{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f6dd41a9",
   "metadata": {},
   "source": [
    "# 8. Rotational Spectra of Methane\n",
    "\n",
    "The rotational spectrum of methane, a nonlinear molecule, is computed by the phase-space sampling (see also section III B of the paper). \n",
    "\n",
    "| Redundant space | Potential | Integrator | Physical space |\n",
    "|---|---|---|---|\n",
    "| Quaternion (4 DOFs) with 1 constraint (norm) | none | `ImplicitVerlet` | Euler angles (3 DOFs) |\n",
    "\n",
    "- **Rigid rotor**: The rotation is propagated directly by the quaternion, as in the *Direct Dynamics* tutorial.\n",
    "Since the potential energy is constant for the rigid rotation, no potential is given, and no Hessian evaluation is needed.\n",
    "\n",
    "- **Initial states**: Coherent states in the Euler angles centered at the reference orientation ($\\psi, \\theta, \\phi$) = (0, $\\pi / 2$, 0), with the rotational kinetic energies of 50, 200 and 500 $\\textrm{cm}^{-1}$ and the widths of 0.2 rad.\n",
    "\n",
    "- **Sampling**: As in the paper, the initial orientation is fixed at the center of the initial states, and only the angular momenta are sampled: the direction is uniform on the unit sphere, and the rotational kinetic energy is uniform.\n",
    "\n",
    "- **Coordinate singularities**: The trajectories pass through the gimbal lock of the Euler angles ($\\theta = 0, \\pi$) depending on the direction of the angular momentum. The steps where the symplectic condition is not satisfied are excluded.\n",
    "\n",
    "- **Reference**: Since methane is a spherical top molecule, the rotational levels are given analytically by $E_J = B J(J+1)$, the same formula as for a linear molecule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "24727517",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import necessary libraries\n",
    "\n",
    "import time\n",
    " \n",
    "import numpy as np\n",
    " \n",
    "from pyscivr.basis import get_overlap\n",
    "from pyscivr.coordinates import QuaternionCoordinates, quaternion_metric\n",
    "from pyscivr.integrators import ImplicitVerlet\n",
    "from pyscivr.scivr import get_action, get_lagrangian, get_prefactor, get_ta_spectrum_fft\n",
    "from pyscivr.units import CmInv, FemtoSec, HBar\n",
    "from pyscivr.utils import get_geom, get_inertia, get_mass_center\n",
    "from pyscivr.variations import make_jacobi_func, make_vari_propagator_implicit, propagate_variation_implicit, to_internal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdc6caf4",
   "metadata": {},
   "source": [
    "## System and coordinates\n",
    "\n",
    "The system and the coordinates are the same as in the *Direct Dynamics* tutorial.\n",
    "\n",
    "The reference structure must be centered at the origin and oriented along the principal axes, so that the moments of inertia can be passed to `quaternion_metric`.\n",
    "\n",
    "`QuaternionCoordinates` defines the Euler angles (yaw, pitch and roll) and the norm condition of the quaternion, where the Euler angles are active. The Jacobian functions are made once and reused for all trajectories.\n",
    "\n",
    "\n",
    "## Sampling of initial conditions\n",
    "\n",
    "`angular_momentum` gives the angular momentum in the body frame with the rotational kinetic energy `K_rot` along the direction `L_dir`, where $K_{\\text{rot}} = \\frac{L^T I^{-1} L}{2}$.\n",
    "\n",
    "`sample_momenta` samples the direction uniformly on the unit sphere and `K_rot` uniformly, and converts the angular momenta into the quaternion momenta by $p = 2 S(q)^T L_{\\text{body}}$.\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 `ImplicitVerlet` with `normalize=True`.\n",
