(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 12910, 367] NotebookOptionsPosition[ 11485, 322] NotebookOutlinePosition[ 12167, 345] CellTagsIndexPosition[ 12124, 342] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["\<\ (* C9H20 molecule after Kimball, parametrized with G2//6-311g(Propane) *)\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659185640745*^9}, { 3.566659668929594*^9, 3.5666597080700626`*^9}, {3.566660290746686*^9, 3.566660291386287*^9}}], Cell["\<\ Clear[k1,k2,k3,s1,s2,s3]; n = 9.; z = 6.; z2 = z*z;\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.5666591808359365`*^9}}], Cell["\<\ (* Terms automatic with ChemEdu/Kimball/Alkan.sys *)\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.5666592286968207`*^9}, { 3.566659647105156*^9, 3.5666596589143763`*^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.;\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659223346011*^9}, { 3.566660259109831*^9, 3.5666602776738634`*^9}}], Cell["\<\ T = 2.25*n*k1/P^2+2.25*(n-1.0)*k2/Q^2+4.5*(n+1.0)*k3/R^2;\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659240178441*^9}}], Cell["\<\ Vee = 3.0*n*s1/P+3.0*(n-1.0)*s2/Q+6.0*(n+1.0)*s3/R+80/r+32/(2*q)+ 136/Sqrt[vd*qr+4*q2+r2]+64/q+108/Sqrt[dd*q2]+112/Sqrt[dd*q2+r2]+ 56/Sqrt[cd*q2]+24/Sqrt[md*q2]+96/Sqrt[vd*qr+md*q2+r2]+48/Sqrt[17*q2]+ 76/Sqrt[hd*q2]+80/Sqrt[hd*q2+r2]+40/Sqrt[33*q2]+8/Sqrt[dd*qr+hd*q2+r2]+ 52/Sqrt[ad*r2]+80/Sqrt[ad*qr+4*q2+vd*r2]+64/Sqrt[ad*qr+4*q2+4*r2]+ 136/Sqrt[zd*qr+q2+r2]+56/Sqrt[dd*q2+ad*r2]+112/Sqrt[zd*qr+cd*q2+r2]+ 48/Sqrt[ad*qr+md*q2+vd*r2]+48/Sqrt[ad*qr+md*q2+4*r2]+96/Sqrt[zd*qr+17*\ q2+r2]+ 40/Sqrt[hd*q2+ad*r2]+80/Sqrt[zd*qr+33*q2+r2]+16/Sqrt[dd*qr+hd*q2+ad*r2]+ 16/Sqrt[68*q2]+64/Sqrt[vd*qr+68*q2+r2]+32/Sqrt[163/3*q2]+ 8/Sqrt[kd*qr+md*q2+r2]+8/Sqrt[12*qr+68*q2+r2]+32/Sqrt[ad*qr+68*q2+4*r2]+ 32/Sqrt[ad*qr+68*q2+vd*r2]+64/Sqrt[zd*qr+163/3*q2+r2]+16/Sqrt[8*qr+md*\ q2+vd*r2]+ 16/Sqrt[40/3*qr+68*q2+vd*r2]+28/Sqrt[ad*q2]+20/Sqrt[24*q2]+8/Sqrt[26/3*\ qr+33*q2+r2]+ 8/Sqrt[34/3*qr+163/3*q2+r2]+44/Sqrt[96*q2]+48/Sqrt[96*q2+r2]+24/Sqrt[81*\ q2]+ 8/Sqrt[sd*qr+dd*q2+r2]+8/Sqrt[16*qr+96*q2+r2]+24/Sqrt[96*q2+ad*r2]+ 48/Sqrt[zd*qr+81*q2+r2]+16/Sqrt[sd*qr+dd*q2+ad*r2]+16/Sqrt[16*qr+96*q2+\ ad*r2]+ 12/Sqrt[200/3*q2]+8/Sqrt[6*qr+17*q2+r2]+8/Sqrt[14*qr+81*q2+r2]+8/Sqrt[\ 132*q2]+ 32/Sqrt[vd*qr+132*q2+r2]+16/Sqrt[113*q2]+8/Sqrt[52/3*qr+132*q2+r2]+ 