bosonic_ham_h2mol.ipynb

{"cells":[{"cell_type":"markdown","metadata":{"id":"iDTWPfBf__xJ"},"source":["# FCI calculations for H$_2$ molecule in the minimal basis"]},{"cell_type":"markdown","metadata":{"id":"vRk4SHLFc-Ax"},"source":["We will compare the fermionic and bosonic Hamiltonians representing the electronic structure of H$_2$ molecule in the minimal basis.\n","All the Hamiltonian matrices should be the same, so it is a way to check that our Hamiltonian mapping is correct."]},{"cell_type":"markdown","metadata":{"id":"VMRG6-TRD4Pw"},"source":["## Prerequisite"]},{"cell_type":"markdown","metadata":{"id":"a6TiEFnRx_9J"},"source":["Installation cells for Google Colab users."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":32861,"status":"ok","timestamp":1723357758151,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":240},"id":"LlyutVWtDvnW","outputId":"85adbfb7-0d14-42e2-8840-440f3665b1d7"},"outputs":[{"output_type":"stream","name":"stdout","text":["Collecting qutip\n","  Downloading qutip-5.0.3.post1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (9.2 kB)\n","Requirement already satisfied: numpy>=1.22 in /usr/local/lib/python3.10/dist-packages (from qutip) (1.26.4)\n","Requirement already satisfied: scipy>=1.9 in /usr/local/lib/python3.10/dist-packages (from qutip) (1.13.1)\n","Requirement already satisfied: packaging in /usr/local/lib/python3.10/dist-packages (from qutip) (24.1)\n","Downloading qutip-5.0.3.post1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (28.0 MB)\n","\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m28.0/28.0 MB\u001b[0m \u001b[31m22.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n","\u001b[?25hInstalling collected packages: qutip\n","Successfully installed 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Colab","userId":"04968770630191453479"},"user_tz":240},"id":"pllef8LIGwWv","outputId":"29e0bfe7-733a-45ad-c424-00befb8c3fbd"},"outputs":[{"output_type":"stream","name":"stdout","text":["Requirement already satisfied: seaborn in /usr/local/lib/python3.10/dist-packages (0.13.1)\n","Requirement already satisfied: numpy!=1.24.0,>=1.20 in /usr/local/lib/python3.10/dist-packages (from seaborn) (1.26.4)\n","Requirement already satisfied: pandas>=1.2 in /usr/local/lib/python3.10/dist-packages (from seaborn) (2.1.4)\n","Requirement already satisfied: matplotlib!=3.6.1,>=3.4 in /usr/local/lib/python3.10/dist-packages (from seaborn) (3.7.1)\n","Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib!=3.6.1,>=3.4->seaborn) (1.2.1)\n","Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.10/dist-packages (from matplotlib!=3.6.1,>=3.4->seaborn) (0.12.1)\n","Requirement already satisfied: fonttools>=4.22.0 in 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matplotlib.pyplot as plt"]},{"cell_type":"markdown","metadata":{"id":"qki5bXQ-yXz2"},"source":["## Functions"]},{"cell_type":"markdown","metadata":{"id":"mv0a8TTnDL3F"},"source":["Molecular data object after Hartree-Fock calculation."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Pzl0mEVrl58n"},"outputs":[],"source":["def h2mol_data(hhdis):\n","    \"\"\"\n","    Molecular data for H2 molecule in a minimal basis.