{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "99a57203-1a92-426f-b3b7-fbc0bed73dd7",
   "metadata": {},
   "source": [
    "# Helmholtz Free Energy\n",
    "The thermodynamic phase stability can be evaluated by comparing the Helmholtz free energy of different phases. So being able to calculate the Helmholtz free energy is an essential step towards calculating the full phase diagram. In the following there approximations are introduced to calculate the Helmholtz free energy, starting with the harmonic approximation, followed by the quasi-harmonic approximation which also includes the volume expansion and finally thermodynamic integration is used to quantify the anharmonic contributions. This addiabative approach to calculate the Helmholtz free energy is typically used in combination with ab-initio simulation methods like density functional theory, still here the approach is demonstrated with the [LAMMPS](https://lammps.org/) simulation code and the Morse potential."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dab82b2f-7bbe-4898-918b-229f870c2c8a",
   "metadata": {},
   "source": [
    "Starting with the import of the required python modules: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7006743f-6ea0-48c5-9b0f-f5dd66f25ee2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ase.build import bulk\n",
    "import numpy as np\n",
    "from atomistics.workflows import optimize_positions_and_volume, LangevinWorkflow, PhonopyWorkflow, QuasiHarmonicWorkflow\n",
    "from atomistics.calculators import evaluate_with_lammps_library, evaluate_with_lammps, get_potential_by_name, evaluate_with_hessian\n",
    "from pylammpsmpi import LammpsASELibrary\n",
    "from phonopy.units import VaspToTHz\n",
    "from tqdm import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas\n",
    "import scipy.constants "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9bd610f-3d04-45be-a2af-b4b2757d3966",
   "metadata": {},
   "source": [
    "Followed by the selection of the reference element and the definition of the Morse interatomic potential:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "edeb4cee-e7c6-408a-90b3-32dd14c0ebc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "structure_bulk = bulk(\"Al\", cubic=True)\n",
    "df_pot_selected = pandas.DataFrame({\n",
    "    \"Config\": [[\n",
    "        \"pair_style morse/smooth/linear 9.0\",\n",
    "        \"pair_coeff * * 0.5 1.8 2.95\"\n",
    "    ]],\n",
    "    \"Filename\": [[]],\n",
    "    \"Model\": [\"Morse\"],\n",
    "    \"Name\": [\"Morse\"],\n",
    "    \"Species\": [[\"Al\"]],\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77476c60-a03b-4b03-9ecd-969eadb34d5d",
   "metadata": {},
   "source": [
    "As a prerequisite the volume and positions of the atomistic structure are optimized to calculate the Helmholtz of the equilibrium structure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "16b51316-c39c-4aba-aa2f-fa92f4f854c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/janssen/projects/pylammpsmpi/pylammpsmpi/wrapper/ase.py:165: UserWarning: Warning: setting upper trangular matrix might slow down the calculation\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "task_dict = optimize_positions_and_volume(structure=structure_bulk)\n",
    "result_dict = evaluate_with_lammps(\n",
    "    task_dict=task_dict,\n",
    "    potential_dataframe=df_pot_selected,\n",
    ")\n",
    "structure_opt = result_dict[\"structure_with_optimized_positions_and_volume\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d660527-0817-48ab-a97d-f641eda0a419",
   "metadata": {},
   "source": [
    "Finally, the size of the atomistic structure is increased by repeating the structure in all three directions three times: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b080f3ce-4eba-493d-b4b5-3b90354a84f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "structure = structure_opt.repeat([3, 3, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a39b4c0d-3a8f-4f1c-b6f7-f604f2b856e0",
   "metadata": {},
   "source": [
    "The increased structure is required for all three approximations, for the harmonic and quasi-harmonic approximation it is required to evaluate the phonons up to an interaction range of 10 Angstrom and for the thermodynamic integration the larger supercell provides improved thermodynamic stability when calculating molecular dynamics trajectories at finite temperatures."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3823c713-38eb-40aa-ab4c-51e254390320",
