "      <td>-0.346116</td>\n",
       "      <td>0.992399</td>\n",
       "      <td>1.721098</td>\n",
       "      <td>344.819311</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>347</th>\n",
       "      <td>FlFl</td>\n",
       "      <td>ORBv2</td>\n",
       "      <td>[6.0, 5.989982779999999, 5.979965579999999, 5....</td>\n",
       "      <td>[-1.6584091186523438, -1.6582937240600586, -1....</td>\n",
       "      <td>[0.0, 2.79e-06, 0.0, 4.8e-07, -1.968e-05, 7.6e...</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>414.590097</td>\n",
       "      <td>11</td>\n",
       "      <td>37.387570</td>\n",
       "      <td>...</td>\n",
       "      <td>18.537373</td>\n",
       "      <td>46.828852</td>\n",
       "      <td>-0.979767</td>\n",
       "      <td>0.996953</td>\n",
       "      <td>-0.347458</td>\n",
       "      <td>0.997401</td>\n",
       "      <td>1.522742</td>\n",
       "      <td>353.778117</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>348</th>\n",
       "      <td>McMc</td>\n",
       "      <td>ORBv2</td>\n",
       "      <td>[6.0, 5.989982779999999, 5.979965579999999, 5....</td>\n",
       "      <td>[0.09161853790283203, 0.09169960021972656, 0.0...</td>\n",
       "      <td>[0.0, -9.4e-07, 0.0, -2.38e-06, 0.0, 0.0, 0.0,...</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>429.250003</td>\n",
       "      <td>4</td>\n",
       "      <td>74.488620</td>\n",
       "      <td>...</td>\n",
       "      <td>28.765408</td>\n",
       "      <td>29.080300</td>\n",
       "      <td>-0.825820</td>\n",
       "      <td>0.849567</td>\n",
       "      <td>-0.262398</td>\n",
       "      <td>0.978996</td>\n",
       "      <td>1.466244</td>\n",
       "      <td>332.199750</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>349</th>\n",
       "      <td>LvLv</td>\n",
       "      <td>ORBv2</td>\n",
       "      <td>[6.0, 5.989982779999999, 5.979965579999999, 5....</td>\n",
       "      <td>[0.1532306671142578, 0.15334033966064453, 0.15...</td>\n",
       "      <td>[0.0, -3.56e-06, 0.0, 6.36e-06, -4.78e-06, 8.1...</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>412.500944</td>\n",
       "      <td>4</td>\n",
       "      <td>32.615990</td>\n",
       "      <td>...</td>\n",
       "      <td>21.352589</td>\n",
       "      <td>35.098622</td>\n",
       "      <td>-0.982043</td>\n",
       "      <td>0.959481</td>\n",
       "      <td>-0.644378</td>\n",
       "      <td>0.999991</td>\n",
       "      <td>1.982194</td>\n",
       "      <td>344.140646</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>350</th>\n",
       "      <td>TsTs</td>\n",
       "      <td>ORBv2</td>\n",
       "      <td>[6.0, 5.989982779999999, 5.979965579999999, 5....</td>\n",
       "      <td>[0.2908821105957031, 0.2906169891357422, 0.290...</td>\n",
       "      <td>[0.0, 4.57e-06, 0.0, -3.1e-07, -1.051e-05, -2....</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>393.376749</td>\n",
       "      <td>6</td>\n",
       "      <td>90.260724</td>\n",
       "      <td>...</td>\n",
       "      <td>21.170416</td>\n",
       "      <td>30.675171</td>\n",
       "      <td>-0.991744</td>\n",
       "      <td>0.996975</td>\n",
       "      <td>-0.868141</td>\n",
       "      <td>0.796969</td>\n",
       "      <td>2.002857</td>\n",
       "      <td>334.536066</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>234 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     name method                                                  R  \\\n",
       "117    HH    ORB  [3.7199999999999998, 3.70996794, 3.69993586, 3...   \n",
       "118  HeHe    ORB  [4.433, 4.42297362, 4.41294724, 4.40292086, 4....   \n",
       "119  LiLi    ORB  [6.572, 6.56198152, 6.55196304, 6.54194454, 6....   \n",
       "120  BeBe    ORB  [6.138, 6.12797338, 6.11794676, 6.10792016, 6....   \n",
       "121    BB    ORB  [5.921, 5.91097088, 5.90094174, 5.89091262, 5....   \n",
       "..    ...    ...                                                ...   \n",
       "346  NhNh  ORBv2  [6.0, 5.989982779999999, 5.979965579999999, 5....   \n",
       "347  FlFl  ORBv2  [6.0, 5.989982779999999, 5.979965579999999, 5....   \n",
       "348  McMc  ORBv2  [6.0, 5.989982779999999, 5.979965579999999, 5....   \n",
       "349  LvLv  ORBv2  [6.0, 5.989982779999999, 5.979965579999999, 5....   \n",
       "350  TsTs  ORBv2  [6.0, 5.989982779999999, 5.979965579999999, 5....   \n",
       "\n",
       "                                                     E  \\\n",
       "117  [-2.253027916, -2.2530450821, -2.2531223297, -...   \n",
       "118  [-0.0489044189, -0.0488109589, -0.0487890244, ...   \n",
       "119  [-0.6005258560000001, -0.600976944, -0.6010656...   \n",
       "120  [0.1439437866, 0.1446228027, 0.1446933746, 0.1...   \n",
       "121  [-1.7345266341999999, -1.7349262238, -1.735033...   \n",
       "..                                                 ...   \n",
       "346  [-1.2127504348754883, -1.2130546569824219, -1....   \n",
       "347  [-1.6584091186523438, -1.6582937240600586, -1....   \n",
       "348  [0.09161853790283203, 0.09169960021972656, 0.0...   \n",
       "349  [0.1532306671142578, 0.15334033966064453, 0.15...   \n",
       "350  [0.2908821105957031, 0.2906169891357422, 0.290...   \n",
       "\n",
       "                                                     F S^2 force-flip-times  \\\n",
       "117  [0.00029414, 0.00030291, 0.00033964, 0.0003847...  []                4   \n",
       "118  [0.00020237, 0.00022884, 0.00022473, 0.0002023...  []                2   \n",
