{ "cells": [ { "cell_type": "markdown", "id": "c0110cd5", "metadata": {}, "source": [ "# Introduction to real-time time-dependent Hartree-Fock theory\n", "\n", "This notebook is written for graduate students who already understand the\n", "**two-level system (TLS)** and want to make the conceptual jump to\n", "**real-time mean-field electronic dynamics** in molecules.\n", "\n", "We take $\\rm{H}_2$, the smallest closed-shell molecule, as an example.\n" ] }, { "cell_type": "markdown", "id": "79854e5e", "metadata": {}, "source": [ "## 0. Roadmap: from a two-level system to many-electron mean field\n", "\n", "Recall the canonical TLS:\n", "\n", "$$H_0 = \\tfrac{1}{2}\\,\\omega_0\\,\\sigma_z, \\qquad\n", "\\hat{\\mu} = \\mu_0\\,\\sigma_x, \\qquad\n", "i\\,\\dot{\\rho} = [H_0,\\rho].$$\n", "\n", "A weak delta kick along the dipole, $U_{\\text{kick}} = e^{\\,i\\kappa\\hat\\mu}$,\n", "prepares a small coherence between the two eigenstates. The induced dipole\n", "then oscillates,\n", "\n", "$$\\Delta\\mu(t) \\propto \\sin(\\omega_0\\, t),$$\n", "\n", "and its FFT yields a single peak at $\\omega = \\omega_0$.\n", "\n", "Real-time time-dependent Hartree–Fock (RT-TDHF) applies the same idea to a\n", "many-electron system.\n", "\n", "Below is the comparison between TLS dynamics and RT-TDHF:\n", "\n", "| concept | TLS | RT-TDHF |\n", "|------------------------|----------------------------------|---------------------------------------------------------------|\n", "| state | $\\rho$ ($2\\times 2$) | density matrix $P$ in the AO basis ($N\\times N$) |\n", "| Hamiltonian | $H_0$ (constant) | Fock $F[P] = H_{\\text{core}}+J[P]-\\tfrac12 K[P]$ (depends on $P$!) |\n", "| equation of motion | $i\\dot\\rho=[H_0,\\rho]$ | $i\\dot P=[F[P],P]$ (Liouville–von Neumann, **nonlinear**) |\n", "| dipole operator | $\\mu_0\\sigma_x$ | AO matrix $\\boldsymbol\\mu = -\\mathbf r$ (electronic) + nuclei |\n", "| eigenbasis | $\\sigma_z$ basis | orthogonal AO basis using $X = S^{-1/2}$ transform |\n", "| linear-response peaks | one, at $\\omega_0$ | many, such as bonding→antibonding ($\\sigma\\to\\sigma^*$). |\n", "\n", "The *only* non-trivial twist is the second row: in mean-field electronic\n", "theory, the effective Hamiltonian $F[P]$ depends on the state $P$ itself.\n", "In Hartree-Fock theory,\n", "as electrons feel the average potential of all other electrons, the Hamiltonian\n", "becomes **nonlinear**, which makes it difficult to maintain the stability of\n", "numerical propagation as a function of time. \n" ] }, { "cell_type": "markdown", "id": "7cdbcc0e", "metadata": {}, "source": [ "## 1. Recall the TLS dynamics\n", "\n", "Before moving to $\\rm{H}_2$, let us run the time-resolved dynamics for a single TLS.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "22113e70", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.linalg import expm\n", "import matplotlib.pyplot as plt\n", "\n", "omega0 = 0.5 # TLS gap (a.u.)\n", "mu0 = 1.0 # transition dipole (a.u.)