{ "cells": [ { "cell_type": "markdown", "id": "cfb42b0f", "metadata": {}, "source": [ "# 12. Spectra with Custom Initial States\n", "\n", "So far, products of coherent states have been used as the initial states to observe the peaks. In practical spectrum calculations, however, the initial state is not always so simple, and users may want to use their own initial states.\n", "\n", "In the SC-IVR calculation, the propagation of the trajectories and the calculation of the spectrum are independent: the initial state $|\\Psi\\rangle$ enters only through the overlap with the coherent states along the trajectories, $\\langle \\Psi | q_t, p_t \\rangle$. Therefore, by defining the overlap, users can compute the dynamics of various initial states with the same trajectories, prefactors and actions. In a previous study, this property was used to compute accurate IR spectra by the semiclassical propagation of matrix product state (MPS) wave functions [1].\n", "\n", "In this tutorial, the DVR eigenfunctions obtained in the tutorial *Pyramidal Inversion Spectra of Ammonia* are used as the initial states, and we examine whether the corresponding eigenenergies are reproduced.\n", "\n", "**References**\n", "\n", "[1] M. Tsumura and Y. Kurashige, \"On-The-Fly Dynamics of Multiconfigurational Wave Packets by a Semiclassical Method,\" *J. Chem. Theory Comput.* **21**, 11401-11414 (2025)." ] }, { "cell_type": "code", "execution_count": 1, "id": "ddebefb6", "metadata": {}, "outputs": [], "source": [ "# import necessary libraries\n", "\n", "import numpy as np\n", "import jax.numpy as jnp\n", "import matplotlib.pyplot as plt\n", "from scipy.interpolate import CubicSpline\n", "from scipy.optimize import minimize_scalar\n", "import time\n", "\n", "from pyscf import gto, dft\n", "from pyscf.geomopt import berny_solver\n", "\n", "from pyscivr.basis import get_overlap\n", "from pyscivr.coordinates import InternalCoordinates, get_bond_angle, rigid_scan_1d\n", "from pyscivr.integrators import ImplicitVerlet\n", "from pyscivr.potentials import DFTPotential\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\n", "from pyscivr.variations import make_vari_propagator_implicit, propagate_variation_implicit" ] }, { "cell_type": "markdown", "id": "bb5f9ba8", "metadata": {}, "source": [ "## System and coordinates" ] }, { "cell_type": "code", "execution_count": null, "id": "421e8331", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Build complete: 12 coordinates\n", "InternalCoordinates:\n", " 0: translation_x value_ref=0.000000\n", " 1: translation_y value_ref=0.000000\n", " 2: translation_z value_ref=0.000000\n", " 3: rotation_x value_ref=0.000000\n", " 4: rotation_y value_ref=0.000000\n", " 5: rotation_z value_ref=0.000000\n", " 6: bond(0, 1) value_ref=1.013605\n", " 7: bond(0, 2) value_ref=1.013604\n", " 8: bond(0, 3) value_ref=1.013604\n", " 9: oop(0, 1, 2, 3) value_ref=1.946712\n", " 10: angle_diff(0, 1, 2, 3) value_ref=0.000000\n", " 11: angle_diff(0, 2, 3, 1) value_ref=0.000006\n" ] } ], "source": [ "OOP_SCAN = np.array([0.5235987756, 0.5958192964, 0.6680398171, 0.7402603379, 0.8124808587, 0.8847013795,\n", " 0.9569219002, 1.029142421 , 1.1013629418, 1.1735834625, 1.2458039833, 1.3180245041,\n", " 1.3902450249, 1.4624655456, 1.5346860664, 1.6069065872, 1.679127108 , 1.7513476287,\n", " 1.8235681495, 1.8957886703, 1.968009191 , 2.0402297118, 2.1124502326, 2.1846707534,\n", " 2.2568912741, 2.3291117949, 2.4013323157, 2.4735528364, 2.5457733572, 2.617993878 ])\n", "POT_EQ = -1539.7748000136369\n", "POT = np.array([-1533.3679150656, -1535.1978467492, -1536.5575481381, -1537.5803862589, -1538.345944936 , -1538.9100711545,\n", " -1539.3104632371, -1539.5718410517, -1539.7174374798, -1539.772203703 , -1539.762164368 , -1539.71349007 ,\n", " -1539.6510261586, -1539.5961483686, -1539.5645513721, -1539.5645494026, -1539.5961454029, -1539.651020247 ,\n", " -1539.7134757022, -1539.7621470889, -1539.7721886233, -1539.7174254704, -1539.5718420652, -1539.3104803338,\n", " -1538.910099893 , -1538.3459989588, -1537.5804707855, -1536.5576441559, -1535.1979697891, -1533.3680075153])\n", "METRIC = np.array([0.3368193733, 0.3409331328, 0.3454019241, 0.350153029 , 0.3551018741, 0.3601522101,\n", " 0.3651970043, 0.3701202188, 0.3747995901, 0.3791104437, 0.3829304521, 0.3861451042,\n", " 0.3886535057, 0.3903740098, 0.3912491197, 0.3912491197, 0.3903740098, 0.3886535057,\n", " 0.3861451042, 0.3829304521, 0.3791104437, 0.3747995901, 0.3701202188, 0.3651970043,\n", " 0.3601522101, 0.3551018741, 0.350153029 , 0.3454019241, 0.3409331328, 0.3368193733])\n", "\n", "XYZSTR = \"\"\"\n", "N 0.25086005 -0.36549644 0.00000000\n", "H 0.28755613 0.64744429 0.00000000\n", "H 0.75879191 -0.68597392 0.81651207\n", "H 0.75879191 -0.68597392 -0.81651207\n", "\"\"\"\n", "\n", "# out of plane angle function\n", "def oop_func(p):\n", " n = jnp.cross(p[2] - p[1], p[3] - p[1]) # normal vector to the plane defined by H1-H2 and H1-H3\n", " u = p[0] - p[1] # vector from N to H1\n", " x = jnp.dot(n, u) # |n||u|cos(theta)\n", " y = jnp.linalg.norm(jnp.cross(n, u)) # |n||u|sin(theta)\n", " return jnp.arctan2(y, x) # angle between the normal vector and the vector from H1 to N\n", "\n", "# difference of bond angles (1-0-2) - (1-0-3)\n", "def get_angle_diff(p):\n", " return get_bond_angle(jnp.stack([p[1], p[0], p[2]])) - get_bond_angle(jnp.stack([p[1], p[0], p[3]]))\n", "\n", "SYMBOLS, POSI_REF, MASS = get_geom(XYZSTR)\n", "\n", "COORD_ALL = InternalCoordinates(POSI_REF, MASS, move_reference=True)\n", "COORD_ALL.register_kind(\"oop\", oop_func, 4, topology=\"I-\")\n", "COORD_ALL.register_kind(\"angle_diff\", get_angle_diff, 4, topology=\"R\") # this topology is not used in later calculations.\n", "\n", "COORD_ALL.add_translation()\n", "COORD_ALL.add_rotation()\n", "COORD_ALL.add_bond(0, 1)\n", "COORD_ALL.add_bond(0, 2)\n", "COORD_ALL.add_bond(0, 3)\n", "\n", "COORD_ALL.add_local(\"oop\", (0, 1, 2, 3))\n", "COORD_ALL.add_local(\"angle_diff\", (0, 1, 2, 3))\n", "COORD_ALL.add_local(\"angle_diff\", (0, 2, 3, 1))\n", "\n", "COORD_ALL.build()\n", "print(COORD_ALL)\n", "\n", "def make_spline_1d(x, y, bc_type='not-a-knot', period=None) -> callable:\n", " \"\"\"Jax-differentiable cubic spline. Coefficients are computed using scipy.\n", "\n", " x : (n,) ascending array of x values\n", " y : (n,) array of y values\n", " bc_type : boundary condition type, see scipy.interpolate.CubicSpline\n", " period : period of the coordinate (use bc_type=\"periodic\")\n", " \"\"\"\n", "\n", " cs = CubicSpline(x, y, bc_type=bc_type, extrapolate=True)\n", " knots = jnp.asarray(cs.x)\n", " coef = jnp.asarray(cs.c)\n", "\n", " def f(q):\n", " if period is not None:\n", " q = knots[0] + (q - knots[0]) % period\n", " i = jnp.clip(jnp.searchsorted(knots, q) - 1, 0, len(knots) - 2)\n", " t = q - knots[i]\n", " c = coef[:, i]\n", " return ((c[0] * t + c[1]) * t + c[2]) * t + c[3]\n", "\n", " return f\n", "\n", "POT_SPLINE = make_spline_1d(OOP_SCAN, POT)\n", "METRIC_SPLINE = make_spline_1d(OOP_SCAN, METRIC)\n", "POSI_EQ = 1.1949167175700643 # equilibrium value of the oop