    "2. Propagate the variation and compute the monodromy matrix in the Euler angles.\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 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 and the monodromy matrix is shared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e8b02a5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constants\n",
    "XYZSTR = \"\"\"\n",
    "C        -0.000000000000       0.000000000000      -0.000000000000\n",
    "H         0.627615334142       0.627615334142       0.627615334142\n",
    "H        -0.627615334142      -0.627615334142       0.627615334142\n",
    "H         0.627615334142      -0.627615334142      -0.627615334142\n",
    "H        -0.627615334142       0.627615334142      -0.627615334142\n",
    "\"\"\"\n",
    "SYMBOLS, POSI_REF, MASS = get_geom(XYZSTR)\n",
    "assert np.allclose(get_mass_center(POSI_REF, MASS), 0.0) # centered at the origin\n",
    "INERTIA_TENSOR = get_inertia(POSI_REF, MASS)\n",
    "assert np.allclose(INERTIA_TENSOR, np.diag(np.diag(INERTIA_TENSOR))) # principal axis frame\n",
    "INERTIA = np.diag(INERTIA_TENSOR) # (3,) principal moments of inertia\n",
    "\n",
    "METRIC_FUNC = quaternion_metric(INERTIA)\n",
    "Q_INIT = np.array([1.0, 0.0, 0.0, 0.0]) # reference orientation (no rotation)\n",
    "\n",
    "# Coordinates (Euler angles and the norm condition)\n",
    "COORD_ALL = QuaternionCoordinates()\n",
    "ACTIVE_IDX = np.array([0, 1, 2]) # yaw, pitch, roll\n",
    "TOPOLOGIES = [COORD_ALL.topology[i] for i in ACTIVE_IDX] # S1, I-, S1\n",
    "\n",
    "JACOBI_FUNC, JACOBI_REV_FUNC, INTERNAL_FUNC, MONODROMY_FUNC = make_jacobi_func(COORD_ALL, ACTIVE_IDX)\n",
    "\n",
    "\n",
    "def get_S(q):\n",
    "    \"\"\"omega_body = 2 S(q) dq/dt, p = 2 S(q)^T L_body, L_body = S(q) p / 2 (|q| = 1).\"\"\"\n",
    "    q0, q1, q2, q3 = q\n",
    "    return np.array([[-q1, q0, q3, -q2],\n",
    "                     [-q2, -q3, q0, q1],\n",
    "                     [-q3, q2, -q1, q0]])\n",
    "\n",
    "\n",
    "def angular_momentum(K_rot, L_dir):\n",
    "    \"\"\"Angular momentum in the body frame with the rotational kinetic energy K_rot [cm^-1] along L_dir.\"\"\"\n",
    "    L_dir = np.atleast_2d(L_dir)\n",
    "    return np.sqrt(2.0 * np.atleast_1d(K_rot)[:, None] * CmInv / np.sum(L_dir**2 / INERTIA, axis=1, keepdims=True)) * L_dir\n",
    "\n",
    "\n",
    "def sample_momenta(n_sample, K_rot_range, seed=10202):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    L_dir = rng.normal(size=(n_sample, 3))\n",
    "    L_dir /= np.linalg.norm(L_dir, axis=1, keepdims=True) # uniform on the unit sphere\n",
    "    K_rot = rng.uniform(*K_rot_range, size=n_sample)\n",
    "    mome = 2.0 * angular_momentum(K_rot, L_dir) @ get_S(Q_INIT) # (n_sample, 4)\n",
    "    return mome, K_rot\n",
    "\n",
    "\n",
    "def run(mome_sample_list, K_rot_list, mome_ref_list, gamma_ref_list, fpath_list,\n",
    "        dt, n_step, n_fft, symp_err_tol=1e-2):\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 Euler angles\n",
    "    posi_ref_int, mome_ref_int = zip(*[INTERNAL_FUNC(Q_INIT, p) for p in mome_ref_list])\n",
    "\n",
    "    n_sample = len(mome_sample_list)\n",
    "    n_ref = len(mome_ref_list)\n",
    "    spectra = [0.0] * n_ref\n",
    "    vari_propagator = make_vari_propagator_implicit(METRIC_FUNC, dt, normalize=True)\n",
    "\n",
    "    t_start = time.perf_counter()\n",
    "    for i in range(n_sample):\n",
    "        # Get trajectory\n",
    "        traj = ImplicitVerlet(Q_INIT, mome_sample_list[i], dt, METRIC_FUNC, normalize=True).run(n_step)\n",
    "        posi, mome = traj[\"posi\"], traj[\"mome\"]\n",
    "\n",
    "        # Get variation\n",
    "        J_rev_init = JACOBI_REV_FUNC(posi[0], mome[0])\n",
