{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aeb1ebff",
   "metadata": {},
   "source": [
    "# 6. Rotational Spectra of Hydrogen\n",
    "\n",
    "The rotational spectrum of hydrogen, a linear molecule, is computed by the phase-space sampling (see also section III A of the paper).\n",
    "\n",
    "| Redundant space | Potential | Integrator | Physical space |\n",
    "|---|---|---|---|\n",
    "| Cartesian (6 DOFs) with 4 constraints (bond and 3 translations) | `ZeroPotential` | `ShakeRattle` | 2D sphere (polar $\\theta$ and azimuthal angle $\\phi$) |\n",
    "\n",
    "- **Rigid rotor**: The bond length and the center of mass are fixed by constraints. Since the potential energy is constant for the rigid rotation, `ZeroPotential` is used (see the *Constrained Dynamics* tutorial), and no Hessian evaluation is needed.\n",
    "\n",
    "- **Initial states**: Coherent states in $(\\theta, \\phi)$ centered at the reference structure along the x-axis ($\\theta = \\pi / 2$, $\\phi = 0$), with the rotational kinetic energies of 500, 2000 and 5000 $\\textrm{cm}^{-1}$ and the widths of 0.2 rad.\n",
    "\n",
    "- **Sampling**: The initial positions are fixed at the center of the initial states, and the initial momenta perpendicular to the bond are sampled uniformly in the 2D momentum space (the rotational kinetic energy and the direction of the rotation plane are sampled uniformly).\n",
    "\n",
    "- **Coordinate singularities**: The trajectories pass through the singular points ($\\theta = 0, \\pi$) depending on the direction of the rotation. The steps where the symplectic condition is not satisfied are excluded.\n",
    "\n",
    "\n",
    "- **Reference**: The peaks are compared with the analytical rotational levels $E_J = B J(J+1)$."
   ]
  },
  {
   "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 ZeroPotential\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 *Constrained Dynamics* tutorial:\n",
    "\n",
    "`COORD_CONST` defines the constraints (bond length and center of mass), and `COORD_ALL` defines the full set of coordinates, where the polar and azimuthal angles are active.\n",
    "\n",
    "The Jacobian functions between the redundant and physical spaces are made once and reused for all trajectories.\n",
    "\n",
    "## Sampling of initial conditions\n",
    "\n",
    "`initial_momenta` gives the momenta of rigid rotation with the rotational kinetic energy `K_rot`\n",
    "in the plane tilted by `tilt` from the xy-plane, as in the *Constrained Dynamics* tutorial.\n",
    "\n",
    "`sample_momenta` samples `K_rot` and `tilt` uniformly, which corresponds to the uniform sampling\n",
    "of the momenta perpendicular to the bond in the 2D momentum space.\n",
    "The vibrational kinetic energy `K_vib` is set to zero for the pure rotation.\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 zero for `ZeroPotential`.\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": null,
   "id": "11cdb216",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Build complete: 4 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",
    "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 = ZeroPotential()\n",
    "ENER_REF = CALC.energy(POSI_REF)\n",
    "\n",