coordinate\n", "OOP_IDX, _, _, TOPOLOGY = COORD_ALL.find_coordinate(\"oop\", (0, 1, 2, 3))\n", "\n", "ACTIVE_IDX = np.array([OOP_IDX])\n", "TOPOLOGIES = [TOPOLOGY] # I-\n", "POSI_EQ = np.array([POSI_EQ])\n", "ENER_EQ = POT_EQ\n", "\n", "METRIC_FUNC = lambda q: METRIC_SPLINE(q).reshape(1, 1) # must return a 2D array\n", "POTENTIAL_FUNC = lambda q: POT_SPLINE(q)[0] # must return a scalar value\n", "\n", "SKEW = np.block(\n", " [[np.zeros((len(ACTIVE_IDX), len(ACTIVE_IDX))), np.eye(len(ACTIVE_IDX))],\n", " [-np.eye(len(ACTIVE_IDX)), np.zeros((len(ACTIVE_IDX), len(ACTIVE_IDX)))]]\n", ")" ] }, { "cell_type": "markdown", "id": "145d3871", "metadata": {}, "source": [ "## DVR reference\n", "\n", "The reference eigenenergies of the 1D Hamiltonian are obtained by the DVR method using sine bases." ] }, { "cell_type": "code", "execution_count": 3, "id": "838151df", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First 16 DVR eigenenergies (cm^-1): [ 508. 510. 1383. 1460. 2013. 2397. 2924. 3489. 4101. 4752. 5437. 6153. 6898. 7669. 8464. 9282.]\n" ] }, { "data": { 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def dvr_1d_sine(a, b, N, K, cs_g, cs_V):\n", "\n", " L = b - a\n", " chi = a + L * (np.arange(N) + 0.5) / N\n", " w = L / N\n", " n = np.arange(1, K + 1)\n", " arg = np.outer(chi - a, n) * np.pi / L\n", " X = np.sqrt(2 / L) * np.sin(arg) # chi_n(chi_j)\n", " dX = np.sqrt(2 / L) * (n * np.pi / L) * np.cos(arg) # chi_n'(chi_j)\n", "\n", " g = cs_g(chi)\n", " gm14 = g ** -0.25\n", " dgm14 = -0.25 * cs_g(chi, 1) * g ** -1.25\n", "\n", " U = dgm14[:, None] * X + gm14[:, None] * dX # d/dchi [g^{-1/4} chi_n]\n", " T = 0.5 * HBar**2 * w * (U.T @ (g[:, None] ** -0.5 * U))\n", " Vm = w * (X.T @ ((cs_V(chi)[:, None]) * X))\n", " H = T + Vm\n", " H = (H + H.T) / 2\n", " return np.linalg.eigvalsh(H), H\n", "\n", "if __name__ == \"__main__\":\n", " a = OOP_SCAN[0]\n", " b = OOP_SCAN[-1]\n", " N, K = 401, 200\n", " cs_g = CubicSpline(OOP_SCAN, 1.0 / METRIC)\n", " cs_V = CubicSpline(OOP_SCAN, POT - POT_EQ)\n", " E, H = dvr_1d_sine(a, b, N, K, cs_g, cs_V)\n", " _, C = np.linalg.eigh(H) # get eigenvectors of the Hamiltonian\n", "\n", " E_dvr = E / CmInv\n", " print(f\"First 16 DVR eigenenergies (cm^-1): {np.round(E_dvr[:16], 0)}\")\n", "\n", " L = b - a\n", " w = L / N\n", " chi_p = np.linspace(a, b, 1000)\n", " n_b = np.arange(1, K + 1)\n", " X_p = np.sqrt(2 / L) * np.sin(np.outer(chi_p - a, n_b) * np.pi / L) # Sine basis\n", "\n", " for i, n in enumerate(range(10)):\n", " psi_t = X_p @ C[:, n] # amplitude w.r.t. d(phi)\n", " y = psi_t * 150 + E[n] / CmInv # signed amplitude shows the parity\n", " plt.plot(np.degrees(chi_p), y, label=f'$E_{{{n}}}$')\n", " plt.hlines(E[n] / CmInv, np.degrees(a), np.degrees(b), lw=0.5)\n", "\n", " plt.title(\"DVR eigenstates\")\n", " plt.plot(np.degrees(chi_p), (cs_V(chi_p)) / CmInv, ls='dashed', c='gray')\n", " plt.axvline(90, c='gray', lw=0.5)\n", " xticks = np.arange(30, 151, 15)\n", " plt.xticks(xticks, labels=[f'{int(t)}°' for t in xticks], fontsize=12)\n", " plt.xlim(np.degrees(a), np.degrees(b))\n", " plt.ylim(0, 5000)\n", " plt.legend(loc=(1.05, 0), fontsize=12)\n", " plt.xlabel(r'out-of-plane angle $\\chi$ / degree', fontsize=12)\n", " plt.ylabel(r'energy / cm$^{-1}$', fontsize=12)\n", " plt.show()" ] }, { "cell_type": "markdown", "id": "f1fbd444", "metadata": {}, "source": [ "## Overlap with the initial states\n", "\n", "In the SC-IVR calculation, the initial state $|\\Psi\\rangle$ enters only through the overlap with the coherent states along the trajectories, $\\langle \\Psi | q_t, p_t \\rangle$.