    "        vari = propagate_variation_implicit(vari_propagator, posi, mome, traj[\"mome_half\"], J_rev_init)\n",
    "        posi_int, mome_int, mono_int, symplectic_error = to_internal(MONODROMY_FUNC, posi, mome, vari)\n",
    "\n",
    "        # Points with large symplectic error are treated as singularities\n",
    "        valid = judge_func(symplectic_error)\n",
    "\n",
    "        lag = get_lagrangian(traj[\"total_energy\"], traj[\"potential_energy\"])   # V = 0\n",
    "        action = get_action(lag, dt)\n",
    "\n",
    "        for j in range(n_ref):\n",
    "            gamma = gamma_ref_list[j]\n",
    "            prefactor = get_prefactor(mono_int, gamma, valid=valid)\n",
    "            overlap = get_overlap(TOPOLOGIES, posi_ref_int[j], mome_ref_int[j], posi_int, mome_int, gamma)\n",
    "            ener_grid, 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}, \"\n",
    "                  f\"max symp error = {np.max(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": "2a6d2450",
   "metadata": {},
   "source": [
    "## Execute calculation\n",
    "\n",
    "The total propagation time is 2000 fs.\n",
    "\n",
    "A time step of 1 fs is sufficient for the slow rotation of methane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6d432c2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     1 / 2000, K_rot = 439.3, max symp error = 5.819e-13, (1.1 sec)\n",
      "    11 / 2000, K_rot = 67.9, max symp error = 5.046e-13, (1.9 sec)\n",
      "    21 / 2000, K_rot = 336.4, max symp error = 9.443e-13, (2.6 sec)\n",
      "    31 / 2000, K_rot = 739.7, max symp error = 1.821e-12, (3.3 sec)\n",
      "    41 / 2000, K_rot = 307.7, max symp error = 1.533e-12, (4.0 sec)\n",
      "    51 / 2000, K_rot = 890.7, max symp error = 1.272e-12, (4.7 sec)\n",
      "    61 / 2000, K_rot = 367.5, max symp error = 7.165e-13, (5.4 sec)\n",
      "    71 / 2000, K_rot = 590.6, max symp error = 8.061e-13, (6.1 sec)\n",
      "    81 / 2000, K_rot = 822.9, max symp error = 8.603e-13, (6.8 sec)\n",
      "    91 / 2000, K_rot = 676.4, max symp error = 1.498e-12, (7.5 sec)\n",
      "   101 / 2000, K_rot = 964.9, max symp error = 1.716e-12, (8.2 sec)\n",
      "   111 / 2000, K_rot = 46.4, max symp error = 2.675e-13, (8.9 sec)\n",
      "   121 / 2000, K_rot = 169.4, max symp error = 1.049e-12, (9.6 sec)\n",
      "   131 / 2000, K_rot = 216.6, max symp error = 9.727e-13, (10.3 sec)\n",
      "   141 / 2000, K_rot = 889.7, max symp error = 2.480e-12, (11.0 sec)\n",
      "   151 / 2000, K_rot = 564.2, max symp error = 1.064e-10, (11.7 sec)\n",
      "   161 / 2000, K_rot = 26.2, max symp error = 1.954e-13, (12.4 sec)\n",
      "   171 / 2000, K_rot = 955.0, max symp error = 2.483e-12, (13.2 sec)\n",
      "   181 / 2000, K_rot = 725.0, max symp error = 4.058e-11, (13.9 sec)\n",
      "   191 / 2000, K_rot = 19.3, max symp error = 1.167e-13, (14.6 sec)\n",
      "   201 / 2000, K_rot = 55.8, max symp error = 3.434e-13, (15.3 sec)\n",
      "   211 / 2000, K_rot = 662.7, max symp error = 2.407e-12, (16.1 sec)\n",
      "   221 / 2000, K_rot = 944.3, max symp error = 1.750e-10, (16.8 sec)\n",
      "   231 / 2000, K_rot = 480.9, max symp error = 9.874e-13, (17.5 sec)\n",
      "   241 / 2000, K_rot = 421.0, max symp error = 2.400e-12, (18.2 sec)\n",
      "   251 / 2000, K_rot = 190.7, max symp error = 5.120e-13, (18.9 sec)\n",
      "   261 / 2000, K_rot = 134.6, max symp error = 1.481e-13, (19.6 sec)\n",
      "   271 / 2000, K_rot = 410.8, max symp error = 7.184e-12, (20.3 sec)\n",
      "   281 / 2000, K_rot = 492.0, max symp error = 1.124e-12, (21.0 sec)\n",
      "   291 / 2000, K_rot = 674.8, max symp error = 6.907e-13, (21.7 sec)\n",
      "   301 / 2000, K_rot = 516.9, max symp error = 5.276e-13, (22.5 sec)\n",
