{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution of N2 exercise: Handling the log files\n",
    "\n",
    "In this tutorial, we will learn how to avoid to read directly the logfiles [log.yaml](./log.yaml), [log-LDA.yaml](./log-LDA.yaml), [log-HF.yaml](./log-HF.yaml) and [log-PBE0.yaml](./log-PBE0.yaml) where all information about the calculation are stored.\n",
    "\n",
    "because the logfile is a serialized python dictionary written in yaml, it is possible using the yaml module to convert it into a python dictionary and process it.\n",
    "\n",
    "In order to simplify this step, we will use the *Logfile* class which has nice method to extract easily the information. This [tutorial](../notebooks/Logfile-Basics.ipynb) explains the basics of the *Logfile* class.\n",
    "\n",
    "\n",
    "<h2>Exercise</h2>\n",
    "\n",
    "Compare the values of the HOMO and HOMO-1 eigenvalues for the LDA and the HF run.\n",
    "Change the values of the hgrid and crmult to find the converged values.\n",
    "Note that, both in the LDA and in the HF calculation, a norm-conserving PSP is used.\n",
    "The results can be compared to all-electron calculations, done with different basis sets, from references (units are eV)\n",
    "(1) S.&nbsp;Hamel <i>et&nbsp;al.</i> J. Electron Spectrospcopy and Related Phenomena 123 (2002) 345-363 and (2) P.&nbsp;Politzer, F.&nbsp;Abu-Awwad, Theor. Chem. Acc. (1998), 99, 83-87:\n",
    "\n",
    "<table>\n",
    "  <tr> <td></td>                      <td>LDA(1)</td>  <td>HF(1)</td>   <td>HF(2)</td>   <td>(Exp.)</td></tr>\n",
    "  <tr> <td>3&sigma;<sub>g</sub></td>  <td>10.36</td>   <td>17.25</td>   <td>17.31</td>   <td>(15.60)</td></tr>\n",
    " <tr> <td>1&pi;<sub>u</sub></td>      <td>11.84</td>   <td>16.71</td>   <td>17.02</td>   <td>(16.98)</td></tr>\n",
    " <tr> <td>2&sigma;<sub>u</sub></td>   <td>13.41</td>   <td>21.25</td>   <td>21.08</td>   <td>(18.78)</td></tr>\n",
    "</table>\n",
    " \n",
    "The results depends, of course, on the precision chosen for the calculation, and of the presence of the pseudopotential.\n",
    "As it is well-known, the pseudopotential appoximation is however much less severe than the approximation induced by typical XC functionals. We might see that, even in the HF case, the presence of a LDA-based pseudopotential (of rather good quality) does not alter so much the results. Here you can find the values from BigDFT calculation using a very good precision (*hgrid=0.3*, *crmult=7.0*). \n",
    "Note that 1 ha=27.21138386 eV.\n",
    " \n",
    "<table>\n",
    "  <tr> <td></td>                        <td>LDA</td>    <td>HF</td></tr>\n",
    "  <tr> <td> 3&sigma;<sub>g</sub></td>   <td>10.40</td>  <td>17.32</td></tr>\n",
    "  <tr> <td> 1&pi;<sub>u</sub></td>      <td>11.75</td>  <td>16.62</td></tr>\n",
    "  <tr> <td> 2&sigma;<sub>u</sub></td>   <td>13.52</td>  <td>21.30</td></tr>\n",
    "</table>\n",
    "\n",
    "How much do these values differ from the calculation with default parameters? Do they converge to a given value?\n",
    "What is the *correlation* for the N2 molecule in (PSP) LDA?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialize a Calculator with OMP_NUM_THREADS=2 and command /local/binaries/gfortran-fpe-1.8/install/bin/bigdft\n",
      "Creating the yaml input file \"./LDA.yaml\"\n",
      "Executing command:  /local/binaries/gfortran-fpe-1.8/install/bin/bigdft -n LDA -s Yes\n",
      "Creating the yaml input file \"./HF.yaml\"\n",
      "Executing command:  /local/binaries/gfortran-fpe-1.8/install/bin/bigdft -n HF -s Yes\n",
      "Creating the yaml input file \"./PBE0.yaml\"\n",
      "Executing command:  /local/binaries/gfortran-fpe-1.8/install/bin/bigdft -n PBE0 -s Yes\n"
     ]
    }
   ],
   "source": [
    "from BigDFT import Calculators as calc #Import the python modules needed\n",
    "from BigDFT import Logfiles as lf\n",
    "from BigDFT import InputActions as A\n",
    "\n",
    "HtoeV = 27.21138386 #Conversion Hartree to meV\n",
    "\n",
    "\n",
    "dico = dict()\n",
    "\n",
    "A.set_atomic_positions(dico,'posinp.xyz')\n",
    "study = calc.SystemCalculator() #Create a calculator\n",
    "\n",
    "A.set_xc(dico,'LDA')\n",
    "LDA = study.run(name=\"LDA\",input=dico,skip=True) #Run the code with the name scheme LDA\n",
    "A.set_xc(dico,'HF')\n",
    "HF = study.run(name=\"HF\",input=dico,skip=True) #Run the code with the name scheme HF\n",
    "A.set_xc(dico,'PBE0')\n",
    "PBE0 = study.run(name=\"PBE0\",input=dico,skip=True) #Run the code with the name scheme HF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variables *first*, *LDA*, *HF* and *PBE0* are instances of the class *BigDFT.Logfiles.Logfile* which contain all information as the total energy.\n",
    "We should also use directly this call loading the corresponding output file as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "PBE0 = lf.Logfile(\"log-PBE0.yaml\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We compare the values of HOMO-1 and HOMO for LDA and HF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LDA [-11.72069487 -11.72068562 -10.37327265]\n",