\n", "\n", "The out-of-plane angle $\\chi$ has the topology `\"I-\"` with the boundaries at $\\chi = 0$ and $\\pi$. In this system, however, the potential diverges toward the boundaries and the trajectories never approach them, so that the boundary conditions can be ignored and a single Gaussian (topology $\\mathbb{R}^1$) is sufficient,\n", "\n", "\\begin{align*}\n", "\\langle \\chi | q, p \\rangle_{\\mathbb{R}^1} = \\left( \\frac{\\gamma}{\\pi} \\right)^{1/4} \\exp \\left[ -\\frac{\\gamma}{2} (\\chi - q)^2 + \\frac{i}{\\hbar} p (\\chi - q) \\right].\n", "\\end{align*}\n", "\n", "If the boundary conditions cannot be ignored, the sum over the images should be taken (see Section II E 2 or Appendix H of the paper).\n", "\n", "Since the coherent state is a Gaussian, its overlap with various basis functions can be computed easily. The DVR eigenstates are expanded in the sine basis on $[a, b] = [\\pi/6, 5\\pi/6]$ with $L = b - a$,\n", "\n", "\\begin{align*}\n", "\\Phi_n(\\chi) = \\sqrt{\\frac{2}{L}} \\sin \\left( k_n (\\chi - a) \\right), \\quad k_n = \\frac{n \\pi}{L}.\n", "\\end{align*}\n", "\n", "Extending the integration range to the whole real line, the overlap is obtained analytically,\n", "\n", "\\begin{align*}\n", "\\langle \\Phi_n | q, p \\rangle = \\sqrt{\\frac{2}{L}} \\left( \\frac{\\gamma}{\\pi} \\right)^{1/4} \\sqrt{\\frac{2\\pi}{\\gamma}} \\frac{1}{2i}\n", "\\left[ e^{i k_n (q - a)} e^{-(p/\\hbar + k_n)^2 / (2\\gamma)} - e^{-i k_n (q - a)} e^{-(p/\\hbar - k_n)^2 / (2\\gamma)} \\right],\n", "\\end{align*}\n", "\n", "and the overlap with the eigenstate $|E_m\\rangle = \\sum_n C_{nm} |\\Phi_n\\rangle$ is $\\langle E_m | q, p \\rangle = \\sum_n C_{nm} \\langle \\Phi_n | q, p \\rangle$.\n", "\n", "Since the sine basis vanishes outside $[a, b]$, the extension of the integration range introduces an error when the coherent state extends beyond the boundaries. We verify the analytical overlap against the numerical integration on a fine grid within $[a, b]$. The width parameter $\\gamma$ can be chosen arbitrarily (it may affect the convergence), and we set $\\gamma = 100$ to make the Gaussian narrow. Note that the same $\\gamma$ must be used in the overlap and in the prefactor." ] }, { "cell_type": "code", "execution_count": 4, "id": "d892998b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "oop (deg) = 30.000, max error = 1.774e-01\n", "oop (deg) = 32.449, max error = 1.137e-01\n", "oop (deg) = 34.898, max error = 6.445e-02\n", "oop (deg) = 37.347, max error = 3.192e-02\n", "oop (deg) = 39.796, max error = 1.367e-02\n", "oop (deg) = 42.245, max error = 5.025e-03\n", "oop (deg) = 44.694, max error = 1.574e-03\n", "oop (deg) = 47.143, max error = 4.188e-04\n", "oop (deg) = 49.592, max error = 9.418e-05\n", "oop (deg) = 52.041, max error = 1.787e-05\n", "oop (deg) = 54.490, max error = 2.852e-06\n", "oop (deg) = 56.939, max error = 3.824e-07\n", "oop (deg) = 59.388, max error = 4.304e-08\n", "oop (deg) = 61.837, max error = 4.059e-09\n", "oop (deg) = 64.286, max error = 3.207e-10\n", "oop (deg) = 66.735, max error = 2.120e-11\n", "oop (deg) = 69.184, max error = 1.173e-12\n", "oop (deg) = 71.633, max error = 5.427e-14\n", "oop (deg) = 74.082, max error = 6.217e-15\n", "oop (deg) = 76.531, max error = 6.106e-15\n", "oop (deg) = 78.980, max error = 7.661e-15\n", "oop (deg) = 81.429, max error = 3.664e-15\n", "oop (deg) = 83.878, max error = 4.829e-15\n", "oop (deg) = 86.327, max error = 7.994e-15\n", "oop (deg) = 88.776, max error = 7.216e-15\n", "oop (deg) = 91.224, max error = 4.552e-15\n", "oop (deg) = 93.673, max error = 7.550e-15\n", "oop (deg) = 96.122, max error = 2.887e-15\n", "oop (deg) = 98.571, max error = 5.440e-15\n", "oop (deg) = 101.020, max error = 5.107e-15\n", "oop (deg) = 103.469, max error = 4.052e-15\n", "oop (deg) = 105.918, max error = 6.106e-15\n", "oop (deg) = 108.367, max error = 5.427e-14\n", "oop (deg) = 110.816, max error = 1.173e-12\n", "oop (deg) = 113.265, max error = 2.120e-11\n", "oop (deg) = 115.714, max error = 3.207e-10\n", "oop (deg) = 118.163, max error = 4.059e-09\n", "oop (deg) = 120.612, max error = 4.304e-08\n", "oop (deg) = 123.061, max error = 3.824e-07\n", "oop (deg) = 125.510, max error = 2.852e-06\n", "oop (deg) = 127.959, max error = 1.787e-05\n", "oop (deg) = 130.408, max error = 9.418e-05\n", "oop (deg) = 132.857, max error = 4.188e-04\n", "oop (deg) = 135.306, max error = 1.574e-03\n", "oop (deg) = 137.755, max error = 5.025e-03\n", "oop (deg) = 140.204, max error = 1.367e-02\n", "oop (deg) = 142.653, max error = 3.192e-02\n", "oop (deg) = 145.102, max error = 6.445e-02\n", "oop (deg) = 147.551, max error = 1.137e-01\n", "oop (deg) = 150.000, max error = 1.774e-01\n" ] } ], "source": [ "def coherent_state(x, q, p, gamma):\n", " return (gamma / np.pi) ** 0.25 * np.exp(-0.5 * gamma * (x - q) ** 2 + 1j * p * (x - q) / HBar)\n", "\n", "def basis_overlap(n, a, L, q, p, gamma):\n", " k = n * np.pi / L\n", " kappa = p / HBar\n", " pref = np.sqrt(2 / L) * (gamma / np.pi) ** 0.25 * np.sqrt(2 * np.pi / gamma) / 2j\n", " return pref * (np.exp(1j * k * (q - a) - (kappa + k) ** 2 / (2 * gamma))\n", " - np.exp(-1j * k * (q - a) - (kappa - k) ** 2 / (2 * gamma)))\n", "\n", "def get_eigen_overlap(posi, mome, gamma, coeff):\n", " \"\"\" along the trajectory; coeff = C[:, m].\"\"\"\n", " S = basis_overlap(n_b, a, L, posi[:, 0][:, None], mome[:, 0][:, None], gamma) # (T, K)\n", " return S @ coeff\n", "\n", "if __name__ == \"__main__\":\n", " # fine grid for Riemann sum\n", " N_fine = 20000\n", " chi_fine = a + L * (np.arange(N_fine) + 0.5) / N_fine\n", " w_fine = L / N_fine\n", " X_fine = np.sqrt(2 / L) * np.sin(np.outer(chi_fine - a, n_b) * np.pi / L) # Sine basis\n", "\n", " gamma = 100.0\n", " q = np.linspace(OOP_SCAN[0], OOP_SCAN[-1], 50)\n", "\n", " S_grid = w_fine * coherent_state(chi_fine[None, :], q[:, None], 0.0, gamma) @ X_fine # (50, K)\n", " S_analytical = basis_overlap(n_b, a, L, q[:, None], 0.0, gamma) # (50, K)\n", "\n", " err = np.max(np.abs(S_grid - S_analytical))\n", " for x, e in zip(q, np.max(np.abs(S_grid - S_analytical), axis=1)):\n", " print(f\"oop (deg) = {x/np.pi * 180:.3f}, max error = {e:.3e}\")" ] }, { "cell_type": "markdown", "id": "06123e95", "metadata": {}, "source": [ "The error is significant only when the center of the coherent state is close to the boundaries, where the Gaussian (width $1/\\sqrt{\\gamma} \\approx 0.1$ rad) extends beyond $[a, b]$. Within 45-135 degrees, the error is smaller than about $10^{-3}$, and it decreases rapidly toward the center (smaller than $10^{-5}$ within 55-125 degrees). In this tutorial, the eigenstates $E_0$ to $E_9$ are used as the initial states, which are localized within 45-135 degrees, and the trajectories also stay within this range." ] }, { "cell_type": "code", "execution_count": 5, "id": "92cf0f29", "metadata": {}, "outputs": [], "source": [ "def run(posi_sample_list, mome_sample_list, gamma,\n", " fpath_list, coeff_list,\n", " dt, n_step, n_fft, symp_err_tol=1e-2):\n", "\n", " assert len(fpath_list) == len(coeff_list[1]), \"fpath_list