\n", "kappa_tls = 1.0e-3 # weak kick\n", "dt_tls = 0.05\n", "nstep_tls = 4000\n", "\n", "# 1. Hamiltonian and dipole operator\n", "H0 = 0.5 * omega0 * np.array([[ 1, 0], [ 0,-1]], dtype=complex) # sigma_z\n", "mu_op = mu0 * np.array([[ 0, 1], [ 1, 0]], dtype=complex) # sigma_x\n", "\n", "# 2. Ground state density: |1><1| (lower eigenstate of sigma_z)\n", "rho = np.array([[0, 0], [0, 1]], dtype=complex)\n", "\n", "# 3. Delta kick: rho -> exp(+i kappa mu) rho exp(-i kappa mu)\n", "U_kick = expm(1j * kappa_tls * mu_op)\n", "rho = U_kick @ rho @ U_kick.conj().T\n", "\n", "# 4. Field-free unitary propagation: rho -> exp(-i H0 dt) rho exp(+i H0 dt)\n", "U_dt = expm(-1j * dt_tls * H0)\n", "times_tls, dip_tls = [0.0], [np.trace(mu_op @ rho).real]\n", "for n in range(1, nstep_tls + 1):\n", " rho = U_dt @ rho @ U_dt.conj().T\n", " times_tls.append(n * dt_tls)\n", " dip_tls.append(np.trace(mu_op @ rho).real)\n", "times_tls = np.array(times_tls)\n", "dip_tls = np.array(dip_tls) - dip_tls[0]\n", "\n", "# 5. FFT of the induced dipole\n", "sig_tls = dip_tls * np.exp(-1e-3 * times_tls)\n", "fft_tls = np.fft.rfft(sig_tls)\n", "omega_tls = 2.0 * np.pi * np.fft.rfftfreq(sig_tls.size, d=dt_tls)\n", "spec_tls = -omega_tls * fft_tls.imag\n", "spec_tls = np.clip(spec_tls / (np.abs(spec_tls).max() + 1e-30), 0.0, None)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(10, 3.4))\n", "ax[0].plot(times_tls, dip_tls, lw=1)\n", "ax[0].set(xlabel=\"time (a.u.)\", ylabel=r\"$\\Delta\\mu(t)$\",\n", " title=fr\"TLS dipole oscillates at $\\omega_0={omega0}$ a.u.\")\n", "ax[1].plot(omega_tls, spec_tls, lw=1.5)\n", "ax[1].axvline(omega0, color=\"k\", ls=\"--\", lw=0.8, label=r\"$\\omega_0$\")\n", "ax[1].set(xlim=(0, 2), xlabel=r\"$\\omega$ (a.u.)\", ylabel=\"spectrum\",\n", " title=\"FFT: a single peak at the gap\"); ax[1].legend()\n", "plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "61be0d33", "metadata": {}, "source": [ "## 2. The same procedure for $\\rm{H}_2$\n", "\n", "Below are the equations we will implement. Compare each line with the TLS\n", "dynamics just above.\n", "\n", "**Closed-shell Fock matrix** (the analog of $H_0$, but state-dependent):\n", "\n", "$$F[P] = H_{\\text{core}} + J[P] - \\tfrac12 K[P], \\qquad\n", "J_{\\mu\\nu}=\\sum_{\\rho\\sigma}(\\mu\\nu|\\rho\\sigma)P_{\\rho\\sigma}, \\quad\n", "K_{\\mu\\nu}=\\sum_{\\rho\\sigma}(\\mu\\rho|\\nu\\sigma)P_{\\rho\\sigma}.$$\n", "\n", "**Symmetric orthogonalization** (going to a clean \"basis\", because\n", "atomic orbitals, or AOs, are not orthogonal):\n", "\n", "$$X = S^{-1/2}, \\qquad U = S^{1/2}, \\qquad\n", "P_{\\text{orth}}=U\\,P\\,U^\\top, \\qquad\n", "F_{\\text{orth}}=X^\\top F X.$$\n", "\n", "**Delta kick** (identical operator structure as in the TLS):\n", "\n", "$$P_{\\text{orth}}(0^+) = e^{\\,i\\kappa\\,\\mu_{z,\\text{orth}}}\\,\n", "P_{\\text{orth}}(0^-)\\, e^{-i\\kappa\\,\\mu_{z,\\text{orth}}}.$$\n", "\n", "**Unitary propagation in the orthogonal basis** (TLS analog: $e^{-iH_0\\Delta t}$):\n", "\n", "$$P(t+\\Delta t)\\approx\n", "e^{-i\\Delta t\\, F[P(t)]}\\,P(t)\\,e^{+i\\Delta t\\, F[P(t)]}.$$\n", "\n", "**Spectrum** (identical formula to the TLS):\n", "\n", "$$\\alpha_{zz}(\\omega)\\approx \\frac{\\Delta t}{\\kappa}\\,\n", "\\text{FFT}\\!\\big[\\Delta\\mu_z(t)\\,e^{-\\eta t}\\big], \\qquad\n", "S(\\omega)\\propto\\omega\\,\\text{Im}\\,\\alpha_{zz}(\\omega).$$\n", "\n", "The single new ingredient compared to the TLS is that **$F$ is rebuilt\n", "from $P$ at every step**.