{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aeb1ebff",
   "metadata": {},
   "source": [
    "# 7. Ro-vibrational Spectra of Hydrogen\n",
    "\n",
    "The ro-vibrational spectrum of hydrogen, a linear molecule, is computed by the phase-space sampling (see also section III D of the paper).\n",
    "\n",
    "| Redundant space | Potential | Integrator | Physical space |\n",
    "|---|---|---|---|\n",
    "| Cartesian (6 DOFs) with 3 constraints (3 translations) | `H2SplinePotential` | `ShakeRattle` | bond length $r$, polar $\\theta$ and azimuthal angle $\\phi$ |\n",
    "\n",
    "- **Ro-vibration**: Only the center of mass is fixed by constraints, so that the molecule vibrates while rotating. The analytical Hessian of `H2SplinePotential` is used at every step.\n",
    "\n",
    "- **Initial states**: Coherent states centered at the equilibrium structure, in the vibrational ground state ($v = 0$) with the rotational kinetic energies of 500, 2000 and 5000 $\\textrm{cm}^{-1}$.\n",
    "  \n",
    "- **Sampling**: As in the pure rotation, the initial positions are fixed at the equilibrium structure, and only the momenta are sampled, including the vibrational momenta (see below).\n",
    "\n",
    "- **Reference**: The peaks are compared with the Dunham expansion for $v = 0$ using the experimental parameters.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5b33a829",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import necessary libraries\n",
    "\n",
    "import sys\n",
    "import time\n",
    "from pathlib import Path\n",
    "\n",
    "sys.path.insert(0, str(Path.cwd().parent))\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from pyscivr.units import FemtoSec, CmInv, HBar\n",
    "from pyscivr.potentials import H2SplinePotential\n",
    "from pyscivr.coordinates import InternalCoordinates\n",
    "from pyscivr.integrators import ShakeRattle\n",
    "from pyscivr.variations import make_vari_propagator, propagate_variation, make_jacobi_func, to_internal\n",
    "from pyscivr.basis import get_overlap\n",
    "from pyscivr.scivr import get_lagrangian, get_action, get_prefactor, get_ta_spectrum_fft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a2e7be4",
   "metadata": {},
   "source": [
    "## System and coordinates\n",
    "\n",
    "The system and the coordinates are the same as in the *Hessian and Variation* tutorial:\n",
    "`COORD_CONST` defines the constraints (center of mass), and `COORD_ALL` defines the full set of coordinates,\n",
    "where the bond length and the polar and azimuthal angles are active.\n",
    "\n",
    "## Sampling of initial conditions\n",
    "\n",
    "`sample_momenta` samples `K_rot`, `tilt`, the vibrational kinetic energy `K_vib` and the sign of the vibrational\n",
    "momentum uniformly.\n",
    "\n",
    "The vibrational momenta are sampled even for the vibrational ground state.\n",
    "In the ground state, the molecule still vibrates with the zero-point motion, and the rotational levels are determined by the rotational constant averaged over this motion, $B_0$, which is smaller than that at the equilibrium structure, $B_e$. \n",
    "Sampling the vibrational momenta takes this ro-vibrational coupling into account.\n",
    "\n",
    "## Calculation of spectra\n",
    "\n",
    "`run` computes the spectra for all the initial states by the following steps for each trajectory:\n",
    "\n",
    "1. Propagate the trajectory by `ShakeRattle`.\n",
    "2. Propagate the variation and compute the monodromy matrix in the physical space.\n",
    "   The Hessian is evaluated at every step using `H2SplinePotential`.\n",
    "3. Exclude the steps where the symplectic condition is not satisfied.\n",
    "4. Compute the action, the prefactor and the overlap with each initial state, and the spectrum\n",
    "   by the FFT.\n",
    "\n",
    "The spectra are averaged over the trajectories and saved for each initial state.\n",
    "Note that each trajectory is used for all the initial states, so that the cost of the dynamics\n",
    "and the monodromy matrix is shared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "11cdb216",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Build complete: 3 coordinates\n",
      "Build complete: 6 coordinates\n"
     ]
    }
   ],
   "source": [
    "# Constants\n",
    "MASS = np.array([1.008, 1.008]) # mass of hydrogen atoms [amu (atomic mass unit)]\n",
    "OMEGA_E = 4401.226  # vibrational frequency of bond stretching [cm^-1]\n",
    "R_E = 0.74160392 # equilibrium bond length [Angs]\n",