      "   311 / 2000, K_rot = 598.9, max symp error = 1.916e-12, (23.2 sec)\n",
      "   321 / 2000, K_rot = 317.9, max symp error = 3.925e-13, (23.9 sec)\n",
      "   331 / 2000, K_rot = 459.9, max symp error = 1.296e-12, (24.6 sec)\n",
      "   341 / 2000, K_rot = 150.7, max symp error = 5.621e-13, (25.3 sec)\n",
      "   351 / 2000, K_rot = 300.8, max symp error = 1.211e-12, (26.0 sec)\n",
      "   361 / 2000, K_rot = 265.6, max symp error = 5.056e-13, (26.7 sec)\n",
      "   371 / 2000, K_rot = 974.8, max symp error = 1.288e-12, (27.4 sec)\n",
      "   381 / 2000, K_rot = 918.6, max symp error = 8.231e-13, (28.2 sec)\n",
      "   391 / 2000, K_rot = 864.9, max symp error = 2.891e-12, (28.9 sec)\n",
      "   401 / 2000, K_rot = 592.6, max symp error = 2.066e-12, (29.6 sec)\n",
      "   411 / 2000, K_rot = 973.3, max symp error = 1.934e-12, (30.3 sec)\n",
      "   421 / 2000, K_rot = 704.8, max symp error = 1.541e-12, (31.0 sec)\n",
      "   431 / 2000, K_rot = 884.7, max symp error = 2.846e-12, (31.8 sec)\n",
      "   441 / 2000, K_rot = 566.6, max symp error = 3.688e-07, (32.5 sec)\n",
      "   451 / 2000, K_rot = 412.0, max symp error = 1.637e-12, (33.2 sec)\n",
      "   461 / 2000, K_rot = 413.9, max symp error = 9.813e-13, (33.9 sec)\n",
      "   471 / 2000, K_rot = 349.1, max symp error = 3.858e-13, (34.6 sec)\n",
      "   481 / 2000, K_rot = 321.3, max symp error = 1.112e-11, (35.3 sec)\n",
      "   491 / 2000, K_rot = 392.0, max symp error = 1.092e-12, (36.1 sec)\n",
      "   501 / 2000, K_rot = 223.7, max symp error = 1.262e-12, (36.8 sec)\n",
      "   511 / 2000, K_rot = 735.3, max symp error = 6.344e-13, (37.4 sec)\n",
      "   521 / 2000, K_rot = 270.9, max symp error = 1.805e-12, (38.1 sec)\n",
      "   531 / 2000, K_rot = 956.4, max symp error = 1.850e-12, (38.8 sec)\n",
      "   541 / 2000, K_rot = 493.2, max symp error = 1.146e-11, (39.4 sec)\n",
      "   551 / 2000, K_rot = 40.8, max symp error = 4.507e-13, (40.1 sec)\n",
      "   561 / 2000, K_rot = 252.0, max symp error = 4.614e-12, (40.8 sec)\n",
      "   571 / 2000, K_rot = 676.3, max symp error = 1.138e-12, (41.4 sec)\n",
      "   581 / 2000, K_rot = 422.3, max symp error = 1.358e-12, (42.1 sec)\n",
      "   591 / 2000, K_rot = 23.1, max symp error = 3.315e-13, (42.8 sec)\n",
      "   601 / 2000, K_rot = 396.8, max symp error = 7.155e-13, (43.6 sec)\n",
      "   611 / 2000, K_rot = 531.2, max symp error = 2.885e-10, (44.3 sec)\n",
      "   621 / 2000, K_rot = 853.8, max symp error = 2.194e-12, (45.1 sec)\n",
      "   631 / 2000, K_rot = 550.3, max symp error = 1.615e-12, (45.9 sec)\n",
      "   641 / 2000, K_rot = 244.1, max symp error = 2.024e-12, (46.6 sec)\n",
      "   651 / 2000, K_rot = 638.0, max symp error = 1.224e-12, (47.3 sec)\n",
      "   661 / 2000, K_rot = 923.9, max symp error = 8.687e-13, (48.0 sec)\n",
      "   671 / 2000, K_rot = 309.8, max symp error = 4.636e-13, (48.7 sec)\n",
      "   681 / 2000, K_rot = 527.0, max symp error = 1.904e-12, (49.4 sec)\n",
      "   691 / 2000, K_rot = 345.0, max symp error = 9.063e-13, (50.1 sec)\n",
      "   701 / 2000, K_rot = 28.2, max symp error = 1.209e-13, (50.8 sec)\n",
      "   711 / 2000, K_rot = 46.5, max symp error = 5.237e-13, (51.5 sec)\n",
      "   721 / 2000, K_rot = 174.9, max symp error = 5.636e-13, (52.2 sec)\n",
      "   731 / 2000, K_rot = 298.7, max symp error = 1.559e-12, (52.9 sec)\n",
      "   741 / 2000, K_rot = 61.9, max symp error = 2.521e-13, (53.6 sec)\n",
      "   751 / 2000, K_rot = 405.6, max symp error = 9.015e-13, (54.3 sec)\n",
      "   761 / 2000, K_rot = 359.3, max symp error = 1.092e-12, (55.0 sec)\n",
      "   771 / 2000, K_rot = 631.8, max symp error = 7.547e-13, (55.7 sec)\n",