\n","\n","    Argument:\n","    hhdis -- bond distance in Angstrom\n","    \"\"\"\n","\n","    # Parameters\n","    basis = \"sto-3g\"\n","    multiplicity = 1\n","    charge = 0\n","\n","    # XYZ coordinates\n","    geometry = [(\"H\", (0,0,0)), (\"H\", (0,0,hhdis))]\n","\n","    # Define molecule\n","    molecule = MolecularData(geometry, basis, multiplicity, charge)\n","\n","    # Run HF calculation\n","    hf_molecule = run_pyscf(molecule, run_scf=1)\n","\n","    return hf_molecule"]},{"cell_type":"markdown","metadata":{"id":"_tHkRA0tEZmG"},"source":["### Fermionic"]},{"cell_type":"markdown","metadata":{"id":"QnfCjUBZ1s1C"},"source":["Compute the molecular integrals to build the fermionic Hamiltonian.\n","Note that we choose to write the molecular electronic structure Hamiltonian as:\n","\n","$$ H = h_{\\text{nuc}}\n","+ \\sum_{pq} h_q^p \\: f_p^\\dagger f_q\n","+ \\frac{1}{2} \\sum_{pqrs} v_{rs}^{pq} \\: f_p^\\dagger f_q^\\dagger f_r f_s,\n","$$\n","whereas the `OpenFermion` convention is\n","\n","$$ H = h_{\\text{nuc}}\n","+ \\sum_{pq} h_q^p \\: f_p^\\dagger f_q\n","+ \\sum_{pqrs} h_{rs}^{pq} \\: f_p^\\dagger f_q^\\dagger f_r f_s.\n","$$"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"seoPKwnWDQj0"},"outputs":[],"source":["def h2mol_integrals(hhdis):\n","    \"\"\"\n","    Hamiltonian coefficients in the bosonic representation.\n","\n","    Argument:\n","    hhdis -- bond distance in Angstrom\n","    \"\"\"\n","\n","    # Molecular data\n","    hf_molecule = h2mol_data(hhdis)\n","\n","    # HF energy\n","    ehf = hf_molecule.hf_energy\n","\n","    # Nuclear repulsion scalar\n","    hnuc = hf_molecule.nuclear_repulsion\n","\n","    # Electron intergals\n","    h1, h2 = get_tensors_from_integrals(hf_molecule.one_body_integrals, \\\n","                                        hf_molecule.two_body_integrals)\n","    v2 = h2 * 2\n","\n","    return ehf, hnuc, h1, v2"]},{"cell_type":"markdown","metadata":{"id":"cLjEuIg93Go7"},"source":["Compute the matrix elements\n","$ \\langle p, q | \\: H \\: |r, s \\rangle $.\n","The Slater determinants are:\n","$ | 0, 1 \\rangle_F, | 0, 2 \\rangle_F, | 0, 3 \\rangle_F, | 1, 2 \\rangle_F, | 1, 3 \\rangle_F $, and $ | 2, 3 \\rangle_F $."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"be8KQxrv3HCl"},"outputs":[],"source":["def ham_fermi_mat(hhdis):\n","    \"\"\"\n","    Build the FCI Hamiltonian matrix in the fermionic representation.\n","    We will use OpenFermion.\n","\n","    Argument:\n","    hhdis -- bond distance in Angstrom\n","    \"\"\"\n","\n","    # Molecular data\n","    hf_molecule = h2mol_data(hhdis)\n","\n","    # Ham operator\n","    ham_op = get_fermion_operator(hf_molecule.get_molecular_hamiltonian())\n","\n","    # Vacuum\n","    n_qubit = 4\n","    vac_state = np.zeros(2 ** n_qubit)\n","    vac_state[0] = 1.0\n","\n","    # Ket operators\n","    ket_list = [FermionOperator('0^ 1^'), \\\n","                FermionOperator('0^ 2^'), \\\n","                FermionOperator('0^ 3^'), \\\n","                FermionOperator('1^ 2^'), \\\n","                FermionOperator('1^ 3^'), \\\n","                FermionOperator('2^ 3^') ]\n","\n","    # Bra operators\n","    bra_list = [FermionOperator('1 0'), \\\n","                FermionOperator('2 0'), \\\n","                FermionOperator('3 0'), \\\n","                FermionOperator('2 1'), \\\n","                FermionOperator('3 1'), \\\n","                FermionOperator('3 2') ]\n","\n","    # Hamiltonian\n","    M2 = np.zeros([6, 6])\n","    j = 0\n","    for bra in bra_list:\n","        j += 1\n","        k = 0\n","        for ket in ket_list:\n","            k += 1\n","            op_mat = get_sparse_operator( bra * ham_op * ket )\n","            M2[j-1, k-1] = np.real( expectation(op_mat, vac_state) )\n","\n","    