(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 20700, 683] NotebookOptionsPosition[ 19417, 642] NotebookOutlinePosition[ 20099, 665] CellTagsIndexPosition[ 20056, 662] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["\<\ (* C20H42 molecule after Kimball, parametrized with G2//6-311g (Propane) V-terms automatic with ChemEdu/Kimball/alkan.sys *) Clear[k0,k1,k2,sig0,sig1,sig2,u,c]; n = 20.; z = 6.; z2 = z*z; (* Parameterlist c, fit for propane with G2//6-311g *) c = {k0 -> 1.02246687, k1 -> 1.37426345, k2 -> 1.20537762, sig0 -> 0.30582536, sig1 -> 0.30677632, sig2 -> 0.35441063};\ \>", "Input", CellChangeTimes->{{3.566660425624523*^9, 3.5666606074272423`*^9}}], Cell["\<\ p = X; p2 = p*p; q = P+Q; r = P+R; q2 = q*q; r2 = r*r; r2p2 = r2*p2; r2p = r2*p; qr = q*r; qrp = qr*p; ad = 8./3.; cd = 19./3.; dd = 32./3.; fd = 512./3.; gd = 64./3.; hd = 128./3.; jd = 10./3.; kd = 20./3.; md = 76./3.; sd = 16./3.; vd = 4./3.; zd = 2./3.; bd = 800.0/3.0; p=X; p2=p*p; q=P+Q; r=P+R; q2=q*q; r2=r*r; r2p2=r2*p2; r2p=r2*p; qr=q*r; qrp=qr*p;\ \>", "Input", CellChangeTimes->{{3.566660425624523*^9, 3.5666608351408424`*^9}}], Cell["\<\ T = 2.25*n*k0/P^2+2.25*(n-1.0)*k1/Q^2+4.5*(n+1.0)*k2/R^2 /. c;\ \>", "Input", CellChangeTimes->{{3.566660425624523*^9, 3.5666608489468665`*^9}}], Cell["\<\ Vee=3.0*n*sig0/P+(n-1.0)*3.0*sig1/Q+ (n+1.0)*6.0*sig2/R+ 104/Sqrt[113*q2]+ 104/Sqrt[ad*qr+132*q2+4*r2]+ 104/Sqrt[ad*qr+132*q2+vd*r2]+ 112/Sqrt[81*q2]+ 112/Sqrt[96*q2+ad*r2]+ 112/Sqrt[vd*qr+452*q2+r2]+ 112/Sqrt[zd*qr+417*q2+r2]+ 12/Sqrt[772*q2]+ 120/Sqrt[163/3*q2]+ 120/Sqrt[ad*qr+68*q2+4*r2]+ 120/Sqrt[ad*qr+68*q2+vd*r2]+ 124/Sqrt[384*q2]+ 128/Sqrt[33*q2]+ 128/Sqrt[384*q2+r2]+ 128/Sqrt[hd*q2+ad*r2]+ 128/Sqrt[zd*qr+353*q2+r2]+ 136/Sqrt[17*q2]+ 136/Sqrt[ad*qr+md*q2+4*r2]+ 136/Sqrt[ad*qr+md*q2+vd*r2]+ 144/Sqrt[cd*q2]+ 144/Sqrt[dd*q2+ad*r2]+ 144/Sqrt[vd*qr+324*q2+r2]+ 144/Sqrt[zd*qr+883/3*q2+r2]+ 152/Sqrt[ad*qr+4*q2+4*r2]+ 152/Sqrt[q2]+ 156/Sqrt[bd*q2]+ 16/Sqrt[104/3*qr+452*q2+vd*r2]+ 16/Sqrt[112/3*qr+1568/3*q2+ad*r2]+ 16/Sqrt[136/3*qr+772*q2+vd*r2]+ 16/Sqrt[152/3*qr+964*q2+vd*r2]+ 16/Sqrt[16*qr+96*q2+ad*r2]+ 16/Sqrt[24*qr+652/3*q2+vd*r2]+ 