{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Molecular dynamics simulations of bulk water\n", "\n", "In this example, we show how to perform molecular dynamics of bulk water using the popular interatomic TIP3P potential\n", "([W. L. Jorgensen et. al.](https://doi.org/10.1063/1.445869)) and [LAMMPS](http://lammps.sandia.gov/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "%matplotlib inline \n", "import matplotlib.pylab as plt\n", "from pyiron.project import Project\n", "import ase.units as units" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "pr = Project(\"tip3p_water\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Creating the initial structure\n", "\n", "We will setup a cubic simulation box consisting of 27 water molecules density density is 1 g/cm$^3$. The target density is achieved by determining the required size of the simulation cell and repeating it in all three spatial dimensions" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "2635f5900e0d4ab29f46adec6f56e2a7", "version_major": 2, "version_minor": 0 }, "text/html": [ "
Failed to display Jupyter Widget of type NGLWidget
.
\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "
\n", "\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "
\n" ], "text/plain": [ "NGLWidget()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "density = 1.0e-24 # g/A^3\n", "n_mols = 27\n", "mol_mass_water = 18.015 # g/mol\n", "\n", "# Determining the supercell size size\n", "mass = mol_mass_water * n_mols / units.mol # g\n", "vol_h2o = mass / density # in A^3\n", "a = vol_h2o ** (1./3.) # A\n", "\n", "# Constructing the unitcell\n", "n = int(round(n_mols ** (1. / 3.)))\n", "\n", "dx = 0.7\n", "r_O = [0, 0, 0]\n", "r_H1 = [dx, dx, 0]\n", "r_H2 = [-dx, dx, 0]\n", "unit_cell = (a / n) * np.eye(3)\n", "water = pr.create_atoms(elements=['H', 'H', 'O'], \n", " positions=[r_H1, r_H2, r_O], \n", " cell=unit_cell)\n", "water.set_repeat([n, n, n])\n", "water.plot3d()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'H54O27'" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "water.get_chemical_formula()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Equilibrate water structure\n", "\n", "The initial water structure is obviously a poor starting point and requires equilibration (Due to the highly artificial structure a MD simulation with a standard time step of 1fs shows poor convergence). Molecular dynamics using a time step that is two orders of magnitude smaller allows us to generate an equilibrated water structure. We use the NVT ensemble for this calculation:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['H2O_tip3p', 'H2O_tip3p_slab']" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "job_name = \"water_slow\"\n", "ham = pr.create_job(\"Lammps\", job_name)\n", "ham.structure = water\n", "# Listing available potentials for this structure\n", "ham.list_potentials()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use the `H2O_tip3p` potential. The `H2O_tip3p_slab` should be used if you want to switch off the periodic boundary conditions along the z-axis " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "ham.potential = 'H2O_tip3p'\n", "ham.calc_md(temperature=300, \n", " n_ionic_steps=1e4, \n", " time_step=0.01)\n", "ham.run()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "383b3d53a6324a9eace3d6bb81c16f58", "version_major": 2, "version_minor": 0 }, "text/html": [ "Failed to display Jupyter Widget of type NGLWidget
.
\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "
\n", "\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "
\n" ], "text/plain": [ "NGLWidget(count=101)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "view = ham.animate_structure()\n", "view" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Full equilibration\n", "\n", "At the end of this simulation, we have obtained a structure that approximately resembles water. Now we increase the time step to get a reasonably equilibrated structure " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Get the final structure from the previous simulation\n", "struct = ham.get_structure(iteration_step=-1)\n", "job_name = \"water_fast\"\n", "ham_eq = pr.create_job(\"Lammps\", job_name)\n", "ham_eq.structure = struct\n", "ham_eq.potential = 'H2O_tip3p'\n", "ham_eq.calc_md(temperature=300, \n", " n_ionic_steps=1e4,\n", " n_print=10, \n", " time_step=1)\n", "ham_eq.run()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e9996981cf4047d4bca6bd6a62db4fb0", "version_major": 2, "version_minor": 0 }, "text/html": [ "Failed to display Jupyter Widget of type NGLWidget
.
\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "
\n", "\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "
\n" ], "text/plain": [ "NGLWidget(count=1001)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "view = ham_eq.animate_structure()\n", "view" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now plot the trajectories" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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