      "   781 / 2000, K_rot = 926.7, max symp error = 1.986e-12, (56.4 sec)\n",
      "   791 / 2000, K_rot = 152.1, max symp error = 9.646e-13, (57.2 sec)\n",
      "   801 / 2000, K_rot = 888.9, max symp error = 1.833e-12, (57.9 sec)\n",
      "   811 / 2000, K_rot = 961.4, max symp error = 1.823e-12, (58.6 sec)\n",
      "   821 / 2000, K_rot = 739.9, max symp error = 1.502e-12, (59.4 sec)\n",
      "   831 / 2000, K_rot = 550.3, max symp error = 1.277e-12, (60.1 sec)\n",
      "   841 / 2000, K_rot = 28.5, max symp error = 3.684e-12, (60.8 sec)\n",
      "   851 / 2000, K_rot = 436.9, max symp error = 1.659e-12, (61.5 sec)\n",
      "   861 / 2000, K_rot = 504.7, max symp error = 1.304e-12, (62.2 sec)\n",
      "   871 / 2000, K_rot = 159.4, max symp error = 9.337e-13, (62.9 sec)\n",
      "   881 / 2000, K_rot = 136.8, max symp error = 3.470e-13, (63.6 sec)\n",
      "   891 / 2000, K_rot = 559.4, max symp error = 1.319e-12, (64.3 sec)\n",
      "   901 / 2000, K_rot = 696.9, max symp error = 4.045e-12, (65.1 sec)\n",
      "   911 / 2000, K_rot = 963.7, max symp error = 9.500e-13, (65.8 sec)\n",
      "   921 / 2000, K_rot = 674.8, max symp error = 1.039e-12, (66.5 sec)\n",
      "   931 / 2000, K_rot = 794.3, max symp error = 1.931e-12, (67.3 sec)\n",
      "   941 / 2000, K_rot = 193.7, max symp error = 1.848e-07, (68.0 sec)\n",
      "   951 / 2000, K_rot = 584.7, max symp error = 3.891e-08, (68.7 sec)\n",
      "   961 / 2000, K_rot = 588.5, max symp error = 2.113e-12, (69.4 sec)\n",
      "   971 / 2000, K_rot = 788.1, max symp error = 1.566e-12, (70.2 sec)\n",
      "   981 / 2000, K_rot = 254.7, max symp error = 1.198e-12, (71.0 sec)\n",
      "   991 / 2000, K_rot = 25.3, max symp error = 9.202e-13, (71.7 sec)\n",
      "  1001 / 2000, K_rot = 342.3, max symp error = 8.701e-13, (72.5 sec)\n",
      "  1011 / 2000, K_rot = 892.1, max symp error = 1.037e-12, (73.2 sec)\n",
      "  1021 / 2000, K_rot = 118.1, max symp error = 2.509e-12, (74.0 sec)\n",
      "  1031 / 2000, K_rot = 385.1, max symp error = 1.127e-12, (74.7 sec)\n",
      "  1041 / 2000, K_rot = 652.7, max symp error = 7.690e-13, (75.4 sec)\n",
      "  1051 / 2000, K_rot = 493.2, max symp error = 1.318e-12, (76.2 sec)\n",
      "  1061 / 2000, K_rot = 400.3, max symp error = 8.285e-13, (76.9 sec)\n",
      "  1071 / 2000, K_rot = 688.1, max symp error = 1.435e-12, (77.6 sec)\n",
      "  1081 / 2000, K_rot = 915.9, max symp error = 2.223e-12, (78.3 sec)\n",
      "  1091 / 2000, K_rot = 251.1, max symp error = 1.153e-12, (79.0 sec)\n",
      "  1101 / 2000, K_rot = 866.7, max symp error = 7.419e-13, (79.7 sec)\n",
      "  1111 / 2000, K_rot = 193.5, max symp error = 1.151e-12, (80.4 sec)\n",
      "  1121 / 2000, K_rot = 493.7, max symp error = 3.579e-13, (81.2 sec)\n",
      "  1131 / 2000, K_rot = 602.3, max symp error = 7.773e-13, (81.9 sec)\n",
      "  1141 / 2000, K_rot = 320.5, max symp error = 3.072e-13, (82.6 sec)\n",
      "  1151 / 2000, K_rot = 82.5, max symp error = 6.062e-12, (83.3 sec)\n",
      "  1161 / 2000, K_rot = 468.3, max symp error = 1.050e-12, (84.0 sec)\n",
      "  1171 / 2000, K_rot = 772.7, max symp error = 1.313e-12, (84.7 sec)\n",
      "  1181 / 2000, K_rot = 677.1, max symp error = 1.576e-12, (85.4 sec)\n",
      "  1191 / 2000, K_rot = 406.5, max symp error = 5.472e-13, (86.1 sec)\n",
      "  1201 / 2000, K_rot = 390.3, max symp error = 4.237e-10, (86.9 sec)\n",
      "  1211 / 2000, K_rot = 592.9, max symp error = 1.819e-11, (87.6 sec)\n",
      "  1221 / 2000, K_rot = 826.9, max symp error = 1.264e-12, (88.3 sec)\n",
      "  1231 / 2000, K_rot = 711.1, max symp error = 2.254e-12, (89.0 sec)\n",
      "  1241 / 2000, K_rot = 596.0, max symp error = 3.994e-12, (89.7 sec)\n",