16/Sqrt[32*qr+384*q2+ad*r2]+ 16/Sqrt[40*qr+1804/3*q2+vd*r2]+ 16/Sqrt[40/3*qr+68*q2+vd*r2]+ 16/Sqrt[48*qr+864*q2+ad*r2]+ 16/Sqrt[56/3*qr+132*q2+vd*r2]+ 16/Sqrt[600*q2]+ 16/Sqrt[8*qr+md*q2+vd*r2]+ 16/Sqrt[80/3*qr+bd*q2+ad*r2]+ 16/Sqrt[817*q2]+ 16/Sqrt[864*q2+ad*r2]+ 16/Sqrt[88/3*qr+324*q2+vd*r2]+ 16/Sqrt[dd*qr+hd*q2+ad*r2]+ 16/Sqrt[gd*qr+fd*q2+ad*r2]+ 16/Sqrt[hd*qr+2048/3*q2+ad*r2]+ 16/Sqrt[sd*qr+dd*q2+ad*r2]+ 16/Sqrt[vd*qr+964*q2+r2]+ 16/Sqrt[zd*qr+913*q2+r2]+ 160/Sqrt[bd*q2+r2]+ 160/Sqrt[zd*qr+241*q2+r2]+ 168/Sqrt[ad*qr+4*q2+vd*r2]+ 168/Sqrt[r2]+ 176/Sqrt[vd*qr+652/3*q2+r2]+ 176/Sqrt[zd*qr+193*q2+r2]+ 188/Sqrt[fd*q2]+ 192/Sqrt[fd*q2+r2]+ 192/Sqrt[zd*qr+451/3*q2+r2]+ 20/Sqrt[1804/3*q2]+ 208/Sqrt[vd*qr+132*q2+r2]+ 208/Sqrt[zd*qr+113*q2+r2]+ 220/Sqrt[96*q2]+ 224/Sqrt[96*q2+r2]+ 224/Sqrt[zd*qr+81*q2+r2]+ 24/Sqrt[1352/3*q2]+ 24/Sqrt[2179/3*q2]+ 24/Sqrt[ad*qr+772*q2+4*r2]+ 24/Sqrt[ad*qr+772*q2+vd*r2]+ 240/Sqrt[vd*qr+68*q2+r2]+ 240/Sqrt[zd*qr+163/3*q2+r2]+ 252/Sqrt[hd*q2]+ 256/Sqrt[hd*q2+r2]+ 256/Sqrt[zd*qr+33*q2+r2]+ 272/Sqrt[vd*qr+md*q2+r2]+ 272/Sqrt[zd*qr+17*q2+r2]+ 28/Sqrt[452*q2]+ 28/Sqrt[864*q2]+ 284/Sqrt[dd*q2]+ 288/Sqrt[dd*q2+r2]+ 288/Sqrt[zd*qr+cd*q2+r2]+ 312/Sqrt[vd*qr+4*q2+r2]+ 312/Sqrt[zd*qr+q2+r2]+ 32/Sqrt[2048/3*q2+ad*r2]+ 32/Sqrt[641*q2]+ 32/Sqrt[864*q2+r2]+ 32/Sqrt[968/3*q2]+ 32/Sqrt[zd*qr+817*q2+r2]+ 36/Sqrt[324*q2]+ 4/Sqrt[296/3*qr+964*q2+4*r2]+ 4/Sqrt[964*q2]+ 40/Sqrt[216*q2]+ 40/Sqrt[561*q2]+ 40/Sqrt[ad*qr+1804/3*q2+4*r2]+ 40/Sqrt[ad*qr+1804/3*q2+vd*r2]+ 44/Sqrt[652/3*q2]+ 48/Sqrt[1459/3*q2]+ 48/Sqrt[1568/3*q2+ad*r2]+ 48/Sqrt[392/3*q2]+ 48/Sqrt[vd*qr+772*q2+r2]+ 48/Sqrt[zd*qr+2179/3*q2+r2]+ 52/Sqrt[132*q2]+ 56/Sqrt[200/3*q2]+ 56/Sqrt[417*q2]+ 56/Sqrt[ad*qr+452*q2+4*r2]+ 56/Sqrt[ad*qr+452*q2+vd*r2]+ 60/Sqrt[2048/3*q2]+ 60/Sqrt[68*q2]+ 64/Sqrt[2048/3*q2+r2]+ 64/Sqrt[24*q2]+ 64/Sqrt[353*q2]+ 64/Sqrt[384*q2+ad*r2]+ 64/Sqrt[zd*qr+641*q2+r2]+ 68/Sqrt[md*q2]+ 72/Sqrt[883/3*q2]+ 72/Sqrt[ad*q2]+ 72/Sqrt[ad*qr+324*q2+4*r2]+ 72/Sqrt[ad*qr+324*q2+vd*r2]+ 76/Sqrt[4*q2]+ 8/Sqrt[100/3*qr+452*q2+r2]+ 8/Sqrt[106/3*qr+1459/3*q2+r2]+ 8/Sqrt[112/3*qr+1568/3*q2+r2]+ 8/Sqrt[116/3*qr+1804/3*q2+r2]+ 