    "POSI_REF = np.array([[-R_E / 2, 0.0, 0.0], [R_E / 2, 0.0, 0.0]])\n",
    "CALC = H2SplinePotential()\n",
    "ENER_REF = CALC.energy(POSI_REF)\n",
    "\n",
    "# Coordinate for constraints\n",
    "COORD_CONST = InternalCoordinates(POSI_REF, MASS)\n",
    "COORD_CONST.add_translation()\n",
    "COORD_CONST.build()\n",
    "\n",
    "# Coordinate for all DOFs\n",
    "COORD_ALL = InternalCoordinates(POSI_REF, MASS)\n",
    "COORD_ALL.add_translation()\n",
    "COORD_ALL.add_polar(0, 1)\n",
    "COORD_ALL.add_azimuthal(0, 1)\n",
    "COORD_ALL.add_bond(0, 1)\n",
    "COORD_ALL.build()\n",
    "\n",
    "ACTIVE_IDX = np.array([COORD_ALL.find_coordinate(kind, (0, 1))[0] for kind in (\"bond\", \"polar\", \"azimuthal\")])\n",
    "TOPOLOGIES = [COORD_ALL.topology[i] for i in ACTIVE_IDX]\n",
    "\n",
    "JACOBI_FUNC, JACOBI_REV_FUNC, INTERNAL_FUNC, MONODROMY_FUNC = make_jacobi_func(COORD_ALL, ACTIVE_IDX)\n",
    "\n",
    "\n",
    "def initial_momenta(K_rot, K_vib, tilt, sign=1):\n",
    "\n",
    "    p_rot = np.sqrt(K_rot * CmInv * MASS[0])\n",
    "    p_vib = np.sqrt(K_vib * CmInv * MASS[0]) * sign\n",
    "    p_rot_y = p_rot * np.cos(tilt)\n",
    "    p_rot_z = p_rot * np.sin(tilt)\n",
    "    return np.array([[-p_vib, -p_rot_y, -p_rot_z], [p_vib, p_rot_y, p_rot_z]])\n",
    "\n",
    "\n",
    "def sample_momenta(n_sample, K_rot_range, K_vib_range, seed=10202):\n",
    "\n",
    "    rng = np.random.default_rng(seed)\n",
    "    K_rot = rng.uniform(*K_rot_range, size=n_sample)\n",
    "    K_vib = rng.uniform(*K_vib_range, size=n_sample)\n",
    "    sign = rng.choice([-1, 1], size=n_sample)\n",
    "    tilt = rng.uniform(0.0, 2.0 * np.pi, size=n_sample)\n",
    "    return [initial_momenta(K_rot[i], K_vib[i], tilt[i], sign[i]) for i in range(n_sample)], K_rot, K_vib\n",
    "\n",
    "\n",
    "def run(posi_sample_list, mome_sample_list, K_rot_list, K_vib_list,\n",
    "        posi_ref_list, mome_ref_list, gamma_ref_list, fpath_list,\n",
    "        dt, n_step, n_fft, symp_err_tol=1e-4):\n",
    "\n",
    "    # Judge function to check if the point is singular or not\n",
    "    judge_func= lambda symp_err : np.isfinite(symp_err) & (symp_err < symp_err_tol)\n",
    "\n",
    "    # Reference positions and momenta in the internal coordinates\n",
    "    posi_ref_int, mome_ref_int = zip(*[INTERNAL_FUNC(p, q) for p, q in zip(posi_ref_list, mome_ref_list)])\n",
    "\n",
    "    n_sample = len(posi_sample_list)\n",
    "    n_ref = len(posi_ref_list)\n",
    "    spectra = [0.0] * n_ref\n",
    "    vari_propagator = make_vari_propagator(COORD_CONST, dt)\n",
    "\n",
    "    t_start = time.perf_counter()\n",
    "    for i in range(n_sample):\n",
    "        # Get trajectory\n",
    "        dyn = ShakeRattle(CALC, posi_sample_list[i], mome_sample_list[i], MASS, dt, COORD_CONST)\n",
    "        traj = dyn.run(n_step)\n",
    "        traj_posi, traj_mome = traj[\"posi\"], traj[\"mome\"]\n",
    "\n",
    "        # get variation\n",
    "        hess = CALC.hessian(traj_posi)\n",
    "        J_rev_init = JACOBI_REV_FUNC(traj_posi[0], traj_mome[0])\n",
    "\n",
    "        vari = propagate_variation(vari_propagator, traj_posi, traj_mome, traj[\"lam\"], traj[\"mu\"], hess, vari_init=J_rev_init)\n",
    "        posi_int, mome_int, mono_int, symplectic_error = to_internal(MONODROMY_FUNC, traj_posi, traj_mome, vari)\n",
    "\n",
    "        # points with large symplectic error are treated as singularities\n",
    "        valid = judge_func(symplectic_error)\n",
    "\n",
    "        ener_grid = 2.0 * np.pi * HBar * np.arange(n_fft) / (dt * n_fft)\n",
    "        lag = get_lagrangian(traj[\"total_energy\"], traj[\"potential_energy\"], ener_ref=ENER_REF)\n",
    "        action = get_action(lag, dt)\n",
    "\n",
    "        for j in range(n_ref):\n",
    "            posi_center, mome_center = posi_ref_int[j], mome_ref_int[j]\n",
    "            gamma = gamma_ref_list[j]\n",
    "            prefactor = get_prefactor(mono_int, gamma, valid=valid)\n",
    "            overlap = get_overlap(TOPOLOGIES, posi_center, mome_center, posi_int, mome_int, gamma)\n",
    "            _, spec = get_ta_spectrum_fft(prefactor, overlap, action, dt, n_fft, valid=valid)\n",
    "            spectra[j] += spec\n",
    "\n",
    "        if i % 10 == 0:\n",
    "            print(f\"{i+1:6d} / {n_sample}, K_rot = {K_rot_list[i]:.1f}, K_vib = {K_vib_list[i]:.1f}, \"\n",
    "                f\"max symp error = {np.max(np.abs(symplectic_error)):.3e}, ({time.perf_counter() - t_start:.1f} sec)\", flush=True)\n",
