how_to_use.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0f8b92b1-80b8-4b9c-bff3-a169aeb6638b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "# Uncomment if you don't want to use GPU\n",
    "#os.environ['CUDA_VISIBLE_DEVICES'] = '-1'\n",
    "os.environ['TF_CPP_MIN_LOG_LEVEL'] = '1' \n",
    "\n",
    "from MultipoleNet import load_model, build_graph_batched, D_Q\n",
    "from rdkit import Chem\n",
    "from rdkit.Chem import AllChem\n",
    "from scipy.spatial.distance import cdist\n",
    "from scipy.spatial.transform import Rotation as R\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "\n",
    "tf.config.list_physical_devices('GPU')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a7260d93-f0d9-4cf6-8393-b8223a8f47df",
   "metadata": {},
   "outputs": [],
   "source": [
    "dtype = np.float32 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "945cb399-387f-4ae9-b0f8-ff9433f3fe73",
   "metadata": {},
   "source": [
    "## Model Loading (Main)\n",
    "Load the model weights: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e55e2bb3-b83f-4845-8e67-011855ec6249",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = load_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e15e295f-66de-4d18-ad58-9fa6a84dc554",
   "metadata": {},
   "source": [
    "## Multipole Prediction for a Single Molecule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a9585de3-97e9-4caa-a592-1592a04964da",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create molecule with RDKit (example: Aspirin)\n",
    "rdkit_mol = Chem.AddHs(Chem.MolFromSmiles('O=C(C)Oc1ccccc1C(=O)O')) \n",
    "elements = [a.GetSymbol() for a in rdkit_mol.GetAtoms()]\n",
    "# Generate a conformation\n",
    "AllChem.EmbedMolecule(rdkit_mol)\n",
    "coordinates = rdkit_mol.GetConformer(0).GetPositions().astype(dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a7a1e05d-37bb-4a7b-bb93-91b3e5b85eb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Predict Multipole for some Conformation:\n",
    "monopoles, dipoles, quadrupoles = model.predict(coordinates, elements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8f4dc9d4-56fb-4009-bc3c-82080d6437ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rotating the dipoles or the molecule shouldn't make a difference...\n",
    "rotation = R.random()\n",
    "r_matrix = rotation.as_matrix().astype(dtype)\n",
    "np.allclose(tf.matmul(model.predict(coordinates, elements)[1], r_matrix.T), \n",
    "            model.predict(tf.matmul(coordinates, r_matrix.T), elements)[1], \n",
    "            atol=np.finfo(dtype).resolution) # atol depends on the used dtype - "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "71968980-a091-4178-8454-f66ac06a8a0e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and quadrupoles\n",
    "np.allclose(tf.matmul(r_matrix, tf.matmul(model.predict(coordinates, elements)[2], r_matrix.T)), \n",
    "            model.predict(tf.matmul(coordinates, r_matrix.T), elements)[2],\n",
    "            atol=np.finfo(dtype).resolution)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffaae51a-67c9-4ad0-9b77-23a4aa48c1b3",
   "metadata": {},
   "source": [
    "## Bached Multipole Prediction\n",
    "If you have the proper hardware available and multiple conformations of the same molecule, this option will be much faster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cc3ddcc8-77b3-4a93-a706-50d1f1be1189",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_conformations = 2500\n",
    "rdkit_mol.RemoveAllConformers()\n",
    "AllChem.EmbedMultipleConfs(rdkit_mol, numConfs=n_conformations)\n",
    "coords_batch = tf.convert_to_tensor(([conformation.GetPositions().astype(dtype) for conformation in rdkit_mol.GetConformers()]))\n",
    "coords_model_input = tf.reshape(coords_batch, [-1, 3]) # The model expects coords in shape Nx3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68dc078d-6058-414d-a177-d9fd4ee8646f",
   "metadata": {},
   "source": [
    "Lets check the timings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2521cd78-51b6-485a-a922-f79cd1b4a173",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.95 ms ± 31 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "graphs = build_graph_batched(coords_batch, elements, cutoff=4.0, num_kernels=32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3deb1997-65c4-47a8-b768-3dbb2d81022f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "411 ms ± 6.45 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "model(graphs, coords_model_input);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8261aeeb-2197-4cb3-a825-63e3a6e18aa6",
   "metadata": {},
   "source": [
    "### Using a Titan V we obtained following timings:\n",
    "\n",
    "411ms for 52'500 atoms / 2500 aspirin conformations (using the main model)\n",
    "\n",
    "Compared to the actual prediction, the graph construction is negligible. As noted in the publication, this step depends on the size of the molecules and can be sped up in applications where multipoles are predicted for the same molecule repeatedly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e388ffb4-496e-49ca-9b15-6b6ca9e3fcd9",
   "metadata": {},
   "source": [
