{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution of the atom within LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we take the code from the Hydrogen project and adopt it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import *\n",
    "from scipy import integrate\n",
    "from scipy import interpolate\n",
    "from scipy import optimize\n",
    "import weave\n",
    "\n",
    "def Numerovc(f, x0_, dx, dh_):\n",
    "    code_Numerov=\"\"\"\n",
    "    double h2 = dh*dh;\n",
    "    double h12 = h2/12.;\n",
    "    \n",
    "    double w0 = x(0)*(1-h12*f(0));\n",
    "    double w1 = x(1)*(1-h12*f(1));\n",
    "    double xi = x(1);\n",
    "    double fi = f(1);\n",
    "    for (int i=2; i<f.size(); i++){\n",
    "        double w2 = 2*w1-w0+h2*fi*xi;  // here fi=f1\n",
    "        fi = f(i);                     // fi=f2\n",
    "        xi = w2/(1-h12*fi);\n",
    "        x(i)=xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "    }\n",
    "    \"\"\"\n",
    "    x = zeros(len(f))\n",
    "    dh=float(dh_)\n",
    "    x[0]=x0_\n",
    "    x[1]=x0_+dh*dx\n",
    "    weave.inline(code_Numerov, ['f','dh','x'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x\n",
    "\n",
    "def fSchrod(En, l, R):\n",
    "    return l*(l+1.)/R**2-2./R-En\n",
    "\n",
    "def ComputeSchrod(En,R,l):\n",
    "    \"Computes Schrod Eq.\" \n",
    "    f = fSchrod(En,l,R[::-1])\n",
    "    ur = Numerovc(f,0.0,-1e-7,-R[1]+R[0])[::-1]\n",
    "    norm = integrate.simps(ur**2,x=R)\n",
    "    return ur*1/sqrt(abs(norm))\n",
    "\n",
    "def Shoot(En,R,l):\n",
    "    ur = ComputeSchrod(En,R,l)\n",
    "    ur = ur/R**l\n",
    "    f0 = ur[0]\n",
    "    f1 = ur[1]\n",
    "    f_at_0 = f0 + (f1-f0)*(0.0-R[0])/(R[1]-R[0])\n",
    "    return f_at_0\n",
    "\n",
    "def FindBoundStates(R,l,nmax,Esearch):\n",
    "    n=0\n",
    "    Ebnd=[]\n",
    "    u0 = Shoot(Esearch[0],R,l)\n",
    "    for i in range(1,len(Esearch)):\n",
    "        u1 = Shoot(Esearch[i],R,l)\n",
    "        if u0*u1<0:\n",
    "            Ebound = optimize.brentq(Shoot,Esearch[i-1],Esearch[i],xtol=1e-16,args=(R,l))\n",
    "            Ebnd.append((l,Ebound))\n",
    "            if len(Ebnd)>nmax: break\n",
    "            n+=1\n",
    "            print 'Found bound state at E=%14.9f E_exact=%14.9f l=%d' % (Ebound, -1.0/(n+l)**2,l)\n",
    "        u0=u1\n",
    "    \n",
    "    return Ebnd\n",
    "\n",
    "def cmpE(x,y):\n",
    "    if abs(x[1]-y[1])>1e-4:\n",
    "        return cmp(x[1],y[1])\n",
    "    else:\n",
    "        return cmp(x[0],y[0])\n",
    "\n",
    "# This is slightly modified code from Hydrogen project\n",
    "def ChargeDensity(bst,R,Zatom):\n",
    "    rho = zeros( len(R) )\n",
    "    N=0\n",
    "    for i,(l,Ei) in enumerate(bst):\n",
    "        dN = 2*(2*l+1)\n",
    "        if N+dN<Zatom:\n",
    "            ferm=1\n",
    "        else:\n",
    "            ferm = (Zatom-N)/float(dN)\n",
    "        u = ComputeSchrod(Ei,R,l)\n",
    "        drho = u**2 / (4*pi*R**2) * dN * ferm\n",
    "        rho += drho\n",
    "        N += dN\n",
    "        print 'Adding state with l=', l, 'and E=', Ei, 'with Z=', N, 'with ferm=', ferm\n",
    "        if N>=Zatom: break\n",
    "    return rho\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999922109 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.249990190 E_exact=  -0.250000000 l=0\n",
      "Found bound state at E=  -0.111108201 E_exact=  -0.111111111 l=0\n",
      "Found bound state at E=  -0.062498772 E_exact=  -0.062500000 l=0\n",
      "Found bound state at E=  -0.039999314 E_exact=  -0.040000000 l=0\n",
      "Found bound state at E=  -0.250000016 E_exact=  -0.250000000 l=1\n",
      "Found bound state at E=  -0.111111117 E_exact=  -0.111111111 l=1\n",
      "Found bound state at E=  -0.062500003 E_exact=  -0.062500000 l=1\n",
      "Found bound state at E=  -0.039999959 E_exact=  -0.040000000 l=1\n",
      "Found bound state at E=  -0.111111111 E_exact=  -0.111111111 l=2\n",
      "Found bound state at E=  -0.062500000 E_exact=  -0.062500000 l=2\n",
      "Found bound state at E=  -0.039999977 E_exact=  -0.040000000 l=2\n",
      "Found bound state at E=  -0.062500000 E_exact=  -0.062500000 l=3\n",
      "Found bound state at E=  -0.039999992 E_exact=  -0.040000000 l=3\n",
      "Adding state with l= 0 and E= -0.999922108956 with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.249990190207 with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.250000015612 with Z= 10 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.111108200823 with Z= 12 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.111111116781 with Z= 18 with ferm= 1\n",
      "Adding state with l= 2 and E= -0.111111111147 with Z= 28 with ferm= 1.0\n"
     ]
    },
    {
     "data": {
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Jeve21fgilS0rC665Bvbe20LCkiV2JoWaRolIaTSSEMjXX9t+9v79Q1cimebUU21RY34+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\niUkhQURERGL6f/5yckOpvBdaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1136d3e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Esearch = -1.2/arange(1,20,0.2)**2\n",
    "\n",
    "R = linspace(1e-8,100,2000)\n",
    "\n",
    "nmax=5\n",
    "Bnd=[]\n",
    "for l in range(nmax-1):\n",
    "    Bnd += FindBoundStates(R,l,nmax-l,Esearch)\n",
    "    \n",
    "Bnd.sort(cmpE)\n",
    "\n",
    "Zatom=28  # Like Ni ion\n",
    "rho = ChargeDensity(Bnd,R,Zatom)\n",
    "\n",
    "from pylab import *\n",
    "%matplotlib inline\n",
    "\n",
    "plot(R,rho*(4*pi*R**2),label='charge density')\n",
    "xlim([0,25])\n",
    "show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def FuncForHartree(y,r,rhoSpline):\n",
    "    return [y[1], -8*pi*r*rhoSpline(r)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rhoSpline = interpolate.UnivariateSpline(R,rho,s=0)\n",
    "U1 = integrate.odeint(FuncForHartree, [0.0,5.], R, args=(rhoSpline,))[:,0]\n",
    "alpha = (2*Zatom-U1[-1])/R[-1]\n",
    "U1 += alpha*R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OQYYNG0Yul2v3qK2tfefzrdWroXdvWLRobtHFOsaMGdPpFqVNTU3kcjlaWlra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\nBBERESnq/wMZSv2s+M+llwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c5e250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(R,U1)\n",
    "grid()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerov again\n",
    "\n",
    "To remind ourselves on Numerov for Poisson equation\n",
    "\n",
    "\\begin{eqnarray}\n",
    "  x(h)+x(-h) = 2x(0)+h^2 (f(0)x(0)+u(0))+\\frac{2}{4!}h^4 x^{(4)}(0)+O(h^6)\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "  x^{(4)}\\sim \\frac{u_{i+1}-2 u_i+u_{i-1}}{h^2}\n",
    "\\end{equation}\n",
    "\n",
    "Inserting the fourth order derivative into the above recursive equation (forth equation in his chapter), we\n",
    "get\n",
    "\n",
    "\\begin{equation}\n",
    "  x_{i+1}-2 x_i+x_{i-1}=h^2 u_i +\\frac{h^2}{12}(u_{i+1}-2 u_i+u_{i-1})\n",
    "\\end{equation}\n",
    "\n",
    "If we switch to a new variable $w_i=x_i-\\frac{h^2}{12}u_i$\n",
    "we are left with the following\n",
    "equation\n",
    "\n",
    "\\begin{equation}\n",
    "  w_{i+1} -2 w_i + w_{i-1} = h^2 u_i+O(h^6)\n",
    "\\end{equation}\n",
    "\n",
    "The variable $x$ needs to be recomputed at each step with\n",
    "$x_i=(w_i+\\frac{h^2}{12}u_i)$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def NumerovUP(U, x0, dx, dt):\n",
    "    \"Python version of Numerov for Poisson equation\"\n",
    "    x = zeros(len(U))\n",
    "    x[0] = x0          # first point\n",
    "    x[1] = dx*dt + x0  # second point\n",
    "    h2 = dt*dt\n",
    "    h12 = h2/12;  \n",
    "    w0 = x[0]-h12*U[0]\n",
    "    w1 = x[1]-h12*U[1]\n",
    "    xi = x[1]\n",
    "    Ui = U[1];      \n",
    "    for i in range(2,len(U)):\n",
    "        w2 = 2*w1 - w0 + h2*Ui\n",
    "        Ui = U[i]\n",
    "        xi = w2+h12*Ui\n",
    "        x[i] = xi\n",
    "        w0 = w1\n",
    "        w1 = w2\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NumerovU(U, x0, dx, dt):\n",
    "    code_NumerovU=\"\"\"\n",
    "      double h2 = dt;\n",
    "      h2 = h2*h2;\n",
    "      double h12 = h2/12;\n",
    "      \n",
    "      double w0 = x(0)-h12*U(0);\n",
    "      double w1 = x(1)-h12*U(1);\n",
    "      double xi = x(1);\n",
    "      double Ux = U(1);\n",
    "      \n",
    "      for (int i=2; i<U.size(); i++){\n",
    "        double w2 = 2*w1 - w0 + h2*Ux;\n",
    "        Ux = U(i);\n",
    "        xi = w2+h12*Ux;\n",
    "        x(i) = xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "      }\n",
    "    \"\"\"\n",
    "    x = zeros(len(U))\n",
    "    x[0] = x0          # first point\n",
    "    x[1] = dx*dt + x0  # second point\n",
    "    \n",
    "    weave.inline(code_NumerovU, ['U', 'x', 'dt'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ux = -8*pi*R*rho\n",
    "U2 = NumerovU(ux, 0.0, 0.1, R[1]-R[0])\n",
    "alpha2 = (2*Zatom-U2[-1])/R[-1]\n",
    "U2 += alpha2*R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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+qfN4KdiPQL6xZQU99o2ib+/i0FEKkj6m5J8690+d+6fO46Vgh4R19SsYhE41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\np87jJTJDwl63g37dNCT4Ulp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c06bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(R,U1)\n",
    "plot(R,U2)\n",
    "grid()\n",
    "show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we add exchange correlation potential. Make sure \"excor.py\" is in your working directory, so that we can import it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MhCruVNmzZ88SO2qmpKSQm5tr/zkgIAB/f3/A1HI88sgjZGVl8ccff5Q5UAC0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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c3a810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from excor import ExchangeCorrelation\n",
    "exc = ExchangeCorrelation()\n",
    "def rs(rho):\n",
    "    \"Given density, returns rs.\"\n",
    "    if rho<1e-100: return 1e100\n",
    "    return pow(3/(4*pi*rho),1/3.)\n",
    "\n",
    "mrs = linspace(0.5,100,300)\n",
    "Ex = array([2*exc.Ex(rs) for rs in mrs])\n",