    "\n",
    "    for j in range(n_ref):\n",
    "        spectra[j] /= n_sample\n",
    "\n",
    "    for j in range(n_ref):\n",
    "        np.savez(fpath_list[j], ener_grid=ener_grid, spectrum=spectra[j])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3429c526",
   "metadata": {},
   "source": [
    "## Execute calculation\n",
    "\n",
    "The total propagation time is 500 fs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa882e2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     1 / 2000, K_rot = 2788.2, K_vib = 2483.7, max symp error = 1.547e-09, (1.2 sec)\n",
      "    11 / 2000, K_rot = 4946.9, K_vib = 1226.6, max symp error = 3.852e-10, (5.9 sec)\n",
      "    21 / 2000, K_rot = 9808.5, K_vib = 3522.1, max symp error = 4.342e-10, (10.7 sec)\n",
      "    31 / 2000, K_rot = 8930.5, K_vib = 2197.7, max symp error = 4.411e-10, (15.3 sec)\n",
      "    41 / 2000, K_rot = 1592.5, K_vib = 1338.6, max symp error = 1.241e-09, (19.7 sec)\n",
      "    51 / 2000, K_rot = 7396.6, K_vib = 900.2, max symp error = 1.002e-09, (24.1 sec)\n",
      "    61 / 2000, K_rot = 2192.0, K_vib = 3063.7, max symp error = 7.122e-10, (28.6 sec)\n",
      "    71 / 2000, K_rot = 6597.3, K_vib = 3239.4, max symp error = 2.918e-10, (33.2 sec)\n",
      "    81 / 2000, K_rot = 2769.8, K_vib = 3814.3, max symp error = 1.893e-09, (38.0 sec)\n",
      "    91 / 2000, K_rot = 2161.3, K_vib = 2645.7, max symp error = 1.017e-09, (42.5 sec)\n",
      "   101 / 2000, K_rot = 3024.0, K_vib = 1407.6, max symp error = 1.212e-09, (47.0 sec)\n",
      "   111 / 2000, K_rot = 4798.8, K_vib = 2901.8, max symp error = 1.571e-09, (52.1 sec)\n",
      "   121 / 2000, K_rot = 6286.0, K_vib = 521.7, max symp error = 3.860e-10, (60.1 sec)\n",
      "   131 / 2000, K_rot = 5551.3, K_vib = 304.8, max symp error = 5.869e-10, (65.1 sec)\n",
      "   141 / 2000, K_rot = 4030.5, K_vib = 101.7, max symp error = 1.311e-09, (70.2 sec)\n",
      "   151 / 2000, K_rot = 1705.5, K_vib = 3088.0, max symp error = 1.029e-09, (75.2 sec)\n",
      "   161 / 2000, K_rot = 2817.6, K_vib = 3.2, max symp error = 7.516e-11, (80.0 sec)\n",
      "   171 / 2000, K_rot = 3701.8, K_vib = 1368.5, max symp error = 5.450e-10, (85.0 sec)\n",
      "   181 / 2000, K_rot = 7288.7, K_vib = 1800.7, max symp error = 3.011e-10, (89.8 sec)\n",
      "   191 / 2000, K_rot = 6585.2, K_vib = 134.9, max symp error = 5.543e-10, (94.8 sec)\n",
      "   201 / 2000, K_rot = 7396.7, K_vib = 1439.0, max symp error = 6.702e-10, (99.6 sec)\n",
      "   211 / 2000, K_rot = 9867.3, K_vib = 2770.9, max symp error = 3.976e-10, (104.8 sec)\n",
      "   221 / 2000, K_rot = 7455.7, K_vib = 3599.9, max symp error = 5.752e-10, (109.6 sec)\n",
      "   231 / 2000, K_rot = 3787.1, K_vib = 3608.2, max symp error = 5.457e-10, (114.5 sec)\n",
      "   241 / 2000, K_rot = 3470.1, K_vib = 4191.9, max symp error = 1.220e-09, (119.3 sec)\n",
      "   251 / 2000, K_rot = 1747.2, K_vib = 3873.8, max symp error = 3.657e-10, (124.4 sec)\n",
      "   261 / 2000, K_rot = 9973.6, K_vib = 3839.2, max symp error = 6.849e-10, (129.3 sec)\n",
      "   271 / 2000, K_rot = 4377.4, K_vib = 2260.9, max symp error = 1.189e-09, (134.5 sec)\n",
      "   281 / 2000, K_rot = 9515.0, K_vib = 4348.2, max symp error = 4.160e-10, (139.3 sec)\n",
      "   291 / 2000, K_rot = 6893.6, K_vib = 1516.3, max symp error = 1.276e-09, (143.9 sec)\n",
      "   301 / 2000, K_rot = 5376.0, K_vib = 4257.9, max symp error = 5.235e-10, (148.3 sec)\n",
      "   311 / 2000, K_rot = 5321.8, K_vib = 1053.0, max symp error = 5.579e-10, (152.8 sec)\n",
      "   321 / 2000, K_rot = 9159.7, K_vib = 2362.1, max symp error = 5.578e-10, (157.2 sec)\n",
      "   331 / 2000, K_rot = 5392.6, K_vib = 3831.9, max symp error = 3.662e-10, (161.7 sec)\n",
      "   341 / 2000, K_rot = 487.6, K_vib = 2345.0, max symp error = 1.201e-09, (166.2 sec)\n",
      "   351 / 2000, K_rot = 6850.8, K_vib = 3830.6, max symp error = 7.851e-10, (170.7 sec)\n",
      "   361 / 2000, K_rot = 219.6, K_vib = 3923.8, max symp error = 5.729e-10, (175.2 sec)\n",
      "   371 / 2000, K_rot = 7582.7, K_vib = 3769.7, max symp error = 8.757e-10, (179.7 sec)\n",
      "   381 / 2000, K_rot = 7779.4, K_vib = 1281.0, max symp error = 3.308e-10, (184.3 sec)\n",
      "   391 / 2000, K_rot = 4940.4, K_vib = 493.9, max symp error = 2.802e-10, (188.7 sec)\n",
      "   401 / 2000, K_rot = 8660.0, K_vib = 458.3, max symp error = 7.543e-10, (193.1 sec)\n",
      "   411 / 2000, K_rot = 1841.7, K_vib = 2777.0, max symp error = 1.155e-10, (197.7 sec)\n",