    "# Coordinate for constraints\n",
    "COORD_CONST = InternalCoordinates(POSI_REF, MASS)\n",
    "COORD_CONST.add_bond(0, 1)\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 (\"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": 3,
   "id": "fa882e2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     1 / 2000, K_rot = 2788.2, K_vib = 0.0, max symp error = 2.680e-09, (1.2 sec)\n",
      "    11 / 2000, K_rot = 4946.9, K_vib = 0.0, max symp error = 3.705e-10, (5.6 sec)\n",
      "    21 / 2000, K_rot = 9808.5, K_vib = 0.0, max symp error = 2.921e-10, (10.0 sec)\n",
      "    31 / 2000, K_rot = 8930.5, K_vib = 0.0, max symp error = 1.116e-09, (14.7 sec)\n",
      "    41 / 2000, K_rot = 1592.5, K_vib = 0.0, max symp error = 7.402e-10, (19.2 sec)\n",
      "    51 / 2000, K_rot = 7396.6, K_vib = 0.0, max symp error = 1.458e-10, (23.8 sec)\n",
      "    61 / 2000, K_rot = 2192.0, K_vib = 0.0, max symp error = 1.056e-09, (28.5 sec)\n",
      "    71 / 2000, K_rot = 6597.3, K_vib = 0.0, max symp error = 5.435e-10, (33.0 sec)\n",
      "    81 / 2000, K_rot = 2769.8, K_vib = 0.0, max symp error = 1.855e-09, (37.6 sec)\n",
      "    91 / 2000, K_rot = 2161.3, K_vib = 0.0, max symp error = 1.721e-09, (42.1 sec)\n",
      "   101 / 2000, K_rot = 3024.0, K_vib = 0.0, max symp error = 1.338e-09, (46.7 sec)\n",
      "   111 / 2000, K_rot = 4798.8, K_vib = 0.0, max symp error = 8.624e-10, (51.1 sec)\n",
      "   121 / 2000, K_rot = 6286.0, K_vib = 0.0, max symp error = 1.251e-09, (55.6 sec)\n",
      "   131 / 2000, K_rot = 5551.3, K_vib = 0.0, max symp error = 1.501e-09, (60.1 sec)\n",
      "   141 / 2000, K_rot = 4030.5, K_vib = 0.0, max symp error = 1.468e-10, (64.8 sec)\n",
      "   151 / 2000, K_rot = 1705.5, K_vib = 0.0, max symp error = 1.197e-09, (69.5 sec)\n",
      "   161 / 2000, K_rot = 2817.6, K_vib = 0.0, max symp error = 1.689e-09, (74.2 sec)\n",
      "   171 / 2000, K_rot = 3701.8, K_vib = 0.0, max symp error = 2.316e-09, (78.8 sec)\n",
      "   181 / 2000, K_rot = 7288.7, K_vib = 0.0, max symp error = 6.891e-10, (83.5 sec)\n",
      "   191 / 2000, K_rot = 6585.2, K_vib = 0.0, max symp error = 1.260e-09, (88.1 sec)\n",
      "   201 / 2000, K_rot = 7396.7, K_vib = 0.0, max symp error = 1.210e-09, (92.6 sec)\n",
      "   211 / 2000, K_rot = 9867.3, K_vib = 0.0, max symp error = 8.693e-10, (97.1 sec)\n",
      "   221 / 2000, K_rot = 7455.7, K_vib = 0.0, max symp error = 1.696e-09, (101.6 sec)\n",
      "   231 / 2000, K_rot = 3787.1, K_vib = 0.0, max symp error = 9.178e-10, (106.2 sec)\n",
      "   241 / 2000, K_rot = 3470.1, K_vib = 0.0, max symp error = 5.026e-11, (110.9 sec)\n",
      "   251 / 2000, K_rot = 1747.2, K_vib = 0.0, max symp error = 9.645e-11, (115.7 sec)\n",
      "   261 / 2000, K_rot = 9973.6, K_vib = 0.0, max symp error = 5.150e-10, (120.4 sec)\n",
      "   271 / 2000, K_rot = 4377.4, K_vib = 0.0, max symp error = 4.803e-10, (125.2 sec)\n",
      "   281 / 2000, K_rot = 9515.0, K_vib = 0.0, max symp error = 2.860e-10, (130.0 sec)\n",
      "   291 / 2000, K_rot = 6893.6, K_vib = 0.0, max symp error = 9.438e-10, (134.7 sec)\n",
      "   301 / 2000, K_rot = 5376.0, K_vib = 0.0, max symp error = 1.139e-09, (139.3 sec)\n",