return M2"]},{"cell_type":"markdown","metadata":{"id":"Hb7uJJGTEc-y"},"source":["### Bosonic"]},{"cell_type":"markdown","metadata":{"id":"pET12uPQtBlV"},"source":["We write the same Hamiltonian of dihydrogen molecule as a system of two qumodes or quantum harmonic oscillators (QHOs), as derived in the equation 46 of [arXiv: 2404.10222v2](https://arxiv.org/abs/2404.10222v2)\n","\n","\\begin{align}\n","H_B\n","&= g_1 |0, 0 \\rangle \\langle 0, 0 |\n","+ g_2 |0, 2 \\rangle \\langle 0, 2|\n","+ g_3 \\big( |0, 1 \\rangle \\langle 0, 1|\n","+ |2, 0 \\rangle \\langle 2, 0| \\big)  \n","+ g_4 \\big( |1, 0, \\rangle \\langle 1, 0 |\n","+ |1, 1 \\rangle \\langle 1, 1| \\big)  \n","\\\\\n","&+ g_5 \\: \\big( |0, 0 \\rangle \\langle 0, 2| + \\text{h.c.} \\big)\n","- g_5 \\: \\big( |2, 0 \\rangle \\langle 0, 1| + \\text{h.c.} \\big),\n","\\end{align}\n","where $\\{ g_j \\}$ are functions of one-electron and two-electron integrals\n","\n","\\begin{align}\n","g_1\n","&= h^0_0 + h^1_1 + v^{01}_{10},\n","\\\\\n","g_2\n","&= 2 h^2_2 + v^{23}_{32},\n","\\\\\n","g_3\n","&= h^0_0 + h^2_2 + v^{02}_{20},\n","\\\\\n","g_4\n","&= h^0_0 + h^2_2 + v^{02}_{20} - v^{02}_{02},\n","\\\\\n","g_5\n","&= v^{02}_{20}.\n","\\end{align}\n","\n","This was the first time a molecular electronic structure Hamiltonian was represented as a bosonic Hamiltonian.\n"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"A1xv3INZ8ju3"},"outputs":[],"source":["def ham_bose_coeffs(h1, v2):\n","    \"\"\"\n","    Hamiltonian coefficients in the bosonic representation.\n","\n","    Arguments:\n","    h1 -- one-electron integrals\n","    v2 -- two-electron integrals\n","    \"\"\"\n","\n","    g1 = np.zeros([5])\n","\n","    g1[0] = h1[0, 0] + h1[1, 1] + v2[0, 1, 1, 0]\n","    g1[1] = ( 2 * h1[2, 2] ) + v2[2, 3, 3, 2]\n","    g1[2] = h1[1, 1] + h1[3, 3] + v2[0, 2, 2, 0]\n","    g1[3] = h1[0, 0] + h1[2, 2] + v2[0, 2, 2, 0] - v2[0, 2, 0, 2]\n","    g1[4] = v2[0, 2, 0, 2]\n","\n","    return g1"]},{"cell_type":"markdown","metadata":{"id":"P7RwrzEE95iZ"},"source":["Compute the matrix elements\n","$ \\langle p, q | \\: H \\: |r, s \\rangle $.\n","The basis states are:\n","$ | 0, 0 \\rangle_B, | 1, 0 \\rangle_B, | 2, 0 \\rangle_B, | 0, 1 \\rangle_B, | 1, 1 \\rangle_B $, and $ | 0, 2 \\rangle_B $."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"_L8Whf9o6CQV"},"outputs":[],"source":["def ham_bose_mat(hnuc, g1):\n","    \"\"\"\n","    Build the FCI Hamiltonian matrix in the bosonic representation.\n","    We will use QuTip.\n","\n","    Arguments:\n","    hnuc -- nuclear repulsion scalar\n","    g1 -- bosonic Hamiltonian coefficients\n","    \"\"\"\n","\n","    # Scalar part of H\n","    ham_bose = hnuc * qt.tensor( qt.qeye(3), qt.qeye(3) )\n","\n","    # Symmetric part of H\n","    ham_bose += g1[0] * qt.tensor( qt.basis(3, 0) * qt.basis(3, 0).dag(), \\\n","                                   qt.basis(3, 0) * qt.basis(3, 0).dag() )\n","    ham_bose += g1[1] * qt.tensor( qt.basis(3, 0) * qt.basis(3, 0).dag(), \\\n","                                   qt.basis(3, 2) * qt.basis(3, 2).dag() )\n","    ham_bose += g1[2] * qt.tensor( qt.basis(3, 0) * qt.basis(3, 0).dag(), \\\n","                                   qt.basis(3, 1) * qt.basis(3, 1).dag() )\n","    ham_bose += g1[2] * qt.tensor( qt.basis(3, 2) * qt.basis(3, 2).dag(), \\\n","                                   qt.basis(3, 0) * qt.basis(3, 0).dag() )\n","    ham_bose += g1[3] * qt.tensor( qt.basis(3, 1) * qt.basis(3, 