and coeff_list must have the same length\"\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", " n_sample = len(mome_sample_list)\n", " n_ref = len(fpath_list)\n", " spectra = [0.0] * n_ref\n", " vari_propagator = make_vari_propagator_implicit(METRIC_FUNC, dt,\n", " potential_func=POTENTIAL_FUNC, normalize=False)\n", "\n", " t_start = time.perf_counter()\n", " for i in range(n_sample):\n", " # Get trajectory\n", " traj = ImplicitVerlet(posi_sample_list[i], mome_sample_list[i], dt, METRIC_FUNC,\n", " potential_func=POTENTIAL_FUNC, normalize=False).run(n_step)\n", " posi, mome = traj[\"posi\"], traj[\"mome\"]\n", "\n", " # Get variation\n", " mono_init = np.eye(len(ACTIVE_IDX) * 2)\n", " mono = propagate_variation_implicit(vari_propagator, posi, mome, traj[\"mome_half\"], mono_init)\n", " symplectic_error = np.max(np.abs(mono.transpose(0, 2, 1) @ SKEW @ mono - SKEW), axis=(1, 2))\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\"], ener_ref=ENER_EQ)\n", " action = get_action(lag, dt)\n", " prefactor = get_prefactor(mono, gamma, valid=valid)\n", " overlap_sine = get_eigen_overlap(posi, mome, gamma, coeff_list)\n", "\n", " for j in range(n_ref):\n", " ener_grid, spec = get_ta_spectrum_fft(prefactor, overlap_sine[:, j], action, dt, n_fft, valid=valid)\n", "\n", " spectra[j] += spec\n", "\n", " if i % 10 == 0:\n", " print(f\"{i+1:6d} / {n_sample}, E = {(traj['total_energy'][-1]-ENER_EQ)/CmInv:.1f} cm^-1, \"\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": "28a449ab", "metadata": {}, "source": [ "## Execute calculation\n", "\n", "The total propagation time is 5 ps (10000 steps of 0.5 fs), and 400 trajectories are sampled up to the kinetic energy of 5000 $\\textrm{cm}^{-1}$." ] }, { "cell_type": "code", "execution_count": 6, "id": "d9947949", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1 / 400, E = 0.0 cm^-1, max symp error = 6.883e-15, (0.6 sec)\n", " 11 / 400, E = 3.8 cm^-1, max symp error = 2.143e-14, (2.9 sec)\n", " 21 / 400, E = 13.8 cm^-1, max symp error = 1.354e-14, (5.2 sec)\n", " 31 / 400, E = 30.0 cm^-1, max symp error = 2.087e-14, (7.5 sec)\n", " 41 / 400, E = 52.5 cm^-1, max symp error = 1.121e-14, (9.8 sec)\n", " 51 / 400, E = 81.3 cm^-1, max symp error = 1.088e-14, (12.2 sec)\n", " 61 / 400, E = 116.3 cm^-1, max symp error = 2.109e-14, (14.5 sec)\n", " 71 / 400, E = 157.5 cm^-1, max symp error = 3.397e-14, (16.9 sec)\n", " 81 / 400, E = 205.0 cm^-1, max symp error = 1.910e-14, (19.2 sec)\n", " 91 / 400, E = 258.8 cm^-1, max symp error = 2.798e-14, (21.5 sec)\n", " 101 / 400, E = 318.8 cm^-1, max symp error = 4.952e-14, (23.9 sec)\n", " 111 / 400, E = 385.0 cm^-1, max symp error = 4.463e-14, (26.2 sec)\n", " 121 / 400, E = 457.6 cm^-1, max symp error = 4.285e-14, (28.3 sec)\n", " 131 / 400, E = 536.3 cm^-1, max symp error = 1.006e-13, (30.4 sec)\n", " 141 / 400, E = 621.3 cm^-1, max symp error = 6.817e-14, (32.5 sec)\n", " 151 / 400, E = 712.6 cm^-1, max symp error = 9.326e-14, (34.6 sec)\n", " 161 / 400, E = 810.1 cm^-1, max symp error = 7.694e-14, (37.0 sec)\n", " 171 / 400, E = 913.9 cm^-1, max symp error = 1.019e-13, (39.3 sec)\n", " 181 / 400, E = 1023.8 cm^-1, max symp error = 9.948e-14, (41.3 sec)\n", " 191 / 400, E = 1140.2 cm^-1, max symp error = 1.135e-13, (43.4 sec)\n", " 201 / 400, E = 1262.6 cm^-1, max symp error = 2.673e-13, (45.8 sec)\n", " 211 / 400, E = 1391.3 cm^-1, max symp error = 2.087e-12, (48.0 sec)\n", " 221 / 400, E = 1526.3 cm^-1, max symp error = 4.855e-12, (50.3 sec)\n", " 231 / 400, E = 1667.7 cm^-1, max