deploy: af0ee75

_sources/ch08/demo_benzene.ipynb

@@ -43,7 +43,180 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Build and Visualize Molecules"
+    "### Diatomics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from pyscf import gto, scf, tools\n",
+    "\n",
+    "def compute_h2_bond_curve(distances, basis='sto-3g'):\n",
+    "    \"\"\"\n",
+    "    Computes the total energy of H2 molecule at various bond distances.\n",
+    "    \n",
+    "    Parameters:\n",
+    "    - distances (array-like): List of H-H bond distances to calculate energy.\n",
+    "    - basis (str): Basis set for the calculation.\n",
+    "    \n",
+    "    Returns:\n",
+    "    - energies (list): Total electronic energies for each bond distance.\n",
+    "    - mo_energies_list (list of lists): Molecular orbital energies for each distance.\n",
+    "    - mo_coeffs_list (list of arrays): Molecular orbital coefficients for each distance.\n",
+    "    \"\"\"\n",
+    "    energies = []\n",
+    "    mo_energies_list = []\n",
+    "    mo_coeffs_list = []\n",
+    "\n",
+    "    for r in distances:\n",
+    "        mol = gto.Mole()\n",
+    "        mol.atom = f'H 0 0 0; H 0 0 {r}'\n",
+    "        mol.basis = basis\n",
+    "        mol.spin = 0  # Singlet state\n",
+    "        mol.build()\n",
+    "        \n",
+    "        # Perform Hartree-Fock calculation\n",
+    "        mf = scf.RHF(mol)\n",
+    "        total_energy = mf.kernel()\n",
+    "        \n",
+    "        # Store results\n",
+    "        energies.append(total_energy)\n",
+    "        mo_energies_list.append(mf.mo_energy)\n",
+    "        mo_coeffs_list.append(mf.mo_coeff)\n",
+    "        \n",
+    "        print(f\"Bond distance: {r:.2f} Å, Total Energy: {total_energy:.6f} Hartree\")\n",
+    "    \n",
+    "    return energies, mo_energies_list, mo_coeffs_list\n",
+    "\n",
+    "def plot_bond_curve(distances, energies):\n",
+    "    \"\"\"\n",
+    "    Plots the bond energy curve of H2 molecule.\n",
+    "    \n",
+    "    Parameters:\n",
+    "    - distances (array-like): H-H bond distances.\n",
+    "    - energies (list): Total electronic energies for each bond distance.\n",
+    "    \"\"\"\n",
+    "    plt.figure(figsize=(8, 5))\n",
+    "    plt.plot(distances, energies, marker='o', label='Total Energy (HF)')\n",
+    "    plt.xlabel('H-H Bond Distance (Å)')\n",
+    "    plt.ylabel('Total Energy (Hartree)')\n",
+    "    plt.title('Bond Curve for H2 (HF/STO-3G)')\n",
+    "    plt.grid(True)\n",
+    "    plt.legend()\n",
+    "    plt.show()\n",
+    "\n",
+    "def plot_molecular_orbitals(distances, mo_energies_list):\n",
+    "    \"\"\"\n",
+    "    Plots the molecular orbital energies as a function of bond distance.\n",
+    "    \n",
+    "    Parameters:\n",
+    "    - distances (array-like): H-H bond distances.\n",
+    "    - mo_energies_list (list of lists): Molecular orbital energies for each distance.\n",
+    "    \"\"\"\n",
+    "    plt.figure(figsize=(8, 5))\n",
+    "    for i in range(len(mo_energies_list[0])):  # Number of orbitals\n",
+    "        orbital_energies = [mo_energies[i] for mo_energies in mo_energies_list]\n",
+    "        plt.plot(distances, orbital_energies, marker='o', label=f'MO {i+1}')\n",
+    "    \n",
+    "    plt.xlabel('H-H Bond Distance (Å)')\n",
+    "    plt.ylabel('Molecular Orbital Energy (Hartree)')\n",