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "53b51e37", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import psi4\n", "import matplotlib.pyplot as plt\n", "from scipy.linalg import expm, fractional_matrix_power\n", "\n", "# Unit conversions\n", "au_to_fs = 0.024188843265857\n", "hartree_to_ev = 27.211386245988\n", "\n", "# Simulation parameters\n", "R_angstrom = 0.74 # H-H bond length\n", "dt = 0.04 # time step in atomic units\n", "nsteps = 1200 # total number of propagation steps\n", "kappa = 1.0e-3 # delta-kick strength (a.u.)\n", "eta = 1.0e-3 # optional exponential damping for FFT (a.u.^-1)\n", "\n", "# Make plots a bit larger\n", "plt.rcParams[\"figure.figsize\"] = (7, 4)\n", "plt.rcParams[\"font.size\"] = 12" ] }, { "cell_type": "markdown", "id": "67feec60", "metadata": {}, "source": [ "## 3. Step 1 - Ground state: solve RHF to get $P_0$\n", "\n", "In the TLS we picked the ground state $|1\\rangle\\langle 1|$ by hand. For\n", "a real molecule we have to *solve* the static problem first: a\n", "self-consistent diagonalization of $F[P]$, i.e. ordinary RHF.\n", "\n", "We place $\\rm{H}_2$ along the $z$ axis with the bond midpoint at the origin so\n", "that the permanent dipole is zero by symmetry.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "a3e6e66a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Memory set to 953.674 MiB by Python driver.\n", " Threads set to 1 by Python driver.\n", "Ground-state RHF energy = -1.128700093561 Eh\n" ] } ], "source": [ "psi4.core.clean()\n", "psi4.set_memory(\"1 GB\")\n", "psi4.core.set_num_threads(1)\n", "psi4.core.set_output_file(\"psi4_h2_rt_tdhf.out\", False)\n", "\n", "mol = psi4.geometry(f'''\n", "units angstrom\n", "nocom\n", "noreorient\n", "symmetry c1\n", "0 1\n", "H 0.0 0.0 {-R_angstrom/2.0}\n", "H 0.0 0.0 {+R_angstrom/2.0}\n", "''')\n", "\n", "psi4.set_options({\n", " \"basis\": \"cc-pvdz\",\n", " \"reference\": \"rhf\",\n", " \"scf_type\": \"pk\",\n", " \"e_convergence\": 1e-12,\n", " \"d_convergence\": 1e-12,\n", "})\n", "\n", "E_scf, wfn = psi4.energy(\"scf\", return_wfn=True)\n", "print(f\"Ground-state RHF energy = {E_scf:.12f} Eh\")" ] }, { "cell_type": "markdown", "id": "c914ce3c", "metadata": {}, "source": [ "## 4. Step 2 - Build $F$, $\\boldsymbol\\mu$, and the orthogonalizer\n", "\n", "The \"Hamiltonian\" of an electronic problem in a finite AO basis is the\n", "Fock matrix $F[P]$. Building it requires:\n", "\n", "- the **overlap** $S$ (because AOs are not orthogonal),\n", "- the **core Hamiltonian** $H_{\\text{core}}$ (kinetic + electron–nucleus),\n", "- the **two-electron integrals** $(\\mu\\nu|\\rho\\sigma)$, from which $J[P]$\n", " and $K[P]$ are contracted at every step,\n", "- the **dipole integrals**, which become the AO matrix of $\\hat\\mu$.\n", "\n", "We then build $X=S^{-1/2}$ once. Multiplying by $X$ on both sides plays\n", "the same role as moving a TLS Hamiltonian into the basis where $\\sigma_z$\n", "is diagonal: in that basis the propagator has the simple form\n", "$P\\to e^{-iF\\Delta t}\\,P\\,e^{+iF\\Delta t}$.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "2dbfe493", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of AO functions = 10\n", "Ground-state total dipole (a.u.) = 3.497202527569243e-15\n" ] } ], "source": [ "mints = psi4.core.MintsHelper(wfn.basisset())\n", "\n", "S = np.asarray(wfn.S())\n", "Hcore = np.asarray(wfn.H())\n", "ERI = np.asarray(mints.ao_eri())\n", "\n", "# Psi4 returns position integrals .\n", "# The electronic dipole operator is -r, so we add the minus sign here.