1).dag(), \\\n","                                   qt.basis(3, 0) * qt.basis(3, 0).dag() )\n","    ham_bose += g1[3] * qt.tensor( qt.basis(3, 1) * qt.basis(3, 1).dag(), \\\n","                                   qt.basis(3, 1) * qt.basis(3, 1).dag() )\n","    # Transition part of H\n","    ham_bose += g1[4] * qt.tensor( qt.basis(3, 0) * qt.basis(3, 0).dag(), \\\n","                                   qt.basis(3, 0) * qt.basis(3, 2).dag() )\n","    ham_bose += g1[4] * qt.tensor( qt.basis(3, 0) * qt.basis(3, 0).dag(), \\\n","                                   qt.basis(3, 2) * qt.basis(3, 0).dag() )\n","    ham_bose -= g1[4] * qt.tensor( qt.basis(3, 2) * qt.basis(3, 0).dag(), \\\n","                                   qt.basis(3, 0) * qt.basis(3, 1).dag() )\n","    ham_bose -= g1[4] * qt.tensor( qt.basis(3, 0) * qt.basis(3, 2).dag(), \\\n","                                   qt.basis(3, 1) * qt.basis(3, 0).dag() )\n","\n","\n","    # States\n","    ket_list = [qt.tensor( qt.basis(3, 0), qt.basis(3, 0) ), \\\n","                qt.tensor( qt.basis(3, 1), qt.basis(3, 0) ), \\\n","                qt.tensor( qt.basis(3, 2), qt.basis(3, 0) ), \\\n","                qt.tensor( qt.basis(3, 0), qt.basis(3, 1) ), \\\n","                qt.tensor( qt.basis(3, 1), qt.basis(3, 1) ), \\\n","                qt.tensor( qt.basis(3, 0), qt.basis(3, 2) ) ]\n","\n","    # Hamiltonian matrix\n","    M2 = np.zeros([6, 6])\n","    j = 0\n","    for bra in ket_list:\n","        j += 1\n","        k = 0\n","        for ket in ket_list:\n","            k += 1\n","            M2[j-1, k-1] = np.real( ham_bose.matrix_element( bra.dag(), ket) )\n","\n","    return M2"]},{"cell_type":"markdown","metadata":{"id":"KiMJZ33zF4Z2"},"source":["## Tests"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"A_vU_Vfg-52n"},"outputs":[],"source":["hhdis = 0.7414\n","ehf, hnuc, h1, v2 = h2mol_integrals(hhdis)\n","g1 = ham_bose_coeffs(h1, v2)\n","\n","MF = ham_fermi_mat(hhdis)\n","MB = ham_bose_mat(hnuc, g1)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":9,"status":"ok","timestamp":1723357770435,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":240},"id":"yC7A92aK0u_B","outputId":"7f856609-628d-4ba7-f4ec-6898ce32d60a"},"outputs":[{"output_type":"stream","name":"stdout","text":["ehf-orig: -1.1166843870853405\n","h00-ferm: -1.116684387085341\n","h00-bose: -1.116684387085341\n"]}],"source":["print(\"ehf-orig:\", ehf)\n","print(\"h00-ferm:\", MF[0, 0])\n","print(\"h00-bose:\", MB[0, 0])"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":6,"status":"ok","timestamp":1723357770435,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":240},"id":"5UY8J6dtDb_J","outputId":"024c7d35-f434-43e8-ef54-bdb66a063130"},"outputs":[{"output_type":"stream","name":"stdout","text":["H-fermi:\n","[[-1.11668439  0.          0.          0.          0.          0.18128881]\n"," [ 0.         -0.53247901  0.          0.          0.          0.        ]\n"," [ 0.          0.         -0.3511902  -0.18128881  0.          0.        ]\n"," [ 0.          0.         -0.18128881 -0.3511902   0.          0.        ]\n"," [ 0.          0.          0.          0.         -0.53247901  0.        ]\n"," [ 0.18128881  0.          0.          0.          0.          0.45925033]]\n","------------\n","H-bose:\n","[[-1.11668439  0.          0.          0.          0.          0.18128881]\n"," [ 0.         -0.53247901  0.          0.          0.          0.        ]\n"," [ 0.          0.         -0.3511902  -0.18128881  0.          0.        ]\n"," [ 0.          0.         -0.18128881 -0.3511902   0.          0.        ]\n"," [ 0.          0.          0.          0.         -0.53247901  0.        ]\n"," [ 0.18128881  0.          0.          0.          0.          0.45925033]]\n"]}],"source":["print(\"H-fermi:\")\n","print(MF)\n","print(\"------------\")\n","print(\"H-bose:\")\n","print(MB)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":5,"status":"ok","timestamp":1723357770435,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":240},"id":"LP5o9me-DfgH","outputId":"ed23f57f-b42e-49fd-9a04-b0a2aa1d6318"},"outputs":[{"output_type":"stream","name":"stdout","text":["H-bose coefficients:\n","[-1.83043838 -0.25450366 -1.06494419 -1.246233    0.18128881]\n"]}],"source":["print(\"H-bose coefficients:\")\n","print(g1)"]},{"cell_type":"markdown","metadata":{"id":"d9K1jBmAEZ-W"},"source":["## Scripts"]},{"cell_type":"markdown","metadata":{"id":"bi0TXMjkOYIh"},"source":["### Heatmaps"]},{"cell_type":"markdown","metadata":{"id":"IiWaVJjRJFrq"},"source":["Print heatmaps of bosonic and fermionic Hamiltonians for the equilibrium H-H bond distance."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"24t1oGZxDcm1"},"outputs":[],"source":["# Distance\n","diseq = 0.7414 # Angstrom\n","\n","# Hamiltonian coefficients\n","ehf, hnuc, h1, v2 = h2mol_integrals(diseq)\n","g1 = ham_bose_coeffs(h1, v2)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"9dupg9GWJKzr"},"outputs":[],"source":["# Hamiltonian matrices\n","M1 = ham_fermi_mat(diseq)\n","M2 = ham_bose_mat(hnuc, g1)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"V5PQqtn1HSqD"},"outputs":[],"source":["# Seaborn themes\n","sns.set_theme(style=\"white\")\n","\n","# Custom colormap\n","cmap = sns.diverging_palette(230, 20, as_cmap=True)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":452},"executionInfo":{"elapsed":525,"status":"ok","timestamp":1723357905171,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":240},"id":"15YRDkBoIFxE","outputId":"492a8480-e9cc-41ce-a784-1bdfa2bad49f"},"outputs":[{"output_type":"execute_result","data":{"text/plain":["<Axes: >"]},"metadata":{},"execution_count":17},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 2 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["# Heatmap #1\n","sns.heatmap(M1, cmap=cmap, vmax=0.3, center=0, square=True, linewidths=.5)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":450},"executionInfo":{"elapsed":333,"status":"ok","timestamp":1709579803477,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":300},"id":"jYrNhaw9JUHK","outputId":"3757d987-818e-43a0-aa23-f56afc0dae19"},"outputs":[{"output_type":"execute_result","data":{"text/plain":["<Axes: >"]},"metadata":{},"execution_count":19},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 2 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["# Heatmap #2\n","sns.heatmap(M2, cmap=cmap, vmax=0.3, center=0, square=True, linewidths=.5)"]},{"cell_type":"markdown","metadata":{"id":"SBbIUuyoOTqa"},"source":["### Bosonic Hamiltonian coefficients"]},{"cell_type":"markdown","metadata":{"id":"S79SV1zlOi-K"},"source":["Plot the $\\{ g_p \\}$ values with respect to H-H bond distances."