    "## Reference Calculations\n",
    "We can use the Psi4 QM library to obtain reference multipoles/ESPs.\n",
    "Let's first generate a surface around the molecule:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b6f6cdb0-d765-4b89-9fbb-bf29efd65e54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1244, 3)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_points, CUTOFF = 400, 4.0\n",
    "monomer_coords = coordinates.copy()\n",
    "surface_points = np.random.normal(size=[N_points, 3])\n",
    "surface_points = (surface_points / np.linalg.norm(surface_points, axis=-1, keepdims=True)) * CUTOFF\n",
    "surface_points = np.reshape(surface_points[None] + monomer_coords[:, None], [-1, 3])\n",
    "surface_points = surface_points[np.where(np.all(cdist(surface_points, monomer_coords) >= (CUTOFF - 1e-1), axis=-1))[0]]\n",
    "surface_points.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a16665a6-1d4b-48c7-827f-b65a375f7c5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('grid.dat', 'w') as file:\n",
    "    for xyz in surface_points:\n",
    "        for c in xyz:\n",
    "            file.write(str(c) + ' ')\n",
    "        file.write('\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9c4e0242-da88-4a77-af92-95ab639d53ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets do a reference calculation.\n",
    "import psi4\n",
    "psi4.set_options({'basis': 'def2-TZVP'})\n",
    "B_to_A = 0.529177249"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ee05dbe1-5014-4bcd-9bb3-e8f3899029e2",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "psi4_mol = psi4.core.Molecule.from_arrays(monomer_coords, elem=elements)\n",
    "psi4.core.set_output_file('output.dat', False)\n",
    "e, wfn = psi4.energy('PBE0', molecule=psi4_mol, return_wfn=True)\n",
    "psi4.oeprop(wfn, 'GRID_ESP', 'MBIS_CHARGES', title='MBIS Multipoles')\n",
    "reference_esp = [float(x) for x in open('grid_esp.dat')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6375d521-f6b3-4c9e-8769-8333d5a7d76a",
   "metadata": {},
   "outputs": [],
   "source": [
    "wfn_variables = wfn.variables()\n",
    "monopoles_ref = wfn_variables['MBIS CHARGES']\n",
    "dipoles_ref = wfn_variables['MBIS DIPOLES'] * B_to_A # Convert to e/A\n",
    "quadrupoles_ref = D_Q(wfn_variables['MBIS QUADRUPOLES'] * B_to_A ** 2).numpy() # Convert to e/A**2 and detrace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "73027816-d248-48ee-943c-e30b3fa950d4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0017258705\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.8246967439537354, 0.9944293067944121)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0, figsize=(10, 10), dpi=100)\n",
    "plt.scatter(monopoles, monopoles_ref, s=5)\n",
    "print(np.mean(np.abs(monopoles - monopoles_ref)))\n",
    "min_x, max_x = np.amin(monopoles_ref) * 1.2, np.amax(monopoles_ref) * 1.2\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(min_x, max_x)\n",
    "ax.set_ylim(min_x, max_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "00b6b399-ba45-4a0f-89ca-a764cea38bb3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0009122615\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.07264698456108318, 0.06805027538363581)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0, figsize=(10, 10), dpi=100)\n",
    "plt.scatter(dipoles, dipoles_ref, s=5)\n",
    "print(np.mean(np.abs(dipoles - dipoles_ref)))\n",
    "min_x, max_x = np.amin(dipoles_ref) * 1.2, np.amax(dipoles_ref) * 1.2\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(min_x, max_x)\n",
    "ax.set_ylim(min_x, max_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f693cb74-1b0e-40ec-9e08-67180365e3a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000476136\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.03363489088641615, 0.05108393590339469)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0, figsize=(10, 10), dpi=100)\n",
    "plt.scatter(quadrupoles, quadrupoles_ref, s=5)\n",
    "print(np.mean(np.abs(quadrupoles - quadrupoles_ref)))\n",
    "min_x, max_x = np.amin(quadrupoles_ref) * 1.2, np.amax(quadrupoles_ref) * 1.2\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(min_x, max_x)\n",
    "ax.set_ylim(min_x, max_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ce21ee36-74af-44ba-b0d6-42fb070a98b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.820202"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checkout the ESP on the surface\n",
    "dmat = cdist(monomer_coords, surface_points)\n",
    "monopoles_esp = tf.reduce_sum(monopoles / dmat, axis=-2) * 1389.35 # eps0\n",
    "ref_esp = np.array(reference_esp) * 2625.5 # Hartree to kJ/mol\n",
    "np.mean(np.abs(monopoles_esp - ref_esp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a0f7f905-db47-4974-83fb-697cbd80b98d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f166c99e9a0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x2000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0, figsize=(20, 20), dpi=100)\n",
    "plt.scatter(monopoles_esp, ref_esp, s=5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "PSI4",
   "language": "python",
   "name": "psi4"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}