+    "    plt.title('Molecular Orbital Energies for H2 (HF/STO-3G)')\n",
+    "    plt.grid(True)\n",
+    "    plt.legend()\n",
+    "    plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Define bond distances (in Ångstroms)\n",
+    "distances = np.linspace(0.5, 3.0, 20)  # From 0.5 to 3.0 Å\n",
+    "\n",
+    "# Run the bond curve calculation\n",
+    "energies, mo_energies_list, mo_coeffs_list = compute_h2_bond_curve(distances)\n",
+    "\n",
+    "# Plot the bond curve\n",
+    "plot_bond_curve(distances, energies)\n",
+    "\n",
+    "# Plot the molecular orbital energies as a function of bond distance\n",
+    "plot_molecular_orbitals(distances, mo_energies_list)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from pyscf import gto, scf, tools\n",
+    "import py3Dmol  # For 3D visualization of orbitals\n",
+    "\n",
+    "def visualize_h2_mo_cubes(bond_distance=0.74, basis='sto-3g', mo_index=0, output_cube_file='mo.cube'):\n",
+    "    \"\"\"\n",
+    "    Generate and visualize cube files for molecular orbitals of H2.\n",
+    "    \n",
+    "    Parameters:\n",
+    "    - bond_distance (float): H-H bond distance (in Ångstroms).\n",
+    "    - basis (str): Basis set for the calculation (e.g., 'sto-3g', '6-31g').\n",
+    "    - mo_index (int): Index of the molecular orbital to visualize (0-indexed).\n",
+    "    - output_cube_file (str): The name of the cube file to save.\n",
+    "    \"\"\"\n",
+    "    # 1. Build the H2 molecule\n",
+    "    mol = gto.Mole()\n",
+    "    mol.atom = f'H 0 0 0; H 0 0 {bond_distance}'\n",
+    "    mol.basis = basis\n",
+    "    mol.spin = 0  # Singlet state\n",
+    "    mol.build()\n",
+    "\n",
+    "    # 2. Perform Hartree-Fock calculation\n",
+    "    mf = scf.RHF(mol)\n",
+    "    mf.kernel()\n",
+    "\n",
+    "    # 3. Generate cube file for the specified molecular orbital (MO)\n",
+    "    print(f\"Generating cube file for MO {mo_index + 1} (0-indexed as {mo_index})\")\n",
+    "    tools.cubegen.orbital(mol, output_cube_file, mf.mo_coeff[:, mo_index], nx=80, ny=80, nz=80)\n",
+    "\n",
+    "    # 4. Visualize the molecular orbital using py3Dmol\n",
+    "    print(f\"Visualizing cube file: {output_cube_file}\")\n",
+    "    cube_view = py3Dmol.view(width=400, height=400)\n",
+    "    with open(output_cube_file, 'r') as cube_file:\n",
+    "        cube_data = cube_file.read()\n",
+    "        \n",
+    "    # Add isosurfaces for positive and negative parts of the orbital\n",
+    "    cube_view.addVolumetricData(cube_data, \"cube\", {'isoval': -0.03, 'color': \"red\", 'opacity': 0.85})\n",
+    "    cube_view.addVolumetricData(cube_data, \"cube\", {'isoval': 0.03, 'color': \"blue\", 'opacity': 0.85})\n",
+    "    \n",
+    "    # Add the molecular structure as well\n",
+    "    cube_view.addModel(mol.tostring(format=\"xyz\"), 'xyz')\n",
+    "    cube_view.setStyle({'stick': {}, 'sphere': {'radius': 0.4}})\n",
+    "    cube_view.setBackgroundColor('0xeeeeee')\n",
+    "    cube_view.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Set the bond distance, basis, and the index of the molecular orbital to visualize\n",
+    "visualize_h2_mo_cubes(bond_distance=0.74, basis='sto-3g', mo_index=1, output_cube_file='mo_1.cube')  # MO 1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Build and Visualize Benzene"
    ]
   },
   {