8/Sqrt[12*qr+68*q2+r2]+ 8/Sqrt[122/3*qr+641*q2+r2]+ 8/Sqrt[130/3*qr+2179/3*q2+r2]+ 8/Sqrt[14*qr+81*q2+r2]+ 8/Sqrt[146/3*qr+913*q2+r2]+ 8/Sqrt[148/3*qr+964*q2+r2]+ 8/Sqrt[16*qr+96*q2+r2]+ 8/Sqrt[22*qr+193*q2+r2]+ 8/Sqrt[2312/3*q2]+ 8/Sqrt[26/3*qr+33*q2+r2]+ 8/Sqrt[28*qr+324*q2+r2]+ 8/Sqrt[30*qr+353*q2+r2]+ 8/Sqrt[32*qr+384*q2+r2]+ 8/Sqrt[34/3*qr+163/3*q2+r2]+ 8/Sqrt[38*qr+561*q2+r2]+ 8/Sqrt[44*qr+772*q2+r2]+ 8/Sqrt[46*qr+817*q2+r2]+ 8/Sqrt[48*qr+864*q2+r2]+ 8/Sqrt[50/3*qr+113*q2+r2]+ 8/Sqrt[52/3*qr+132*q2+r2]+ 8/Sqrt[58/3*qr+451/3*q2+r2]+ 8/Sqrt[6*qr+17*q2+r2]+ 8/Sqrt[68/3*qr+652/3*q2+r2]+ 8/Sqrt[74/3*qr+241*q2+r2]+ 8/Sqrt[80/3*qr+bd*q2+r2]+ 8/Sqrt[82/3*qr+883/3*q2+r2]+ 8/Sqrt[913*q2]+ 8/Sqrt[98/3*qr+417*q2+r2]+ 8/Sqrt[ad*qr+964*q2+4*r2]+ 8/Sqrt[ad*qr+964*q2+vd*r2]+ 8/Sqrt[dd*qr+hd*q2+r2]+ 8/Sqrt[gd*qr+fd*q2+r2]+ 8/Sqrt[hd*qr+2048/3*q2+r2]+ 8/Sqrt[jd*qr+cd*q2+r2]+ 8/Sqrt[kd*qr+md*q2+r2]+ 8/Sqrt[sd*qr+dd*q2+r2]+ 80/Sqrt[241*q2]+ 80/Sqrt[bd*q2+ad*r2]+ 80/Sqrt[vd*qr+1804/3*q2+r2]+ 80/Sqrt[zd*qr+561*q2+r2]+ 88/Sqrt[193*q2]+ 88/Sqrt[ad*qr+652/3*q2+4*r2]+ 88/Sqrt[ad*qr+652/3*q2+vd*r2]+ 92/Sqrt[1568/3*q2]+ 96/Sqrt[1568/3*q2+r2]+ 96/Sqrt[451/3*q2]+ 96/Sqrt[ad*r2]+ 96/Sqrt[fd*q2+ad*r2]+ 96/Sqrt[zd*qr+1459/3*q2+r2];\ \>", "Input", CellChangeTimes->{{3.566660425624523*^9, 3.5666608818785243`*^9}}], Cell["\<\ Vne=-3.0*n*z/P-2.0*(n+1.0)*(3.0-((p-1.0)*(1.0+P/R))^2)/R- 104*z/Sqrt[vd*qr+132*q2+r2]- 104/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+132*q2+r2]- 104/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+132*q2+r2]- 104/Sqrt[vd*qrp+r2p2+132*q2]- 104/Sqrt[zd*qrp+r2p2+113*q2]- 112*z/Sqrt[96*q2+r2]- 112/Sqrt[-2*r2p+r2p2+96*q2+r2]- 112/Sqrt[r2p2+96*q2]- 112/Sqrt[zd*qrp+r2p2+81*q2]- 112/Sqrt[zd*r2p+r2p2+96*q2+r2]- 12*z/Sqrt[2179/3*q2]- 12*z/Sqrt[772*q2]- 120*z/Sqrt[vd*qr+68*q2+r2]- 120/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+68*q2+r2]- 120/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+68*q2+r2]- 120/Sqrt[vd*qrp+r2p2+68*q2]- 120/Sqrt[zd*qrp+r2p2+163/3*q2]- 128*z/Sqrt[hd*q2+r2]- 128/Sqrt[-2*r2p+r2p2+hd*q2+r2]- 128/Sqrt[r2p2+hd*q2]- 128/Sqrt[zd*qrp+r2p2+33*q2]- 