      "   311 / 2000, K_rot = 5321.8, K_vib = 0.0, max symp error = 1.367e-09, (144.0 sec)\n",
      "   321 / 2000, K_rot = 9159.7, K_vib = 0.0, max symp error = 9.742e-10, (148.6 sec)\n",
      "   331 / 2000, K_rot = 5392.6, K_vib = 0.0, max symp error = 1.207e-09, (153.4 sec)\n",
      "   341 / 2000, K_rot = 487.6, K_vib = 0.0, max symp error = 3.172e-10, (158.2 sec)\n",
      "   351 / 2000, K_rot = 6850.8, K_vib = 0.0, max symp error = 1.104e-09, (163.0 sec)\n",
      "   361 / 2000, K_rot = 219.6, K_vib = 0.0, max symp error = 1.266e-09, (167.7 sec)\n",
      "   371 / 2000, K_rot = 7582.7, K_vib = 0.0, max symp error = 4.256e-10, (172.5 sec)\n",
      "   381 / 2000, K_rot = 7779.4, K_vib = 0.0, max symp error = 8.252e-10, (177.2 sec)\n",
      "   391 / 2000, K_rot = 4940.4, K_vib = 0.0, max symp error = 6.222e-10, (181.9 sec)\n",
      "   401 / 2000, K_rot = 8660.0, K_vib = 0.0, max symp error = 4.726e-10, (186.6 sec)\n",
      "   411 / 2000, K_rot = 1841.7, K_vib = 0.0, max symp error = 1.018e-09, (191.4 sec)\n",
      "   421 / 2000, K_rot = 2463.3, K_vib = 0.0, max symp error = 5.678e-10, (196.0 sec)\n",
      "   431 / 2000, K_rot = 7594.3, K_vib = 0.0, max symp error = 1.289e-09, (200.7 sec)\n",
      "   441 / 2000, K_rot = 7529.8, K_vib = 0.0, max symp error = 4.533e-10, (205.3 sec)\n",
      "   451 / 2000, K_rot = 3684.4, K_vib = 0.0, max symp error = 8.943e-10, (209.9 sec)\n",
      "   461 / 2000, K_rot = 390.8, K_vib = 0.0, max symp error = 5.925e-10, (214.5 sec)\n",
      "   471 / 2000, K_rot = 1503.1, K_vib = 0.0, max symp error = 1.107e-09, (219.1 sec)\n",
      "   481 / 2000, K_rot = 2764.9, K_vib = 0.0, max symp error = 1.081e-09, (223.7 sec)\n",
      "   491 / 2000, K_rot = 5392.0, K_vib = 0.0, max symp error = 8.092e-11, (228.4 sec)\n",
      "   501 / 2000, K_rot = 2453.7, K_vib = 0.0, max symp error = 2.457e-09, (233.1 sec)\n",
      "   511 / 2000, K_rot = 9722.6, K_vib = 0.0, max symp error = 9.067e-10, (237.8 sec)\n",
      "   521 / 2000, K_rot = 2164.7, K_vib = 0.0, max symp error = 5.723e-10, (242.5 sec)\n",
      "   531 / 2000, K_rot = 1284.9, K_vib = 0.0, max symp error = 7.824e-10, (247.1 sec)\n",
      "   541 / 2000, K_rot = 3925.6, K_vib = 0.0, max symp error = 1.650e-09, (251.9 sec)\n",
      "   551 / 2000, K_rot = 9981.7, K_vib = 0.0, max symp error = 2.264e-10, (256.6 sec)\n",
      "   561 / 2000, K_rot = 5556.3, K_vib = 0.0, max symp error = 1.349e-09, (261.3 sec)\n",
      "   571 / 2000, K_rot = 7794.8, K_vib = 0.0, max symp error = 9.959e-10, (265.9 sec)\n",
      "   581 / 2000, K_rot = 3518.4, K_vib = 0.0, max symp error = 6.393e-10, (270.5 sec)\n",
      "   591 / 2000, K_rot = 3835.0, K_vib = 0.0, max symp error = 5.076e-10, (275.1 sec)\n",
      "   601 / 2000, K_rot = 817.9, K_vib = 0.0, max symp error = 1.835e-09, (279.7 sec)\n",
      "   611 / 2000, K_rot = 2152.6, K_vib = 0.0, max symp error = 6.105e-10, (284.4 sec)\n",
      "   621 / 2000, K_rot = 2828.7, K_vib = 0.0, max symp error = 6.351e-10, (289.2 sec)\n",
      "   631 / 2000, K_rot = 3203.5, K_vib = 0.0, max symp error = 2.871e-10, (293.9 sec)\n",
      "   641 / 2000, K_rot = 4838.7, K_vib = 0.0, max symp error = 7.875e-11, (298.6 sec)\n",