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":8228,"status":"ok","timestamp":1723357921023,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":240},"id":"5dR6RtcxJXse","outputId":"8caa6b27-1230-4f18-edc5-ef2eb0f85f87"},"outputs":[{"output_type":"stream","name":"stdout","text":["distance: 0.2\n","------------------\n","distance: 0.22\n","------------------\n","distance: 0.24\n","------------------\n","distance: 0.26\n","------------------\n","distance: 0.28\n","------------------\n","distance: 0.30000000000000004\n","------------------\n","distance: 0.32000000000000006\n","------------------\n","distance: 0.3400000000000001\n","------------------\n","distance: 0.3600000000000001\n","------------------\n","distance: 0.3800000000000001\n","------------------\n","distance: 0.40000000000000013\n","------------------\n","distance: 0.42000000000000015\n","------------------\n","distance: 0.44000000000000017\n","------------------\n","distance: 0.4600000000000002\n","------------------\n","distance: 0.4800000000000002\n","------------------\n","distance: 0.5000000000000002\n","------------------\n","distance: 0.5200000000000002\n","------------------\n","distance: 0.5400000000000003\n","------------------\n","distance: 0.5600000000000003\n","------------------\n","distance: 0.5800000000000003\n","------------------\n","distance: 0.6000000000000003\n","------------------\n","distance: 0.6200000000000003\n","------------------\n","distance: 0.6400000000000003\n","------------------\n","distance: 0.6600000000000004\n","------------------\n","distance: 0.6800000000000004\n","------------------\n","distance: 0.7000000000000004\n","------------------\n","distance: 0.7200000000000004\n","------------------\n","distance: 0.7400000000000004\n","------------------\n","distance: 0.7600000000000005\n","------------------\n","distance: 0.7800000000000005\n","------------------\n","distance: 0.8000000000000005\n","------------------\n","distance: 0.8200000000000005\n","------------------\n","distance: 0.8400000000000005\n","------------------\n","distance: 0.8600000000000005\n","------------------\n","distance: 0.8800000000000006\n","------------------\n","distance: 0.9000000000000006\n","------------------\n","distance: 0.9200000000000006\n","------------------\n","distance: 0.9400000000000006\n","------------------\n","distance: 0.9600000000000006\n","------------------\n","distance: 0.9800000000000006\n","------------------\n","distance: 1.0000000000000007\n","------------------\n","distance: 1.0200000000000007\n","------------------\n","distance: 1.0400000000000007\n","------------------\n","distance: 1.0600000000000007\n","------------------\n","distance: 1.0800000000000007\n","------------------\n","distance: 1.1000000000000008\n","------------------\n","distance: 1.1200000000000008\n","------------------\n","distance: 1.1400000000000008\n","------------------\n","distance: 1.1600000000000008\n","------------------\n","distance: 1.1800000000000008\n","------------------\n","distance: 1.2000000000000008\n","------------------\n","distance: 1.2200000000000009\n","------------------\n","distance: 1.2400000000000009\n","------------------\n","distance: 1.260000000000001\n","------------------\n","distance: 1.280000000000001\n","------------------\n","distance: 1.300000000000001\n","------------------\n","distance: 1.320000000000001\n","------------------\n","distance: 1.340000000000001\n","------------------\n","distance: 1.360000000000001\n","------------------\n","distance: 1.380000000000001\n","------------------\n","distance: 1.400000000000001\n","------------------\n","distance: 1.420000000000001\n","------------------\n","distance: 1.440000000000001\n","------------------\n","distance: 