    "Ec = array([2*(exc.EcVc(rs)+exc.Vc(rs)) for rs in mrs])\n",
    "Ek = array([3/5.*(9*pi/4.)**(2/3.) * 1/rs**2 for rs in mrs])\n",
    "semilogy(mrs, -Ex, label='E-Exchange')\n",
    "semilogy(mrs, -Ec, label='E-correlation')\n",
    "semilogy(mrs, Ek, label='E-kinetic')\n",
    "legend(loc='best')\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from excor import ExchangeCorrelation\n",
    "exc = ExchangeCorrelation()\n",
    "def rs(rho):\n",
    "    \"Given density, returns rs.\"\n",
    "    if rho<1e-100: return 1e100\n",
    "    return pow(3/(4*pi*rho),1/3.)\n",
    "\n",
    "Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "\n",
    "Uks = U2-2*Zatom + Vxc*R\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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18W62v//979Flp5xySqn11vb9Vvcz0pB9X1UtEydOZMGCBQCldjmWXUfZ719F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\nWldycrIbPXq0++yzz1zPnj3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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114ae9b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5zh44Rc6RNHKOZpB3IpNLpzOxpmWiMjPwOZuJX3YmtXIyCcrLIPhSJnWsmYSQ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\nIiIh8f+19OMbReIjeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1144914d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(R,Vxc, label='Exchange-correlation contribution to U')\n",
    "legend(loc='best')\n",
    "show()\n",
    "\n",
    "plot(R,Vxc*R,label='Exchange-correlation contribution')\n",
    "plot(R,U2,label='Hartree contribution')\n",
    "plot(R,Uks, label='Uks')\n",
    "legend(loc='best')\n",
    "grid()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now it is time to reorganize the code and feed Hartree+Exchange correlation back to the Schroedinger equation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import *\n",
    "from scipy import integrate\n",
    "from scipy import interpolate\n",
    "from scipy import optimize\n",
    "import weave\n",
    "\n",
    "def Numerovc(f, x0_, dx, dh_):\n",
    "    code_Numerov=\"\"\"\n",
    "    double h2 = dh*dh;\n",
    "    double h12 = h2/12.;\n",
    "    \n",
    "    double w0 = x(0)*(1-h12*f(0));\n",
    "    double w1 = x(1)*(1-h12*f(1));\n",
    "    double xi = x(1);\n",
    "    double fi = f(1);\n",
    "    for (int i=2; i<f.size(); i++){\n",
    "        double w2 = 2*w1-w0+h2*fi*xi;  // here fi=f1\n",
    "        fi = f(i);                     // fi=f2\n",
    "        xi = w2/(1-h12*fi);\n",
    "        x(i)=xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "    }\n",
    "    \"\"\"\n",
    "    x = zeros(len(f))\n",
    "    dh=float(dh_)\n",
    "    x[0]=x0_\n",
    "    x[1]=x0_+dh*dx\n",
    "    weave.inline(code_Numerov, ['f','dh','x'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x\n",
    "\n",
    "def NumerovU(U, x0, dx, dt):\n",
    "    code_NumerovU=\"\"\"\n",
    "      double h2 = dt;\n",
    "      h2 = h2*h2;\n",
    "      double h12 = h2/12;\n",
    "      \n",
    "      double w0 = x(0)-h12*U(0);\n",
    "      double w1 = x(1)-h12*U(1);\n",
    "      double xi = x(1);\n",
    "      double Ux = U(1);\n",
    "      \n",
    "      for (int i=2; i<U.size(); i++){\n",
    "        double w2 = 2*w1 - w0 + h2*Ux;\n",
    "        Ux = U(i);\n",
    "        xi = w2+h12*Ux;\n",
    "        x(i) = xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "      }\n",
    "    \"\"\"\n",
    "    x = zeros(len(U))\n",
    "    x[0] = x0          # first point\n",
    "    x[1] = dx*dt + x0  # second point\n",
    "    \n",
    "    weave.inline(code_NumerovU, ['U', 'x', 'dt'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x\n",
    "\n",
    "def fSchrod2(En, R, l, Uks):\n",
    "    return (l*(l+1.)/R + Uks)/R - En\n",
    "    #return l*(l+1.)/R**2-2./R-En\n",
    "\n",
    "def ComputeSchrod(En,R,l,Uks):\n",
    "    \"Computes Schrod Eq.\" \n",
    "    f = fSchrod2(En,R[::-1],l,Uks[::-1])  # do not forget to turn around Uks!\n",
    "    ur = Numerovc(f,0.0,-1e-7,-R[1]+R[0])[::-1]\n",
    "    norm = integrate.simps(ur**2,x=R)\n",
    "    return ur*1/sqrt(abs(norm))\n",
    "\n",
    "def Shoot(En,R,l,Uks):\n",
    "    ur = ComputeSchrod(En,R,l,Uks)\n",
    "    #ur = ur/R**l\n",
    "    f0 = ur[0]\n",
    "    f1 = ur[1]\n",
    "    f_at_0 = f0 + (f1-f0)*(0.0-R[0])/(R[1]-R[0])\n",
    "    return f_at_0\n",
    "\n",
    "def FindBoundStates(R,l,nmax,Esearch,Uks):\n",
    "    n=0\n",
    "    Ebnd=[]\n",
    "    u0 = Shoot(Esearch[0],R,l,Uks)\n",
    "    for i in range(1,len(Esearch)):\n",
    "        u1 = Shoot(Esearch[i],R,l,Uks)\n",
    "        #print 'looking at energy', Esearch[i], u0,u1\n",
    "        if u0*u1<0:\n",
    "            Ebound = optimize.brentq(Shoot,Esearch[i-1],Esearch[i],xtol=1e-16,args=(R,l,Uks))\n",
    "            Ebnd.append((l,Ebound))\n",
    "            if len(Ebnd)>nmax: break\n",
    "            n+=1\n",
    "            print 'Found bound state at E=%14.9f E[Hartree]=%14.9f l=%d' % (Ebound, Ebound/2,l)\n",
    "        u0=u1\n",
    "    return Ebnd\n",
    "\n",
    "def cmpE(x,y):\n",
    "    if abs(x[1]-y[1])>1e-4:\n",
    "        return cmp(x[1],y[1])\n",
    "    else:\n",
    "        return cmp(x[0],y[0])\n",
    "\n",
    "# This is slightly modified code from Hydrogen project\n",
    "def ChargeDensity(bst,R,Zatom,Uks):\n",
    "    rho = zeros( len(R) )\n",
    "    N=0\n",
    "    for i,(l,Ei) in enumerate(bst):\n",
    "        dN = 2*(2*l+1)\n",
    "        if N+dN<Zatom:\n",
    "            ferm=1\n",
    "        else:\n",
    "            ferm = (Zatom-N)/float(dN)\n",
    "        u = ComputeSchrod(Ei,R,l,Uks)\n",
    "        drho = u**2 / (4*pi*R**2) * dN * ferm\n",
    "        rho += drho\n",
    "        N += dN\n",
    "        print 'Adding state with l=', l, 'and E=', Ei/2, ' Hartree with Z=', N, 'with ferm=', ferm\n",
    "        if N>=Zatom: break\n",
    "    return rho\n",
    "    \n",
    "    \n",
    "def HartreeU(R, rho):\n",
    "    ux = -8*pi*R*rho\n",
    "    dudx=0.1\n",
    "    U = NumerovU(ux, 0.0, dudx, R[1]-R[0])\n",
    "    alpha2 = (2*Zatom-U[-1])/R[-1]\n",
    "    U += alpha2*R\n",
    "    return U\n",
    "\n",
    "def rs(rho):\n",
    "    \"Given density, returns rs.\"\n",
    "    if rho<1e-100: return 1e100\n",
    "    return pow(3/(4*pi*rho),1/3.)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -2.04562577e-12,   4.29560682e+00,   8.29392313e-03, ...,\n",
       "         2.56199726e-49,   1.27942754e-49,   0.00000000e+00])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ComputeSchrod(-1.,R,l,-2*ones(len(R)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999998807 E[Hartree]=  -0.499999403 l=0\n",
      "Found bound state at E=  -0.249999851 E[Hartree]=  -0.124999925 l=0\n",
      "Adding state with l= 0 and E= -0.499999403471  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.124999925296  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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/IpFI0CUkHGXunjJ3T5mHVyiag4IC71l7DvwxcuTIoEtIOMrcPWXunjIPr9A0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\n0wj3Vjj1VNiwAWoELSIiEu8Cu7eCtXY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c3a650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1144577d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E= -12.847578370 E[Hartree]=  -6.423789185 l=0\n",
      "Found bound state at E=  -1.592504356 E[Hartree]=  -0.796252178 l=0\n",
      "Adding state with l= 0 and E= -6.42378918503  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.796252177996  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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SiUTIy8uLWT516lRGjx4ds6yoqIhIJFJt+CwrK2uP1/j269cvcO8jLS0tLt4H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\nREREJMb/Bx4thAAW+yJ3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114b70990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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F76g3z5EkqQG8lr4kSQ1g4EuS1AAGviRJDWDgS5LUAAa+JEkNYOBLktQABr4k\nSQ1g4EuS1AAGviRJDWDgS5LUAAa+JEkN8P8AjaCNR1XrSAQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106212d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = linspace(1e-8,50,2**12+1) # so that we can use Romberg method\n",
    "\n",
    "nmax = 2\n",
    "Zatom = 4\n",
    "\n",
    "E0=-1.2*Zatom**2\n",
    "Eshift=0.5 # sometimes energies can be positive!!!                                                                                                                        \n",
    "Esearch = -logspace(-4,log10(-E0+Eshift),200)[::-1] + Eshift\n",
    "\n",
    "exc = ExchangeCorrelation()\n",
    "Uks = -2.*ones( len(R) )     # First iteration like hydrogen atom\n",
    "\n",
    "for itt in range(2):\n",
    "    Bnd=[]\n",
    "    for l in range(nmax-1):\n",
    "        Bnd += FindBoundStates(R,l,nmax-l,Esearch,Uks)\n",
    "    Bnd.sort( cmpE )\n",
    "    \n",
    "    rho = ChargeDensity(Bnd,R,Zatom,Uks)\n",
    "    \n",
    "    U = HartreeU(R, rho)\n",
    "    \n",
    "    Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "    \n",
    "    Uks = U-2*Zatom + Vxc*R\n",
    "    \n",
    "    print 'Total density has weight=', integrate.simps(rho*(4*pi*R**2), x=R)\n",
    "    \n",
    "    plot(R,U, label='U-hartree')\n",
    "    plot(R,Vxc,label='Vxc')\n",
    "    plot(R, Uks, label='Uks')\n",
    "    legend(loc='best')\n",
    "    grid()\n",
    "    show()\n",
    "    plot(R, rho*(4*pi*R**2))\n",
    "    xlim([0,20])\n",
    "    show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will include charge density mixing, which will improve convergence. We will take a fraction of the new, and a fraction of the old charge density at each iteration.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999998807 E[Hartree]=  -0.499999403 l=0\n",
      "Found bound state at E=  -0.249999851 E[Hartree]=  -0.124999925 l=0\n",
      "Adding state with l= 0 and E= -0.499999403471  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.124999925296  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E= -12.847578370 E[Hartree]=  -6.423789185 l=0\n",
      "Found bound state at E=  -1.592504356 E[Hartree]=  -0.796252178 l=0\n",
