(* 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};

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;

T = 2.25*n*k0/P^2+2.25*(n-1.0)*k1/Q^2+4.5*(n+1.0)*k2/R^2 /. c;

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];

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];

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];

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}]

u = t[[2]];
N[T /. u,10]
N[Vne /. u,10]
N[Vee /. u /. c, 10]
N[Vnn /. u, 10]
dch = 0.529177*X*(P+R) /. u              (* C-H distance *)
dcc = 0.529177*2.*(P+Q) /. u             (* C-C distance *)
N[-(Vne+Vee+Vnn)/T /. u /. c, 8]         (* Virial Theorem *)
(* Next: -E(C20H42) - n*|C| - (2n+2)*0.5 *)
(-t[[1]] - n*37.784301 - n - 1.)*627.50956
(* Atomisationenergie at 0 K in kcal/mol *)