symp error = 3.485e-11, (52.5 sec)\n", " 241 / 400, E = 1815.1 cm^-1, max symp error = 2.167e-11, (54.7 sec)\n", " 251 / 400, E = 1968.9 cm^-1, max symp error = 1.134e-11, (56.9 sec)\n", " 261 / 400, E = 2128.9 cm^-1, max symp error = 8.898e-12, (59.2 sec)\n", " 271 / 400, E = 2295.1 cm^-1, max symp error = 4.181e-12, (61.4 sec)\n", " 281 / 400, E = 2467.7 cm^-1, max symp error = 2.627e-12, (63.8 sec)\n", " 291 / 400, E = 2646.5 cm^-1, max symp error = 3.324e-12, (66.1 sec)\n", " 301 / 400, E = 2831.4 cm^-1, max symp error = 2.754e-12, (68.4 sec)\n", " 311 / 400, E = 3022.8 cm^-1, max symp error = 3.299e-12, (70.7 sec)\n", " 321 / 400, E = 3220.3 cm^-1, max symp error = 2.363e-12, (73.1 sec)\n", " 331 / 400, E = 3424.1 cm^-1, max symp error = 2.800e-12, (75.5 sec)\n", " 341 / 400, E = 3634.0 cm^-1, max symp error = 1.302e-12, (77.9 sec)\n", " 351 / 400, E = 3850.0 cm^-1, max symp error = 1.178e-12, (80.3 sec)\n", " 361 / 400, E = 4072.9 cm^-1, max symp error = 2.052e-12, (82.7 sec)\n", " 371 / 400, E = 4301.4 cm^-1, max symp error = 8.016e-13, (85.2 sec)\n", " 381 / 400, E = 4536.5 cm^-1, max symp error = 2.247e-12, (87.6 sec)\n", " 391 / 400, E = 4778.0 cm^-1, max symp error = 8.331e-13, (90.0 sec)\n" ] } ], "source": [ "if __name__ == \"__main__\":\n", " N_SAMPLE = 400\n", " K_MAX = 5000.0 # cm^-1\n", "\n", " posi_sample_list = np.repeat([POSI_EQ], N_SAMPLE, axis=0)\n", " mome_max = np.sqrt(2 * K_MAX * CmInv / METRIC_SPLINE(POSI_EQ))\n", " # G p^2/2 = K\n", " mome_sample_list = np.linspace(mome_max / N_SAMPLE, mome_max, N_SAMPLE)[:, None]\n", "\n", " state_list = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n", " gamma = np.array([100.0])\n", " dt = 0.1 * FemtoSec\n", " n_step = 10000\n", " n_fft = 2 ** 19\n", " fpath_list = [f\"ammonia_oop_eigen_{m:.0f}_spectra.npz\" for m in state_list]\n", " coeff_list = C[:, state_list]\n", "\n", " run(posi_sample_list, mome_sample_list, gamma,\n", " fpath_list, coeff_list,\n", " dt, n_step, n_fft)" ] }, { "cell_type": "code", "execution_count": 11, "id": "6150c3f1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Peaks (cm^-1) for m = 0: [524.]\n", "Peaks (cm^-1) for m = 1: [524.]\n", "Peaks (cm^-1) for m = 2: [ 527. 1446.]\n", "Peaks (cm^-1) for m = 3: [1447.]\n", "Peaks (cm^-1) for m = 4: [1541. 1951. 2238.]\n", "Peaks (cm^-1) for m = 5: [2395.]\n", "Peaks (cm^-1) for m = 6: [2910.]\n", "Peaks (cm^-1) for m = 7: [3478.]\n", "Peaks (cm^-1) for m = 8: [4091.]\n", "Peaks (cm^-1) for m = 9: [4745.]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "if __name__ == \"__main__\":\n", " import matplotlib.pyplot as plt\n", " from scipy.signal import find_peaks\n", "\n", " fpath_list = [f\"ammonia_oop_eigen_{m:.0f}_spectra.npz\" for m in state_list]\n", "\n", " fig, ax = plt.subplots(1, 1, figsize=(7, 5), sharex=True)\n", "\n", " dvr_ref = E_dvr[state_list]\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 <= 5000])\n", " peaks, _ = find_peaks(spectrum, height=0.1, prominence=0.1)\n", " peaks = peaks[ener_grid[peaks] <= 5000]\n", " print(f\"Peaks (cm^-1) for m = {state_list[i]:.0f}: {np.round(ener_grid[peaks], 0)}\")\n", " \n", " plt.plot(ener_grid, spectrum, label=f\"m = {state_list[i]:.0f}\",\n", " linewidth= 3 if i % 2 == 0 else 1, alpha= 0.5 if i % 2 == 0 else 1,\n", " linestyle= \"-\" if i % 2 == 0 else \"--\")\n", "\n", " plt.suptitle(\"Spectra of Ammonia OOP\")\n", " plt.xlim(0, 5000)\n", " plt.ylim(0, 1.2)\n", " plt.vlines(dvr_ref, 0, 1.2, color='gray', linestyle=\":\")\n", " plt.xlabel(\"Energy (cm$^{-1}$)\")\n", " plt.ylabel(\"Intensity (arb. unit)\")\n", " plt.legend(loc=(1.05, 0))\n", " plt.tight_layout()\n", " plt.show()" ] }, { "cell_type": "markdown", "id": "7ff42bc1", "metadata": {}, "source": [ "The spectra obtained with the DVR eigenstates $|E_m\\rangle$ as the initial states are compared with the DVR eigenvalues and with the peaks obtained with the coherent states in the tutorial *Pyramidal Inversion Spectra of Ammonia* (all in $\\textrm{cm}^{-1}$). For $1^{+}$ and $2^{+}$, the additional peaks are shown in parentheses.