   "metadata": {},
   "source": [
    "## Harmonic Approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "960ffb99-ad07-4512-bf4f-8b617265d635",
   "metadata": {},
   "source": [
    "The harmonic approximation is calculated using the finite displacement method using the [phonopy](https://phonopy.github.io/phonopy/) package. In the `atomistics` package the [phonopy](https://phonopy.github.io/phonopy/) workflow is implemented in the `PhonopyWorkflow` object. Following the typical three step process of generating the structures `generate_structures()` evaluating them with the [LAMMPS](https://lammps.org/) simulation code using the `evaluate_with_lammps()` function and analysing the results using the `analyse_structures()` function the thermodynamic properties can be calculated using the `get_thermal_properties()` function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3eeb5d4-6a99-4b08-a5dd-65743b35e71d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'temperatures': array([1.000e+00, 2.510e+02, 5.010e+02, 7.510e+02, 1.001e+03, 1.251e+03,\n",
       "        1.501e+03]),\n",
       " 'free_energy': array([ 0.3054683 ,  0.26911103,  0.08807443, -0.2090548 , -0.58871765,\n",
       "        -1.03150448, -1.52522672]),\n",
       " 'entropy': array([5.12294911e-14, 4.12565469e+01, 9.50730111e+01, 1.32185181e+02,\n",
       "        1.59664975e+02, 1.81349904e+02, 1.99221616e+02]),\n",
       " 'heat_capacity': array([        nan, 63.97199066, 88.27044589, 94.37971636, 96.67969872,\n",
       "        97.77513519, 98.37869945])}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "workflow_fix = PhonopyWorkflow(\n",
    "    structure=structure_opt,\n",
    "    interaction_range=10,\n",
    "    factor=VaspToTHz,\n",
    "    displacement=0.01,\n",
    "    dos_mesh=20,\n",
    "    primitive_matrix=None,\n",
    "    number_of_snapshots=None,\n",
    ")\n",
    "structure_dict = workflow_fix.generate_structures()\n",
    "result_dict = evaluate_with_lammps(\n",
    "    task_dict=structure_dict,\n",
    "    potential_dataframe=df_pot_selected,\n",
    ")\n",
    "workflow_fix.analyse_structures(output_dict=result_dict)\n",
    "term_base_dict = workflow_fix.get_thermal_properties(\n",
    "    t_min=1,\n",
    "    t_max=1500,\n",
    "    t_step=250,\n",
    "    temperatures=None,\n",
    "    cutoff_frequency=None,\n",
    "    pretend_real=False,\n",
    "    band_indices=None,\n",
    "    is_projection=False,\n",
    ")\n",
    "term_base_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98b4662a-a606-4c2e-8866-fda1f83e4a2b",
   "metadata": {},
   "source": [
    "The dictionary returned by the `get_thermal_properties()` function contains the temperature dependence of the following thermodynamic properties: Helmholtz free energy `free_energy`, Entropy `entropy` and the heat capcity at constant volume `heat_capacity`. In addition, the temperature is also included in the result dictionary to simplify the plotting of the results. The results are compared to the other approximations in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0640a73b-8a76-4eb1-bb64-66e389d0f71c",
   "metadata": {},
   "source": [
    "## Quasi-Harmonic Approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6eca5d10-2d99-46a0-afd0-d132d52b0128",
   "metadata": {},
   "source": [
    "The quasi-harmonic approximation extends the harmonix approximation by including the volume expansion. In the `atomistics` package this is implemented with the `QuasiHarmonicWorkflow` which internally is a combination of the `EnergyVolumeCurveWorkflow` and the `PhonopyWorkflow` introduced above. Consequently, the input parameters for the `QuasiHarmonicWorkflow` are a superset of the inputs of these workflows: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c40054b0-3492-48a2-93ad-34615caca7e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'free_energy': array([ 0.30135185,  0.26231475,  0.07072364, -0.24471851, -0.65110999,\n",
       "        -1.12998338, -1.67042388]),\n",
       " 'entropy': array([3.31166059e-07, 4.25802580e+01, 9.77768688e+01, 1.36322159e+02,\n",
       "        1.65329534e+02, 1.88653045e+02, 2.08300252e+02]),\n",
       " 'heat_capacity': array([        nan, 64.86754373, 88.84137042, 94.80149704, 97.01828281,\n",
       "        98.06138269, 98.62976854]),\n",
       " 'volumes': array([66.78514133, 66.90026195, 67.24614141, 67.66763429, 68.13272595,\n",
       "        68.63838791, 69.19002682]),\n",