      "Adding state with l= 0 and E= -6.42378918503  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.796252177996  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -9.809331493 E[Hartree]=  -4.904665746 l=0\n",
      "Found bound state at E=  -0.759401416 E[Hartree]=  -0.379700708 l=0\n",
      "Adding state with l= 0 and E= -4.90466574638  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.379700708221  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -6.716105845 E[Hartree]=  -3.358052923 l=0\n",
      "Found bound state at E=  -0.215725475 E[Hartree]=  -0.107862738 l=0\n",
      "Adding state with l= 0 and E= -3.35805292251  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.107862737501  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.565176024 E[Hartree]=  -3.782588012 l=0\n",
      "Found bound state at E=  -0.393819734 E[Hartree]=  -0.196909867 l=0\n",
      "Adding state with l= 0 and E= -3.78258801221  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.196909866827  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.907109199 E[Hartree]=  -3.953554600 l=0\n",
      "Found bound state at E=  -0.464424548 E[Hartree]=  -0.232212274 l=0\n",
      "Adding state with l= 0 and E= -3.95355459973  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.232212274037  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.704561385 E[Hartree]=  -3.852280692 l=0\n",
      "Found bound state at E=  -0.409029832 E[Hartree]=  -0.204514916 l=0\n",
      "Adding state with l= 0 and E= -3.85228069231  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.204514915867  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.682331761 E[Hartree]=  -3.841165881 l=0\n",
      "Found bound state at E=  -0.403695002 E[Hartree]=  -0.201847501 l=0\n",
      "Adding state with l= 0 and E= -3.84116588064  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.201847501159  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.718367018 E[Hartree]=  -3.859183509 l=0\n",
      "Found bound state at E=  -0.413194014 E[Hartree]=  -0.206597007 l=0\n",
      "Adding state with l= 0 and E= -3.85918350894  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.206597007022  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.716041250 E[Hartree]=  -3.858020625 l=0\n",
      "Found bound state at E=  -0.412505071 E[Hartree]=  -0.206252536 l=0\n",
      "Adding state with l= 0 and E= -3.85802062506  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.206252535601  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.710600928 E[Hartree]=  -3.855300464 l=0\n",
      "Found bound state at E=  -0.411038588 E[Hartree]=  -0.205519294 l=0\n",
      "Adding state with l= 0 and E= -3.85530046412  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.2055192941  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.711860535 E[Hartree]=  -3.855930268 l=0\n",
      "Found bound state at E=  -0.411383126 E[Hartree]=  -0.205691563 l=0\n",
      "Adding state with l= 0 and E= -3.85593026768  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20569156278  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712535108 E[Hartree]=  -3.856267554 l=0\n",
      "Found bound state at E=  -0.411565239 E[Hartree]=  -0.205782620 l=0\n",
      "Adding state with l= 0 and E= -3.85626755415  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205782619571  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712221919 E[Hartree]=  -3.856110960 l=0\n",
      "Found bound state at E=  -0.411479949 E[Hartree]=  -0.205739974 l=0\n",
      "Adding state with l= 0 and E= -3.8561109595  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739974323  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712163550 E[Hartree]=  -3.856081775 l=0\n",
      "Found bound state at E=  -0.411464155 E[Hartree]=  -0.205732078 l=0\n",
      "Adding state with l= 0 and E= -3.85608177481  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205732077673  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712223689 E[Hartree]=  -3.856111845 l=0\n",
      "Found bound state at E=  -0.411480517 E[Hartree]=  -0.205740258 l=0\n",
      "Adding state with l= 0 and E= -3.85611184467  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205740258488  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712223394 E[Hartree]=  -3.856111697 l=0\n",
      "Found bound state at E=  -0.411480430 E[Hartree]=  -0.205740215 l=0\n",
      "Adding state with l= 0 and E= -3.85611169684  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205740215146  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712213707 E[Hartree]=  -3.856106854 l=0\n",
      "Found bound state at E=  -0.411477795 E[Hartree]=  -0.205738898 l=0\n",
      "Adding state with l= 0 and E= -3.85610685372  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205738897534  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712215324 E[Hartree]=  -3.856107662 l=0\n",
      "Found bound state at E=  -0.411478235 E[Hartree]=  -0.205739118 l=0\n",
      "Adding state with l= 0 and E= -3.85610766187  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20573911762  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216630 E[Hartree]=  -3.856108315 l=0\n",
      "Found bound state at E=  -0.411478591 E[Hartree]=  -0.205739295 l=0\n",
      "Adding state with l= 0 and E= -3.85610831498  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739295317  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216157 E[Hartree]=  -3.856108078 l=0\n",
      "Found bound state at E=  -0.411478462 E[Hartree]=  -0.205739231 l=0\n",
      "Adding state with l= 0 and E= -3.85610807842  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739230934  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216022 E[Hartree]=  -3.856108011 l=0\n",
      "Found bound state at E=  -0.411478425 E[Hartree]=  -0.205739213 l=0\n",
      "Adding state with l= 0 and E= -3.856108011  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739212588  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216120 E[Hartree]=  -3.856108060 l=0\n",
      "Found bound state at E=  -0.411478452 E[Hartree]=  -0.205739226 l=0\n",
      "Adding state with l= 0 and E= -3.85610806021  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739225981  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216126 E[Hartree]=  -3.856108063 l=0\n",
      "Found bound state at E=  -0.411478454 E[Hartree]=  -0.205739227 l=0\n",
      "Adding state with l= 0 and E= -3.85610806315  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739226775  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216109 E[Hartree]=  -3.856108055 l=0\n",
      "Found bound state at E=  -0.411478449 E[Hartree]=  -0.205739224 l=0\n",
      "Adding state with l= 0 and E= -3.85610805471  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224482  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216111 E[Hartree]=  -3.856108056 l=0\n",
      "Found bound state at E=  -0.411478449 E[Hartree]=  -0.205739225 l=0\n",
      "Adding state with l= 0 and E= -3.85610805559  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224718  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216114 E[Hartree]=  -3.856108057 l=0\n",
      "Found bound state at E=  -0.411478450 E[Hartree]=  -0.205739225 l=0\n",
      "Adding state with l= 0 and E= -3.85610805681  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739225051  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216113 E[Hartree]=  -3.856108056 l=0\n",
      "Found bound state at E=  -0.411478450 E[Hartree]=  -0.205739225 l=0\n",
      "Adding state with l= 0 and E= -3.85610805647  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224957  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216113 E[Hartree]=  -3.856108056 l=0\n",
      "Found bound state at E=  -0.411478450 E[Hartree]=  -0.205739225 l=0\n",
      "Adding state with l= 0 and E= -3.85610805633  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20573922492  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216113 E[Hartree]=  -3.856108056 l=0\n",
      "Found bound state at E=  -0.411478450 E[Hartree]=  -0.205739225 l=0\n",
      "Adding state with l= 0 and E= -3.8561080564  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224937  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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g8b621WEFERGRYLg+56AlYIGN+1tRIwfuLF68zz5NfKDM3VPm7inz2OWsOTDG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\n/vjf/4a//Q2WL4ehQ727Ica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B4HpgIZAC9KrNto0Ld0CrVl6DIL5LT08PuoSEo8zdU+bu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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11063c7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rDHvvDR/4QH6iQpJUDIaEEh15JIwfn/9qr6f/+i84+GBYujQ/1njllfkxzUay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\n2ZOk/DQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114b70590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = linspace(1e-8,50,2**12+1) # so that we can use Romberg method\n",
    "\n",
    "nmax = 2\n",
    "Zatom = 4\n",
    "mixr = 0.5\n",
    "\n",
    "E0=-1.2*Zatom**2\n",
    "Eshift=0.5 # sometimes energies can be positive!!!                                                                                                                        \n",
    "Esearch = -logspace(-4,log10(-E0+Eshift),200)[::-1] + Eshift\n",
    "\n",
    "exc = ExchangeCorrelation()\n",
    "Uks = -2.*ones( len(R) )     # First iteration like hydrogen atom\n",
    "\n",
    "for itt in range(30):\n",
    "    Bnd=[]\n",
    "    for l in range(nmax-1):\n",
    "        Bnd += FindBoundStates(R,l,nmax-l,Esearch,Uks)\n",
    "    Bnd.sort( cmpE )\n",
    "    \n",
    "    rho_new = ChargeDensity(Bnd,R,Zatom,Uks)\n",
    "    \n",
    "    if itt>0:\n",
    "        rho = rho_new*mixr + (1-mixr)*rho_old\n",
    "    else:\n",
    "        rho = rho_new\n",
    "    rho_old = copy(rho_new)\n",
    "    \n",
    "    U = HartreeU(R, rho)\n",
    "    \n",
    "    Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "    \n",
    "    Uks = U-2*Zatom + Vxc*R\n",
    "    \n",
    "    print 'Total density has weight=', integrate.simps(rho*(4*pi*R**2), x=R)\n",