1.460000000000001\n","------------------\n","distance: 1.480000000000001\n","------------------\n","distance: 1.500000000000001\n","------------------\n","distance: 1.5200000000000011\n","------------------\n","distance: 1.5400000000000011\n","------------------\n","distance: 1.5600000000000012\n","------------------\n","distance: 1.5800000000000012\n","------------------\n","distance: 1.6000000000000012\n","------------------\n","distance: 1.6200000000000012\n","------------------\n","distance: 1.6400000000000012\n","------------------\n","distance: 1.6600000000000013\n","------------------\n","distance: 1.6800000000000013\n","------------------\n","distance: 1.7000000000000013\n","------------------\n","distance: 1.7200000000000013\n","------------------\n","distance: 1.7400000000000013\n","------------------\n","distance: 1.7600000000000013\n","------------------\n","distance: 1.7800000000000014\n","------------------\n","distance: 1.8000000000000014\n","------------------\n","distance: 1.8200000000000014\n","------------------\n","distance: 1.8400000000000014\n","------------------\n","distance: 1.8600000000000014\n","------------------\n","distance: 1.8800000000000014\n","------------------\n","distance: 1.9000000000000015\n","------------------\n","distance: 1.9200000000000015\n","------------------\n","distance: 1.9400000000000015\n","------------------\n","distance: 1.9600000000000015\n","------------------\n","distance: 1.9800000000000015\n","------------------\n","distance: 2.0000000000000013\n","------------------\n","distance: 2.0200000000000014\n","------------------\n","distance: 2.0400000000000014\n","------------------\n","distance: 2.0600000000000014\n","------------------\n","distance: 2.0800000000000014\n","------------------\n","distance: 2.1000000000000014\n","------------------\n","distance: 2.1200000000000014\n","------------------\n","distance: 2.1400000000000015\n","------------------\n","distance: 2.1600000000000015\n","------------------\n","distance: 2.1800000000000015\n","------------------\n","distance: 2.2000000000000015\n","------------------\n","distance: 2.2200000000000015\n","------------------\n","distance: 2.2400000000000015\n","------------------\n","distance: 2.2600000000000016\n","------------------\n","distance: 2.2800000000000016\n","------------------\n","distance: 2.3000000000000016\n","------------------\n","distance: 2.3200000000000016\n","------------------\n","distance: 2.3400000000000016\n","------------------\n","distance: 2.3600000000000017\n","------------------\n","distance: 2.3800000000000017\n","------------------\n","distance: 2.4000000000000017\n","------------------\n","distance: 2.4200000000000017\n","------------------\n","distance: 2.4400000000000017\n","------------------\n","distance: 2.4600000000000017\n","------------------\n","distance: 2.4800000000000018\n","------------------\n","distance: 2.5000000000000018\n","------------------\n","distance: 2.520000000000002\n","------------------\n","distance: 2.540000000000002\n","------------------\n","distance: 2.560000000000002\n","------------------\n","distance: 2.580000000000002\n","------------------\n","distance: 2.600000000000002\n","------------------\n","distance: 2.620000000000002\n","------------------\n","distance: 2.640000000000002\n","------------------\n","distance: 2.660000000000002\n","------------------\n","distance: 2.680000000000002\n","------------------\n","distance: 2.700000000000002\n","------------------\n","distance: 