e=(-2*a^11*b^2 + a^12*b^2 - 16*a^10*b^3 + 8*a^11*b^3 - 56*a^9*b^4 + 
     29*a^10*b^4 - 204*a^8*b^5 + 64*a^9*b^5 - 426*a^7*b^6 + 226*a^8*b^6 - 
     426*a^6*b^7 + 368*a^7*b^7 - 204*a^5*b^8 + 226*a^6*b^8 - 56*a^4*b^9 + 
     64*a^5*b^9 - 16*a^3*b^10 + 29*a^4*b^10 - 2*a^2*b^11 + 8*a^3*b^11 + 
     a^2*b^12 - 6*a^11*b*c + 3*a^12*b*c - 48*a^10*b^2*c + 24*a^11*b^2*c - 
     170*a^9*b^3*c + 85*a^10*b^3*c - 360*a^8*b^4*c + 176*a^9*b^4*c - 
     1232*a^7*b^5*c + 165*a^8*b^5*c - 2000*a^6*b^6*c + 1147*a^7*b^6*c - 
     1232*a^5*b^7*c + 1147*a^6*b^7*c - 360*a^4*b^8*c + 165*a^5*b^8*c - 
     170*a^3*b^9*c + 176*a^4*b^9*c - 48*a^2*b^10*c + 85*a^3*b^10*c - 
     6*a*b^11*c + 24*a^2*b^11*c + 3*a*b^12*c - 6*a^11*c^2 + 3*a^12*c^2 - 
     48*a^10*b*c^2 + 24*a^11*b*c^2 - 171*a^9*b^2*c^2 + 86*a^10*b^2*c^2 - 
     364*a^8*b^3*c^2 + 184*a^9*b^3*c^2 - 536*a^7*b^4*c^2 + 269*a^8*b^4*c^2 - 
     2363*a^6*b^5*c^2 + 48*a^7*b^5*c^2 - 2363*a^5*b^6*c^2 + 
     2868*a^6*b^6*c^2 - 536*a^4*b^7*c^2 + 48*a^5*b^7*c^2 - 364*a^3*b^8*c^2 + 
     269*a^4*b^8*c^2 - 171*a^2*b^9*c^2 + 184*a^3*b^9*c^2 - 48*a*b^10*c^2 + 
     86*a^2*b^10*c^2 - 6*b^11*c^2 + 24*a*b^11*c^2 + 3*b^12*c^2)/
   (2*(a^10*b^2 + 8*a^9*b^3 + 28*a^8*b^4 + 120*a^7*b^5 + 198*a^6*b^6 + 
       120*a^5*b^7 + 28*a^4*b^8 + 8*a^3*b^9 + a^2*b^10 + 3*a^10*b*c + 
       24*a^9*b^2*c + 86*a^8*b^3*c + 184*a^7*b^4*c + 823*a^6*b^5*c + 
       823*a^5*b^6*c + 184*a^4*b^7*c + 86*a^3*b^8*c + 24*a^2*b^9*c + 
       3*a*b^10*c + 3*a^10*c^2 + 24*a^9*b*c^2 + 87*a^8*b^2*c^2 + 
       192*a^7*b^3*c^2 + 294*a^6*b^4*c^2 + 1872*a^5*b^5*c^2 + 
       294*a^4*b^6*c^2 + 192*a^3*b^7*c^2 + 87*a^2*b^8*c^2 + 24*a*b^9*c^2 + 
       3*b^10*c^2))

plote=Table[ContourPlot[Evaluate[e /. c-> c1], {a, .15, 1.25}, {b,.15, 1.25},
Contours->{-.52,-.5,-.48,-.46,-.44,-.42,-.4,-.38,-.36,-.34,-.32},
ColorFunction ->Hue,DisplayFunction->Identity],{c1,0,1,.05}]
ListAnimate[plote]

FindMinimum[e,{a,1.1},{b,.5},{c,.35}]
Out[4]= {-0.525919, {a -> 1.07487, b -> 0.477447, c -> 0.312549}}



e2=e /. c->0
FindMinimum[e2,{a,1.1},{b,.3}]
Out[6]= {{-0.513303, {a -> 1.03923, b -> 0.283221}}

The H (where Z=1) the energy unit is a hartree: me2*alpha^2=27.211 eV

me2*alpha^2*1e6*-0.525919= -14.311 eV
me2*alpha^2*1e6*-0.513303=-13.968 

For ionization energy final state energy is -1/2, so Delta E is:
me2*alpha^2*1e6*(.5-0.513303)=-0.36199 
me2*alpha^2*1e6*(.5-0.525919)=-0.70529 

HW: old exam: 2005/346t304.pdf #5