\n", "x_ao, y_ao, z_ao = [np.asarray(m) for m in mints.ao_dipole()]\n", "mu_x_ao = -x_ao\n", "mu_y_ao = -y_ao\n", "mu_z_ao = -z_ao\n", "\n", "# Closed-shell total density P = 2 * D_alpha (density matrix of the alpha electron)\n", "P0 = 2.0 * np.asarray(wfn.Da())\n", "\n", "# Symmetric orthogonalization matrices\n", "X = fractional_matrix_power(S, -0.5)\n", "U = fractional_matrix_power(S, 0.5)\n", "\n", "# Nuclear dipole (in a.u.); for midpoint-centered H2 this is zero\n", "R_bohr = np.array([[mol.x(A), mol.y(A), mol.z(A)] for A in range(mol.natom())])\n", "Z = np.array([mol.Z(A) for A in range(mol.natom())])\n", "mu_nuc = (Z[:, None] * R_bohr).sum(axis=0)\n", "\n", "print(\"Number of AO functions =\", S.shape[0])\n", "print(\"Ground-state total dipole (a.u.) =\", np.trace(P0 @ mu_z_ao).real + mu_nuc[2])" ] }, { "cell_type": "markdown", "id": "3a2d3e8f", "metadata": {}, "source": [ "### Inspect the orbital structure: the closest analog of $\\omega_0$\n", "\n", "The bare HOMO–LUMO gap is the simplest analog of the TLS gap $\\omega_0$.\n", "But the actual RT-TDHF (and LR-TDHF) excitation energy is shifted from\n", "this gap by the electron–electron interaction in $J[P]-\\tfrac12K[P]$.\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "0cc82b74", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "All MO energies (Eh):\n", " MO 0 HOMO e = -0.59241 Eh\n", " MO 1 LUMO e = 0.19744 Eh\n", " MO 2 e = 0.47932 Eh\n", " MO 3 e = 0.93732 Eh\n", " MO 4 e = 1.29290 Eh\n", " MO 5 e = 1.29290 Eh\n", " MO 6 e = 1.95702 Eh\n", " MO 7 e = 2.04352 Eh\n", " MO 8 e = 2.04352 Eh\n", " MO 9 e = 3.61047 Eh\n", "\n", "HOMO–LUMO gap = 0.7899 Eh = 21.493 eV\n", "\n", "We will see below that the lowest RT-TDHF / LR-TDHF peak is *not*\n", "at this bare gap. Instead, it is shifted by electron-electron interactions,\n", "which is precisely the nonlinear part of F[P].\n" ] } ], "source": [ "eps = np.asarray(wfn.epsilon_a())\n", "nocc = wfn.nalpha() # number of doubly-occupied MOs (= 1 for H2)\n", "\n", "print(f\"All MO energies (Eh):\")\n", "for i, e in enumerate(eps):\n", " label = \"HOMO\" if i == nocc - 1 else \"LUMO\" if i == nocc else \" \"\n", " print(f\" MO {i:2d} {label} e = {e: .5f} Eh\")\n", "\n", "gap = eps[nocc] - eps[nocc - 1]\n", "print(f\"\\nHOMO–LUMO gap = {gap:.4f} Eh = {gap*hartree_to_ev:.3f} eV\")\n", "print(\"\\nWe will see below that the lowest RT-TDHF / LR-TDHF peak is *not*\")\n", "print(\"at this bare gap. Instead, it is shifted by electron-electron interactions,\")\n", "print(\"which is precisely the nonlinear part of F[P].\")\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "515a5584", "metadata": {}, "outputs": [], "source": [ "def build_fock(P):\n", " \"\"\"Closed-shell RHF Fock matrix built from the total AO density P.\"\"\"\n", " J = np.einsum(\"pqrs,rs->pq\", ERI, P, optimize=True)\n", " K = np.einsum(\"prqs,rs->pq\", ERI, P, optimize=True)\n", " F = Hcore + J - 0.5 * K\n", " return 0.5 * (F + F.conj().T)\n", "\n", "\n", "def ao_to_orth_density(P):\n", " return U @ P @ U.conj().T\n", "\n", "\n", "def orth_to_ao_density(P_orth):\n", " return X @ P_orth @ X.conj().T\n", "\n", "\n", "def ao_to_orth_operator(A):\n", " return X.conj().T @ A @ X\n", "\n", "\n", "def dipole_z(P):\n", " \"\"\"Total molecular dipole along z (electrons + nuclei).\"\"\"\n", " return np.trace(P @ mu_z_ao).real + mu_nuc[2]\n", "\n", "\n", "def rhf_energy(P, F):\n", " \"\"\"Closed-shell RHF total energy from the total density P.