       " 'temperatures': array([1.000e+00, 2.510e+02, 5.010e+02, 7.510e+02, 1.001e+03, 1.251e+03,\n",
       "        1.501e+03])}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "workflow_qh = QuasiHarmonicWorkflow(\n",
    "    structure=structure_opt,\n",
    "    num_points=11,\n",
    "    vol_range=0.05,\n",
    "    interaction_range=10,\n",
    "    factor=VaspToTHz,\n",
    "    displacement=0.01,\n",
    "    dos_mesh=20,\n",
    "    primitive_matrix=None,\n",
    "    number_of_snapshots=None,\n",
    ")\n",
    "structure_dict = workflow_qh.generate_structures()\n",
    "result_dict = evaluate_with_lammps(\n",
    "    task_dict=structure_dict,\n",
    "    potential_dataframe=df_pot_selected,\n",
    ")\n",
    "workflow_qh.analyse_structures(output_dict=result_dict)\n",
    "term_qh_dict = workflow_qh.get_thermal_properties(\n",
    "    t_min=1,\n",
    "    t_max=1500,\n",
    "    t_step=250,\n",
    "    temperatures=None,\n",
    "    cutoff_frequency=None,\n",
    "    pretend_real=False,\n",
    "    band_indices=None,\n",
    "    is_projection=False,\n",
    "    quantum_mechanical=True,\n",
    ")\n",
    "term_qh_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f2fafa0-2fa2-44bd-9682-6cf2e3dbc9c4",
   "metadata": {},
   "source": [
    "In analogy to the `get_thermal_properties()` function of the `PhonopyWorkflow` the `get_thermal_properties()` function of the `QuasiHarmonicWorkflow` returns a dictionary with the temperature dependence of the thermodynamic properties. The volume at finite temperature is included as an additional output. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17420568-77a1-4000-9b4e-6e9f610c65b1",
   "metadata": {},
   "source": [
    "Furthermore, the `QuasiHarmonicWorkflow` adds the ability to calculate the volume expansion with the classical harmonic oscillator rather than the quantum mechanical osicllator which is used by default:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7647bde8-8b7c-4325-875c-1e1ec32e7f6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'free_energy': array([ 0.00653974,  0.20391846,  0.04183779, -0.26289749, -0.66376056,\n",
       "        -1.13921853]),\n",
       " 'volumes': array([66.29913676, 66.70960432, 67.13998119, 67.59365054, 68.07505673,\n",
       "        68.5902383 ]),\n",
       " 'temperatures': array([   1,  251,  501,  751, 1001, 1251])}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "term_qh_cl_dict = workflow_qh.get_thermal_properties(\n",
    "    t_min=1,\n",
    "    t_max=1500,\n",
    "    t_step=250,\n",
    "    temperatures=None,\n",
    "    cutoff_frequency=None,\n",
    "    pretend_real=False,\n",
    "    band_indices=None,\n",
    "    is_projection=False,\n",
    "    quantum_mechanical=False,\n",
    ")\n",
    "term_qh_cl_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b1d4099-4a9b-4712-91f9-2253825d6eb4",
   "metadata": {},
   "source": [
    "In this case the dictionary of thermal properties calculated by the `get_thermal_properties()` function only contains the Helmholtz free energy `free_energy`, the volume at finite temperature `volumes` and the corresponding temperature `termpatures`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f151704-c29d-4e6a-8c4a-13de7f882a26",
   "metadata": {},
   "source": [
    "For the comparison of the harmonic approximation and the quasi-harmonic approximation the thermodynamic properties are visualized in the following. Given the coarse sampling of the temperature dependence these graphs look a bit rough. A better choice for the temperature step would be 50K rather than 250K. Here the larger temperature step is chosen to minimize the computational cost. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7b7a7475-9db7-4548-8aac-564bcaf7baef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1353b8eb0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Helmholtz Free Energy\")\n",
    "plt.plot(term_base_dict['temperatures'], term_base_dict['free_energy'], label=\"Harmonic\")\n",
    "plt.plot(term_qh_dict['temperatures'], term_qh_dict['free_energy'], label=\"Quasi-Harmonic (qm)\")\n",
    "plt.plot(term_qh_cl_dict['temperatures'], term_qh_cl_dict['free_energy'], label=\"Quasi-Harmonic (cl)\")\n",
    "plt.xlabel(\"Temperature (K)\")\n",
    "plt.ylabel(\"Helmholtz Free Energy (eV)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b8055310-1120-4502-8f17-d5cc5fb1e890",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1379268c0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Entropy\")\n",