      "   651 / 2000, K_rot = 4176.6, K_vib = 0.0, max symp error = 7.929e-10, (303.2 sec)\n",
      "   661 / 2000, K_rot = 2076.9, K_vib = 0.0, max symp error = 7.046e-10, (307.7 sec)\n",
      "   671 / 2000, K_rot = 7519.9, K_vib = 0.0, max symp error = 1.352e-09, (312.2 sec)\n",
      "   681 / 2000, K_rot = 9171.1, K_vib = 0.0, max symp error = 7.952e-10, (316.9 sec)\n",
      "   691 / 2000, K_rot = 5976.7, K_vib = 0.0, max symp error = 4.052e-10, (321.6 sec)\n",
      "   701 / 2000, K_rot = 5310.1, K_vib = 0.0, max symp error = 1.088e-09, (326.3 sec)\n",
      "   711 / 2000, K_rot = 7895.5, K_vib = 0.0, max symp error = 2.454e-10, (330.9 sec)\n",
      "   721 / 2000, K_rot = 9576.3, K_vib = 0.0, max symp error = 1.343e-09, (335.7 sec)\n",
      "   731 / 2000, K_rot = 9017.8, K_vib = 0.0, max symp error = 1.400e-09, (340.3 sec)\n",
      "   741 / 2000, K_rot = 6847.5, K_vib = 0.0, max symp error = 2.638e-10, (345.0 sec)\n",
      "   751 / 2000, K_rot = 6915.3, K_vib = 0.0, max symp error = 1.021e-09, (349.8 sec)\n",
      "   761 / 2000, K_rot = 2417.0, K_vib = 0.0, max symp error = 6.727e-10, (354.7 sec)\n",
      "   771 / 2000, K_rot = 4178.8, K_vib = 0.0, max symp error = 2.217e-09, (359.4 sec)\n",
      "   781 / 2000, K_rot = 9218.0, K_vib = 0.0, max symp error = 4.434e-11, (364.1 sec)\n",
      "   791 / 2000, K_rot = 2660.2, K_vib = 0.0, max symp error = 9.337e-10, (368.7 sec)\n",
      "   801 / 2000, K_rot = 2507.7, K_vib = 0.0, max symp error = 1.147e-09, (373.6 sec)\n",
      "   811 / 2000, K_rot = 5999.4, K_vib = 0.0, max symp error = 5.702e-10, (378.4 sec)\n",
      "   821 / 2000, K_rot = 282.7, K_vib = 0.0, max symp error = 1.887e-09, (383.3 sec)\n",
      "   831 / 2000, K_rot = 6042.2, K_vib = 0.0, max symp error = 1.155e-09, (388.1 sec)\n",
      "   841 / 2000, K_rot = 3275.4, K_vib = 0.0, max symp error = 5.697e-10, (392.9 sec)\n",
      "   851 / 2000, K_rot = 2054.4, K_vib = 0.0, max symp error = 5.034e-10, (397.6 sec)\n",
      "   861 / 2000, K_rot = 4978.0, K_vib = 0.0, max symp error = 1.589e-09, (402.3 sec)\n",
      "   871 / 2000, K_rot = 4786.3, K_vib = 0.0, max symp error = 1.403e-09, (407.0 sec)\n",
      "   881 / 2000, K_rot = 3213.5, K_vib = 0.0, max symp error = 1.004e-09, (411.8 sec)\n",
      "   891 / 2000, K_rot = 1980.6, K_vib = 0.0, max symp error = 1.929e-10, (416.7 sec)\n",
      "   901 / 2000, K_rot = 9113.5, K_vib = 0.0, max symp error = 1.709e-09, (421.5 sec)\n",
      "   911 / 2000, K_rot = 7299.0, K_vib = 0.0, max symp error = 1.198e-09, (426.2 sec)\n",
      "   921 / 2000, K_rot = 4054.4, K_vib = 0.0, max symp error = 8.651e-10, (430.9 sec)\n",
      "   931 / 2000, K_rot = 9594.0, K_vib = 0.0, max symp error = 5.862e-10, (435.5 sec)\n",
      "   941 / 2000, K_rot = 7537.2, K_vib = 0.0, max symp error = 7.554e-10, (440.2 sec)\n",
      "   951 / 2000, K_rot = 9288.8, K_vib = 0.0, max symp error = 5.175e-10, (444.9 sec)\n",
      "   961 / 2000, K_rot = 2782.4, K_vib = 0.0, max symp error = 1.324e-09, (449.5 sec)\n",
      "   971 / 2000, K_rot = 7003.2, K_vib = 0.0, max symp error = 2.273e-10, (454.2 sec)\n",
      "   981 / 2000, K_rot = 2347.4, K_vib = 0.0, max symp error = 9.900e-10, (458.9 sec)\n",
      "   991 / 2000, K_rot = 3765.6, K_vib = 0.0, max symp error = 1.279e-09, (463.6 sec)\n",