    "  \n",
    "\n",
    "plot(R,U, label='U-hartree')\n",
    "plot(R,Vxc,label='Vxc')\n",
    "plot(R, Uks, label='Uks')\n",
    "legend(loc='best')\n",
    "grid()\n",
    "show()\n",
    "plot(R, rho*(4*pi*R**2))\n",
    "xlim([0,10])\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we add the total energy. At each iteration, we will evaluate \n",
    "\n",
    "\\begin{eqnarray}\n",
    "E^{LDA}_{total} &=& \\sum_{i\\in occupied}\\int d\\vec{r}\n",
    "\\psi_i^*(\\vec{r})[-\\nabla^2]\\psi_i(\\vec{r}) +\\nonumber\\\\\n",
    " &+& \\int d\\vec{r} \\rho(\\vec{r}) [V_{nucleous}(\\vec{r})+\\epsilon_H(\\vec{r}) +\n",
    "   \\epsilon_{XC}(\\vec{r})]\\nonumber\\\\\n",
    " &=& \\sum_{i\\in occupied}\\int d\\vec{r}\n",
    "\\psi_i^*(\\vec{r})[-\\nabla^2+V_{nucleous}+V_H+V_{XC}]\\psi_i(\\vec{r})\n",
    " \\nonumber\\\\\n",
    " &+& \\int d\\vec{r} \\rho(\\vec{r}) [\\epsilon_H(\\vec{r})-V_H(\\vec{r}) +\n",
    "   \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\\nonumber\\\\\n",
    " &=& \\sum_{i\\in occupied}\\epsilon_i + \\int d\\vec{r} \\rho(\\vec{r}) [\\epsilon_H(\\vec{r})-V_H(\\vec{r}) +\n",
    "   \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\\nonumber\\\\\n",
    " &=& \\sum_{i\\in occupied}\\epsilon_i + \\int d\\vec{r} \\rho(\\vec{r}) [-\\epsilon_H(\\vec{r}) + \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\\\\\n",
    "  &=& \\sum_{i\\in occupied}\\epsilon_i + \\int d\\vec{r} \\rho(\\vec{r})[\n",
    "  -\\frac{1}{2} V_H(\\vec{r}) + \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\n",
    "\\end{eqnarray}\n",
    "\n",
    "Here we used\n",
    "\n",
    "\\begin{eqnarray}\n",
    "&& E_y[\\rho] \\equiv \\int d\\vec{r}\\; \\rho(\\vec{r})\\; \\epsilon_y[\\rho(\\vec{r})]\\\\\n",
    "&& V_y[\\rho]\\equiv \\frac{\\delta E_y[\\rho]}{\\delta \\rho(\\vec{r})}\n",
    "\\end{eqnarray}\n",
    "where $y$ is one of $H$, $x$ or $c$. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare these values with NIST database at:\n",
    "https://www.nist.gov/pml/data/atomic-total-energies-and-eigenvalues-html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999998525 E[Hartree]=  -0.499999263 l=0\n",
      "Found bound state at E=  -0.225612420 E[Hartree]=  -0.112806210 l=0\n",
      "Found bound state at E=  -0.237719089 E[Hartree]=  -0.118859545 l=1\n",
      "Adding state with l= 0 and E= -0.499999262651  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.11885954472  Hartree with Z= 8 with ferm= 1.0\n",
      "Itteration 0 Etot[Ry]= -18.6894880818 Etot[Hartre]= -9.3447440409 Diff= 18.6894880818\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -58.434784810 E[Hartree]= -29.217392405 l=0\n",
      "Found bound state at E= -10.657763975 E[Hartree]=  -5.328881987 l=0\n",
      "Found bound state at E= -10.573657920 E[Hartree]=  -5.286828960 l=1\n",
      "Adding state with l= 0 and E= -29.217392405  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -5.32888198725  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -5.28682895997  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 1 Etot[Ry]= -222.78914458 Etot[Hartre]= -111.39457229 Diff= 204.099656498\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -44.666807253 E[Hartree]= -22.333403627 l=0\n",
      "Found bound state at E=  -4.494571717 E[Hartree]=  -2.247285859 l=0\n",
      "Found bound state at E=  -3.483793215 E[Hartree]=  -1.741896608 l=1\n",
      "Adding state with l= 0 and E= -22.3334036266  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -2.24728585855  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -1.74189660768  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 2 Etot[Ry]= -206.175980551 Etot[Hartre]= -103.087990276 Diff= 16.613164029\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -31.323729185 E[Hartree]= -15.661864593 l=0\n",
      "Found bound state at E=  -0.325863389 E[Hartree]=  -0.162931694 l=0\n",
      "Found bound state at E=   0.162691446 E[Hartree]=   0.081345723 l=1\n",
      "Adding state with l= 0 and E= -15.6618645926  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.162931694387  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= 0.0813457227617  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 3 Etot[Ry]= -116.906288649 Etot[Hartre]= -58.4531443247 Diff= 89.2696919019\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -39.821454422 E[Hartree]= -19.910727211 l=0\n",
      "Found bound state at E=  -3.513907181 E[Hartree]=  -1.756953590 l=0\n",
      "Found bound state at E=  -2.440575758 E[Hartree]=  -1.220287879 l=1\n",
      "Adding state with l= 0 and E= -19.9107272112  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -1.75695359044  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -1.22028787882  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 4 Etot[Ry]= -147.809875724 Etot[Hartre]= -73.904937862 Diff= 30.9035870746\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -40.741447329 E[Hartree]= -20.370723665 l=0\n",
      "Found bound state at E=  -3.782278358 E[Hartree]=  -1.891139179 l=0\n",
      "Found bound state at E=  -2.736552096 E[Hartree]=  -1.368276048 l=1\n",
      "Adding state with l= 0 and E= -20.3707236647  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -1.89113917881  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -1.36827604793  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 5 Etot[Ry]= -177.467770526 Etot[Hartre]= -88.7338852628 Diff= 29.6578948016\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -35.340389182 E[Hartree]= -17.670194591 l=0\n",
      "Found bound state at E=  -0.967563303 E[Hartree]=  -0.483781651 l=0\n",
      "Found bound state at E=  -0.017375274 E[Hartree]=  -0.008687637 l=1\n",
      "Adding state with l= 0 and E= -17.670194591  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.483781651309  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.00868763714349  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 6 Etot[Ry]= -136.449954598 Etot[Hartre]= -68.2249772992 Diff= 41.017815927\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -38.177001672 E[Hartree]= -19.088500836 l=0\n",
      "Found bound state at E=  -2.214708097 E[Hartree]=  -1.107354049 l=0\n",
      "Found bound state at E=  -1.136160963 E[Hartree]=  -0.568080482 l=1\n",
      "Adding state with l= 0 and E= -19.0885008358  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -1.10735404862  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.568080481503  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 7 Etot[Ry]= -145.858022964 Etot[Hartre]= -72.9290114821 Diff= 9.40806836579\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -39.022022508 E[Hartree]= -19.511011254 l=0\n",
      "Found bound state at E=  -2.526267445 E[Hartree]=  -1.263133722 l=0\n",
      "Found bound state at E=  -1.461705876 E[Hartree]=  -0.730852938 l=1\n",
      "Adding state with l= 0 and E= -19.5110112539  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -1.26313372238  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.730852938169  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 8 Etot[Ry]= -161.624522674 Etot[Hartre]= -80.8122613371 Diff= 15.7664997098\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -36.400750644 E[Hartree]= -18.200375322 l=0\n",
      "Found bound state at E=  -1.316719555 E[Hartree]=  -0.658359777 l=0\n",
      "Found bound state at E=  -0.284342831 E[Hartree]=  -0.142171416 l=1\n",
      "Adding state with l= 0 and E= -18.2003753222  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.658359777319  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.142171415521  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 9 Etot[Ry]= -143.798851323 Etot[Hartre]= -71.8994256617 Diff= 17.8256713506\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.572003685 E[Hartree]= -18.786001843 l=0\n",
      "Found bound state at E=  -1.809061488 E[Hartree]=  -0.904530744 l=0\n",
      "Found bound state at E=  -0.739909698 E[Hartree]=  -0.369954849 l=1\n",
      "Adding state with l= 0 and E= -18.7860018427  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.904530744064  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.369954848882  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 10 Etot[Ry]= -146.04912323 Etot[Hartre]= -73.024561615 Diff= 2.2502719065\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -38.273020848 E[Hartree]= -19.136510424 l=0\n",
      "Found bound state at E=  -2.079942188 E[Hartree]=  -1.039971094 l=0\n",
      "Found bound state at E=  -1.011347844 E[Hartree]=  -0.505673922 l=1\n",
      "Adding state with l= 0 and E= -19.1365104242  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -1.0399710942  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.505673921879  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 11 Etot[Ry]= -154.481920258 Etot[Hartre]= -77.2409601292 Diff= 8.43279702851\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.058719393 E[Hartree]= -18.529359697 l=0\n",
      "Found bound state at E=  -1.563071066 E[Hartree]=  -0.781535533 l=0\n",
      "Found bound state at E=  -0.505512927 E[Hartree]=  -0.252756464 l=1\n",
      "Adding state with l= 0 and E= -18.5293596965  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.781535532793  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.252756463528  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 12 Etot[Ry]= -147.463655302 Etot[Hartre]= -73.731827651 Diff= 7.01826495645\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.395531101 E[Hartree]= -18.697765551 l=0\n",
      "Found bound state at E=  -1.703300390 E[Hartree]=  -0.851650195 l=0\n",
      "Found bound state at E=  -0.638412369 E[Hartree]=  -0.319206184 l=1\n",
      "Adding state with l= 0 and E= -18.6977655506  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.851650195143  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.31920618429  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 13 Etot[Ry]= -146.85519989 Etot[Hartre]= -73.4275999449 Diff= 0.608455412228\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.884173003 E[Hartree]= -18.942086501 l=0\n",
      "Found bound state at E=  -1.896593146 E[Hartree]=  -0.948296573 l=0\n",