\n", "\n", "| Level | $E$ (DVR) | $E$ (SC-IVR, eigenstate) | $E$ (SC-IVR, coherent state) |\n", "|---|---|---|---|\n", "| $0^{+}$ / $0^{-}$ | 508 / 510 | 524 / 524 | 520 |\n", "| $1^{+}$ / $1^{-}$ | 1383 / 1460 | 1446 (527) / 1447 | 1445 |\n", "| $2^{+}$ / $2^{-}$ | 2013 / 2397 | 1951 (1541, 2238) / 2395 | 1950 / 2396 |\n", "| $3^{+}$ / $3^{-}$ | 2924 / 3489 | 2910 / 3478 | 2912 / 3480 |\n", "| $4^{+}$ / $4^{-}$ | 4101 / 4752 | 4091 / 4745 | 4093 / 4744 |\n", "\n", "- **Peak positions**: The peaks obtained with the eigenstates agree with those obtained with the coherent states within a few $\\textrm{cm}^{-1}$. The peak positions are determined by the semiclassical propagation itself, and the initial state only selects which levels appear and with what intensities.\n", "\n", "- **Levels well above the barrier**: Each eigenstate ($m = 5$ to $9$) gives a single sharp peak at the corresponding level, and the individual levels are extracted without ambiguity in the assignment.\n", "\n", "- **Tunneling doublets**: Both $0^{+}$ and $0^{-}$ give a single peak at the same position, and so do $1^{+}$ and $1^{-}$. Even with the exact eigenstates as the initial states, the semiclassical propagation with classical trajectories does not distinguish the two levels of each doublet.\n", "\n", "- **Levels near the barrier top**: For $1^{+}$, a peak also appears at the ground level (527 $\\textrm{cm}^{-1}$), although the exact eigenstates are orthogonal to each other. For $2^{+}$, which lies just above the barrier top, the main peak is shifted by about $-60$ $\\textrm{cm}^{-1}$ and the intensity leaks to other energies (1541 and 2238 $\\textrm{cm}^{-1}$). The semiclassical approximation breaks down most severely near the barrier top." ] }, { "cell_type": "markdown", "id": "91e1179a", "metadata": {}, "source": [ "In summary, any initial state can be used in SC-IVR by defining the overlap $\\langle \\Psi | q_t, p_t \\rangle$, while the trajectories, prefactors and actions are shared among all the initial states.\n", "\n", "More generally, PySCIVR does not bundle the SC-IVR calculation into a single function by design. The actions, prefactors, overlaps and spectra are computed by separate functions, so that each component can be replaced independently. For example, the prefactor can be computed by other methods: various approximations of the prefactor have been proposed to avoid the instability caused by chaotic trajectories and to reduce the computational cost.[1] Likewise, the trajectories are not tied to the calculation of spectra, and other properties can be computed from the same set of trajectories by combining the components in different ways.\n", "\n", "**References** \n", "\n", "[1] G. Di Liberto and M. Ceotto, “The importance of the pre-exponential factor in semiclassical molecular dynamics,” *J. of Chem Phys* **145** (2016)" ] } ], "metadata": { "kernelspec": { "display_name": "pyscivr (3.13.11)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.11" } }, "nbformat": 4, "nbformat_minor": 5 }