16/Sqrt[ad*qr+132*q2+4*r2]+16/Sqrt[ad*qr+132*q2+vd*r2]+32/Sqrt[zd*qr+\ 113*q2+r2]+ 16/Sqrt[56/3*qr+132*q2+vd*r2]+8/Sqrt[jd*qr+cd*q2+r2]+8/Sqrt[50/3*qr+113*\ q2+r2]+ 12/Sqrt[fd*q2]+16/Sqrt[fd*q2+r2]+8/Sqrt[451/3*q2]+8/Sqrt[gd*qr+fd*q2+r2]+ 8/Sqrt[fd*q2+ad*r2]+16/Sqrt[zd*qr+451/3*q2+r2]+16/Sqrt[gd*qr+fd*q2+ad*\ r2]+ 4/Sqrt[392/3*q2]+8/Sqrt[58/3*qr+451/3*q2+r2]+4/Sqrt[hd*qr+fd*q2+ad*r2];\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659271862097*^9}, { 3.566659602239477*^9, 3.566659606872685*^9}, {3.5666597270864964`*^9, 3.5666600900991335`*^9}}], Cell["\<\ Vne = -3.0*n*z/P-2.0*(n+1.0)*(3.0-((p-1.0)*(1.0+P/R))^2)/R-40*z/r-40/(r*p)-32*\ z/(2*q)- 68*z/Sqrt[vd*qr+4*q2+r2]- 68/Sqrt[vd*qrp+r2p2+4*q2]- 32*z/q- 28*z/Sqrt[dd*q2]- 56*z/Sqrt[dd*q2+r2]- 56/Sqrt[r2p2+dd*q2]- 28*z/Sqrt[cd*q2]- 24*z/Sqrt[md*q2]- 48*z/Sqrt[vd*qr+md*q2+r2]- 48/Sqrt[vd*qrp+r2p2+md*q2]- 24*z/Sqrt[17*q2]- 20*z/Sqrt[hd*q2]- 40*z/Sqrt[hd*q2+r2]- 40/Sqrt[r2p2+hd*q2]- 20*z/Sqrt[33*q2]- 4*z/Sqrt[dd*qr+hd*q2+r2]- 4/Sqrt[dd*qrp+r2p2+hd*q2]- 52/Sqrt[zd*r2p+r2p2+r2]- 80/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+4*q2+r2]- 64/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+4*q2+r2]- 56/Sqrt[-2*r2p+r2p2+dd*q2+r2]- 56/Sqrt[zd*r2p+r2p2+dd*q2+r2]- 48/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+md*q2+r2]- 48/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+md*q2+r2]- 40/Sqrt[-2*r2p+r2p2+hd*q2+r2]- 40/Sqrt[zd*r2p+r2p2+hd*q2+r2]- 8/Sqrt[dd*qrp+zd*r2p+r2p2+hd*q2+r2]- 68/Sqrt[zd*qrp+r2p2+q2]- 56/Sqrt[zd*qrp+r2p2+cd*q2]- 48/Sqrt[zd*qrp+r2p2+17*q2]- 40/Sqrt[zd*qrp+r2p2+33*q2]- 8/Sqrt[dd*qr+zd*r2p+r2p2+hd*q2+r2]- 16*z/Sqrt[68*q2]- 32*z/Sqrt[vd*qr+68*q2+r2]- 32/Sqrt[vd*qrp+r2p2+68*q2]- 16*z/Sqrt[163/3*q2]- 4*z/Sqrt[kd*qr+md*q2+r2]- 4/Sqrt[kd*qrp+r2p2+md*q2]- 4*z/Sqrt[12*qr+68*q2+r2]- 4/Sqrt[12*qrp+r2p2+68*q2]- 32/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+68*q2+r2]- 32/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+68*q2+r2]- 8/Sqrt[vd*qr+kd*qrp-zd*r2p+r2p2+md*q2+r2]- 8/Sqrt[vd*qr+12*qrp-zd*r2p+r2p2+68*q2+r2]- 32/Sqrt[zd*qrp+r2p2+163/3*q2]- 8/Sqrt[kd*qr+vd*qrp-zd*r2p+r2p2+md*q2+r2]- 8/Sqrt[12*qr+vd*qrp-zd*r2p+r2p2+68*q2+r2]- 4/Sqrt[26/3*qrp+r2p2+33*q2]- 4/Sqrt[34/3*qrp+r2p2+163/3*q2]- 12*z/Sqrt[96*q2]- 24*z/Sqrt[96*q2+r2]- 24/Sqrt[r2p2+96*q2]- 12*z/Sqrt[81*q2]- 4*z/Sqrt[sd*qr+dd*q2+r2]- 4/Sqrt[sd*qrp+r2p2+dd*q2]- 4*z/Sqrt[16*qr+96*q2+r2]- 