128/Sqrt[zd*r2p+r2p2+hd*q2+r2]- 136*z/Sqrt[vd*qr+md*q2+r2]- 136/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+md*q2+r2]- 136/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+md*q2+r2]- 136/Sqrt[vd*qrp+r2p2+md*q2]- 136/Sqrt[zd*qrp+r2p2+17*q2]- 144*z/Sqrt[dd*q2+r2]- 144/Sqrt[-2*r2p+r2p2+dd*q2+r2]- 144/Sqrt[r2p2+dd*q2]- 144/Sqrt[zd*qrp+r2p2+cd*q2]- 144/Sqrt[zd*r2p+r2p2+dd*q2+r2]- 152/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+4*q2+r2]- 156*z/Sqrt[vd*qr+4*q2+r2]- 156/Sqrt[vd*qrp+r2p2+4*q2]- 156/Sqrt[zd*qrp+r2p2+q2]- 16*z/Sqrt[2048/3*q2]- 16*z/Sqrt[641*q2]- 16*z/Sqrt[864*q2+r2]- 16/Sqrt[-2*r2p+r2p2+864*q2+r2]- 16/Sqrt[r2p2+864*q2]- 16/Sqrt[zd*qrp+r2p2+817*q2]- 16/Sqrt[zd*r2p+r2p2+864*q2+r2]- 168/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+4*q2+r2]- 20*z/Sqrt[1804/3*q2]- 20*z/Sqrt[561*q2]- 24*z/Sqrt[1459/3*q2]- 24*z/Sqrt[1568/3*q2]- 24*z/Sqrt[vd*qr+772*q2+r2]- 24/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+772*q2+r2]- 24/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+772*q2+r2]- 24/Sqrt[vd*qrp+r2p2+772*q2]- 24/Sqrt[zd*qrp+r2p2+2179/3*q2]- 28*z/Sqrt[417*q2]- 28*z/Sqrt[452*q2]- 32*z/Sqrt[2048/3*q2+r2]- 32*z/Sqrt[353*q2]- 32*z/Sqrt[384*q2]- 32/Sqrt[-2*r2p+r2p2+2048/3*q2+r2]- 32/Sqrt[r2p2+2048/3*q2]- 32/Sqrt[zd*qrp+r2p2+641*q2]- 32/Sqrt[zd*r2p+r2p2+2048/3*q2+r2]- 36*z/Sqrt[324*q2]- 36*z/Sqrt[883/3*q2]- 4*z/Sqrt[100/3*qr+452*q2+r2]- 4*z/Sqrt[112/3*qr+1568/3*q2+r2]- 4*z/Sqrt[116/3*qr+1804/3*q2+r2]- 4*z/Sqrt[12*qr+68*q2+r2]- 4*z/Sqrt[148/3*qr+964*q2+r2]- 4*z/Sqrt[16*qr+96*q2+r2]- 4*z/Sqrt[28*qr+324*q2+r2]- 4*z/Sqrt[32*qr+384*q2+r2]- 4*z/Sqrt[44*qr+772*q2+r2]- 4*z/Sqrt[48*qr+864*q2+r2]- 4*z/Sqrt[52/3*qr+132*q2+r2]- 4*z/Sqrt[68/3*qr+652/3*q2+r2]- 4*z/Sqrt[80/3*qr+bd*q2+r2]- 4*z/Sqrt[913*q2]- 4*z/Sqrt[964*q2]- 4*z/Sqrt[dd*qr+hd*q2+r2]- 4*z/Sqrt[gd*qr+fd*q2+r2]- 4*z/Sqrt[hd*qr+2048/3*q2+r2]- 4*z/Sqrt[kd*qr+md*q2+r2]- 4*z/Sqrt[sd*qr+dd*q2+r2]- 4/Sqrt[100/3*qrp+r2p2+452*q2]- 4/Sqrt[106/3*qrp+r2p2+1459/3*q2]- 4/Sqrt[112/3*qrp+r2p2+1568/3*q2]- 4/Sqrt[116/3*qrp+r2p2+1804/3*q2]- 4/Sqrt[12*qrp+r2p2+68*q2]- 4/Sqrt[122/3*qrp+r2p2+641*q2]- 4/Sqrt[130/3*qrp+r2p2+2179/3*q2]- 