      "  1251 / 2000, K_rot = 178.6, max symp error = 1.025e-12, (90.4 sec)\n",
      "  1261 / 2000, K_rot = 428.3, max symp error = 6.344e-13, (91.1 sec)\n",
      "  1271 / 2000, K_rot = 548.2, max symp error = 2.137e-12, (91.8 sec)\n",
      "  1281 / 2000, K_rot = 630.7, max symp error = 8.693e-13, (92.5 sec)\n",
      "  1291 / 2000, K_rot = 124.0, max symp error = 3.351e-13, (93.2 sec)\n",
      "  1301 / 2000, K_rot = 238.2, max symp error = 1.339e-12, (93.9 sec)\n",
      "  1311 / 2000, K_rot = 809.4, max symp error = 4.970e-13, (94.6 sec)\n",
      "  1321 / 2000, K_rot = 777.6, max symp error = 1.594e-12, (95.3 sec)\n",
      "  1331 / 2000, K_rot = 543.0, max symp error = 1.616e-10, (96.0 sec)\n",
      "  1341 / 2000, K_rot = 935.0, max symp error = 1.266e-12, (96.7 sec)\n",
      "  1351 / 2000, K_rot = 914.0, max symp error = 1.710e-12, (97.4 sec)\n",
      "  1361 / 2000, K_rot = 522.2, max symp error = 4.010e-12, (98.2 sec)\n",
      "  1371 / 2000, K_rot = 479.7, max symp error = 1.568e-12, (98.9 sec)\n",
      "  1381 / 2000, K_rot = 166.4, max symp error = 1.385e-11, (99.6 sec)\n",
      "  1391 / 2000, K_rot = 421.4, max symp error = 9.244e-13, (100.3 sec)\n",
      "  1401 / 2000, K_rot = 389.9, max symp error = 1.806e-12, (101.0 sec)\n",
      "  1411 / 2000, K_rot = 727.5, max symp error = 1.458e-12, (101.8 sec)\n",
      "  1421 / 2000, K_rot = 538.9, max symp error = 1.274e-12, (102.5 sec)\n",
      "  1431 / 2000, K_rot = 756.7, max symp error = 1.519e-12, (103.2 sec)\n",
      "  1441 / 2000, K_rot = 204.9, max symp error = 1.366e-12, (103.9 sec)\n",
      "  1451 / 2000, K_rot = 829.9, max symp error = 5.990e-12, (104.6 sec)\n",
      "  1461 / 2000, K_rot = 758.5, max symp error = 1.374e-12, (105.3 sec)\n",
      "  1471 / 2000, K_rot = 951.8, max symp error = 1.421e-12, (106.0 sec)\n",
      "  1481 / 2000, K_rot = 503.8, max symp error = 1.353e-12, (106.7 sec)\n",
      "  1491 / 2000, K_rot = 508.0, max symp error = 1.102e-12, (107.4 sec)\n",
      "  1501 / 2000, K_rot = 63.6, max symp error = 2.597e-13, (108.2 sec)\n",
      "  1511 / 2000, K_rot = 213.3, max symp error = 9.822e-13, (108.9 sec)\n",
      "  1521 / 2000, K_rot = 316.3, max symp error = 1.023e-12, (109.6 sec)\n",
      "  1531 / 2000, K_rot = 834.3, max symp error = 5.648e-12, (110.3 sec)\n",
      "  1541 / 2000, K_rot = 634.7, max symp error = 1.911e-12, (111.0 sec)\n",
      "  1551 / 2000, K_rot = 931.7, max symp error = 3.078e-12, (111.8 sec)\n",
      "  1561 / 2000, K_rot = 752.3, max symp error = 1.758e-12, (112.5 sec)\n",
      "  1571 / 2000, K_rot = 941.9, max symp error = 1.179e-12, (113.2 sec)\n",
      "  1581 / 2000, K_rot = 425.1, max symp error = 1.168e-11, (113.9 sec)\n",
      "  1591 / 2000, K_rot = 112.6, max symp error = 3.246e-13, (114.6 sec)\n",
      "  1601 / 2000, K_rot = 325.2, max symp error = 1.210e-11, (115.3 sec)\n",
      "  1611 / 2000, K_rot = 768.0, max symp error = 9.784e-13, (116.0 sec)\n",
      "  1621 / 2000, K_rot = 654.5, max symp error = 1.152e-12, (116.7 sec)\n",
      "  1631 / 2000, K_rot = 802.5, max symp error = 1.976e-12, (117.5 sec)\n",
      "  1641 / 2000, K_rot = 927.4, max symp error = 6.437e-13, (118.2 sec)\n",
      "  1651 / 2000, K_rot = 233.0, max symp error = 5.927e-13, (118.9 sec)\n",
      "  1661 / 2000, K_rot = 633.1, max symp error = 1.559e-12, (119.6 sec)\n",
      "  1671 / 2000, K_rot = 143.9, max symp error = 6.444e-13, (120.3 sec)\n",
      "  1681 / 2000, K_rot = 292.2, max symp error = 5.467e-13, (121.0 sec)\n",
      "  1691 / 2000, K_rot = 30.5, max symp error = 4.867e-13, (121.8 sec)\n",
      "  1701 / 2000, K_rot = 55.5, max symp error = 9.172e-13, (122.5 sec)\n",
      "  1711 / 2000, K_rot = 41.2, max symp error = 1.004e-13, (123.2 sec)\n",