4/Sqrt[16*qrp+r2p2+96*q2]- 24/Sqrt[zd*r2p+r2p2+96*q2+r2]- 24/Sqrt[-2*r2p+r2p2+96*q2+r2]- 8/Sqrt[sd*qrp+zd*r2p+r2p2+dd*q2+r2]- 8/Sqrt[16*qrp+zd*r2p+r2p2+96*q2+r2]- 24/Sqrt[zd*qrp+r2p2+81*q2]- 8/Sqrt[sd*qr+zd*r2p+r2p2+dd*q2+r2]- 8/Sqrt[16*qr+zd*r2p+r2p2+96*q2+r2]- 4/Sqrt[6*qrp+r2p2+17*q2]- 4/Sqrt[14*qrp+r2p2+81*q2]- 8*z/Sqrt[132*q2]- 16*z/Sqrt[vd*qr+132*q2+r2]- 16/Sqrt[vd*qrp+r2p2+132*q2]- 8*z/Sqrt[113*q2]- 4*z/Sqrt[52/3*qr+132*q2+r2]- 4/Sqrt[52/3*qrp+r2p2+132*q2]- 16/Sqrt[vd*qr+vd*qrp+2*r2p+r2p2+132*q2+r2]- 16/Sqrt[vd*qr+vd*qrp-zd*r2p+r2p2+132*q2+r2]- 8/Sqrt[vd*qr+52/3*qrp-zd*r2p+r2p2+132*q2+r2]- 16/Sqrt[zd*qrp+r2p2+113*q2]- 8/Sqrt[52/3*qr+vd*qrp-zd*r2p+r2p2+132*q2+r2]- 4/Sqrt[jd*qrp+r2p2+cd*q2]- 4/Sqrt[50/3*qrp+r2p2+113*q2]- 4*z/Sqrt[fd*q2]- 8*z/Sqrt[fd*q2+r2]- 8/Sqrt[r2p2+fd*q2]- 4*z/Sqrt[451/3*q2]- 4*z/Sqrt[gd*qr+fd*q2+r2]- 4/Sqrt[gd*qrp+r2p2+fd*q2]- 8/Sqrt[zd*r2p+r2p2+fd*q2+r2]- 8/Sqrt[-2*r2p+r2p2+fd*q2+r2]- 8/Sqrt[gd*qrp+zd*r2p+r2p2+fd*q2+r2]- 8/Sqrt[zd*qrp+r2p2+451/3*q2]- 8/Sqrt[gd*qr+zd*r2p+r2p2+fd*q2+r2]- 4/Sqrt[58/3*qrp+r2p2+451/3*q2]- 4/Sqrt[gd*qr+gd*qrp+zd*r2p+r2p2+fd*q2+r2];\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.5666592896305275`*^9}, { 3.5666601115959716`*^9, 3.5666601350584126`*^9}}], Cell["\<\ Vnn = 20*z/(r*p)+ 8*z2/(2*q)+ 34*z/Sqrt[vd*qrp+r2p2+4*q2]+ 14/Sqrt[dd*q2]+ 7*z2/Sqrt[dd*q2]+ 28*z/Sqrt[r2p2+dd*q2]+ 6*z2/Sqrt[md*q2]+ 24*z/Sqrt[vd*qrp+r2p2+md*q2]+ 10/Sqrt[hd*q2]+ 5*z2/Sqrt[hd*q2]+ 20*z/Sqrt[r2p2+hd*q2]+ 2*z/Sqrt[dd*qrp+r2p2+hd*q2]+ 13/Sqrt[ad*r2p2]+ 20/Sqrt[ad*qrp+vd*r2p2+4*q2]+ 16/Sqrt[ad*qrp+4*r2p2+4*q2]+ 14/Sqrt[ad*r2p2+dd*q2]+ 12/Sqrt[ad*qrp+vd*r2p2+md*q2]+ 12/Sqrt[ad*qrp+4*r2p2+md*q2]+ 10/Sqrt[ad*r2p2+hd*q2]+ 4/Sqrt[dd*qrp+ad*r2p2+hd*q2]+ 4*z2/Sqrt[68*q2]+ 16*z/Sqrt[vd*qrp+r2p2+68*q2]+ 2*z/Sqrt[kd*qrp+r2p2+md*q2]+ 2*z/Sqrt[12*qrp+r2p2+68*q2]+ 8/Sqrt[ad*qrp+4*r2p2+68*q2]+ 8/Sqrt[ad*qrp+vd*r2p2+68*q2]+ 4/Sqrt[8*qrp+vd*r2p2+md*q2]+ 4/Sqrt[40/3*qrp+vd*r2p2+68*q2]+ 6/Sqrt[96*q2]+ 3*z2/Sqrt[96*q2]+ 12*z/Sqrt[r2p2+96*q2]+ 2*z/Sqrt[sd*qrp+r2p2+dd*q2]+ 2*z/Sqrt[16*qrp+r2p2+96*q2]+ 6/Sqrt[ad*r2p2+96*q2]+ 4/Sqrt[sd*qrp+ad*r2p2+dd*q2]+ 4/Sqrt[16*qrp+ad*r2p2+96*q2]+ 2*z2/Sqrt[132*q2]+ 8*z/Sqrt[vd*qrp+r2p2+132*q2]+ 2*z/Sqrt[52/3*qrp+r2p2+132*q2]+ 4/Sqrt[ad*qrp+4*r2p2+132*q2]+ 4/Sqrt[ad*qrp+vd*r2p2+132*q2]+ 4/Sqrt[56/3*qrp+vd*r2p2+132*q2]+ 2/Sqrt[fd*q2]+ z2/Sqrt[fd*q2]+ 4*z/Sqrt[r2p2+fd*q2]+ 