    "plt.plot(term_base_dict['temperatures'], term_base_dict['entropy'], label=\"harmonic\")\n",
    "plt.plot(term_qh_dict['temperatures'], term_qh_dict['entropy'], label=\"quasi-harmonic (qm)\")\n",
    "plt.xlabel(\"Temperature (K)\")\n",
    "plt.ylabel(\"Entropy (J/K/mol)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2b3420f5-9f0c-4510-a097-fc47bf7c4001",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x137a130a0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Heat Capacity\")\n",
    "plt.plot(term_base_dict['temperatures'], term_base_dict['heat_capacity'], label=\"harmonic\")\n",
    "plt.plot(term_qh_dict['temperatures'], term_qh_dict['heat_capacity'], label=\"quasi-harmonic\")\n",
    "plt.axhline(3 * scipy.constants.Boltzmann * scipy.constants.Avogadro * len(structure_opt), color=\"black\", linestyle=\"--\", label=\"$3Nk_B$\")\n",
    "plt.xlabel(\"Temperature (K)\")\n",
    "plt.ylabel(\"Heat Capacity (J/K/mol)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cd12417-574b-48c3-966d-4428c8cbe9b0",
   "metadata": {},
   "source": [
    "## Thermo Dynamic Integration"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4645998f-9a85-4c95-96fd-16c838c20ea8",
   "metadata": {},
   "source": [
    "To include the anharmonic contribution to the free energy thermo dynamic integration is used to integrate the internal energy between the quasi-harmonic reference and the full anharmonic molecular dynamics calculation. For the choice of computational efficiency molecular dynamics trajectories with 3000 steps are using and a set of five lambda values between 0.0 and 1.0. Again, increasing the number of lambda values from 5 to 11 can improve the approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "85f88cb8-07dc-4cfb-b466-9dff81077088",
   "metadata": {},
   "outputs": [],
   "source": [
    "steps = 3000\n",
    "steps_lst = list(range(steps))\n",
    "lambda_lst = np.linspace(0.0, 1.0, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10ad9a6b-6590-40fd-a172-99ef8e3caffe",
   "metadata": {},
   "source": [
    "From the finite temperature volume of the `QuasiHarmonicWorkflow` above the finite temperature lattice constant is calculated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "05b3a33f-7071-4d71-82ce-4f769b95ee6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice_constant_lst = np.array(term_qh_dict['volumes']) ** (1/3)\n",
    "temperature_lst = term_qh_dict['temperatures']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a97716c-0f94-4e36-bbca-8b055e42f44c",
   "metadata": {},
   "source": [
    "The thermodynamic integration workflow consists of two loops. The first loop iterates over the different temperatures and the corresponding finite temperature lattice constants while the second inner loop iterates over the different lambda parameters. In the outter loop the `PhonopyWorkflow` workflow is used to calculate the finite temperature force constants which can be accessed from the `PhonopyWorkflow` using the `get_hesse_matrix()` function. In addition the `evaluate_with_lammps()` function is used in the outter loop as well to calculate the equilibrium energy at finite volume. Finally, in the inner loop the `LangevinWorkflow` is used to calculate the molecular dynamics trajectory with both the forces and the energy being mixed in dependence of the lambda parameter from the Hessian calculation `evaluate_with_hessian()` and the [LAMMPS](https://lammps.org/) calculation `evaluate_with_lammps_library()`. Here the [LAMMPS](https://lammps.org/) library interface is used to evaluate multiple structures one after another. Finally the lambda dependence is fitted and the integral from 0 to 1 is calculated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a2aafca6-faa2-48ff-9f40-86483acd2389",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████| 3000/3000 [00:06<00:00, 498.47it/s]\n",
      "100%|██████████████████████████████████████| 3000/3000 [00:05<00:00, 501.21it/s]\n",
      "100%|██████████████████████████████████████| 3000/3000 [00:05<00:00, 509.76it/s]\n",
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     ]
    }
   ],
   "source": [
    "free_energy_lst, eng_lambda_dependence_lst = [], []\n",
    "for lattice_constant, temperature in zip(lattice_constant_lst, temperature_lst):\n",
    "    structure = bulk(\"Al\", a=lattice_constant, cubic=True).repeat([3, 3, 3])\n",