      "  1001 / 2000, K_rot = 9447.7, K_vib = 0.0, max symp error = 1.079e-09, (468.3 sec)\n",
      "  1011 / 2000, K_rot = 4098.7, K_vib = 0.0, max symp error = 3.597e-10, (473.0 sec)\n",
      "  1021 / 2000, K_rot = 2402.9, K_vib = 0.0, max symp error = 7.812e-10, (477.7 sec)\n",
      "  1031 / 2000, K_rot = 7194.7, K_vib = 0.0, max symp error = 1.044e-09, (482.4 sec)\n",
      "  1041 / 2000, K_rot = 2557.9, K_vib = 0.0, max symp error = 2.052e-09, (487.3 sec)\n",
      "  1051 / 2000, K_rot = 7609.2, K_vib = 0.0, max symp error = 3.957e-10, (492.0 sec)\n",
      "  1061 / 2000, K_rot = 4817.1, K_vib = 0.0, max symp error = 1.236e-09, (496.8 sec)\n",
      "  1071 / 2000, K_rot = 5458.6, K_vib = 0.0, max symp error = 3.431e-10, (501.5 sec)\n",
      "  1081 / 2000, K_rot = 4589.1, K_vib = 0.0, max symp error = 1.135e-09, (506.2 sec)\n",
      "  1091 / 2000, K_rot = 5344.1, K_vib = 0.0, max symp error = 1.134e-09, (510.9 sec)\n",
      "  1101 / 2000, K_rot = 9410.6, K_vib = 0.0, max symp error = 5.722e-10, (515.6 sec)\n",
      "  1111 / 2000, K_rot = 3666.5, K_vib = 0.0, max symp error = 8.712e-10, (520.4 sec)\n",
      "  1121 / 2000, K_rot = 240.3, K_vib = 0.0, max symp error = 4.725e-10, (525.2 sec)\n",
      "  1131 / 2000, K_rot = 6294.3, K_vib = 0.0, max symp error = 1.975e-09, (529.9 sec)\n",
      "  1141 / 2000, K_rot = 4357.6, K_vib = 0.0, max symp error = 9.068e-10, (534.8 sec)\n",
      "  1151 / 2000, K_rot = 9056.6, K_vib = 0.0, max symp error = 1.128e-09, (539.6 sec)\n",
      "  1161 / 2000, K_rot = 7166.2, K_vib = 0.0, max symp error = 2.227e-11, (544.4 sec)\n",
      "  1171 / 2000, K_rot = 8916.5, K_vib = 0.0, max symp error = 1.021e-09, (549.1 sec)\n",
      "  1181 / 2000, K_rot = 451.6, K_vib = 0.0, max symp error = 4.935e-10, (553.9 sec)\n",
      "  1191 / 2000, K_rot = 2126.8, K_vib = 0.0, max symp error = 1.139e-09, (558.5 sec)\n",
      "  1201 / 2000, K_rot = 9789.0, K_vib = 0.0, max symp error = 8.513e-10, (563.1 sec)\n",
      "  1211 / 2000, K_rot = 5422.0, K_vib = 0.0, max symp error = 1.167e-10, (567.7 sec)\n",
      "  1221 / 2000, K_rot = 3624.6, K_vib = 0.0, max symp error = 3.619e-10, (572.3 sec)\n",
      "  1231 / 2000, K_rot = 2296.3, K_vib = 0.0, max symp error = 7.671e-10, (576.9 sec)\n",
      "  1241 / 2000, K_rot = 2172.9, K_vib = 0.0, max symp error = 1.472e-09, (581.5 sec)\n",
      "  1251 / 2000, K_rot = 5639.4, K_vib = 0.0, max symp error = 5.967e-10, (586.3 sec)\n",
      "  1261 / 2000, K_rot = 4547.6, K_vib = 0.0, max symp error = 9.726e-10, (591.1 sec)\n",
      "  1271 / 2000, K_rot = 350.1, K_vib = 0.0, max symp error = 2.029e-09, (595.8 sec)\n",
      "  1281 / 2000, K_rot = 3161.5, K_vib = 0.0, max symp error = 8.883e-10, (600.6 sec)\n",
      "  1291 / 2000, K_rot = 2615.2, K_vib = 0.0, max symp error = 9.626e-10, (605.4 sec)\n",
      "  1301 / 2000, K_rot = 3493.6, K_vib = 0.0, max symp error = 1.142e-09, (610.1 sec)\n",
      "  1311 / 2000, K_rot = 2293.5, K_vib = 0.0, max symp error = 6.199e-10, (614.9 sec)\n",
      "  1321 / 2000, K_rot = 1026.4, K_vib = 0.0, max symp error = 2.312e-09, (619.7 sec)\n",
      "  1331 / 2000, K_rot = 8248.1, K_vib = 0.0, max symp error = 3.949e-10, (624.5 sec)\n",