4/Sqrt[14*qrp+r2p2+81*q2]- 4/Sqrt[146/3*qrp+r2p2+913*q2]- 4/Sqrt[148/3*qr+148/3*qrp+2*r2p+r2p2+964*q2+r2]- 4/Sqrt[148/3*qrp+r2p2+964*q2]- 4/Sqrt[16*qrp+r2p2+96*q2]- 4/Sqrt[22*qrp+r2p2+193*q2]- 4/Sqrt[26/3*qrp+r2p2+33*q2]- 4/Sqrt[28*qrp+r2p2+324*q2]- 4/Sqrt[30*qrp+r2p2+353*q2]- 4/Sqrt[32*qrp+r2p2+384*q2]- 4/Sqrt[34/3*qrp+r2p2+163/3*q2]- 4/Sqrt[38*qrp+r2p2+561*q2]- 4/Sqrt[44*qrp+r2p2+772*q2]- 4/Sqrt[46*qrp+r2p2+817*q2]- 4/Sqrt[48*qrp+r2p2+864*q2]- 4/Sqrt[50/3*qrp+r2p2+113*q2]- 4/Sqrt[52/3*qrp+r2p2+132*q2]- 4/Sqrt[58/3*qrp+r2p2+451/3*q2]- 4/Sqrt[6*qrp+r2p2+17*q2]- 4/Sqrt[68/3*qrp+r2p2+652/3*q2]- 4/Sqrt[74/3*qrp+r2p2+241*q2]- 4/Sqrt[80/3*qrp+r2p2+bd*q2]- 4/Sqrt[82/3*qrp+r2p2+883/3*q2]- 4/Sqrt[98/3*qrp+r2p2+417*q2]- 4/Sqrt[dd*qrp+r2p2+hd*q2]- 4/Sqrt[gd*qrp+r2p2+fd*q2]- 4/Sqrt[hd*qrp+r2p2+2048/3*q2]- 4/Sqrt[jd*qrp+r2p2+cd*q2]- 4/Sqrt[kd*qrp+r2p2+md*q2]- 4/Sqrt[sd*qrp+r2p2+dd*q2]- 40*z/Sqrt[241*q2]- 40*z/Sqrt[bd*q2]- 40*z/Sqrt[vd*qr+1804/3*q2+r2]- 40/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+1804/3*q2+r2]- 40/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+1804/3*q2+r2]- 40/Sqrt[vd*qrp+r2p2+1804/3*q2]- 40/Sqrt[zd*qrp+r2p2+561*q2]- 44*z/Sqrt[193*q2]- 44*z/Sqrt[652/3*q2]- 48*z/Sqrt[1568/3*q2+r2]- 48*z/Sqrt[451/3*q2]- 48*z/Sqrt[fd*q2]- 48/Sqrt[-2*r2p+r2p2+1568/3*q2+r2]- 48/Sqrt[r2p2+1568/3*q2]- 48/Sqrt[zd*qrp+r2p2+1459/3*q2]- 48/Sqrt[zd*r2p+r2p2+1568/3*q2+r2]- 52*z/Sqrt[113*q2]- 52*z/Sqrt[132*q2]- 56*z/Sqrt[81*q2]- 56*z/Sqrt[96*q2]- 56*z/Sqrt[vd*qr+452*q2+r2]- 56/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+452*q2+r2]- 56/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+452*q2+r2]- 56/Sqrt[vd*qrp+r2p2+452*q2]- 56/Sqrt[zd*qrp+r2p2+417*q2]- 60*z/Sqrt[163/3*q2]- 60*z/Sqrt[68*q2]- 64*z/Sqrt[33*q2]- 64*z/Sqrt[384*q2+r2]- 64*z/Sqrt[hd*q2]- 64/Sqrt[-2*r2p+r2p2+384*q2+r2]- 64/Sqrt[r2p2+384*q2]- 64/Sqrt[zd*qrp+r2p2+353*q2]- 64/Sqrt[zd*r2p+r2p2+384*q2+r2]- 68*z/Sqrt[17*q2]- 68*z/Sqrt[md*q2]- 72*z/Sqrt[cd*q2]- 72*z/Sqrt[dd*q2]- 72*z/Sqrt[vd*qr+324*q2+r2]- 72/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+324*q2+r2]- 72/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+324*q2+r2]- 