\"\"\"\n", " return 0.5 * np.trace(P @ (Hcore + F)).real + mol.nuclear_repulsion_energy()" ] }, { "cell_type": "markdown", "id": "47d6fcc7", "metadata": {}, "source": [ "## 5. Step 3 - Kick the molecule (same operator as in the TLS)\n", "\n", "In the TLS we applied $e^{i\\kappa\\sigma_x}$ to the ground state. Here we\n", "apply $e^{i\\kappa\\hat\\mu_z}$ to the orthogonalized density, which\n", "generates a small coherence between every occupied MO and every virtual\n", "MO with non-zero $z$-dipole matrix element to it (in $\\rm{H}_2$, the dominant\n", "channel is $\\sigma_g \\to \\sigma_u^*$).\n", "\n", "Because $\\kappa$ is small, we stay in the linear-response regime: the Fourier\n", "transform of $\\Delta\\mu_z(t)$ samples the linear-response polarizability\n", "$\\alpha_{zz}(\\omega)$. \n" ] }, { "cell_type": "code", "execution_count": 7, "id": "953695dc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Induced dipole immediately after the kick = 3.941292e-15 a.u.\n" ] } ], "source": [ "P0_orth = ao_to_orth_density(P0)\n", "mu_z_orth = ao_to_orth_operator(mu_z_ao)\n", "\n", "U_kick = expm(1j * kappa * mu_z_orth)\n", "P_kicked_orth = U_kick @ P0_orth @ U_kick.conj().T\n", "P_kicked = orth_to_ao_density(P_kicked_orth)\n", "P_kicked = 0.5 * (P_kicked + P_kicked.conj().T)\n", "\n", "print(f\"Induced dipole immediately after the kick = {dipole_z(P_kicked): .6e} a.u.\")" ] }, { "cell_type": "markdown", "id": "e3282d96", "metadata": {}, "source": [ "## 6. Step 4 - Real-time propagation\n", "\n", "We use the simplest possible scheme: at each step, build $F$ from the\n", "current $P$, then take a unitary step\n", "\n", "$$P(t+\\Delta t) = e^{-i\\Delta t\\, F[P(t)]}\\,P(t)\\,e^{+i\\Delta t\\, F[P(t)]}.$$\n", "\n", "This is **first-order accurate** because $F$ is evaluated at the start of\n", "the step. In other words, the energy drift \n", "following this unitary propagation scheme scales in the order of $\\Delta t$.\n", "\n", "For improving the energy conservation, a midpoint or modified-midpoint scheme (the \"MMUT\" propagator\n", "used in production codes) can be applied, but this is outside the scope of this tutorial.\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "1a5ab5f4", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.linalg import expm\n", "\n", "def propagate_naive_unitary(P_start_orth, dt, nsteps):\n", " \"\"\"Naive first-order RT-TDHF propagation in the orthonormal basis.\n", "\n", " Propagation rule:\n", " F_n = F[P_n]\n", " U_n = exp(-i dt F_n)\n", " P_{n+1} = U_n P_n U_n^dagger\n", "\n", " This is simpler than MMUT because it does not use a midpoint density or\n", " half-step bootstrap. It is unitary, but only first-order accurate in time\n", " for nonlinear TDHF.\n", " \"\"\"\n", "\n", " # Initial density\n", " P_orth = P_start_orth.copy()\n", " P_orth = 0.5 * (P_orth + P_orth.conj().T)\n", "\n", " # Initial AO density and observables\n", " P_ao = orth_to_ao_density(P_orth)\n", " P_ao = 0.5 * (P_ao + P_ao.conj().T)\n", "\n", " F_ao = build_fock(P_ao)\n", " F_ao = 0.5 * (F_ao + F_ao.conj().T)\n", "\n", " times = [0.0]\n", " dipoles = [dipole_z(P_ao)]\n", " energies = [rhf_energy(P_ao, F_ao)]\n", "\n", " for step in range(1, nsteps + 1):\n", " # Fock from the density at the beginning of the step\n", " P_ao = orth_to_ao_density(P_orth)\n", " P_ao = 0.5 * (P_ao + P_ao.conj().T)\n", "\n", " F_ao = build_fock(P_ao)\n", " F_ao = 0.5 * (F_ao + F_ao.conj().T)\n", "\n", " F_orth = ao_to_orth_operator(F_ao)\n", " F_orth = 0.5 * (F_orth + F_orth.conj().T)\n", "\n", " # Naive full-step unitary propagation\n", " U_step = expm(-1j * dt * F_orth)\n", " P_orth = U_step @ P_orth @ U_step.conj().T\n", " P_orth = 0.5 * (P_orth + P_orth.conj().T)\n", "\n", " # Back to AO basis for analysis\n", " P_ao = orth_to_ao_density(P_orth)\n", " P_ao = 0.5 * (P_ao + P_ao.conj().T)\n", "\n", " F_ao = build_fock(P_ao)\n", " F_ao = 0.5 * (F_ao + F_ao.conj().T)\n", "\n", " times.append(step * dt)\n", " dipoles.append(dipole_z(P_ao))\n", " energies.append(rhf_energy(P_ao, F_ao))\n", "\n", " return np.array(times), np.array(dipoles), np.array(energies)" ] }, { "cell_type": "code", "execution_count": 9, "id": "1ac0ef94", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total propagation time = 1.161 fs\n", "Max energy drift = 3.190e-07 Eh\n" ] } ], "source": [ "times_au, dipoles_z, energies = propagate_naive_unitary(P_kicked_orth, dt, nsteps)\n", "times_fs = times_au * au_to_fs\n", "\n", "print(f\"Total propagation time = {times_fs[-1]:.3f} fs\")\n", "print(f\"Max energy drift = {np.max(np.abs(energies - energies[0])):.3e} Eh\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "c8e9ab30", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "delta_mu = dipoles_z - dipoles_z[0]\n", "\n", "plt.plot(times_fs, delta_mu, lw=1.0)\n", "plt.xlabel(\"Time (fs)\")\n", "plt.ylabel(r\"$\\Delta \\mu_z(t)$ (a.u.)\")\n", "plt.title(\"Induced dipole after a delta kick\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d1b01653", "metadata": {}, "source": [ "Here, just like the TLS dynamics, $\\Delta\\mu_z(t)$ is a\n", "small oscillation around zero. However, unlike the TLS, it is **not** a single\n", "sinusoid: it is a sum of contributions from every dipole-allowed\n", "excitation that the kick excited.\n" ] }, { "cell_type": "markdown", "id": "ef655e71", "metadata": {}, "source": [ "## 7. Step 5 - Spectrum from the dipole trajectory\n", "\n", "The FFT step is identical to the TLS procedure. The damping factor\n", "$e^{-\\eta t}$ below broadens the discrete peaks into Lorentzians.\n", "\n", "The absorption-like spectrum is\n", "\n", "$$\\alpha_{zz}(\\omega) \\approx \\frac{\\Delta t}{\\kappa}\\,\n", "\\text{FFT}\\!\\big[\\Delta\\mu_z(t)\\,e^{-\\eta t}\\big], \\qquad\n", "S(\\omega)\\propto \\omega\\,\\text{Im}\\,\\alpha_{zz}(\\omega).$$\n", "\n", "The factor of $\\omega$ is the standard convention that turns the\n", "polarizability into an oscillator-strength-like quantity.\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "2f0199a5", "metadata": {}, "outputs": [], "source": [ "signal = delta_mu * np.exp(-eta * times_au)\n", "\n", "fft_vals = np.fft.rfft(signal)\n", "omega_au = 2.0 * np.pi * np.fft.rfftfreq(signal.size, d=dt)\n", "energy_ev = omega_au * hartree_to_ev\n", "\n", "# A simple absorption-like spectrum from the NumPy FFT.