{ "cells": [ { "cell_type": "markdown", "id": "a27d63fc-7bef-48af-ad11-1cb14fb6b4ec", "metadata": {}, "source": [ "# Observing Marcus Inverted Region" ] }, { "cell_type": "markdown", "id": "196a8dc4-7e25-4cd2-8472-8ced3d2e46d3", "metadata": {}, "source": [ "## Overview\n", "\n", "In this notebook we will simulate the charge transfer between two molecules using the Marcus model\n", "\n", "$$\n", " \\hat H = -V(a^\\dagger_0 a_1 + a^\\dagger_1 a_0) + \\Delta G a^\\dagger_1 a_1 + \\omega \\sum_{i=0, 1} b^\\dagger_i b_i + g \\omega \\sum_{i=0, 1} a^\\dagger_i a_i (b^\\dagger_i + b_i)\n", "$$\n", "\n", "with transfer integral $V=-0.1$, dimensionless coupling constant $g=1$, vibration frequency $\\omega=0.5$.\n", "We will show that, by decreasing the reaction Gibbs free energy change $\\Delta G$, the reaction rate will first increase and then decrease, as predicted by the Marcus theory." ] }, { "cell_type": "markdown", "id": "43e4b11c-f5ec-4e65-8838-ef91e87e11ee", "metadata": {}, "source": [ "## Define the Hamiltonian and initial state" ] }, { "cell_type": "code", "execution_count": 1, "id": "f0e54566-edab-423e-81d6-e9d9365e331c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "jax_backend" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "\n", "from tencirchem import Op, BasisMultiElectron, BasisSHO, TimeEvolution, set_backend\n", "\n", "set_backend(\"jax\")" ] }, { "cell_type": "code", "execution_count": 2, "id": "35139f14-b5f6-4720-96b2-100c57106271", "metadata": {}, "outputs": [], "source": [ "v = -0.1\n", "g = 1\n", "omega = 0.5\n", "nbas = 8" ] }, { "cell_type": "code", "execution_count": 3, "id": "8dadf496-f732-4442-9c4e-71417950924f", "metadata": {}, "outputs": [], "source": [ "def get_hamiltonian(delta_g):\n", " ham_terms = v * Op(r\"a^\\dagger a\", [\"e0\", \"e1\"]) + v * Op(r\"a^\\dagger a\", [\"e1\", \"e0\"])\n", " ham_terms += delta_g * Op(r\"a^\\dagger a\", \"e1\")\n", " for i in range(2):\n", " ham_terms += omega * Op(r\"b^\\dagger b\", f\"v{i}\")\n", " ham_terms += g * omega * Op(r\"a^\\dagger a\", f\"e{i}\") * Op(r\"b^\\dagger+b\", f\"v{i}\")\n", " basis = [BasisMultiElectron([\"e0\", \"e1\"], [0, 0]), BasisSHO(\"v0\", omega, nbas), BasisSHO(\"v1\", omega, nbas)]\n", " return ham_terms, basis" ] }, { "cell_type": "code", "execution_count": 4, "id": "c847063d-c59e-4e71-931e-a69064a61a24", "metadata": {}, "outputs": [], "source": [ "# using a relaxed initial state\n", "def get_init_condition():\n", " basis = BasisSHO(0, omega, nbas)\n", " state = np.linalg.eigh(basis.op_mat(r\"b^\\dagger b\") + g * basis.op_mat(r\"b^\\dagger+b\"))[1][:, 0]\n", " return {\"v0\": state}" ] }, { "cell_type": "markdown", "id": "5e306a49-9390-4770-ba9e-bbb749b312ca", "metadata": {}, "source": [ "## Run simulation\n", "Next, we run the simulation using the `TimeEvolution` class with the custom initial state. \n", "The execution may take 10-20 minutes since it's a 7-qubit system and 5 trajectories are generated." ] }, { "cell_type": "code", "execution_count": 5, "id": "b9dbd075-9597-4ee1-90be-a73059bdb4e8", "metadata": {}, "outputs": [], "source": [ "n_list = []\n", "delta_g_list = np.linspace(0, -2, 5)\n", "for delta_g in delta_g_list:\n", " ham_terms, basis = get_hamiltonian(delta_g)\n", " init_condition = get_init_condition()\n", " te = TimeEvolution(ham_terms, basis, init_condition=init_condition, property_op_dict={\"n\": Op(\"a^\\dagger a\", \"e0\")})\n", " for i in range(40):\n", " te.kernel(0.2)\n", " n_list.append(te.property_dict[\"n\"].real)" ] }, { "cell_type": "markdown", "id": "db87a1b8-9eb9-4f11-841b-5c16d2b900b1", "metadata": {}, "source": [ "## Analyze and plot" ] }, { "cell_type": "code", "execution_count": 6, "id": "68ecf449-59f9-4a53-80fc-38ffafaf467f", "metadata": {}, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "import mpl_config" ] }, { "cell_type": "code", "execution_count": 7, "id": "60df9730-334d-4fe7-af4f-a237afedd7d7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.arange(41) * 0.2\n", "for i, n in enumerate(n_list):\n", " label = r\"$\\Delta G =\" + str(delta_g_list[i]) + \"$\"\n", " plt.plot(t, n.real[:, 0], label=label, linestyle=\"--\")\n", "plt.xlabel(\"$t$\")\n", "plt.ylabel(r\"Occupation $\\langle a^\\dagger_0 a_0 \\rangle$\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "974d31d5-004a-49bf-a785-43814d20e7b7", "metadata": {}, "source": [ "The Marcus rate is\n", "\n", "$$\n", "k = \\frac{V^2}{\\hbar} \\sqrt{\\frac{\\pi\\beta}{\\lambda}} \\exp{\\left (-\\frac{\\beta(\\lambda + \\Delta G)^2}{4\\lambda} \\right )}\n", "$$\n", "where $\\lambda = 2g^2\\omega$ is the reorganization energy.