      "HF [-17.31174049 -16.60642809 -16.60642409]\n"
     ]
    }
   ],
   "source": [
    "lda_evals = LDA.evals[0][0]\n",
    "hf_evals = HF.evals[0][0]\n",
    "print \"LDA\",lda_evals[-3:]*HtoeV\n",
    "print \"HF\", hf_evals[-3:]*HtoeV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modifications of the calculation parameters\n",
    "Then we do a convergence curve varying *hgrid* which controls the grid step of the Daubechies basis set and *crmult* the extension. The default values are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hgrids [0.45, 0.45, 0.45]\n",
      "rmult [5.0, 8.0]\n"
     ]
    }
   ],
   "source": [
    "print 'hgrids',LDA.log['dft']['hgrids']\n",
    "print 'rmult',LDA.log['dft']['rmult']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*hgrids* is an array of 3 values for the x, y, and z direction. A simple scalar can be indicated for the input.\n",
    "*rmult* is composed into two multiplied factors, one for the coarse grid, and the second one for the fine grid.\n",
    "We build our script for LDA and run it (on one core, it takes 10 minutes roughly for all calculations).\n",
    "\n",
    "Todo:\n",
    "  This part has to be modernized with the new input file syntax and dataset retrieval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating from a dictionary the yaml input file \"LDA-0.45-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.45-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.40-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.40-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.35-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.35-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.30-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.30-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.25-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.25-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.45-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.45-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.40-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.40-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.35-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.35-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.30-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.30-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.25-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.25-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.45-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.45-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.40-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.40-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.35-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.35-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.30-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.30-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.25-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.25-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.45-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.45-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.40-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.40-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.35-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.35-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.30-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.30-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"LDA-0.25-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n LDA-0.25-09.0 -s Yes\n"
     ]
    }
   ],
   "source": [
    "Hgrids = [0.45, 0.40, 0.35, 0.30, 0.25]\n",
    "Crmult = [3.0, 5.0, 7.0, 9.0]\n",
    "dico = lf.Logfile('LDA.yaml').log #Build the dictionary in order to change it (yaml.load with import yaml could be another way)\n",
    "dico['dft'] = LDA.log['dft'] #Add the dictionary coming from the logfile (which can be also used as an input file)\n",
    "log_LDA = {}\n",
    "emin_LDA = 0.0\n",
    "for crmult in Crmult:\n",
    "    log_LDA[crmult] = []\n",
    "    for hgrid in Hgrids:\n",
    "        A.set_hgrid(dico,hgrid)\n",
    "        dico['dft']['rmult'] = [ crmult, 8.0]\n",
    "        name = \"LDA-%4.2f-%04.1f\" % (hgrid,crmult)\n",
    "        log = study.run(name=name,input=dico,skip=True)\n",
    "        log_LDA[crmult].append( log )\n",