      "Found bound state at E=  -0.828013088 E[Hartree]=  -0.414006544 l=1\n",
      "Adding state with l= 0 and E= -18.9420865014  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.948296572757  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.414006543873  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 14 Etot[Ry]= -151.202416826 Etot[Hartre]= -75.6012084132 Diff= 4.34721693654\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.376441340 E[Hartree]= -18.688220670 l=0\n",
      "Found bound state at E=  -1.687570537 E[Hartree]=  -0.843785268 l=0\n",
      "Found bound state at E=  -0.623455859 E[Hartree]=  -0.311727930 l=1\n",
      "Adding state with l= 0 and E= -18.6882206701  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.843785268251  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.311727929664  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 15 Etot[Ry]= -148.886760087 Etot[Hartre]= -74.4433800434 Diff= 2.3156567395\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.390331414 E[Hartree]= -18.695165707 l=0\n",
      "Found bound state at E=  -1.693605554 E[Hartree]=  -0.846802777 l=0\n",
      "Found bound state at E=  -0.629248069 E[Hartree]=  -0.314624035 l=1\n",
      "Adding state with l= 0 and E= -18.6951657071  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.846802777027  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.31462403461  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 16 Etot[Ry]= -147.689102468 Etot[Hartre]= -73.8445512342 Diff= 1.19765761848\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.679878079 E[Hartree]= -18.839939040 l=0\n",
      "Found bound state at E=  -1.809734026 E[Hartree]=  -0.904867013 l=0\n",
      "Found bound state at E=  -0.742210632 E[Hartree]=  -0.371105316 l=1\n",
      "Adding state with l= 0 and E= -18.8399390396  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.904867013108  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.371105316064  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 17 Etot[Ry]= -149.751737816 Etot[Hartre]= -74.8758689078 Diff= 2.0626353473\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.496870854 E[Hartree]= -18.748435427 l=0\n",
      "Found bound state at E=  -1.735296263 E[Hartree]=  -0.867648131 l=0\n",
      "Found bound state at E=  -0.669538626 E[Hartree]=  -0.334769313 l=1\n",
      "Adding state with l= 0 and E= -18.7484354272  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.867648131447  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.334769313017  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 18 Etot[Ry]= -149.235257845 Etot[Hartre]= -74.6176289225 Diff= 0.516479970723\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.431430320 E[Hartree]= -18.715715160 l=0\n",
      "Found bound state at E=  -1.708607494 E[Hartree]=  -0.854303747 l=0\n",
      "Found bound state at E=  -0.643731025 E[Hartree]=  -0.321865512 l=1\n",
      "Adding state with l= 0 and E= -18.7157151601  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.854303747204  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.321865512267  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 19 Etot[Ry]= -148.295916561 Etot[Hartre]= -74.1479582803 Diff= 0.939341284331\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.580211765 E[Hartree]= -18.790105883 l=0\n",
      "Found bound state at E=  -1.768718612 E[Hartree]=  -0.884359306 l=0\n",
      "Found bound state at E=  -0.702061538 E[Hartree]=  -0.351030769 l=1\n",
      "Adding state with l= 0 and E= -18.7901058826  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.884359306056  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.351030769098  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 20 Etot[Ry]= -149.16587051 Etot[Hartre]= -74.582935255 Diff= 0.86995394936\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.530151148 E[Hartree]= -18.765075574 l=0\n",
      "Found bound state at E=  -1.748427858 E[Hartree]=  -0.874213929 l=0\n",
      "Found bound state at E=  -0.682298563 E[Hartree]=  -0.341149281 l=1\n",
      "Adding state with l= 0 and E= -18.765075574  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.874213929043  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.341149281461  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 21 Etot[Ry]= -149.211574102 Etot[Hartre]= -74.605787051 Diff= 0.0457035919248\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.469858107 E[Hartree]= -18.734929053 l=0\n",
      "Found bound state at E=  -1.723864453 E[Hartree]=  -0.861932227 l=0\n",
      "Found bound state at E=  -0.658478619 E[Hartree]=  -0.329239309 l=1\n",
      "Adding state with l= 0 and E= -18.7349290533  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.861932226586  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.329239309395  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 22 Etot[Ry]= -148.654051022 Etot[Hartre]= -74.3270255108 Diff= 0.557523080342\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.536490985 E[Hartree]= -18.768245493 l=0\n",
      "Found bound state at E=  -1.750877659 E[Hartree]=  -0.875438830 l=0\n",
      "Found bound state at E=  -0.684684255 E[Hartree]=  -0.342342128 l=1\n",
      "Adding state with l= 0 and E= -18.7682454925  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.875438829671  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.34234212772  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 23 Etot[Ry]= -148.962757427 Etot[Hartre]= -74.4813787133 Diff= 0.308706405068\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.532696100 E[Hartree]= -18.766348050 l=0\n",
      "Found bound state at E=  -1.749343874 E[Hartree]=  -0.874671937 l=0\n",
      "Found bound state at E=  -0.683192604 E[Hartree]=  -0.341596302 l=1\n",
      "Adding state with l= 0 and E= -18.7663480498  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.87467193688  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.341596302007  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 24 Etot[Ry]= -149.113943343 Etot[Hartre]= -74.5569716714 Diff= 0.151185916185\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.494507667 E[Hartree]= -18.747253834 l=0\n",
      "Found bound state at E=  -1.733811168 E[Hartree]=  -0.866905584 l=0\n",
      "Found bound state at E=  -0.668113431 E[Hartree]=  -0.334056716 l=1\n",
      "Adding state with l= 0 and E= -18.7472538337  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.866905584125  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.33405671569  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 25 Etot[Ry]= -148.834546045 Etot[Hartre]= -74.4172730224 Diff= 0.279397298054\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.519926521 E[Hartree]= -18.759963260 l=0\n",
      "Found bound state at E=  -1.744130031 E[Hartree]=  -0.872065016 l=0\n",
      "Found bound state at E=  -0.678126618 E[Hartree]=  -0.339063309 l=1\n",
      "Adding state with l= 0 and E= -18.7599632603  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.872065015596  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.33906330879  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 26 Etot[Ry]= -148.912247218 Etot[Hartre]= -74.4561236092 Diff= 0.0777011735939\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.527639853 E[Hartree]= -18.763819927 l=0\n",
      "Found bound state at E=  -1.747260392 E[Hartree]=  -0.873630196 l=0\n",
      "Found bound state at E=  -0.681168170 E[Hartree]=  -0.340584085 l=1\n",
      "Adding state with l= 0 and E= -18.7638199265  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.873630196191  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.340584085062  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 27 Etot[Ry]= -149.034276942 Etot[Hartre]= -74.5171384711 Diff= 0.122029723805\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.507556727 E[Hartree]= -18.753778363 l=0\n",
      "Found bound state at E=  -1.739099860 E[Hartree]=  -0.869549930 l=0\n",
      "Found bound state at E=  -0.673243237 E[Hartree]=  -0.336621618 l=1\n",
      "Adding state with l= 0 and E= -18.7537783634  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.869549930126  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.336621618254  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 28 Etot[Ry]= -148.9131813 Etot[Hartre]= -74.4565906499 Diff= 0.121095642318\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.515050361 E[Hartree]= -18.757525180 l=0\n",
      "Found bound state at E=  -1.742143236 E[Hartree]=  -0.871071618 l=0\n",
      "Found bound state at E=  -0.676197360 E[Hartree]=  -0.338098680 l=1\n",
      "Adding state with l= 0 and E= -18.7575251805  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871071618232  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338098679914  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 29 Etot[Ry]= -148.912681926 Etot[Hartre]= -74.4563409628 Diff= 0.000499374331071\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.522660717 E[Hartree]= -18.761330359 l=0\n",
      "Found bound state at E=  -1.745232060 E[Hartree]=  -0.872616030 l=0\n",
      "Found bound state at E=  -0.679197400 E[Hartree]=  -0.339598700 l=1\n",
      "Adding state with l= 0 and E= -18.7613303587  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.872616030031  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.33959870023  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 30 Etot[Ry]= -148.986220623 Etot[Hartre]= -74.4931103113 Diff= 0.0735386970794\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.513515646 E[Hartree]= -18.756757823 l=0\n",
      "Found bound state at E=  -1.741517845 E[Hartree]=  -0.870758923 l=0\n",
      "Found bound state at E=  -0.675590230 E[Hartree]=  -0.337795115 l=1\n",
      "Adding state with l= 0 and E= -18.7567578228  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.87075892271  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.337795114891  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 31 Etot[Ry]= -148.941990218 Etot[Hartre]= -74.4709951092 Diff= 0.0442304041557\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.514445519 E[Hartree]= -18.757222760 l=0\n",
      "Found bound state at E=  -1.741895569 E[Hartree]=  -0.870947785 l=0\n",