\n", "alpha_w = (dt / kappa) * fft_vals\n", "spectrum = omega_au * (-alpha_w.imag)\n", "\n", "# Clean up the zero-frequency point and any tiny negative noise\n", "spectrum[0] = 0.0\n", "spectrum = np.clip(spectrum, 0.0, None)\n", "\n", "# Normalize for plotting\n", "if spectrum.max() > 0:\n", " spectrum = spectrum / spectrum.max()" ] }, { "cell_type": "code", "execution_count": 12, "id": "72850316", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(energy_ev, spectrum, lw=1.5)\n", "plt.xlim(0, 50)\n", "plt.xlabel(\"Energy (eV)\")\n", "plt.ylabel(\"Normalized intensity\")\n", "plt.title(\"RT-TDHF spectrum of H$_2$ from a NumPy FFT\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "06acd54b", "metadata": {}, "source": [ "## 8. Cross-check: linear response TDHF (LR-TDHF)\n", "\n", "LR-TDHF solves an eigenvalue problem for the linear response of the same\n", "Fock operator. In the **weak-kick limit**, RT-TDHF and LR-TDHF must\n", "predict the same excitation energies and oscillator strengths. The peak\n", "positions in our spectrum should line up with the LR-TDHF stick spectrum.\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "f378aca2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "LR-TDHF excitation energy (eV): [13.91137134 21.31926952 32.05653779]\n", "LR-TDHF oscillator strength: [0.53262017 0. 0.13572863]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from psi4.driver.procrouting.response.scf_response import tdscf_excitations\n", "\n", "psi4.set_options({\n", " \"basis\": \"cc-pvdz\",\n", " \"reference\": \"rhf\",\n", " \"scf_type\": \"pk\",\n", " \"save_jk\": True,\n", "})\n", "\n", "E_lr, wfn_lr = psi4.energy(\"scf\", return_wfn=True, molecule=mol)\n", "lr_res = tdscf_excitations(wfn_lr, states=3, tda=False)\n", "\n", "exc_ev = np.array([r[\"EXCITATION ENERGY\"] for r in lr_res]) * hartree_to_ev\n", "osc = np.array([r[\"OSCILLATOR STRENGTH (LEN)\"] for r in lr_res])\n", "\n", "print(\"LR-TDHF excitation energy (eV):\", exc_ev)\n", "print(\"LR-TDHF oscillator strength:\", osc)\n", "\n", "plt.plot(energy_ev, spectrum, label=\"RT-TDHF (FFT)\")\n", "plt.vlines(exc_ev, 0, osc/np.max(osc), linestyles=\"dashed\", linewidth=1.0, label=\"LR-TDHF stick\")\n", "plt.xlim(0, 50)\n", "plt.xlabel(\"Energy (eV)\")\n", "plt.ylabel(\"Normalized intensity\")\n", "plt.title(\"H$_2$ spectrum: RT-TDHF vs Psi4 LR-TDHF\")\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "953d0bd3", "metadata": {}, "source": [ "## 9. Padé FFT in MaxwellLink: a shorter trajectory suffices\n", "\n", "A plain FFT needs a long trajectory to resolve sharp peaks: the spectral\n", "resolution is $\\Delta\\omega \\sim 2\\pi / T_{\\text{total}}$. The Padé\n", "approximant rewrites the FFT as a rational function and converges much\n", "faster, so you can extract clean peaks from a *shorter* trajectory at\n", "the cost of slightly biased line shapes. This Padé function is shipped within \n", "MaxwellLink.\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "27b73ab0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from maxwelllink.tools import rt_tddft_spectrum\n", "\n", "# call Pade approximation FFT spectrum function\n", "freq_ev, sp_tot, t_fs, mu = rt_tddft_spectrum(delta_mu, dt, e_cutoff_ev=50)\n", "\n", "plt.plot(freq_ev, sp_tot, label=\"RT-TDHF (FFT)\")\n", "plt.vlines(exc_ev, 0, osc/np.max(osc), linestyles=\"dashed\", linewidth=1.0, label=\"LR-TDHF stick\")\n", "plt.xlim(0, 50)\n", "plt.xlabel(\"Energy (eV)\")\n", "plt.ylabel(\"Normalized intensity\")\n", "plt.title(\"H$_2$ spectrum: RT-TDHF vs Psi4 LR-TDHF\")\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "mxl-install", "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 }