\n", "Since temperature is not considered in this simulation, $\\beta$ need to be fitted." ] }, { "cell_type": "code", "execution_count": 8, "id": "2d720e7a-6fb5-4fb2-9e0d-325dcffd150b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.014047289363197032,\n", " 0.02814188436474036,\n", " 0.029197240764329252,\n", " 0.019342655847204578,\n", " 0.01011515881320177]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# fit charge transfer rate\n", "rate = [-np.polyfit(t[10:], n[:, 0][10:], 1)[0] for n in n_list]\n", "rate" ] }, { "cell_type": "markdown", "id": "dc87b3f7-9a07-47f2-8ca2-325c33e33cd2", "metadata": {}, "source": [ "Next, compare the simulated rate with the Marcus rate and the nuclear tunneling charge transfer rate ([*Phys. Rev. B* **2009**, *79*, 115203](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.115203))" ] }, { "cell_type": "code", "execution_count": 9, "id": "026b6cfb-d170-4cdc-86ca-9f01fc248969", "metadata": {}, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "import mpl_config\n", "import numpy as np\n", "\n", "delta_g_list = np.linspace(0, -2, 5)\n", "rate = [0.014048168006004535, 0.028141822635725088, 0.02919731407299346, 0.019324510938040215, 0.01011515881320177]" ] }, { "cell_type": "code", "execution_count": 10, "id": "c918bdf5-31d2-458b-bf68-382ccc33cf6f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# marcus rate\n", "def marcus_rate(delta_g, beta):\n", " lam = 2 * g**2 * omega\n", " return v**2 * np.sqrt(np.pi * beta / lam) * np.exp(-(beta * (lam + delta_g) ** 2) / (4 * lam))\n", "\n", "\n", "# fit temperature\n", "from scipy.optimize import curve_fit\n", "\n", "beta = curve_fit(marcus_rate, delta_g_list, rate)[0][0]\n", "from scipy.integrate import trapezoid\n", "\n", "\n", "# nuclear tunneling rate\n", "def nuclear_tunneling_rate(delta_g):\n", " s = g**2\n", " t = np.linspace(-6, 6, int(1e3))\n", " integrand = v**2 * np.exp(\n", " 1j * delta_g * t - s * (1 - np.exp(1j * omega * t)) - s * (-1j * omega * t + omega**2 * t**2)\n", " )\n", " return trapezoid(integrand.real, t.ravel())\n", "\n", "\n", "dense_delta_g = np.linspace(-3, 1)\n", "plt.plot(\n", " dense_delta_g,\n", " np.log10([marcus_rate(delta_g, beta) for delta_g in dense_delta_g]),\n", " linestyle=\"-.\",\n", " label=\"Marcus rate (fitted)\",\n", ")\n", "plt.plot(\n", " dense_delta_g,\n", " np.log10([nuclear_tunneling_rate(delta_g) for delta_g in dense_delta_g]),\n", " linestyle=\"--\",\n", " label=\"Full quantum rate\",\n", ")\n", "plt.plot(delta_g_list, np.log10(rate), linestyle=\"\", marker=\"o\", markersize=6, label=\"Simulation\")\n", "plt.xlabel(r\"$\\Delta G$\")\n", "plt.ylabel(\"Transfer rate log$_{10} \\ k$\")\n", "plt.legend(frameon=True)" ] }, { "cell_type": "code", "execution_count": 11, "id": "366beeb6-5522-42fa-9cb2-d5f8319fa486", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8, 3.5), tight_layout=True)\n", "ax1, ax2 = fig.subplots(1, 2)\n", "\n", "plt.sca(ax1)\n", "for i, n in enumerate(n_list):\n", " label = r\"$\\Delta G =\" + str(delta_g_list[i]) + \"$\"\n", " plt.plot(t, n.real[:, 0], label=label, linestyle=\"--\")\n", "plt.xlabel(\"$t$\")\n", "plt.ylabel(r\"Occupation $\\langle a^\\dagger_0 a_0 \\rangle$\")\n", "plt.text(-2.2, 1.02, r\"$(\\bf{a})$\", fontsize=\"x-large\")\n", "plt.legend()\n", "\n", "plt.sca(ax2)\n", "plt.plot(\n", " dense_delta_g,\n", " np.log10([marcus_rate(delta_g, beta) for delta_g in dense_delta_g]),\n", " linestyle=\"-.\",\n", " label=\"Marcus rate (fitted)\",\n", ")\n", "plt.plot(\n", " dense_delta_g,\n", " np.log10([nuclear_tunneling_rate(delta_g) for delta_g in dense_delta_g]),\n", " linestyle=\"--\",\n", " label=\"Full quantum rate\",\n", ")\n", "plt.plot(delta_g_list, np.log10(rate), linestyle=\"\", marker=\"o\", markersize=6, label=\"Simulation rate\")\n", "plt.xlabel(r\"$\\Delta G$\")\n", "plt.ylabel(\"Transfer rate log$_{10} \\ k$\")\n", "plt.text(-4.2, -1.43, r\"$(\\bf{b})$\", fontsize=\"x-large\")\n", "plt.legend(frameon=True)\n", "plt.savefig(\"marcus.pdf\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.7.13" } }, "nbformat": 4, "nbformat_minor": 5 }