2*z/Sqrt[gd*qrp+r2p2+fd*q2]+ 2/Sqrt[ad*r2p2+fd*q2]+ 4/Sqrt[gd*qrp+ad*r2p2+fd*q2]+ 1/Sqrt[hd*qrp+ad*r2p2+fd*q2];\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659301533349*^9}}], Cell["func = T + Vee + Vne + Vnn;", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659319988181*^9}}], Cell["\<\ (* Parameterliste c, angepasst f\[UDoubleDot]r Propan an G2//6-311g *) c = {k1 -> 1.02246687, k2 -> 1.37426345, k3 -> 1.20537762, s1 -> 0.30582536, s2 -> 0.30677632, s3 -> 0.35441063};\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659328708596*^9}}], Cell[CellGroupData[{ Cell["\<\ func = func /. c; t = FindMinimum[func, {P, 0.26112}, {Q, 1.187}, {R, 1.2769}, {X, 1.3559},{Method->\"Newton\", MaxIterations-> 500}]\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659337163811*^9}, { 3.566659440685593*^9, 3.5666594710900464`*^9}, {3.5666595253157415`*^9, 3.5666595375305634`*^9}, 3.566660185165701*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "354.22332774448904`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"P", "\[Rule]", "0.2612365595907857`"}], ",", RowBox[{"Q", "\[Rule]", "1.1869177800201292`"}], ",", RowBox[{"R", "\[Rule]", "1.2768409578656097`"}], ",", RowBox[{"X", "\[Rule]", "1.3557946068327773`"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.566659573956627*^9, 3.5666601906101103`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ u = t[[2]]; N[Vne /. u,10] N[Vee /. u /. c, 10] N[Vnn /. u, 10] dch = 0.529177*X*(P+R) /. u (* C-H Abstand *) dcc = 0.529177*2.*(P+Q) /. u (* C-C Abstand *) N[-(Vne+Vee+Vnn)/T /. u /. c, 8] (* Virial Theorem *) (-t[[1]] - n*37.784301 - n - 1.)*627.50956 (* Atomisierungsenergie bei 0 K in kcal/mol *)\ \>", "Input", CellChangeTimes->{{3.5666591697755175`*^9, 3.566659354011841*^9}, { 3.566659398627919*^9, 3.5666594310759764`*^9}}], Cell[BoxData[ RowBox[{"-", "1729.1191143880922`"}]], "Output", CellChangeTimes->{3.566659574019027*^9, 3.5666601906257105`*^9}], Cell[BoxData["572.5385683821505`"], "Output", CellChangeTimes->{3.566659574019027*^9, 3.5666601906257105`*^9}], Cell[BoxData["448.13389051630736`"], "Output", CellChangeTimes->{3.566659574019027*^9, 3.5666601906257105`*^9}], Cell[BoxData["1.103501901562691`"], "Output", CellChangeTimes->{3.566659574019027*^9, 3.5666601906257105`*^9}], Cell[BoxData["1.5326599379445702`"], "Output", 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