      "   421 / 2000, K_rot = 2463.3, K_vib = 3043.4, max symp error = 2.053e-10, (202.2 sec)\n",
      "   431 / 2000, K_rot = 7594.3, K_vib = 676.2, max symp error = 3.350e-10, (206.9 sec)\n",
      "   441 / 2000, K_rot = 7529.8, K_vib = 1375.6, max symp error = 6.600e-10, (211.7 sec)\n",
      "   451 / 2000, K_rot = 3684.4, K_vib = 2426.1, max symp error = 1.455e-09, (216.2 sec)\n",
      "   461 / 2000, K_rot = 390.8, K_vib = 1589.5, max symp error = 2.390e-09, (220.6 sec)\n",
      "   471 / 2000, K_rot = 1503.1, K_vib = 2211.0, max symp error = 5.834e-10, (225.1 sec)\n",
      "   481 / 2000, K_rot = 2764.9, K_vib = 717.1, max symp error = 1.334e-09, (229.8 sec)\n",
      "   491 / 2000, K_rot = 5392.0, K_vib = 2641.8, max symp error = 7.976e-10, (234.5 sec)\n",
      "   501 / 2000, K_rot = 2453.7, K_vib = 3233.2, max symp error = 4.626e-10, (239.1 sec)\n",
      "   511 / 2000, K_rot = 9722.6, K_vib = 4054.7, max symp error = 5.191e-10, (243.6 sec)\n",
      "   521 / 2000, K_rot = 2164.7, K_vib = 2386.7, max symp error = 8.077e-10, (248.5 sec)\n",
      "   531 / 2000, K_rot = 1284.9, K_vib = 100.8, max symp error = 1.945e-10, (253.1 sec)\n",
      "   541 / 2000, K_rot = 3925.6, K_vib = 1523.9, max symp error = 7.747e-10, (257.6 sec)\n",
      "   551 / 2000, K_rot = 9981.7, K_vib = 240.5, max symp error = 4.452e-10, (262.2 sec)\n",
      "   561 / 2000, K_rot = 5556.3, K_vib = 328.1, max symp error = 1.488e-09, (266.8 sec)\n",
      "   571 / 2000, K_rot = 7794.8, K_vib = 4344.3, max symp error = 2.749e-10, (271.4 sec)\n",
      "   581 / 2000, K_rot = 3518.4, K_vib = 4241.0, max symp error = 1.184e-09, (275.9 sec)\n",
      "   591 / 2000, K_rot = 3835.0, K_vib = 775.0, max symp error = 1.092e-09, (280.5 sec)\n",
      "   601 / 2000, K_rot = 817.9, K_vib = 1561.8, max symp error = 1.009e-09, (285.1 sec)\n",
      "   611 / 2000, K_rot = 2152.6, K_vib = 3333.5, max symp error = 1.169e-09, (289.7 sec)\n",
      "   621 / 2000, K_rot = 2828.7, K_vib = 2157.5, max symp error = 1.876e-10, (294.3 sec)\n",
      "   631 / 2000, K_rot = 3203.5, K_vib = 994.2, max symp error = 1.074e-09, (298.9 sec)\n",
      "   641 / 2000, K_rot = 4838.7, K_vib = 4078.5, max symp error = 1.174e-09, (303.4 sec)\n",
      "   651 / 2000, K_rot = 4176.6, K_vib = 3858.7, max symp error = 2.300e-10, (307.9 sec)\n",
      "   661 / 2000, K_rot = 2076.9, K_vib = 578.9, max symp error = 3.775e-10, (312.7 sec)\n",
      "   671 / 2000, K_rot = 7519.9, K_vib = 3621.0, max symp error = 6.933e-10, (317.5 sec)\n",
      "   681 / 2000, K_rot = 9171.1, K_vib = 2870.4, max symp error = 6.783e-10, (322.2 sec)\n",
      "   691 / 2000, K_rot = 5976.7, K_vib = 432.7, max symp error = 1.181e-09, (326.7 sec)\n",
      "   701 / 2000, K_rot = 5310.1, K_vib = 3735.4, max symp error = 6.075e-10, (331.2 sec)\n",
      "   711 / 2000, K_rot = 7895.5, K_vib = 1044.6, max symp error = 4.220e-10, (335.7 sec)\n",
      "   721 / 2000, K_rot = 9576.3, K_vib = 786.6, max symp error = 4.420e-10, (340.1 sec)\n",
      "   731 / 2000, K_rot = 9017.8, K_vib = 1438.3, max symp error = 5.052e-10, (344.5 sec)\n",
      "   741 / 2000, K_rot = 6847.5, K_vib = 1233.1, max symp error = 4.541e-10, (349.0 sec)\n",
      "   751 / 2000, K_rot = 6915.3, K_vib = 2984.2, max symp error = 8.296e-10, (353.4 sec)\n",
      "   761 / 2000, K_rot = 2417.0, K_vib = 614.9, max symp error = 7.797e-10, (357.9 sec)\n",
      "   771 / 2000, K_rot = 4178.8, K_vib = 1514.2, max symp error = 6.346e-10, (362.4 sec)\n",
      "   781 / 2000, K_rot = 9218.0, K_vib = 1418.5, max symp error = 6.936e-10, (366.8 sec)\n",
      "   791 / 2000, K_rot = 2660.2, K_vib = 734.1, max symp error = 3.763e-10, (371.3 sec)\n",
      "   801 / 2000, K_rot = 2507.7, K_vib = 2022.8, max symp error = 1.487e-09, (375.9 sec)\n",
      "   811 / 2000, K_rot = 5999.4, K_vib = 2258.1, max symp error = 3.067e-10, (380.6 sec)\n",
      "   821 / 2000, K_rot = 282.7, K_vib = 1278.3, max symp error = 1.292e-09, (385.5 sec)\n",
      "   831 / 2000, K_rot = 6042.2, K_vib = 3129.6, max symp error = 9.717e-10, (390.2 sec)\n",
      "   841 / 2000, K_rot = 3275.4, K_vib = 1746.8, max symp error = 1.292e-09, (394.8 sec)\n",
      "   851 / 2000, K_rot = 2054.4, K_vib = 997.1, max symp error = 5.412e-10, (399.4 sec)\n",
      "   861 / 2000, K_rot = 4978.0, K_vib = 3446.3, max symp error = 9.314e-10, (404.2 sec)\n",
      "   871 / 2000, K_rot = 4786.3, K_vib = 1854.4, max symp error = 4.216e-10, (408.9 sec)\n",
      "   881 / 2000, K_rot = 3213.5, K_vib = 148.8, max symp error = 1.112e-09, (413.5 sec)\n",