      "  1721 / 2000, K_rot = 406.7, max symp error = 9.606e-13, (123.9 sec)\n",
      "  1731 / 2000, K_rot = 586.1, max symp error = 2.692e-12, (124.6 sec)\n",
      "  1741 / 2000, K_rot = 499.9, max symp error = 1.966e-12, (125.3 sec)\n",
      "  1751 / 2000, K_rot = 731.2, max symp error = 3.186e-12, (126.0 sec)\n",
      "  1761 / 2000, K_rot = 10.8, max symp error = 1.192e-11, (126.7 sec)\n",
      "  1771 / 2000, K_rot = 722.8, max symp error = 6.450e-13, (127.5 sec)\n",
      "  1781 / 2000, K_rot = 958.6, max symp error = 2.810e-12, (128.2 sec)\n",
      "  1791 / 2000, K_rot = 626.4, max symp error = 9.325e-13, (128.9 sec)\n",
      "  1801 / 2000, K_rot = 71.5, max symp error = 4.262e-13, (129.6 sec)\n",
      "  1811 / 2000, K_rot = 352.1, max symp error = 5.041e-13, (130.4 sec)\n",
      "  1821 / 2000, K_rot = 380.1, max symp error = 1.133e-12, (131.1 sec)\n",
      "  1831 / 2000, K_rot = 818.7, max symp error = 1.577e-12, (131.8 sec)\n",
      "  1841 / 2000, K_rot = 72.0, max symp error = 1.004e-12, (132.5 sec)\n",
      "  1851 / 2000, K_rot = 112.5, max symp error = 4.005e-13, (133.2 sec)\n",
      "  1861 / 2000, K_rot = 548.9, max symp error = 1.236e-12, (133.9 sec)\n",
      "  1871 / 2000, K_rot = 256.5, max symp error = 1.503e-12, (134.6 sec)\n",
      "  1881 / 2000, K_rot = 166.2, max symp error = 4.501e-13, (135.4 sec)\n",
      "  1891 / 2000, K_rot = 67.2, max symp error = 5.416e-13, (136.1 sec)\n",
      "  1901 / 2000, K_rot = 360.0, max symp error = 6.761e-13, (136.8 sec)\n",
      "  1911 / 2000, K_rot = 745.4, max symp error = 1.371e-12, (137.5 sec)\n",
      "  1921 / 2000, K_rot = 595.9, max symp error = 2.397e-12, (138.2 sec)\n",
      "  1931 / 2000, K_rot = 335.7, max symp error = 2.097e-10, (138.9 sec)\n",
      "  1941 / 2000, K_rot = 400.4, max symp error = 3.903e-13, (139.7 sec)\n",
      "  1951 / 2000, K_rot = 141.0, max symp error = 3.830e-13, (140.5 sec)\n",
      "  1961 / 2000, K_rot = 164.7, max symp error = 2.625e-13, (141.2 sec)\n",
      "  1971 / 2000, K_rot = 169.2, max symp error = 5.982e-13, (142.0 sec)\n",
      "  1981 / 2000, K_rot = 264.3, max symp error = 9.873e-13, (142.7 sec)\n",
      "  1991 / 2000, K_rot = 801.4, max symp error = 7.671e-13, (143.4 sec)\n"
     ]
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    # set parameters\n",
    "    n_sample = 2000\n",
    "    dt = 1.0 * FemtoSec\n",
    "    n_step = 2000\n",
    "    n_fft = 2**19\n",
    " \n",
    "    # set reference states\n",
    "    K_rot_ref_list = [50.0, 200.0, 500.0]\n",
    "    L_dir_ref = np.array([1.0, -1.0, -1.0])\n",
    "    mome_ref_list = [2.0 * angular_momentum(k_rot, L_dir_ref)[0] @ get_S(Q_INIT) for k_rot in K_rot_ref_list]\n",
    " \n",
    "    gamma_ref = [1.0 / (2 * 0.2**2)] * 3   # sqrt(1 / 2 gamma) = 0.2 rad for yaw, pitch, roll\n",
    "    gamma_ref_list = np.asarray([gamma_ref] * len(K_rot_ref_list))\n",
    "    fpath_list = [f\"methane_pure_rot_{k_rot:.0f}_n_{n_sample}_spectra.npz\" for k_rot in K_rot_ref_list]\n",
    " \n",
    "    # sample the initial momenta\n",
    "    mome_sample_list, K_rot_list = sample_momenta(n_sample, K_rot_range=(10.0, 1000.0))\n",
    " \n",
    "    run(mome_sample_list, K_rot_list, mome_ref_list, gamma_ref_list, fpath_list, dt, n_step, n_fft)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e161dd3",
   "metadata": {},
   "source": [
    "## Plot results\n",
    "\n",
    "Since methane is a spherical top with the moment of inertia $I$, the rotational levels are given analytically by $E_J = B J(J+1)$ with $B = \\frac{\\hbar^2}{2I}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8ccf762c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rotational constant B = 5.307 cm^-1\n",