      "  1341 / 2000, K_rot = 9451.1, K_vib = 0.0, max symp error = 1.147e-09, (629.4 sec)\n",
      "  1351 / 2000, K_rot = 6264.2, K_vib = 0.0, max symp error = 6.107e-10, (634.3 sec)\n",
      "  1361 / 2000, K_rot = 4614.2, K_vib = 0.0, max symp error = 3.291e-10, (639.1 sec)\n",
      "  1371 / 2000, K_rot = 8100.1, K_vib = 0.0, max symp error = 8.619e-10, (643.9 sec)\n",
      "  1381 / 2000, K_rot = 6091.0, K_vib = 0.0, max symp error = 3.813e-10, (648.7 sec)\n",
      "  1391 / 2000, K_rot = 3336.7, K_vib = 0.0, max symp error = 2.489e-10, (653.5 sec)\n",
      "  1401 / 2000, K_rot = 9340.1, K_vib = 0.0, max symp error = 2.215e-09, (658.3 sec)\n",
      "  1411 / 2000, K_rot = 3087.2, K_vib = 0.0, max symp error = 1.210e-10, (663.0 sec)\n",
      "  1421 / 2000, K_rot = 6007.2, K_vib = 0.0, max symp error = 2.716e-10, (667.7 sec)\n",
      "  1431 / 2000, K_rot = 8549.9, K_vib = 0.0, max symp error = 1.224e-09, (672.5 sec)\n",
      "  1441 / 2000, K_rot = 3685.4, K_vib = 0.0, max symp error = 1.428e-09, (677.2 sec)\n",
      "  1451 / 2000, K_rot = 1389.7, K_vib = 0.0, max symp error = 1.039e-09, (681.9 sec)\n",
      "  1461 / 2000, K_rot = 5130.7, K_vib = 0.0, max symp error = 7.576e-10, (686.8 sec)\n",
      "  1471 / 2000, K_rot = 866.6, K_vib = 0.0, max symp error = 1.269e-09, (691.4 sec)\n",
      "  1481 / 2000, K_rot = 7205.9, K_vib = 0.0, max symp error = 1.365e-09, (696.1 sec)\n",
      "  1491 / 2000, K_rot = 5494.3, K_vib = 0.0, max symp error = 7.108e-10, (700.9 sec)\n",
      "  1501 / 2000, K_rot = 6408.4, K_vib = 0.0, max symp error = 1.753e-10, (705.6 sec)\n",
      "  1511 / 2000, K_rot = 2938.0, K_vib = 0.0, max symp error = 5.596e-10, (710.5 sec)\n",
      "  1521 / 2000, K_rot = 9885.7, K_vib = 0.0, max symp error = 1.164e-09, (715.1 sec)\n",
      "  1531 / 2000, K_rot = 5770.4, K_vib = 0.0, max symp error = 3.947e-10, (719.9 sec)\n",
      "  1541 / 2000, K_rot = 9285.6, K_vib = 0.0, max symp error = 2.698e-09, (724.5 sec)\n",
      "  1551 / 2000, K_rot = 1669.5, K_vib = 0.0, max symp error = 4.818e-10, (729.3 sec)\n",
      "  1561 / 2000, K_rot = 8796.3, K_vib = 0.0, max symp error = 6.143e-10, (734.1 sec)\n",
      "  1571 / 2000, K_rot = 2098.4, K_vib = 0.0, max symp error = 3.571e-11, (738.8 sec)\n",
      "  1581 / 2000, K_rot = 6521.5, K_vib = 0.0, max symp error = 1.607e-09, (743.4 sec)\n",
      "  1591 / 2000, K_rot = 8306.3, K_vib = 0.0, max symp error = 1.836e-09, (748.2 sec)\n",
      "  1601 / 2000, K_rot = 5014.2, K_vib = 0.0, max symp error = 1.455e-09, (752.9 sec)\n",
      "  1611 / 2000, K_rot = 2860.3, K_vib = 0.0, max symp error = 7.849e-10, (757.6 sec)\n",
      "  1621 / 2000, K_rot = 1863.2, K_vib = 0.0, max symp error = 1.546e-10, (762.4 sec)\n",
      "  1631 / 2000, K_rot = 6431.5, K_vib = 0.0, max symp error = 1.173e-09, (767.0 sec)\n",
      "  1641 / 2000, K_rot = 4589.4, K_vib = 0.0, max symp error = 1.086e-09, (771.8 sec)\n",
      "  1651 / 2000, K_rot = 3933.0, K_vib = 0.0, max symp error = 2.092e-10, (776.6 sec)\n",
      "  1661 / 2000, K_rot = 9232.2, K_vib = 0.0, max symp error = 3.533e-10, (781.4 sec)\n",
      "  1671 / 2000, K_rot = 7627.6, K_vib = 0.0, max symp error = 5.849e-10, (786.2 sec)\n",