      "   891 / 2000, K_rot = 1980.6, K_vib = 4212.3, max symp error = 1.628e-09, (418.2 sec)\n",
      "   901 / 2000, K_rot = 9113.5, K_vib = 1305.4, max symp error = 7.734e-10, (422.9 sec)\n",
      "   911 / 2000, K_rot = 7299.0, K_vib = 1744.8, max symp error = 8.285e-10, (427.5 sec)\n",
      "   921 / 2000, K_rot = 4054.4, K_vib = 3002.2, max symp error = 5.457e-10, (432.3 sec)\n",
      "   931 / 2000, K_rot = 9594.0, K_vib = 652.2, max symp error = 3.325e-10, (437.1 sec)\n",
      "   941 / 2000, K_rot = 7537.2, K_vib = 2377.7, max symp error = 8.212e-10, (441.9 sec)\n",
      "   951 / 2000, K_rot = 9288.8, K_vib = 278.3, max symp error = 2.818e-10, (446.6 sec)\n",
      "   961 / 2000, K_rot = 2782.4, K_vib = 3178.6, max symp error = 1.426e-09, (451.1 sec)\n",
      "   971 / 2000, K_rot = 7003.2, K_vib = 407.0, max symp error = 2.431e-10, (455.7 sec)\n",
      "   981 / 2000, K_rot = 2347.4, K_vib = 2065.2, max symp error = 1.072e-09, (460.3 sec)\n",
      "   991 / 2000, K_rot = 3765.6, K_vib = 1960.8, max symp error = 4.861e-10, (464.8 sec)\n",
      "  1001 / 2000, K_rot = 9447.7, K_vib = 2569.5, max symp error = 4.796e-10, (469.4 sec)\n",
      "  1011 / 2000, K_rot = 4098.7, K_vib = 2410.4, max symp error = 5.334e-10, (474.0 sec)\n",
      "  1021 / 2000, K_rot = 2402.9, K_vib = 3137.9, max symp error = 1.211e-09, (478.7 sec)\n",
      "  1031 / 2000, K_rot = 7194.7, K_vib = 3809.3, max symp error = 5.450e-10, (483.3 sec)\n",
      "  1041 / 2000, K_rot = 2557.9, K_vib = 4334.3, max symp error = 4.228e-10, (487.9 sec)\n",
      "  1051 / 2000, K_rot = 7609.2, K_vib = 1718.9, max symp error = 3.706e-10, (492.5 sec)\n",
      "  1061 / 2000, K_rot = 4817.1, K_vib = 2678.6, max symp error = 5.726e-10, (497.2 sec)\n",
      "  1071 / 2000, K_rot = 5458.6, K_vib = 3853.6, max symp error = 1.011e-09, (501.7 sec)\n",
      "  1081 / 2000, K_rot = 4589.1, K_vib = 2305.1, max symp error = 4.308e-10, (506.2 sec)\n",
      "  1091 / 2000, K_rot = 5344.1, K_vib = 1818.7, max symp error = 3.584e-10, (510.9 sec)\n",
      "  1101 / 2000, K_rot = 9410.6, K_vib = 2516.0, max symp error = 7.857e-10, (515.5 sec)\n",
      "  1111 / 2000, K_rot = 3666.5, K_vib = 3507.4, max symp error = 8.588e-10, (520.0 sec)\n",
      "  1121 / 2000, K_rot = 240.3, K_vib = 3517.0, max symp error = 6.272e-10, (524.6 sec)\n",
      "  1131 / 2000, K_rot = 6294.3, K_vib = 3297.4, max symp error = 6.860e-10, (529.2 sec)\n",
      "  1141 / 2000, K_rot = 4357.6, K_vib = 1741.9, max symp error = 6.422e-10, (533.8 sec)\n",
      "  1151 / 2000, K_rot = 9056.6, K_vib = 2342.0, max symp error = 5.668e-10, (538.4 sec)\n",
      "  1161 / 2000, K_rot = 7166.2, K_vib = 60.6, max symp error = 1.908e-10, (542.9 sec)\n",
      "  1171 / 2000, K_rot = 8916.5, K_vib = 325.7, max symp error = 4.829e-10, (547.6 sec)\n",
      "  1181 / 2000, K_rot = 451.6, K_vib = 2794.4, max symp error = 1.549e-09, (552.3 sec)\n",
      "  1191 / 2000, K_rot = 2126.8, K_vib = 777.3, max symp error = 5.189e-10, (557.2 sec)\n",
      "  1201 / 2000, K_rot = 9789.0, K_vib = 3297.3, max symp error = 6.385e-10, (562.1 sec)\n",
      "  1211 / 2000, K_rot = 5422.0, K_vib = 3283.8, max symp error = 5.213e-10, (566.7 sec)\n",
      "  1221 / 2000, K_rot = 3624.6, K_vib = 2727.0, max symp error = 2.683e-10, (571.3 sec)\n",
      "  1231 / 2000, K_rot = 2296.3, K_vib = 1739.8, max symp error = 5.492e-10, (575.9 sec)\n",
      "  1241 / 2000, K_rot = 2172.9, K_vib = 880.1, max symp error = 8.172e-10, (580.4 sec)\n",
      "  1251 / 2000, K_rot = 5639.4, K_vib = 1741.8, max symp error = 5.743e-10, (585.0 sec)\n",
      "  1261 / 2000, K_rot = 4547.6, K_vib = 1369.5, max symp error = 2.408e-10, (589.5 sec)\n",
      "  1271 / 2000, K_rot = 350.1, K_vib = 1926.1, max symp error = 8.248e-10, (594.0 sec)\n",
      "  1281 / 2000, K_rot = 3161.5, K_vib = 743.2, max symp error = 9.574e-10, (598.5 sec)\n",
      "  1291 / 2000, K_rot = 2615.2, K_vib = 460.4, max symp error = 8.505e-10, (603.1 sec)\n",
      "  1301 / 2000, K_rot = 3493.6, K_vib = 1263.6, max symp error = 9.196e-10, (607.9 sec)\n",
      "  1311 / 2000, K_rot = 2293.5, K_vib = 1831.8, max symp error = 7.507e-10, (612.7 sec)\n",
      "  1321 / 2000, K_rot = 1026.4, K_vib = 635.0, max symp error = 1.644e-09, (617.3 sec)\n",
      "  1331 / 2000, K_rot = 8248.1, K_vib = 4326.5, max symp error = 3.777e-10, (621.9 sec)\n",
      "  1341 / 2000, K_rot = 9451.1, K_vib = 4342.0, max symp error = 1.887e-10, (626.5 sec)\n",
      "  1351 / 2000, K_rot = 6264.2, K_vib = 2723.8, max symp error = 7.169e-10, (631.1 sec)\n",