72/Sqrt[vd*qrp+r2p2+324*q2]- 72/Sqrt[zd*qrp+r2p2+883/3*q2]- 76*z/Sqrt[4*q2]- 76*z/Sqrt[q2]- 8*z/Sqrt[817*q2]- 8*z/Sqrt[864*q2]- 8*z/Sqrt[vd*qr+964*q2+r2]- 8/Sqrt[100/3*qr+vd*qrp-zd*r2p+r2p2+452*q2+r2]- 8/Sqrt[112/3*qr+zd*r2p+r2p2+1568/3*q2+r2]- 8/Sqrt[112/3*qrp+zd*r2p+r2p2+1568/3*q2+r2]- 8/Sqrt[116/3*qr+vd*qrp-zd*r2p+r2p2+1804/3*q2+r2]- 8/Sqrt[12*qr+vd*qrp-zd*r2p+r2p2+68*q2+r2]- 8/Sqrt[148/3*qr+vd*qrp-zd*r2p+r2p2+964*q2+r2]- 8/Sqrt[16*qr+zd*r2p+r2p2+96*q2+r2]- 8/Sqrt[16*qrp+zd*r2p+r2p2+96*q2+r2]- 8/Sqrt[28*qr+vd*qrp-zd*r2p+r2p2+324*q2+r2]- 8/Sqrt[32*qr+zd*r2p+r2p2+384*q2+r2]- 8/Sqrt[32*qrp+zd*r2p+r2p2+384*q2+r2]- 8/Sqrt[44*qr+vd*qrp-zd*r2p+r2p2+772*q2+r2]- 8/Sqrt[48*qr+zd*r2p+r2p2+864*q2+r2]- 8/Sqrt[48*qrp+zd*r2p+r2p2+864*q2+r2]- 8/Sqrt[52/3*qr+vd*qrp-zd*r2p+r2p2+132*q2+r2]- 8/Sqrt[68/3*qr+vd*qrp-zd*r2p+r2p2+652/3*q2+r2]- 8/Sqrt[80/3*qr+zd*r2p+r2p2+bd*q2+r2]- 8/Sqrt[80/3*qrp+zd*r2p+r2p2+bd*q2+r2]- 8/Sqrt[dd*qr+zd*r2p+r2p2+hd*q2+r2]- 8/Sqrt[dd*qrp+zd*r2p+r2p2+hd*q2+r2]- 8/Sqrt[gd*qr+zd*r2p+r2p2+fd*q2+r2]- 8/Sqrt[gd*qrp+zd*r2p+r2p2+fd*q2+r2]- 8/Sqrt[hd*qr+zd*r2p+r2p2+2048/3*q2+r2]- 8/Sqrt[hd*qrp+zd*r2p+r2p2+2048/3*q2+r2]- 8/Sqrt[kd*qr+vd*qrp-zd*r2p+r2p2+md*q2+r2]- 8/Sqrt[sd*qr+zd*r2p+r2p2+dd*q2+r2]- 8/Sqrt[sd*qrp+zd*r2p+r2p2+dd*q2+r2]- 8/Sqrt[vd*qr+100/3*qrp-zd*r2p+r2p2+452*q2+r2]- 8/Sqrt[vd*qr+116/3*qrp-zd*r2p+r2p2+1804/3*q2+r2]- 8/Sqrt[vd*qr+12*qrp-zd*r2p+r2p2+68*q2+r2]- 8/Sqrt[vd*qr+148/3*qrp-zd*r2p+r2p2+964*q2+r2]- 8/Sqrt[vd*qr+28*qrp-zd*r2p+r2p2+324*q2+r2]- 8/Sqrt[vd*qr+44*qrp-zd*r2p+r2p2+772*q2+r2]- 8/Sqrt[vd*qr+52/3*qrp-zd*r2p+r2p2+132*q2+r2]- 8/Sqrt[vd*qr+68/3*qrp-zd*r2p+r2p2+652/3*q2+r2]- 8/Sqrt[vd*qr+kd*qrp-zd*r2p+r2p2+md*q2+r2]- 8/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+964*q2+r2]- 8/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+964*q2+r2]- 8/Sqrt[vd*qrp+r2p2+964*q2]- 8/Sqrt[zd*qrp+r2p2+913*q2]- 80*z/Sqrt[bd*q2+r2]- 80/Sqrt[-2*r2p+r2p2+bd*q2+r2]- 80/Sqrt[r2p2+bd*q2]- 80/Sqrt[zd*qrp+r2p2+241*q2]- 80/Sqrt[zd*r2p+r2p2+bd*q2+r2]- 84*z/Sqrt[r2]- 84/Sqrt[r2p2]- 88*z/Sqrt[vd*qr+652/3*q2+r2]- 88/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+652/3*q2+r2]- 