    "    equilibrium_lammps = evaluate_with_lammps(task_dict={\"calc_energy\": structure}, potential_dataframe=df_pot_selected)['energy']\n",
    "    workflow_fix = PhonopyWorkflow(\n",
    "        structure=structure,\n",
    "        interaction_range=10,\n",
    "        factor=VaspToTHz,\n",
    "        displacement=0.01,\n",
    "        dos_mesh=20,\n",
    "        primitive_matrix=None,\n",
    "        number_of_snapshots=None,\n",
    "    )\n",
    "    structure_dict = workflow_fix.generate_structures()\n",
    "    result_dict = evaluate_with_lammps(\n",
    "        task_dict=structure_dict,\n",
    "        potential_dataframe=df_pot_selected,\n",
    "    )\n",
    "    workflow_fix.analyse_structures(output_dict=result_dict)\n",
    "    energy_pot_all_lst, energy_mean_lst, energy_kin_all_lst = [], [], []\n",
    "    for lambda_parameter in lambda_lst: \n",
    "        thermo_eng_pot_lst, thermo_eng_kin_lst = [], []\n",
    "        workflow_md_thermo = LangevinWorkflow(\n",
    "            structure=structure,\n",
    "            temperature=temperature,\n",
    "            overheat_fraction=2.0,\n",
    "            damping_timescale=100.0,\n",
    "            time_step=1,\n",
    "        )\n",
    "        lmp = LammpsASELibrary(\n",
    "            working_directory=None,\n",
    "            cores=1,\n",
    "            comm=None,\n",
    "            logger=None,\n",
    "            log_file=None,\n",
    "            library=None,\n",
    "            diable_log_file=True,\n",
    "        )\n",
    "        for i in tqdm(steps_lst):\n",
    "            task_dict = workflow_md_thermo.generate_structures()\n",
    "            hessian_dict = evaluate_with_hessian(\n",
    "                task_dict=task_dict,\n",
    "                structure_equilibrium=structure,\n",
    "                force_constants=workflow_fix.get_hesse_matrix(),\n",
    "                bulk_modulus=0,\n",
    "                shear_modulus=0,\n",
    "            )\n",
    "            lammps_dict = evaluate_with_lammps_library(\n",
    "                task_dict=task_dict,\n",
    "                potential_dataframe=df_pot_selected,\n",
    "                lmp=lmp,\n",
    "            )\n",
    "            result_dict = {\n",
    "                \"forces\": {0: (1-lambda_parameter) * hessian_dict[\"forces\"][0] + lambda_parameter * lammps_dict[\"forces\"][0]},\n",
    "                \"energy\": {0: (1-lambda_parameter) * hessian_dict[\"energy\"][0] + lambda_parameter * (lammps_dict[\"energy\"][0] - equilibrium_lammps)},\n",
    "            }\n",
    "            eng_pot, eng_kin = workflow_md_thermo.analyse_structures(output_dict=result_dict)\n",
    "            thermo_eng_pot_lst.append(eng_pot)\n",
    "            thermo_eng_kin_lst.append(eng_kin)\n",
    "        lmp.close()\n",
    "        thermo_energy = np.array(thermo_eng_pot_lst) + np.array(thermo_eng_kin_lst)\n",
    "        energy_mean_lst.append(np.mean(thermo_energy[1000:]))\n",
    "        energy_pot_all_lst.append(thermo_eng_pot_lst)\n",
    "        energy_kin_all_lst.append(thermo_eng_kin_lst)\n",
    "    eng_lambda_dependence_lst.append(np.array(energy_mean_lst) / len(structure) * 1000)\n",
    "    fit = np.poly1d(np.polyfit(lambda_lst, np.array(energy_mean_lst) / len(structure) * 1000, 3))\n",
    "    integral = np.polyint(fit)\n",
    "    free_energy_lst.append(integral(1.0) - integral(0.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61ac00f2-f724-44cf-a587-37edb3db0f13",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3cd7a2b-678a-497a-9b88-176b81e105bc",
   "metadata": {},
   "source": [
    "The Helmholtz free energy for all three approximations is compared in the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "16d54aed-5461-4546-9ef5-92b416805b1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x137a11c60>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Helmholtz Free Energy\")\n",
    "plt.plot(term_base_dict['temperatures'], term_base_dict['free_energy'], label=\"Harmonic\")\n",
    "plt.plot(term_qh_dict['temperatures'], term_qh_dict['free_energy'], label=\"Quasi-Harmonic\")\n",
    "plt.plot(term_qh_dict['temperatures'], term_qh_dict['free_energy'] - np.array(free_energy_lst) / 1000, label=\"Thermodynamic Integration\")\n",
    "plt.xlabel(\"Temperature (K)\")\n",
    "plt.ylabel(\"Helmholtz Free Energy (eV)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4d96b6c1-bc84-4172-a981-4d7ec8ac280b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}