      "  1361 / 2000, K_rot = 4614.2, K_vib = 1380.0, max symp error = 4.753e-10, (635.7 sec)\n",
      "  1371 / 2000, K_rot = 8100.1, K_vib = 343.3, max symp error = 5.250e-10, (640.3 sec)\n",
      "  1381 / 2000, K_rot = 6091.0, K_vib = 1225.5, max symp error = 1.007e-09, (644.8 sec)\n",
      "  1391 / 2000, K_rot = 3336.7, K_vib = 3789.3, max symp error = 1.017e-09, (649.4 sec)\n",
      "  1401 / 2000, K_rot = 9340.1, K_vib = 1438.4, max symp error = 2.340e-10, (654.0 sec)\n",
      "  1411 / 2000, K_rot = 3087.2, K_vib = 4160.6, max symp error = 6.153e-10, (658.6 sec)\n",
      "  1421 / 2000, K_rot = 6007.2, K_vib = 3360.5, max symp error = 1.029e-09, (663.5 sec)\n",
      "  1431 / 2000, K_rot = 8549.9, K_vib = 975.1, max symp error = 4.291e-10, (668.3 sec)\n",
      "  1441 / 2000, K_rot = 3685.4, K_vib = 2469.4, max symp error = 9.055e-10, (672.9 sec)\n",
      "  1451 / 2000, K_rot = 1389.7, K_vib = 509.4, max symp error = 3.514e-10, (677.4 sec)\n",
      "  1461 / 2000, K_rot = 5130.7, K_vib = 3560.5, max symp error = 7.755e-10, (681.9 sec)\n",
      "  1471 / 2000, K_rot = 866.6, K_vib = 854.5, max symp error = 1.545e-09, (686.3 sec)\n",
      "  1481 / 2000, K_rot = 7205.9, K_vib = 2784.5, max symp error = 7.075e-10, (690.8 sec)\n",
      "  1491 / 2000, K_rot = 5494.3, K_vib = 2530.7, max symp error = 5.348e-10, (695.4 sec)\n",
      "  1501 / 2000, K_rot = 6408.4, K_vib = 111.1, max symp error = 5.867e-10, (700.2 sec)\n",
      "  1511 / 2000, K_rot = 2938.0, K_vib = 4235.7, max symp error = 2.310e-10, (705.0 sec)\n",
      "  1521 / 2000, K_rot = 9885.7, K_vib = 1728.6, max symp error = 4.125e-10, (709.5 sec)\n",
      "  1531 / 2000, K_rot = 5770.4, K_vib = 795.9, max symp error = 4.784e-10, (714.1 sec)\n",
      "  1541 / 2000, K_rot = 9285.6, K_vib = 1281.8, max symp error = 4.266e-10, (718.9 sec)\n",
      "  1551 / 2000, K_rot = 1669.5, K_vib = 1074.7, max symp error = 1.146e-09, (723.6 sec)\n",
      "  1561 / 2000, K_rot = 8796.3, K_vib = 2569.7, max symp error = 6.655e-10, (728.1 sec)\n",
      "  1571 / 2000, K_rot = 2098.4, K_vib = 776.9, max symp error = 2.883e-09, (732.6 sec)\n",
      "  1581 / 2000, K_rot = 6521.5, K_vib = 1206.9, max symp error = 2.943e-10, (737.4 sec)\n",
      "  1591 / 2000, K_rot = 8306.3, K_vib = 3139.3, max symp error = 8.134e-10, (742.0 sec)\n",
      "  1601 / 2000, K_rot = 5014.2, K_vib = 4385.6, max symp error = 5.634e-10, (746.8 sec)\n",
      "  1611 / 2000, K_rot = 2860.3, K_vib = 3898.4, max symp error = 1.571e-09, (751.5 sec)\n",
      "  1621 / 2000, K_rot = 1863.2, K_vib = 3050.5, max symp error = 5.345e-10, (756.5 sec)\n",
      "  1631 / 2000, K_rot = 6431.5, K_vib = 1493.9, max symp error = 3.303e-10, (761.4 sec)\n",
      "  1641 / 2000, K_rot = 4589.4, K_vib = 1564.1, max symp error = 1.162e-09, (766.1 sec)\n",
      "  1651 / 2000, K_rot = 3933.0, K_vib = 1785.4, max symp error = 5.184e-10, (770.8 sec)\n",
      "  1661 / 2000, K_rot = 9232.2, K_vib = 474.1, max symp error = 3.365e-10, (775.7 sec)\n",
      "  1671 / 2000, K_rot = 7627.6, K_vib = 2090.2, max symp error = 7.010e-10, (780.6 sec)\n",
      "  1681 / 2000, K_rot = 6536.5, K_vib = 1957.2, max symp error = 4.526e-10, (785.5 sec)\n",
      "  1691 / 2000, K_rot = 897.3, K_vib = 1412.1, max symp error = 1.139e-09, (790.3 sec)\n",
      "  1701 / 2000, K_rot = 1867.7, K_vib = 3648.6, max symp error = 2.817e-10, (795.2 sec)\n",
      "  1711 / 2000, K_rot = 1623.7, K_vib = 2682.8, max symp error = 1.224e-09, (799.9 sec)\n",
      "  1721 / 2000, K_rot = 5538.5, K_vib = 1783.7, max symp error = 6.541e-10, (804.5 sec)\n",
      "  1731 / 2000, K_rot = 5618.3, K_vib = 3934.1, max symp error = 1.223e-09, (809.2 sec)\n",
      "  1741 / 2000, K_rot = 8806.9, K_vib = 2356.1, max symp error = 4.143e-10, (813.8 sec)\n",
      "  1751 / 2000, K_rot = 5849.4, K_vib = 3275.8, max symp error = 6.418e-10, (818.3 sec)\n",
      "  1761 / 2000, K_rot = 192.3, K_vib = 1805.9, max symp error = 6.478e-11, (822.9 sec)\n",
      "  1771 / 2000, K_rot = 4075.3, K_vib = 1004.7, max symp error = 8.884e-10, (827.5 sec)\n",
      "  1781 / 2000, K_rot = 5590.7, K_vib = 3830.3, max symp error = 4.418e-10, (832.1 sec)\n",
      "  1791 / 2000, K_rot = 2198.4, K_vib = 3373.9, max symp error = 1.232e-09, (836.7 sec)\n",
      "  1801 / 2000, K_rot = 6597.9, K_vib = 3443.8, max symp error = 1.006e-09, (841.2 sec)\n",
      "  1811 / 2000, K_rot = 4280.0, K_vib = 976.2, max symp error = 9.927e-10, (845.8 sec)\n",
      "  1821 / 2000, K_rot = 4019.1, K_vib = 807.5, max symp error = 2.038e-09, (850.5 sec)\n",