88/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+652/3*q2+r2]- 88/Sqrt[vd*qrp+r2p2+652/3*q2]- 88/Sqrt[zd*qrp+r2p2+193*q2]- 96*z/Sqrt[fd*q2+r2]- 96/Sqrt[-2*r2p+r2p2+fd*q2+r2]- 96/Sqrt[r2p2+fd*q2]- 96/Sqrt[zd*qrp+r2p2+451/3*q2]- 96/Sqrt[zd*r2p+r2p2+fd*q2+r2]- 96/Sqrt[zd*r2p+r2p2+r2];\ \>", "Input", CellChangeTimes->{{3.566660425624523*^9, 3.566660898726554*^9}}], Cell["\<\ Vnn=1/Sqrt[296/3*qrp+4*r2p2+964*q2]+ 10*z2/Sqrt[bd*q2]+ 10/Sqrt[ad*qrp+4*r2p2+1804/3*q2]+ 10/Sqrt[ad*qrp+vd*r2p2+1804/3*q2]+ 11*z2/Sqrt[652/3*q2]+ 12*z/Sqrt[vd*qrp+r2p2+772*q2]+ 12*z2/Sqrt[fd*q2]+ 12/Sqrt[1568/3*q2]+ 12/Sqrt[ad*r2p2+1568/3*q2]+ 13*z2/Sqrt[132*q2]+ 14*z2/Sqrt[96*q2]+ 14/Sqrt[ad*qrp+4*r2p2+452*q2]+ 14/Sqrt[ad*qrp+vd*r2p2+452*q2]+ 15*z2/Sqrt[68*q2]+ 16*z/Sqrt[r2p2+2048/3*q2]+ 16*z2/Sqrt[hd*q2]+ 16/Sqrt[384*q2]+ 16/Sqrt[ad*r2p2+384*q2]+ 17*z2/Sqrt[md*q2]+ 18*z2/Sqrt[dd*q2]+ 18/Sqrt[ad*qrp+4*r2p2+324*q2]+ 18/Sqrt[ad*qrp+vd*r2p2+324*q2]+ 19*z2/Sqrt[4*q2]+ 2*z/Sqrt[100/3*qrp+r2p2+452*q2]+ 2*z/Sqrt[112/3*qrp+r2p2+1568/3*q2]+ 2*z/Sqrt[116/3*qrp+r2p2+1804/3*q2]+ 2*z/Sqrt[12*qrp+r2p2+68*q2]+ 2*z/Sqrt[148/3*qrp+r2p2+964*q2]+ 2*z/Sqrt[16*qrp+r2p2+96*q2]+ 2*z/Sqrt[28*qrp+r2p2+324*q2]+ 2*z/Sqrt[32*qrp+r2p2+384*q2]+ 2*z/Sqrt[44*qrp+r2p2+772*q2]+ 2*z/Sqrt[48*qrp+r2p2+864*q2]+ 2*z/Sqrt[52/3*qrp+r2p2+132*q2]+ 2*z/Sqrt[68/3*qrp+r2p2+652/3*q2]+ 2*z/Sqrt[80/3*qrp+r2p2+bd*q2]+ 2*z/Sqrt[dd*qrp+r2p2+hd*q2]+ 2*z/Sqrt[gd*qrp+r2p2+fd*q2]+ 2*z/Sqrt[hd*qrp+r2p2+2048/3*q2]+ 2*z/Sqrt[kd*qrp+r2p2+md*q2]+ 2*z/Sqrt[sd*qrp+r2p2+dd*q2]+ 2*z2/Sqrt[864*q2]+ 2/Sqrt[ad*qrp+4*r2p2+964*q2]+ 2/Sqrt[ad*qrp+vd*r2p2+964*q2]+ 20*z/Sqrt[vd*qrp+r2p2+1804/3*q2]+ 20/Sqrt[ad*r2p2+bd*q2]+ 20/Sqrt[bd*q2]+ 22/Sqrt[ad*qrp+4*r2p2+652/3*q2]+ 22/Sqrt[ad*qrp+vd*r2p2+652/3*q2]+ 24*z/Sqrt[r2p2+1568/3*q2]+ 24/Sqrt[ad*r2p2]+ 24/Sqrt[ad*r2p2+fd*q2]+ 24/Sqrt[fd*q2]+ 26/Sqrt[ad*qrp+4*r2p2+132*q2]+ 26/Sqrt[ad*qrp+vd*r2p2+132*q2]+ 28*z/Sqrt[vd*qrp+r2p2+452*q2]+ 28/Sqrt[96*q2]+ 28/Sqrt[ad*r2p2+96*q2]+ 3*z2/Sqrt[772*q2]+ 30/Sqrt[ad*qrp+4*r2p2+68*q2]+ 30/Sqrt[ad*qrp+vd*r2p2+68*q2]+ 32*z/Sqrt[r2p2+384*q2]+ 32/Sqrt[ad*r2p2+hd*q2]+ 32/Sqrt[hd*q2]+ 34/Sqrt[ad*qrp+4*r2p2+md*q2]+ 