      "  1681 / 2000, K_rot = 6536.5, K_vib = 0.0, max symp error = 5.926e-10, (790.8 sec)\n",
      "  1691 / 2000, K_rot = 897.3, K_vib = 0.0, max symp error = 1.001e-09, (795.5 sec)\n",
      "  1701 / 2000, K_rot = 1867.7, K_vib = 0.0, max symp error = 1.550e-09, (800.2 sec)\n",
      "  1711 / 2000, K_rot = 1623.7, K_vib = 0.0, max symp error = 4.588e-10, (805.1 sec)\n",
      "  1721 / 2000, K_rot = 5538.5, K_vib = 0.0, max symp error = 8.589e-10, (809.8 sec)\n",
      "  1731 / 2000, K_rot = 5618.3, K_vib = 0.0, max symp error = 1.106e-09, (814.7 sec)\n",
      "  1741 / 2000, K_rot = 8806.9, K_vib = 0.0, max symp error = 1.843e-09, (819.4 sec)\n",
      "  1751 / 2000, K_rot = 5849.4, K_vib = 0.0, max symp error = 1.731e-09, (824.1 sec)\n",
      "  1761 / 2000, K_rot = 192.3, K_vib = 0.0, max symp error = 1.355e-09, (828.9 sec)\n",
      "  1771 / 2000, K_rot = 4075.3, K_vib = 0.0, max symp error = 2.365e-09, (833.7 sec)\n",
      "  1781 / 2000, K_rot = 5590.7, K_vib = 0.0, max symp error = 1.645e-09, (838.4 sec)\n",
      "  1791 / 2000, K_rot = 2198.4, K_vib = 0.0, max symp error = 1.520e-09, (843.2 sec)\n",
      "  1801 / 2000, K_rot = 6597.9, K_vib = 0.0, max symp error = 1.272e-09, (848.0 sec)\n",
      "  1811 / 2000, K_rot = 4280.0, K_vib = 0.0, max symp error = 1.775e-10, (852.7 sec)\n",
      "  1821 / 2000, K_rot = 4019.1, K_vib = 0.0, max symp error = 1.308e-09, (857.5 sec)\n",
      "  1831 / 2000, K_rot = 3659.6, K_vib = 0.0, max symp error = 6.542e-10, (862.2 sec)\n",
      "  1841 / 2000, K_rot = 4965.5, K_vib = 0.0, max symp error = 2.012e-09, (866.9 sec)\n",
      "  1851 / 2000, K_rot = 2757.4, K_vib = 0.0, max symp error = 1.790e-10, (871.8 sec)\n",
      "  1861 / 2000, K_rot = 9182.1, K_vib = 0.0, max symp error = 1.243e-09, (876.5 sec)\n",
      "  1871 / 2000, K_rot = 8172.8, K_vib = 0.0, max symp error = 6.560e-10, (881.0 sec)\n",
      "  1881 / 2000, K_rot = 3323.9, K_vib = 0.0, max symp error = 5.745e-10, (885.6 sec)\n",
      "  1891 / 2000, K_rot = 5787.3, K_vib = 0.0, max symp error = 5.782e-10, (890.1 sec)\n",
      "  1901 / 2000, K_rot = 128.8, K_vib = 0.0, max symp error = 8.916e-10, (894.6 sec)\n",
      "  1911 / 2000, K_rot = 4775.1, K_vib = 0.0, max symp error = 3.214e-10, (899.2 sec)\n",
      "  1921 / 2000, K_rot = 7999.3, K_vib = 0.0, max symp error = 7.878e-10, (903.9 sec)\n",
      "  1931 / 2000, K_rot = 650.4, K_vib = 0.0, max symp error = 5.829e-10, (908.7 sec)\n",
      "  1941 / 2000, K_rot = 2412.1, K_vib = 0.0, max symp error = 1.661e-09, (913.4 sec)\n",
      "  1951 / 2000, K_rot = 9588.3, K_vib = 0.0, max symp error = 1.619e-10, (918.2 sec)\n",
      "  1961 / 2000, K_rot = 9360.6, K_vib = 0.0, max symp error = 1.845e-09, (922.8 sec)\n",
      "  1971 / 2000, K_rot = 9367.1, K_vib = 0.0, max symp error = 8.983e-10, (927.5 sec)\n",
      "  1981 / 2000, K_rot = 9965.5, K_vib = 0.0, max symp error = 1.212e-09, (932.2 sec)\n",
      "  1991 / 2000, K_rot = 2330.2, K_vib = 0.0, max symp error = 8.930e-10, (936.9 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",
    "    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",