      "  1831 / 2000, K_rot = 3659.6, K_vib = 1709.2, max symp error = 4.123e-10, (855.1 sec)\n",
      "  1841 / 2000, K_rot = 4965.5, K_vib = 2212.8, max symp error = 6.215e-10, (859.6 sec)\n",
      "  1851 / 2000, K_rot = 2757.4, K_vib = 3108.4, max symp error = 6.709e-10, (864.5 sec)\n",
      "  1861 / 2000, K_rot = 9182.1, K_vib = 3572.3, max symp error = 2.572e-10, (869.3 sec)\n",
      "  1871 / 2000, K_rot = 8172.8, K_vib = 4193.5, max symp error = 5.430e-10, (874.1 sec)\n",
      "  1881 / 2000, K_rot = 3323.9, K_vib = 2253.9, max symp error = 5.853e-10, (879.0 sec)\n",
      "  1891 / 2000, K_rot = 5787.3, K_vib = 3324.0, max symp error = 1.406e-09, (883.8 sec)\n",
      "  1901 / 2000, K_rot = 128.8, K_vib = 3748.5, max symp error = 6.703e-10, (888.7 sec)\n",
      "  1911 / 2000, K_rot = 4775.1, K_vib = 1557.6, max symp error = 8.290e-10, (893.5 sec)\n",
      "  1921 / 2000, K_rot = 7999.3, K_vib = 1498.7, max symp error = 2.526e-10, (898.2 sec)\n",
      "  1931 / 2000, K_rot = 650.4, K_vib = 1933.2, max symp error = 1.772e-10, (902.8 sec)\n",
      "  1941 / 2000, K_rot = 2412.1, K_vib = 1297.5, max symp error = 4.961e-10, (907.6 sec)\n",
      "  1951 / 2000, K_rot = 9588.3, K_vib = 3472.6, max symp error = 4.916e-10, (912.4 sec)\n",
      "  1961 / 2000, K_rot = 9360.6, K_vib = 4297.3, max symp error = 1.074e-09, (917.1 sec)\n",
      "  1971 / 2000, K_rot = 9367.1, K_vib = 3811.7, max symp error = 2.225e-10, (921.7 sec)\n",
      "  1981 / 2000, K_rot = 9965.5, K_vib = 4154.6, max symp error = 5.324e-10, (926.2 sec)\n",
      "  1991 / 2000, K_rot = 2330.2, K_vib = 1885.9, max symp error = 2.760e-09, (930.8 sec)\n"
     ]
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    # set parameters\n",
    "    n_sample = 2000\n",
    "    dt = 0.1 * FemtoSec\n",
    "    n_step = 5000\n",
    "    n_fft = 2**19\n",
    "\n",
    "    # set reference state\n",
    "    K_rot_ref_list = [500.0, 2000.0, 5000.0]\n",
    "\n",
    "    # no vibrational kinetic energy for the reference state to target the vibrational ground state (v=0)\n",
    "    mome_ref_list = [initial_momenta(k_rot, 0.0, np.pi / 4) for k_rot in K_rot_ref_list]\n",
    "    posi_ref_list = [POSI_REF] * len(K_rot_ref_list)\n",
    "\n",
    "    omega_e = OMEGA_E * CmInv / HBar  # convert to internal unit\n",
    "    gamma_ref = [MASS[0] * omega_e / (2.0 * HBar), # harmonic width (m_H * omega / 2 hbar)\n",
    "                 1.0 / (2 * 0.2 ** 2),  # sqrt(1 / 2 gamma) = 0.2 rad\n",
    "                 1.0 / (2 * 0.2 ** 2)]\n",
    "    gamma_ref_list = [gamma_ref] * len(K_rot_ref_list)\n",
    "    fpath_list = [f\"hydrogen_rovib_{k_rot:.0f}_v0_n_{n_sample}_spectra.npz\" for k_rot in K_rot_ref_list]\n",
    "\n",
    "    posi_ref_list = np.asarray(posi_ref_list)\n",
    "    mome_ref_list = np.asarray(mome_ref_list)\n",
    "    gamma_ref_list = np.asarray(gamma_ref_list)\n",
    "\n",
    "    K_rot_range = (10.0, 10000.0)\n",
    "    K_vib_range = (0.0, OMEGA_E)\n",
    "    mome_sample_list, K_rot_list, K_vib_list = sample_momenta(n_sample, K_rot_range, K_vib_range)\n",
    "    posi_sample_list = np.asarray([POSI_REF] * n_sample)\n",
    "\n",
    "    run(posi_sample_list, mome_sample_list, K_rot_list, K_vib_list,\n",
    "        posi_ref_list, mome_ref_list, gamma_ref_list, fpath_list,\n",
    "        dt, n_step, n_fft)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7baabc9d",
   "metadata": {},
   "source": [
    "## Plot results\n",
    "\n",
    "The reference levels are the experimental ro-vibrational levels of H2 in the vibrational ground state,\n",
    "given by the Dunham expansion\n",
    "\n",
    "$$\n",
    "E_J = E_{\\text{ZPE}} + B J(J+1) - D [J(J+1)]^2 + H [J(J+1)]^3 + L [J(J+1)]^4\n",
    "$$\n",
    "\n",
    "with the coefficients from D. E. Jennings and J. W. Brault, J. Mol. Spectrosc. **102**, 265-272 (1983).\n",
    "\n",
    "The zero-point energy is set to $E_{\\text{ZPE}}$ = 2183 $\\textrm{cm}^{-1}$ here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "67f6c0e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analytical energies (cm^-1): [2183.  2301.5 2537.4 2888.5 3351.8 3923.2 4597.9 5370.5 6234.9 7184.9\n",
      " 8213.7 9314.4]\n",
      "Peaks (cm^-1) for K = 500: [2289.1 2537.9 2883.4 3341.4 3915.3 4594.2 5362.1]\n",
      "Peaks (cm^-1) for K = 2000: [2541.7 2882.1 3340.2 3913.4 4592.3 5362.1 6226.1 7174.7 8204.1]\n",
      "Peaks (cm^-1) for K = 5000: [3338.3 3912.1 4591.  5361.5 6225.4 7174.1 8203.5 9308.6]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x, B, D, H, L):\n",