      "Found bound state at E=  -0.675956950 E[Hartree]=  -0.337978475 l=1\n",
      "Adding state with l= 0 and E= -18.7572227597  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.870947784535  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.337978475069  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 32 Etot[Ry]= -148.924263673 Etot[Hartre]= -74.4621318367 Diff= 0.0177265450819\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.519414924 E[Hartree]= -18.759707462 l=0\n",
      "Found bound state at E=  -1.743912921 E[Hartree]=  -0.871956461 l=0\n",
      "Found bound state at E=  -0.677916014 E[Hartree]=  -0.338958007 l=1\n",
      "Adding state with l= 0 and E= -18.759707462  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871956460725  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338958006969  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 33 Etot[Ry]= -148.961744105 Etot[Hartre]= -74.4808720525 Diff= 0.0374804315697\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.515844461 E[Hartree]= -18.757922231 l=0\n",
      "Found bound state at E=  -1.742463082 E[Hartree]=  -0.871231541 l=0\n",
      "Found bound state at E=  -0.676508001 E[Hartree]=  -0.338254000 l=1\n",
      "Adding state with l= 0 and E= -18.7579222307  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871231540851  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338254000261  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 34 Etot[Ry]= -148.94978914 Etot[Hartre]= -74.4748945702 Diff= 0.0119549646056\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.514997560 E[Hartree]= -18.757498780 l=0\n",
      "Found bound state at E=  -1.742119181 E[Hartree]=  -0.871059591 l=0\n",
      "Found bound state at E=  -0.676174078 E[Hartree]=  -0.338087039 l=1\n",
      "Adding state with l= 0 and E= -18.7574987799  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871059590665  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338087039198  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 35 Etot[Ry]= -148.934339712 Etot[Hartre]= -74.467169856 Diff= 0.0154494284\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.517670583 E[Hartree]= -18.758835291 l=0\n",
      "Found bound state at E=  -1.743204448 E[Hartree]=  -0.871602224 l=0\n",
      "Found bound state at E=  -0.677227935 E[Hartree]=  -0.338613968 l=1\n",
      "Adding state with l= 0 and E= -18.7588352913  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871602223879  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338613967552  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 36 Etot[Ry]= -148.950922154 Etot[Hartre]= -74.4754610769 Diff= 0.0165824418804\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516565448 E[Hartree]= -18.758282724 l=0\n",
      "Found bound state at E=  -1.742755720 E[Hartree]=  -0.871377860 l=0\n",
      "Found bound state at E=  -0.676792169 E[Hartree]=  -0.338396084 l=1\n",
      "Adding state with l= 0 and E= -18.7582827241  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871377859933  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338396084464  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 37 Etot[Ry]= -148.950237524 Etot[Hartre]= -74.4751187619 Diff= 0.000684630013097\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.515616337 E[Hartree]= -18.757808168 l=0\n",
      "Found bound state at E=  -1.742370314 E[Hartree]=  -0.871185157 l=0\n",
      "Found bound state at E=  -0.676417927 E[Hartree]=  -0.338208963 l=1\n",
      "Adding state with l= 0 and E= -18.7578081683  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871185157169  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338208963253  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 38 Etot[Ry]= -148.940614546 Etot[Hartre]= -74.4703072728 Diff= 0.0096229781069\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516859589 E[Hartree]= -18.758429794 l=0\n",
      "Found bound state at E=  -1.742875116 E[Hartree]=  -0.871437558 l=0\n",
      "Found bound state at E=  -0.676908114 E[Hartree]=  -0.338454057 l=1\n",
      "Adding state with l= 0 and E= -18.7584297944  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871437558211  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338454057052  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 39 Etot[Ry]= -148.946852687 Etot[Hartre]= -74.4734263436 Diff= 0.00623814152075\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516681583 E[Hartree]= -18.758340791 l=0\n",
      "Found bound state at E=  -1.742802840 E[Hartree]=  -0.871401420 l=0\n",
      "Found bound state at E=  -0.676837927 E[Hartree]=  -0.338418964 l=1\n",
      "Adding state with l= 0 and E= -18.7583407913  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871401420108  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338418963733  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 40 Etot[Ry]= -148.948901586 Etot[Hartre]= -74.4744507932 Diff= 0.00204889922324\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516036797 E[Hartree]= -18.758018398 l=0\n",
      "Found bound state at E=  -1.742541019 E[Hartree]=  -0.871270509 l=0\n",
      "Found bound state at E=  -0.676583684 E[Hartree]=  -0.338291842 l=1\n",
      "Adding state with l= 0 and E= -18.7580183985  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871270509283  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338291841939  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 41 Etot[Ry]= -148.943885561 Etot[Hartre]= -74.4719427805 Diff= 0.00501602539367\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516534787 E[Hartree]= -18.758267393 l=0\n",
      "Found bound state at E=  -1.742743224 E[Hartree]=  -0.871371612 l=0\n",
      "Found bound state at E=  -0.676780036 E[Hartree]=  -0.338390018 l=1\n",
      "Adding state with l= 0 and E= -18.7582673934  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871371612243  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338390018164  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 42 Etot[Ry]= -148.945681401 Etot[Hartre]= -74.4728407005 Diff= 0.00179583987676\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516623632 E[Hartree]= -18.758311816 l=0\n",
      "Found bound state at E=  -1.742779300 E[Hartree]=  -0.871389650 l=0\n",
      "Found bound state at E=  -0.676815068 E[Hartree]=  -0.338407534 l=1\n",
      "Adding state with l= 0 and E= -18.758311816  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871389649888  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338407534052  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 43 Etot[Ry]= -148.947630406 Etot[Hartre]= -74.473815203 Diff= 0.0019490051605\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516268443 E[Hartree]= -18.758134221 l=0\n",
      "Found bound state at E=  -1.742635075 E[Hartree]=  -0.871317537 l=0\n",
      "Found bound state at E=  -0.676675016 E[Hartree]=  -0.338337508 l=1\n",
      "Adding state with l= 0 and E= -18.7581342213  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871317537256  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338337508127  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 44 Etot[Ry]= -148.945363786 Etot[Hartre]= -74.4726818931 Diff= 0.00226661990098\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516429648 E[Hartree]= -18.758214824 l=0\n",
      "Found bound state at E=  -1.742700532 E[Hartree]=  -0.871350266 l=0\n",
      "Found bound state at E=  -0.676738579 E[Hartree]=  -0.338369289 l=1\n",
      "Adding state with l= 0 and E= -18.7582148242  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871350265765  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.33836928935  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 45 Etot[Ry]= -148.945556041 Etot[Hartre]= -74.4727780204 Diff= 0.000192254692735\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516547053 E[Hartree]= -18.758273527 l=0\n",
      "Found bound state at E=  -1.742748203 E[Hartree]=  -0.871374102 l=0\n",
      "Found bound state at E=  -0.676784871 E[Hartree]=  -0.338392435 l=1\n",
      "Adding state with l= 0 and E= -18.7582735267  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871374101551  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338392435493  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 46 Etot[Ry]= -148.946811528 Etot[Hartre]= -74.4734057638 Diff= 0.00125548680617\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516378424 E[Hartree]= -18.758189212 l=0\n",
      "Found bound state at E=  -1.742679731 E[Hartree]=  -0.871339866 l=0\n",
      "Found bound state at E=  -0.676718380 E[Hartree]=  -0.338359190 l=1\n",
      "Adding state with l= 0 and E= -18.7581892119  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871339865598  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338359190168  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 47 Etot[Ry]= -148.945935275 Etot[Hartre]= -74.4729676375 Diff= 0.000876252640637\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516409428 E[Hartree]= -18.758204714 l=0\n",
      "Found bound state at E=  -1.742692321 E[Hartree]=  -0.871346160 l=0\n",
      "Found bound state at E=  -0.676730605 E[Hartree]=  -0.338365303 l=1\n",
      "Adding state with l= 0 and E= -18.758204714  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871346160307  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338365302707  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 48 Etot[Ry]= -148.945705754 Etot[Hartre]= -74.472852877 Diff= 0.000229521081337\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516492724 E[Hartree]= -18.758246362 l=0\n",
      "Found bound state at E=  -1.742726142 E[Hartree]=  -0.871363071 l=0\n",
      "Found bound state at E=  -0.676763448 E[Hartree]=  -0.338381724 l=1\n",
      "Adding state with l= 0 and E= -18.7582463619  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871363071067  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338381724135  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 49 Etot[Ry]= -148.946375007 Etot[Hartre]= -74.4731875034 Diff= 0.000669252860575\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516423545 E[Hartree]= -18.758211772 l=0\n",
