(* 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[ 64637, 2941] NotebookOptionsPosition[ 63233, 2897] NotebookOutlinePosition[ 63772, 2917] CellTagsIndexPosition[ 63729, 2914] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ (* Acetylene with two fused methanes at face with CH4 data CH4Mt(min).nb \ 04.07.2012 *) Clear[z,sig1,sig2,sig4,k1,k2,k4,nc,R1,R2,R3,R4,w,p,vee,vne,vnn, xc,yc,zc,xn,yn,zn,oc,ch,rr,cs,ss,d1,d2,d3,d4,d5,pi,i,j,d,t]; z=6.0; nc=7; (* number of clouds *) sig1=0.3; sig2=0.3; sig4=0.3; (* screening const. from e-e interaction in \ doubly occ. clouds *) k1=1.0; k2=1.0; k4=1.0; (* parameters for kinetic energy of clouds; k=1.0 \ Kimball's lowest value *) bohr=0.529177; rad=57.29578; (* C He-shells *) Ekin = 2*(2.25*k1/R1^2); vee=2*(3.0*sig1/R1); vne=-2*(3.0*z/R1); (* this is the common face assumption *) R4=R2; k4=k2; sig4=sig2; (* bonding pairs *) Ekin = Ekin + 2.25*(2*k2/R2^2+3*k4/R4^2); vee=vee+3.0*(2*sig2/R2+3*sig4/R4); vne=vne-2*(3-(p/R2)^2)/R2; (* cloud occupation *) oc={-2,-2,-2,-2,-2,-2,-2}; (* nuclear charges for C1,C2,H3,H4,face1,face2,face3 *) ch={6,6,1,1,0,0,0}; (* cloud radii in the same order *) rr={R1,R1,R2,R2,R4,R4,R4}; (* w is half angle between two C-H of CH4, i.e. 109.47\[Degree]/2 *) w=ArcCos[-1/3]/2; cs=Cos[w]; ss=Sin[w]; (* edge length of tetrahedron of 4 equal clouds *) a=4*(R1+R2)/Sqrt[6]; (* 4/Sqrt[6] is also Sqrt[8/3] *) (* x is C-C bond axis, xz one mirrorplane of D3h molecule *) (* R1+R2 is radius of circumsphere for each tetrahedron of equal clouds *) d1=R1+R4; d2=R1+R2; (* cloud coordinates in terms of radii *) d3=d2+d1/3; d4=d1*Sqrt[2/3]; d5=d1*Sqrt[8]/3; xc={-d1/3,d1/3,-d3,d3,0,0,0}; yc={0,0,0,0,0,-d4,d4}; zc={0,0,0,0,d5,-d5/2,-d5/2}; (* 'eclipsed' conformation *) (* nuclear coordinates in terms of radii; C nuclei assumed in center of C(1s) \ cloud *) (* CH units span radius R1+R2+p of circumsphere through H, if tetrahedral! *) d6=R1+R2+p; d7=d1/3+d6; xn={-d1/3,d1/3,-d7,d7,0,0,0}; yn={0,0,0,0,0,0,0}; zn={0,0,0,0,0,0,0}; (* potential energy of protons in CH-clouds with eccentricity p *) (* cc: sum of cloud-cloud potential energies *) For[i = 1, i < nc, i++, For[j = i+1, j < nc+1, j++, vee = vee + \ oc[[i]]*oc[[j]]/Sqrt[(xc[[i]]-xc[[j]])^2+(yc[[i]]-yc[[j]])^2+(zc[[i]]-zc[[j]])\ ^2]]] (* nn: sum of nuclei-nuclei potential energies *) vnn = 0.0; For[i = 1, i < nc-3, i++, For[j = i+1, j < nc-2, j++, vnn = vnn + \ ch[[i]]*ch[[j]]/Sqrt[(xn[[i]]-xn[[j]])^2+(yn[[i]]-yn[[j]])^2+(zn[[i]]-zn[[j]])\ ^2]]] (* cn: sum of cloud-nuclei potential energies *) For[i = 1, i < nc+1, i++, For[j = 1, j < nc-2, j++, If[i != j, vne = vne + \ oc[[i]]*ch[[j]]/Sqrt[(xc[[i]]-xn[[j]])^2+(yc[[i]]-yn[[j]])^2+(zc[[i]]-zn[[j]])\ ^2]]]] Epot=vne+vee+vnn; func=Ekin+Epot; (* results of CH4 computation; if this is not available, decomment the \ minimize function *) (* R1=0.2623610; R2=1.2461360; p=0.53986226; *) (* minimization function for R1, R2, p *) t = FindMinimum[func,{R1,0.26},{R2,1.29},{p,0.54},{Method -> Automatic}, \ {MaxIterations -> 500}] (* func *) vne /. t[[2]] vee /. t[[2]] vnn /. t[[2]] -Epot/Ekin /. t[[2]] 2*d1/3*bohr /. t[[2]] (R1+R2+p)*bohr /. t[[2]] (R1+R2)*bohr /. t[[2]] 2*w*rad /. t[[2]]\ \>", "Input", PageWidth->WindowWidth, FontSize->16], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "74.2253079502582`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"R1", "\[Rule]", "0.2580355953488826`"}], ",", RowBox[{"R2", "\[Rule]", "1.302033245353087`"}], ",", RowBox[{"p", "\[Rule]", "0.6513964113041653`"}]}], "}"}]}], "}"}]], "Output"], Cell[BoxData[ RowBox[{"-", "245.31970982515324`"}]], "Output"], 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