      "Analytical rotational energies (cm^-1): [  0.   10.6  31.8  63.7 106.1 159.2 222.9 297.2 382.1 477.6 583.8 700.5\n",
      " 827.9 965.9]\n",
      "Peaks (cm^-1) for K = 50: [ 30.7  63.3 104.7 158.5 220.6 295.4]\n",
      "Peaks (cm^-1) for K = 200: [ 30.5  62.5 104.5 158.  219.8 294.3 382.2 475.6 581.6]\n",
      "Peaks (cm^-1) for K = 500: [104.6 157.1 219.4 293.5 381.6 475.3 580.9 697.9 826.6 965.7]\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",
    "    B = HBar**2 / (2.0 * INERTIA[0]) / CmInv\n",
    "    analytical_energies = np.array([B * J * (J + 1) for J in range(20)])\n",
    "    analytical_energies = analytical_energies[analytical_energies <= 1000]\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[ener_grid <= 1000])\n",
    "        peaks, _ = find_peaks(spectrum, height=0.1, prominence=0.1)\n",
    "        peaks = peaks[ener_grid[peaks] <= 1000]\n",
    "        print(f\"Peaks (cm^-1) for K = {K_rot_ref_list[i]:.0f}: {np.round(ener_grid[peaks], 1)}\")\n",
    " \n",
    "        ax[i].plot(ener_grid, spectrum, label=f\"K = {K_rot_ref_list[i]:.0f}\", color=colors[i])\n",
    "        ax[i].plot(ener_grid[peaks], spectrum[peaks], \"x\", color=\"black\")\n",
    "        ax[i].vlines(analytical_energies, 0.0, 1.2, color=\"gray\", linestyle=\"--\", label=\"analytical\")\n",
    "        ax[i].set_ylim(0, 1.2)\n",
    "        ax[i].legend()\n",
    " \n",
    "    ax[-1].set_xlim(0, 1000)\n",
    "    ax[-1].set_xlabel(\"Energy (cm$^{-1}$)\")\n",
    "    ax[0].set_ylabel(\"Intensity (arb. unit)\")\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0579d41",
   "metadata": {},
   "source": [
    "The computed peak positions for $K = 500$ $\\textrm{cm}^{-1}$ are compared with the analytical eigenenergies\n",
    "$E_J = B J(J+1)$ with $B = 5.307$ $\\textrm{cm}^{-1}$ (all in $\\textrm{cm}^{-1}$).\n",
    "\n",
    "| $J$ | Computed | $B J(J+1)$ | Deviation |\n",
    "|---|---|---|---|\n",
    "| 4 | 104.6 | 106.1 | −1.5 |\n",
    "| 5 | 157.1 | 159.2 | −2.1 |\n",
    "| 6 | 219.4 | 222.9 | −3.5 |\n",
    "| 7 | 293.5 | 297.2 | −3.7 |\n",
    "| 8 | 381.6 | 382.1 | −0.5 |\n",
    "| 9 | 475.3 | 477.6 | −2.3 |\n",
    "| 10 | 580.9 | 583.8 | −2.9 |\n",
    "| 11 | 697.9 | 700.5 | −2.6 |\n",
    "| 12 | 826.6 | 827.9 | −1.3 |\n",
    "| 13 | 965.7 | 965.9 | −0.2 |\n",
    "\n",
    "- **Quantitative agreement**: The computed peaks agree with the analytical eigenenergies with an RMSE of about\n",
    "2.3 $\\textrm{cm}^{-1}$, well below the intrinsic resolution determined by the propagation time.\n",
    "The same peak positions are obtained for all the initial states, up to $J = 13$ (about 970 $\\textrm{cm}^{-1}$) for $K = 500$ $\\textrm{cm}^{-1}$. The rotational spectrum of the nonlinear molecule is thus reproduced by the quaternion-based propagation, even though the trajectories pass through the gimbal lock of the Euler angles.\n",
    "\n",
    "- **Line shape**: As in the case of H2, each peak has an asymmetric line shape with a sharp edge at the eigenenergy\n",
    "  and a tail on the low-energy side, which originates from the time-averaging expression (see Appendix K of the paper).\n",
    "- **Dependence on the initial state**: The intensity distribution follows the rotational kinetic energy of the\n",
    "  initial state: the strongest peaks appear around 105, 158 and 475 $\\textrm{cm}^{-1}$ for the initial states\n",
    "  with $K$ = 50, 200 and 500 $\\textrm{cm}^{-1}$, respectively."
   ]
  }
 ],
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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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   "nbconvert_exporter": "python",
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}