      "Found bound state at E=  -1.742698053 E[Hartree]=  -0.871349026 l=0\n",
      "Found bound state at E=  -0.676736172 E[Hartree]=  -0.338368086 l=1\n",
      "Adding state with l= 0 and E= -18.7582117724  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871349026313  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338368085781  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 50 Etot[Ry]= -148.946108865 Etot[Hartre]= -74.4730544325 Diff= 0.000266141804616\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516415001 E[Hartree]= -18.758207500 l=0\n",
      "Found bound state at E=  -1.742694583 E[Hartree]=  -0.871347292 l=0\n",
      "Found bound state at E=  -0.676732803 E[Hartree]=  -0.338366401 l=1\n",
      "Adding state with l= 0 and E= -18.7582075004  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871347291703  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338366401367  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 51 Etot[Ry]= -148.945864884 Etot[Hartre]= -74.4729324422 Diff= 0.00024398064852\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516462042 E[Hartree]= -18.758231021 l=0\n",
      "Found bound state at E=  -1.742713684 E[Hartree]=  -0.871356842 l=0\n",
      "Found bound state at E=  -0.676751351 E[Hartree]=  -0.338375676 l=1\n",
      "Adding state with l= 0 and E= -18.7582310212  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.8713568422  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338375675503  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 52 Etot[Ry]= -148.946173635 Etot[Hartre]= -74.4730868174 Diff= 0.000308750399711\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438742 E[Hartree]= -18.758219371 l=0\n",
      "Found bound state at E=  -1.742704223 E[Hartree]=  -0.871352112 l=0\n",
      "Found bound state at E=  -0.676742164 E[Hartree]=  -0.338371082 l=1\n",
      "Adding state with l= 0 and E= -18.758219371  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352111702  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371081887  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 53 Etot[Ry]= -148.946134434 Etot[Hartre]= -74.4730672172 Diff= 3.92002743865e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516424373 E[Hartree]= -18.758212186 l=0\n",
      "Found bound state at E=  -1.742698389 E[Hartree]=  -0.871349194 l=0\n",
      "Found bound state at E=  -0.676736498 E[Hartree]=  -0.338368249 l=1\n",
      "Adding state with l= 0 and E= -18.7582121863  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.87134919433  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338368248933  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 54 Etot[Ry]= -148.94597129 Etot[Hartre]= -74.4729856449 Diff= 0.000163144573605\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516447172 E[Hartree]= -18.758223586 l=0\n",
      "Found bound state at E=  -1.742707646 E[Hartree]=  -0.871353823 l=0\n",
      "Found bound state at E=  -0.676745487 E[Hartree]=  -0.338372744 l=1\n",
      "Adding state with l= 0 and E= -18.7582235859  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871353823074  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338372743735  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 55 Etot[Ry]= -148.946093755 Etot[Hartre]= -74.4730468776 Diff= 0.000122465381708\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516442070 E[Hartree]= -18.758221035 l=0\n",
      "Found bound state at E=  -1.742705575 E[Hartree]=  -0.871352787 l=0\n",
      "Found bound state at E=  -0.676743476 E[Hartree]=  -0.338371738 l=1\n",
      "Adding state with l= 0 and E= -18.758221035  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.87135278742  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371738055  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 56 Etot[Ry]= -148.946118378 Etot[Hartre]= -74.4730591892 Diff= 2.4623144526e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516431359 E[Hartree]= -18.758215679 l=0\n",
      "Found bound state at E=  -1.742701225 E[Hartree]=  -0.871350613 l=0\n",
      "Found bound state at E=  -0.676739253 E[Hartree]=  -0.338369626 l=1\n",
      "Adding state with l= 0 and E= -18.7582156794  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871350612732  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338369626294  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 57 Etot[Ry]= -148.946029354 Etot[Hartre]= -74.4730146771 Diff= 8.9024311194e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516440930 E[Hartree]= -18.758220465 l=0\n",
      "Found bound state at E=  -1.742705112 E[Hartree]=  -0.871352556 l=0\n",
      "Found bound state at E=  -0.676743026 E[Hartree]=  -0.338371513 l=1\n",
      "Adding state with l= 0 and E= -18.7582204648  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352555797  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371513131  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 58 Etot[Ry]= -148.946068333 Etot[Hartre]= -74.4730341665 Diff= 3.8978847499e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516441620 E[Hartree]= -18.758220810 l=0\n",
      "Found bound state at E=  -1.742705392 E[Hartree]=  -0.871352696 l=0\n",
      "Found bound state at E=  -0.676743299 E[Hartree]=  -0.338371649 l=1\n",
      "Adding state with l= 0 and E= -18.7582208099  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352695975  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371649255  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 59 Etot[Ry]= -148.946098624 Etot[Hartre]= -74.4730493119 Diff= 3.02907997423e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516435409 E[Hartree]= -18.758217705 l=0\n",
      "Found bound state at E=  -1.742702870 E[Hartree]=  -0.871351435 l=0\n",
      "Found bound state at E=  -0.676740849 E[Hartree]=  -0.338370425 l=1\n",
      "Adding state with l= 0 and E= -18.7582177046  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871351434941  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338370424706  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 60 Etot[Ry]= -148.946056695 Etot[Hartre]= -74.4730283477 Diff= 4.19284119175e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438751 E[Hartree]= -18.758219375 l=0\n",
      "Found bound state at E=  -1.742704227 E[Hartree]=  -0.871352113 l=0\n",
      "Found bound state at E=  -0.676742167 E[Hartree]=  -0.338371084 l=1\n",
      "Adding state with l= 0 and E= -18.7582193753  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352113438  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371083574  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 61 Etot[Ry]= -148.946063741 Etot[Hartre]= -74.4730318704 Diff= 7.0454900083e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516440487 E[Hartree]= -18.758220244 l=0\n",
      "Found bound state at E=  -1.742704932 E[Hartree]=  -0.871352466 l=0\n",
      "Found bound state at E=  -0.676742852 E[Hartree]=  -0.338371426 l=1\n",
      "Adding state with l= 0 and E= -18.7582202436  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352465994  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371425927  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 62 Etot[Ry]= -148.946084853 Etot[Hartre]= -74.4730424263 Diff= 2.11118428126e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516437414 E[Hartree]= -18.758218707 l=0\n",
      "Found bound state at E=  -1.742703684 E[Hartree]=  -0.871351842 l=0\n",
      "Found bound state at E=  -0.676741640 E[Hartree]=  -0.338370820 l=1\n",
      "Adding state with l= 0 and E= -18.7582187069  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871351842022  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338370820012  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 63 Etot[Ry]= -148.946067813 Etot[Hartre]= -74.4730339065 Diff= 1.70397333932e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438223 E[Hartree]= -18.758219111 l=0\n",
      "Found bound state at E=  -1.742704012 E[Hartree]=  -0.871352006 l=0\n",
      "Found bound state at E=  -0.676741959 E[Hartree]=  -0.338370979 l=1\n",
      "Adding state with l= 0 and E= -18.7582191113  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352006117  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338370979353  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 64 Etot[Ry]= -148.946065345 Etot[Hartre]= -74.4730326725 Diff= 2.46785859304e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516439593 E[Hartree]= -18.758219797 l=0\n",
      "Found bound state at E=  -1.742704569 E[Hartree]=  -0.871352285 l=0\n",
      "Found bound state at E=  -0.676742499 E[Hartree]=  -0.338371250 l=1\n",
      "Adding state with l= 0 and E= -18.7582197966  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352284505  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371249689  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 65 Etot[Ry]= -148.946077153 Etot[Hartre]= -74.4730385766 Diff= 1.18081559322e-05\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438274 E[Hartree]= -18.758219137 l=0\n",
      "Found bound state at E=  -1.742704033 E[Hartree]=  -0.871352017 l=0\n",
      "Found bound state at E=  -0.676741979 E[Hartree]=  -0.338370990 l=1\n",
      "Adding state with l= 0 and E= -18.758219137  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352016647  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338370989582  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 66 Etot[Ry]= -148.946071499 Etot[Hartre]= -74.4730357496 Diff= 5.654095105e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438243 E[Hartree]= -18.758219121 l=0\n",
      "Found bound state at E=  -1.742704021 E[Hartree]=  -0.871352010 l=0\n",
      "Found bound state at E=  -0.676741967 E[Hartree]=  -0.338370983 l=1\n",
      "Adding state with l= 0 and E= -18.7582191215  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352010291  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338370983408  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 67 Etot[Ry]= -148.946067774 Etot[Hartre]= -74.4730338872 Diff= 3.72478507416e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516439060 E[Hartree]= -18.758219530 l=0\n",