34/Sqrt[ad*qrp+vd*r2p2+md*q2]+ 36*z/Sqrt[vd*qrp+r2p2+324*q2]+ 36/Sqrt[ad*r2p2+dd*q2]+ 36/Sqrt[dd*q2]+ 38/Sqrt[ad*qrp+4*r2p2+4*q2]+ 4*z/Sqrt[vd*qrp+r2p2+964*q2]+ 4*z2/Sqrt[2048/3*q2]+ 4/Sqrt[104/3*qrp+vd*r2p2+452*q2]+ 4/Sqrt[112/3*qrp+ad*r2p2+1568/3*q2]+ 4/Sqrt[136/3*qrp+vd*r2p2+772*q2]+ 4/Sqrt[152/3*qrp+vd*r2p2+964*q2]+ 4/Sqrt[16*qrp+ad*r2p2+96*q2]+ 4/Sqrt[24*qrp+vd*r2p2+652/3*q2]+ 4/Sqrt[32*qrp+ad*r2p2+384*q2]+ 4/Sqrt[40*qrp+vd*r2p2+1804/3*q2]+ 4/Sqrt[40/3*qrp+vd*r2p2+68*q2]+ 4/Sqrt[48*qrp+ad*r2p2+864*q2]+ 4/Sqrt[56/3*qrp+vd*r2p2+132*q2]+ 4/Sqrt[8*qrp+vd*r2p2+md*q2]+ 4/Sqrt[80/3*qrp+ad*r2p2+bd*q2]+ 4/Sqrt[864*q2]+ 4/Sqrt[88/3*qrp+vd*r2p2+324*q2]+ 4/Sqrt[ad*r2p2+864*q2]+ 4/Sqrt[dd*qrp+ad*r2p2+hd*q2]+ 4/Sqrt[gd*qrp+ad*r2p2+fd*q2]+ 4/Sqrt[hd*qrp+ad*r2p2+2048/3*q2]+ 4/Sqrt[sd*qrp+ad*r2p2+dd*q2]+ 40*z/Sqrt[r2p2+bd*q2]+ 42*z/Sqrt[r2p2]+ 42/Sqrt[ad*qrp+vd*r2p2+4*q2]+ 44*z/Sqrt[vd*qrp+r2p2+652/3*q2]+ 48*z/Sqrt[r2p2+fd*q2]+ 5*z2/Sqrt[1804/3*q2]+ 52*z/Sqrt[vd*qrp+r2p2+132*q2]+ 56*z/Sqrt[r2p2+96*q2]+ 6*z2/Sqrt[1568/3*q2]+ 6/Sqrt[ad*qrp+4*r2p2+772*q2]+ 6/Sqrt[ad*qrp+vd*r2p2+772*q2]+ 60*z/Sqrt[vd*qrp+r2p2+68*q2]+ 64*z/Sqrt[r2p2+hd*q2]+ 68*z/Sqrt[vd*qrp+r2p2+md*q2]+ 7*z2/Sqrt[452*q2]+ 72*z/Sqrt[r2p2+dd*q2]+ 78*z/Sqrt[vd*qrp+r2p2+4*q2]+ 8*z/Sqrt[r2p2+864*q2]+ 8*z2/Sqrt[384*q2]+ 8/Sqrt[2048/3*q2]+ 8/Sqrt[ad*r2p2+2048/3*q2]+ 9*z2/Sqrt[324*q2]+ z2/Sqrt[964*q2]; \ \>", "Input", CellChangeTimes->{{3.566660425624523*^9, 3.5666609130473795`*^9}}], Cell[CellGroupData[{ Cell["\<\ func = T + Vee + Vne + Vnn /. c; t = FindMinimum[func, {P, 0.26112}, {Q, 1.187}, {R, 1.2769}, {X, 1.3559},{Method->\"Newton\", MaxIterations->500}]\ \>", "Input", CellChangeTimes->{{3.566660425624523*^9, 3.566660988567112*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "785.7260612793639`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"P", "\[Rule]", "0.2612085815918361`"}], ",", RowBox[{"Q", "\[Rule]", "1.1874457933170892`"}], ",", RowBox[{"R", "\[Rule]", "1.2783096911829595`"}], ",", RowBox[{"X", "\[Rule]", "1.3553532342501777`"}]}], "}"}]}], "}"}]], "Output", 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