    "        emin_LDA =min(emin_LDA,log.energy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do the same loops to run the Hartree-Fock calculations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating from a dictionary the yaml input file \"HF-0.45-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.45-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.40-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.40-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.35-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.35-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.30-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.30-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.25-03.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.25-03.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.45-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.45-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.40-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.40-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.35-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.35-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.30-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.30-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.25-05.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.25-05.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.45-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.45-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.40-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.40-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.35-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.35-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.30-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.30-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.25-07.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.25-07.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.45-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.45-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.40-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.40-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.35-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.35-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.30-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.30-09.0 -s Yes\n",
      "Creating from a dictionary the yaml input file \"HF-0.25-09.0.yaml\"\n",
      "Executing command:  /local/deutsch/Forge/BigDFT/build-mpif90/install/bin/bigdft -n HF-0.25-09.0 -s Yes\n"
     ]
    }
   ],
   "source": [
    "dico = lf.Logfile('HF.yaml').log #Build the dictionary in order to change it (yaml.load with import yaml could be another way)\n",
    "dico['dft'] = HF.log['dft'] #Add the dictionary coming from the logfile (which can be also used as an input file)\n",
    "log_HF = {}\n",
    "emin_HF = 0.0\n",
    "for crmult in Crmult:\n",
    "    log_HF[crmult] = []\n",
    "    for hgrid in Hgrids:\n",
    "        dico['dft']['hgrids'] = hgrid\n",
    "        dico['dft']['rmult'] = [ crmult, 8.0]\n",
    "        name = \"HF-%4.2f-%04.1f\" % (hgrid,crmult)\n",
    "        log = study.run(name=name,input=dico,skip=True)\n",
    "        log_HF[crmult].append(log)\n",
    "        emin_HF = min(emin_HF,log.energy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa767d06ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "# Lists of markers and colors (for matplotlib)\n",
    "colors = ['#74a9cf', '#2b8cbe', '#045a8d', '#009900', '#FF8000']\n",
    "colors = ['#000000', '#ff0000', '#045a8d', '#009900', '#FF8000']\n",
    "markers = ['o','s','d','d','d']\n",
    "\n",
    "plt.figure(figsize=(15,7))\n",
    "# Plot with matplotlib\n",
    "for i,crmult in enumerate(Crmult):\n",
    "    im = i%len(colors)\n",
    "    ener = [ HtoeV*(l.energy-emin_LDA) for l in log_LDA[crmult] ]\n",
    "    plt.plot(Hgrids, ener, marker=markers[im], \n",
    "             ls='-', label=str(crmult),color=colors[im])  \n",
    "\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Grid step (Bohr)')\n",
    "plt.ylabel('Total energy $\\Delta E$ (eV)')\n",
    "plt.title('Dissociation energy of the N2 dimer for different rmult')\n",
    "plt.legend(loc=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa767d38690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,7))\n",
    "# Plot with matplotlib\n",
    "for i,crmult in enumerate(Crmult):\n",
    "    im = i%len(colors)\n",
    "    ener = [ HtoeV*(l.energy-emin_HF) for l in log_HF[crmult] ]\n",
    "    plt.plot(Hgrids, ener, marker=markers[im], \n",
    "             ls='-', label=str(crmult),color=colors[im])  \n",
    "\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Grid step (Bohr)')\n",
    "plt.ylabel('Total energy $\\Delta E$ (eV)')\n",
    "plt.title('Dissociation energy of the N2 dimer for different crmult')\n",
    "plt.legend(loc=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to converge the result, you need to decrease the grid step and also increase the extension of the mesh. For a given *crmult*, the curve are almost flat. For a *hgrid* value of of 0.35, there is few difference between the values with *crmult*=5.0 and 7.0 but for a *hgrid* value of 0.20 it is important. Now we give the HOMO-1 and HOMO eigenvalues both for LDA and HF functionals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LDA   HF\n",
      "10.40 16.63\n",
      "11.75 16.63\n",
      "11.75 17.32\n",
      "13.52 21.30\n",
      "28.08 39.83\n"
     ]
    }
   ],
   "source": [
    "ih = Hgrids.index(0.3)\n",
    "lda_evals = log_LDA[7.0][ih].evals[0][0]\n",
    "hf_evals = log_HF[7.0][ih].evals[0][0]\n",
    "print \"LDA   HF\"\n",
    "for (l,h) in zip(reversed(lda_evals),reversed(hf_evals)):\n",
    "    print \"%5.2f %5.2f\" % (-HtoeV*l, -HtoeV*h)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}