      "Found bound state at E=  -1.742704353 E[Hartree]=  -0.871352176 l=0\n",
      "Found bound state at E=  -0.676742289 E[Hartree]=  -0.338371145 l=1\n",
      "Adding state with l= 0 and E= -18.7582195302  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352176301  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371144615  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 68 Etot[Ry]= -148.946073453 Etot[Hartre]= -74.4730367263 Diff= 5.67813913221e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438584 E[Hartree]= -18.758219292 l=0\n",
      "Found bound state at E=  -1.742704159 E[Hartree]=  -0.871352080 l=0\n",
      "Found bound state at E=  -0.676742101 E[Hartree]=  -0.338371051 l=1\n",
      "Adding state with l= 0 and E= -18.7582192921  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352079564  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371050675  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 69 Etot[Ry]= -148.946072268 Etot[Hartre]= -74.4730361342 Diff= 1.18418830652e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438378 E[Hartree]= -18.758219189 l=0\n",
      "Found bound state at E=  -1.742704075 E[Hartree]=  -0.871352038 l=0\n",
      "Found bound state at E=  -0.676742020 E[Hartree]=  -0.338371010 l=1\n",
      "Adding state with l= 0 and E= -18.7582191888  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352037671  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371009995  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 70 Etot[Ry]= -148.946069548 Etot[Hartre]= -74.4730347741 Diff= 2.72019792646e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438791 E[Hartree]= -18.758219396 l=0\n",
      "Found bound state at E=  -1.742704243 E[Hartree]=  -0.871352122 l=0\n",
      "Found bound state at E=  -0.676742183 E[Hartree]=  -0.338371092 l=1\n",
      "Adding state with l= 0 and E= -18.7582193955  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.87135212167  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371091568  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 71 Etot[Ry]= -148.946071912 Etot[Hartre]= -74.4730359562 Diff= 2.36432430256e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438666 E[Hartree]= -18.758219333 l=0\n",
      "Found bound state at E=  -1.742704192 E[Hartree]=  -0.871352096 l=0\n",
      "Found bound state at E=  -0.676742134 E[Hartree]=  -0.338371067 l=1\n",
      "Adding state with l= 0 and E= -18.758219333  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352096214  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371066846  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 72 Etot[Ry]= -148.946072129 Etot[Hartre]= -74.4730360646 Diff= 2.16683872623e-07\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438491 E[Hartree]= -18.758219246 l=0\n",
      "Found bound state at E=  -1.742704121 E[Hartree]=  -0.871352061 l=0\n",
      "Found bound state at E=  -0.676742065 E[Hartree]=  -0.338371032 l=1\n",
      "Adding state with l= 0 and E= -18.7582192456  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352060685  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.33837103234  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 73 Etot[Ry]= -148.946070566 Etot[Hartre]= -74.4730352828 Diff= 1.56348016844e-06\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438673 E[Hartree]= -18.758219336 l=0\n",
      "Found bound state at E=  -1.742704195 E[Hartree]=  -0.871352098 l=0\n",
      "Found bound state at E=  -0.676742136 E[Hartree]=  -0.338371068 l=1\n",
      "Adding state with l= 0 and E= -18.7582193363  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352097568  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371068161  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 74 Etot[Ry]= -148.94607138 Etot[Hartre]= -74.4730356902 Diff= 8.14678685401e-07\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438669 E[Hartree]= -18.758219334 l=0\n",
      "Found bound state at E=  -1.742704193 E[Hartree]=  -0.871352097 l=0\n",
      "Found bound state at E=  -0.676742135 E[Hartree]=  -0.338371067 l=1\n",
      "Adding state with l= 0 and E= -18.7582193343  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352096742  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371067356  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 75 Etot[Ry]= -148.946071834 Etot[Hartre]= -74.4730359169 Diff= 4.53573704817e-07\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438561 E[Hartree]= -18.758219281 l=0\n",
      "Found bound state at E=  -1.742704150 E[Hartree]=  -0.871352075 l=0\n",
      "Found bound state at E=  -0.676742092 E[Hartree]=  -0.338371046 l=1\n",
      "Adding state with l= 0 and E= -18.7582192806  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352074868  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371046115  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 76 Etot[Ry]= -148.946071066 Etot[Hartre]= -74.4730355329 Diff= 7.6817207173e-07\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438629 E[Hartree]= -18.758219314 l=0\n",
      "Found bound state at E=  -1.742704177 E[Hartree]=  -0.871352089 l=0\n",
      "Found bound state at E=  -0.676742119 E[Hartree]=  -0.338371059 l=1\n",
      "Adding state with l= 0 and E= -18.7582193143  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352088574  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371059424  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 77 Etot[Ry]= -148.946071255 Etot[Hartre]= -74.4730356275 Diff= 1.89304046216e-07\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438653 E[Hartree]= -18.758219326 l=0\n",
      "Found bound state at E=  -1.742704187 E[Hartree]=  -0.871352094 l=0\n",
      "Found bound state at E=  -0.676742129 E[Hartree]=  -0.338371064 l=1\n",
      "Adding state with l= 0 and E= -18.7582193265  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352093578  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371064287  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 78 Etot[Ry]= -148.946071607 Etot[Hartre]= -74.4730358033 Diff= 3.51544656496e-07\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438597 E[Hartree]= -18.758219299 l=0\n",
      "Found bound state at E=  -1.742704164 E[Hartree]=  -0.871352082 l=0\n",
      "Found bound state at E=  -0.676742107 E[Hartree]=  -0.338371053 l=1\n",
      "Adding state with l= 0 and E= -18.7582192987  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352082232  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371053267  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 79 Etot[Ry]= -148.946071279 Etot[Hartre]= -74.4730356397 Diff= 3.27106505438e-07\n",
      "Total density has weight= 8.0\n",
      "Found bound state at E= -37.516438616 E[Hartree]= -18.758219308 l=0\n",
      "Found bound state at E=  -1.742704172 E[Hartree]=  -0.871352086 l=0\n",
      "Found bound state at E=  -0.676742114 E[Hartree]=  -0.338371057 l=1\n",
      "Adding state with l= 0 and E= -18.758219308  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.871352085984  Hartree with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.338371056908  Hartree with Z= 10 with ferm= 0.666666666667\n",
      "Itteration 80 Etot[Ry]= -148.946071264 Etot[Hartre]= -74.4730356318 Diff= 1.59294302193e-08\n"
     ]
    },
    {
     "data": {
      "image/png": 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0JZKkgcRD+gPMkCHw9a/DnXc6Cp8kqe/s4Q9Ahx8Oe+4Jp58OK1YUXY0kaSDI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\nIhDcn/P1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1148732d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def ChargeDensity(bst,R,Zatom,Uks):\n",
    "    rho = zeros( len(R) )\n",
    "    N=0\n",
    "    Ebs=0.\n",
    "    for i,(l,Ei) in enumerate(bst):\n",
    "        dN = 2*(2*l+1)\n",
    "        if N+dN<Zatom:\n",
    "            ferm=1\n",
    "        else:\n",
    "            ferm = (Zatom-N)/float(dN)\n",
    "        u = ComputeSchrod(Ei,R,l,Uks)\n",
    "        drho = u**2 / (4*pi*R**2) * dN * ferm\n",
    "        rho += drho\n",
    "        N += dN\n",
    "        Ebs += Ei*dN*ferm\n",
    "        print 'Adding state with l=', l, 'and E=', Ei/2, ' Hartree with Z=', N, 'with ferm=', ferm\n",
    "        if N>=Zatom: break\n",
    "    return (rho,Ebs)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "R = linspace(1e-8,10,2**13+1) # so that we can use Romberg method\n",
    "Etol=1e-7\n",
    "nmax = 3\n",
    "Zatom = 8\n",
    "mixr = 0.5\n",
    "\n",
    "E0=-1.2*Zatom**2\n",
    "Eshift=0.5 # sometimes energies can be positive!!!                                                                                                                        \n",
    "Esearch = -logspace(-4,log10(-E0+Eshift),200)[::-1] + Eshift\n",
    "\n",
    "exc = ExchangeCorrelation()\n",
    "Uks = -2.*ones( len(R) )     # First iteration like hydrogen atom\n",
    "Eold=0\n",
    "\n",
    "for itt in range(100):\n",
    "    Bnd=[]\n",
    "    for l in range(nmax-1):\n",
    "        Bnd += FindBoundStates(R,l,nmax-l-1,Esearch,Uks)\n",
    "    Bnd.sort( cmpE )\n",
    "    \n",
    "    (rho_new,Ebs) = ChargeDensity(Bnd,R,Zatom,Uks)\n",
    "    \n",
    "    if itt>0:\n",
    "        rho = rho_new*mixr + (1-mixr)*rho_old\n",
    "    else:\n",
    "        rho = rho_new\n",
    "    rho_old = copy(rho_new)\n",
    "    \n",
    "    U = HartreeU(R, rho)\n",
    "    \n",
    "    Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "    \n",
    "    Uks = U-2*Zatom + Vxc*R\n",
    "    \n",
    "    # Total energy\n",
    "    ExcVxc = array([2*exc.EcVc(rs(rh))+2*exc.ExVx(rs(rh)) for rh in rho])\n",
    "    pot=(ExcVxc*R**2-0.5*U*R)*rho*4*pi\n",
    "    Etot = integrate.romb(pot, R[1]-R[0]) + Ebs\n",
    "    print 'Itteration', itt, 'Etot[Ry]=', Etot, 'Etot[Hartre]=', Etot/2, 'Diff=', abs(Etot-Eold)\n",
    "    if itt>0 and abs(Etot-Eold)<Etol: break\n",
    "    Eold = Etot\n",
    "    \n",
    "    print 'Total density has weight=', integrate.simps(rho*(4*pi*R**2), x=R)\n",
    "  \n",
    "\n",
    "plot(R, rho*(4*pi*R**2),'--', label='rho')\n",
    "legend(loc='best')\n",
    "xlim([0,10])\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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