    "    gamma_ref = [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_pure_rot_{k_rot:.0f}_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, 0.0)  # No vibrational kinetic energy for pure rotational motion\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 rotational energies can be calculated analytically using the formula $E_J = B_e J(J+1)$, where $B_e = \\frac{\\hbar^2}{2I}$ is the rotational constant and $J$ is the rotational quantum number.\n",
    "\n",
    "The moment of inertia $I$ for H2 can be calculated as $I = \\frac{m_H}{2}r_e^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "67f6c0e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rotational constant B = 60.817 cm^-1\n",
      "Analytical rotational energies (cm^-1): [   0.   121.6  364.9  729.8 1216.3 1824.5 2554.3 3405.7 4378.8 5473.5\n",
      " 6689.8 8027.8 9487.4]\n",
      "Peaks (cm^-1) for K = 500: [ 111.3  370.3  730.4 1214.5 1826.6 2553.8 3403.8 4377.9]\n",
      "Peaks (cm^-1) for K = 2000: [ 369.   730.4 1213.3 1825.3 2553.2 3403.2 4376.6 5475.3 6686.1]\n",
      "Peaks (cm^-1) for K = 5000: [1212.  1824.7 2552.5 3403.2 4375.9 5474.7 6685.4 8028.5 9494.4]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
    "    # rotational constant\n",
    "    B = HBar**2 / (2.0 * I) / CmInv\n",
    "    analytical_energies = np.array([B * J * (J + 1) for J in range(20) if B * J * (J + 1) <= 10000])\n",
    "    print(f\"Rotational constant B = {B:.3f} cm^-1\")\n",
    "    print(f\"Analytical rotational 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",
    "        peaks = peaks[ener_grid[peaks] <= 10000]\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=\"analytical\")\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": [
    "The computed peak positions for $K = 2000$ $\\textrm{cm}^{-1}$ are compared with the analytical eigenenergies $E_J = B_e J(J+1)$ with $B_e = 60.817$ $\\textrm{cm}^{-1}$ (all in $\\textrm{cm}^{-1}$).\n",
    "\n",
    "| $J$ | Computed | $B_e J(J+1)$ | Deviation |\n",
    "|---|---|---|---|\n",
    "| 2 | 369.0 | 364.9 | +4.1 |\n",
    "| 3 | 730.4 | 729.8 | +0.6 |\n",
    "| 4 | 1213.3 | 1216.3 | −3.0 |\n",
    "| 5 | 1825.3 | 1824.5 | +0.8 |\n",
    "| 6 | 2553.2 | 2554.3 | −1.1 |\n",
    "| 7 | 3403.2 | 3405.7 | −2.5 |\n",
    "| 8 | 4376.6 | 4378.8 | −2.2 |\n",
    "| 9 | 5475.3 | 5473.5 | +1.8 |\n",
    "| 10 | 6686.1 | 6689.8 | −3.7 |\n",
    "\n",
    "- **Quantitative agreement**: The computed peaks agree with the analytical eigenenergies with an RMSE of about 2.5 $\\textrm{cm}^{-1}$, without systematic dependence on $J$. The same peak positions are obtained for all the initial states, up to $J = 12$ (about 9500 $\\textrm{cm}^{-1}$) for $K$ = 5000 $\\textrm{cm}^{-1}$.\n",
    "\n",
    "- **Line shape**: Each peak has an asymmetric line shape with a sharp edge at the eigenenergy and a tail on the low-energy side, which originates from the time-averaging expression (see Appendix K of the paper).\n",
    "\n",
    "- **Dependence on the initial state**: The intensity distribution follows the rotational kinetic energy of the initial state: the strongest peaks appear around 730, 2550 and 5470 $\\textrm{cm}^{-1}$ for the initial states with $K$ = 500, 2000 and 5000 $\\textrm{cm}^{-1}$, respectively."
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