2.720000000000002\n","------------------\n","distance: 2.740000000000002\n","------------------\n","distance: 2.760000000000002\n","------------------\n","distance: 2.780000000000002\n","------------------\n","distance: 2.800000000000002\n","------------------\n","distance: 2.820000000000002\n","------------------\n","distance: 2.840000000000002\n","------------------\n","distance: 2.860000000000002\n","------------------\n","distance: 2.880000000000002\n","------------------\n","distance: 2.900000000000002\n","------------------\n","distance: 2.920000000000002\n","------------------\n","distance: 2.940000000000002\n","------------------\n","distance: 2.960000000000002\n","------------------\n","distance: 2.980000000000002\n","------------------\n","distance: 3.000000000000002\n","------------------\n","distance: 3.0200000000000022\n","------------------\n","distance: 3.0400000000000023\n","------------------\n","distance: 3.0600000000000023\n","------------------\n","distance: 3.0800000000000023\n","------------------\n","distance: 3.1000000000000023\n","------------------\n","distance: 3.1200000000000023\n","------------------\n","distance: 3.1400000000000023\n","------------------\n","distance: 3.1600000000000024\n","------------------\n","distance: 3.1800000000000024\n","------------------\n","distance: 3.2000000000000024\n","------------------\n"]}],"source":["# Parameters\n","disin = 0.2 # initial distance\n","deltadis = 0.02 # change in distance\n","npoints = 151 # number of points\n","\n","# Initialize\n","gmat = np.zeros([npoints, 5]) # array for coefficients\n","dvec = np.zeros([npoints]) # array for distances\n","dvec[0] = disin # initial distance\n","\n","# Start the loop\n","for j in range(npoints):\n","    # Print\n","    print(\"distance:\", dvec[j])\n","    print(\"------------------\")\n","    # Get coefficients\n","    ehf, hnuc, h1, v2 = h2mol_integrals(dvec[j])\n","    gmat[j, :] = ham_bose_coeffs(h1, v2)\n","    # Exit condition\n","    if j == npoints - 1:\n","        break\n","    # Update\n","    dvec[j + 1] = dvec[j] + deltadis"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":445},"executionInfo":{"elapsed":1172,"status":"ok","timestamp":1723357922193,"user":{"displayName":"Batista Colab","userId":"04968770630191453479"},"user_tz":240},"id":"hSfzm5FklXJa","outputId":"77218c07-de2b-426b-a9a5-cb9025068ed9"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["# Figure and axes\n","fig, ax = plt.subplots()\n","plt.rcParams.update({'font.size': 16})\n","plt.subplots_adjust(left=0.15, bottom=0.15)\n","\n","# Axis labels and title\n","ax.set_xlabel('Bond distance ($\\AA$)')\n","ax.set_ylabel('Coefficients (Hartree)')\n","#ax.set_title('Bosonic Hamiltonian coefficients for dihydrogen')\n","\n","# Plot the curves\n","ax.plot(dvec, gmat[:, 4], '--', color='orange', label='$g_5$')\n","ax.plot(dvec, -gmat[:, 4], '', color='orange', label='$- g_5$')\n","ax.plot(dvec, gmat[:, 1], '', color='blue', label='$g_2$')\n","ax.plot(dvec, gmat[:, 2], '--', color='black', label='$g_3$')\n","ax.plot(dvec, gmat[:, 3], '', color='green', label='$g_4$')\n","ax.plot(dvec, gmat[:, 0], '', color='brown', label='$g_1$')\n","\n","# Legend\n","ax.legend(loc='best')\n","\n","# Save\n","plt.savefig('bosonic_coeffs.pdf', dpi=500)\n","#files.download('bosonic_coeffs.png')\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"colab":{"toc_visible":true,"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0}