       "119  [-5.638e-05, -9.191e-05, -0.000119780000000000...  []                1   \n",
       "120  [0.00024622, 0.00020539, 0.00021473, 0.0002307...  []                1   \n",
       "121  [-5.236e-05, -9.37e-06, 1.198e-05, 1.637e-05, ...  []                1   \n",
       "..                                                 ...  ..              ...   \n",
       "346  [0.0, 7.4e-07, 0.0, 7e-08, 9.54e-06, 4.87e-06,...  []                1   \n",
       "347  [0.0, 2.79e-06, 0.0, 4.8e-07, -1.968e-05, 7.6e...  []                1   \n",
       "348  [0.0, -9.4e-07, 0.0, -2.38e-06, 0.0, 0.0, 0.0,...  []                1   \n",
       "349  [0.0, -3.56e-06, 0.0, 6.36e-06, -4.78e-06, 8.1...  []                1   \n",
       "350  [0.0, 4.57e-06, 0.0, -3.1e-07, -1.051e-05, -2....  []                1   \n",
       "\n",
       "     force-total-variation energy-diff-flip-times  energy-grad-norm-max  ...  \\\n",
       "117             133.563746                      3            102.248369  ...   \n",
       "118             125.775458                      3            133.955726  ...   \n",
       "119              21.673787                      4             11.264810  ...   \n",
       "120              74.423075                      5             17.538560  ...   \n",
       "121             149.497415                      8             33.563880  ...   \n",
       "..                     ...                    ...                   ...  ...   \n",
       "346             418.177464                     10             66.461493  ...   \n",
       "347             414.590097                     11             37.387570  ...   \n",
       "348             429.250003                      4             74.488620  ...   \n",
       "349             412.500944                      4             32.615990  ...   \n",
       "350             393.376749                      6             90.260724  ...   \n",
       "\n",
       "     energy-total-variation  conservation-deviation  \\\n",
       "117               13.361551                3.256510   \n",
       "118               13.115419                2.880469   \n",
       "119                6.484533                0.676364   \n",
       "120               11.756050                3.683254   \n",
       "121               16.196704                5.626231   \n",
       "..                      ...                     ...   \n",
       "346               23.668904               38.121299   \n",
       "347               18.537373               46.828852   \n",
       "348               28.765408               29.080300   \n",
       "349               21.352589               35.098622   \n",
       "350               21.170416               30.675171   \n",
       "\n",
       "     spearman-descending-force  spearman-ascending-force  \\\n",
       "117                  -0.995613                  0.578188   \n",
       "118                  -0.995071                 -0.047308   \n",
       "119                  -0.993505                  0.999677   \n",
       "120                  -1.000000                  0.970939   \n",
       "121                  -1.000000                  0.923103   \n",
       "..                         ...                       ...   \n",
       "346                  -0.939579                  0.981659   \n",
       "347                  -0.979767                  0.996953   \n",
       "348                  -0.825820                  0.849567   \n",
       "349                  -0.982043                  0.959481   \n",
       "350                  -0.991744                  0.996975   \n",
       "\n",
       "     spearman-repulsion-energy  spearman-attraction-energy  tortuosity  \\\n",
       "117                  -0.974646                    0.503110    1.294458   \n",
       "118                  -0.971360                    0.339413    1.462191   \n",
       "119                  -0.999719                    0.948915    1.048659   \n",
       "120                  -0.980368                    0.695956    1.058202   \n",
       "121                  -0.987539                    0.815314    1.190810   \n",
       "..                         ...                         ...         ...   \n",
       "346                  -0.346116                    0.992399    1.721098   \n",
       "347                  -0.347458                    0.997401    1.522742   \n",
       "348                  -0.262398                    0.978996    1.466244   \n",
       "349                  -0.644378                    0.999991    1.982194   \n",
       "350                  -0.868141                    0.796969    2.002857   \n",
       "\n",
       "     force-jump  pbe-energy-mae  pbe-force-mae  \n",
       "117   33.598923        1.380663       2.621806  \n",
       "118   31.778227             NaN            NaN  \n",
       "119    0.069108        0.304063       0.650049  \n",
       "120    0.021102             NaN            NaN  \n",
       "121    0.672005        1.081229       1.333676  \n",
       "..          ...             ...            ...  \n",
       "346  344.819311             NaN            NaN  \n",
       "347  353.778117             NaN            NaN  \n",
       "348  332.199750             NaN            NaN  \n",
       "349  344.140646             NaN            NaN  \n",
       "350  334.536066             NaN            NaN  \n",
       "\n",
       "[234 rows x 21 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
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