    "    return B*x*(x+1)-D*x*x*(x+1)*(x+1)+H*(x**3)*((x+1)**3)+L*(x**4)*((x+1)**4)\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    import matplotlib.pyplot as plt\n",
    "    from scipy.signal import find_peaks\n",
    "\n",
    "    # moment of inertia of H2\n",
    "    I = MASS[0] * R_E**2 / 2.0\n",
    "\n",
    "    # Dunham expansion coefficients for H2 vibrational ground state\n",
    "    # D. E. Jennings and J. W. Brault, \"The ground state of molecular hydrogen\", Journal of Molecular Spectroscopy 102, 265–272 (1983).\n",
    "    B = 59.334547\n",
    "    D = 0.0456821\n",
    "    H = 4.8542e-5\n",
    "    L = -5.411e-8\n",
    "    ZPE = 2183.0  # zero-point energy [cm^-1]\n",
    "\n",
    "    analytical_energies = np.array([f(n, B, D, H, L) + ZPE for n in range(20)])\n",
    "    analytical_energies = analytical_energies[analytical_energies <= 10000]\n",
    "\n",
    "    print(f\"Analytical energies (cm^-1): {np.round(analytical_energies, 1)}\")\n",
    "\n",
    "    fig, ax = plt.subplots(3, 1, figsize=(7, 7), sharex=True)\n",
    "    colors = [\"red\", \"green\", \"blue\"]    \n",
    "\n",
    "    for i, fpath in enumerate(fpath_list):\n",
    "        data = np.load(fpath)\n",
    "        ener_grid = data[\"ener_grid\"] / CmInv\n",
    "        spectrum = data[\"spectrum\"]\n",
    "        spectrum /= np.max(spectrum)\n",
    "        peaks, _ = find_peaks(spectrum, height=0.1, prominence=0.1)\n",
    "        mask = (ener_grid[peaks] <= 10000)\n",
    "        peaks = peaks[mask]\n",
    "\n",
    "        print(f\"Peaks (cm^-1) for K = {K_rot_ref_list[i]:.0f}: {np.round(ener_grid[peaks], 1)}\")\n",
    "        ax[i].plot(ener_grid[peaks], spectrum[peaks], \"x\", color=\"black\")\n",
    "\n",
    "        ax[i].plot(ener_grid, spectrum, label=f\"K = {K_rot_ref_list[i]:.0f}\", color=colors[i])\n",
    "        ax[i].set_xlim(0, 10000)\n",
    "        ax[i].set_ylim(0, 1.2)\n",
    "        ax[i].vlines(analytical_energies, 0.0, 1.2, color=\"gray\", linestyle=\"--\", label=\"reference\")\n",
    "        ax[i].legend()\n",
    "\n",
    "    ax[-1].set_xlabel(\"Energy (cm^-1)\")\n",
    "    ax[1].set_ylabel(\"intensity (arb. unit)\")\n",
    "    ax[-1].set_xlim(0, 10000)\n",
    "    plt.tight_layout()    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc8864af",
   "metadata": {},
   "source": [
    "Since the peak corresponding to the vibrational zero-point energy is not clearly resolved, we evaluate the successive intervals $\\Delta_J \\equiv E_J - E_{J-1}$, which are independent of the choice of the zero-point energy, as in the paper.\n",
    "The computed intervals from the spectrum for $K$ = 2000 $\\textrm{cm}^{-1}$ are compared with the reference values $\\Delta_J^{(\\text{ref})}$ from the Dunham expansion and the rigid-rotor intervals\n",
    "$\\Delta_J^{(\\text{rigid})} = 2 B_e J$ (all in $\\textrm{cm}^{-1}$).\n",
    "\n",
    "| $J$ | $\\Delta_J$ | $\\Delta_J^{(\\text{ref})}$ | $\\Delta_J - \\Delta_J^{(\\text{ref})}$ | $\\Delta_J^{(\\text{rigid})}$ | $\\Delta_J - \\Delta_J^{(\\text{rigid})}$ |\n",
    "|---|---|---|---|---|---|\n",
    "| 3 | 340.4 | 351.1 | −10.7 | 364.9 | −24.5 |\n",
    "| 4 | 458.1 | 463.3 | −5.2 | 486.6 | −28.5 |\n",
    "| 5 | 573.2 | 571.4 | +1.8 | 608.2 | −35.0 |\n",
    "| 6 | 678.9 | 674.7 | +4.2 | 729.8 | −50.9 |\n",
    "| 7 | 769.8 | 772.6 | −2.8 | 851.5 | −81.7 |\n",
    "| 8 | 864.0 | 864.5 | −0.5 | 973.1 | −109.1 |\n",
    "| 9 | 948.6 | 950.0 | −1.4 | 1094.8 | −146.2 |\n",
    "| 10 | 1029.4 | 1028.8 | +0.6 | 1216.4 | −187.0 |\n",
    "\n",
    "- The computed intervals reproduce the reference values with an RMSE of about 5 $\\textrm{cm}^{-1}$, without systematic dependence on $J$.\n",
    "\n",
    "- In contrast, the computed intervals deviate from the rigid-rotor values increasingly with $J$, reaching $-187$ $\\textrm{cm}^{-1}$ at $J = 10$. The computed spectrum thus follows the Dunham expansion rather than the rigid rotor, showing that the ro-vibrational coupling is properly accounted for.\n",
    "\n",
    "- Unlike the single-trajectory spectrum (*Spectrum Calculation* tutorial), which agrees with the reference levels only near the energy of the trajectory, the spectrum with the phase-space sampling reproduces the levels over the whole range."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "pyscivr (3.13.11)",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.11"
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