clc; clear all;format long%Mencari Energi helium %fungsi basis slater 1s dengan nilai-nilai eksponen orbitals1=1.45;s2=2.91; %Integral overlapS11=1;S22=1;S12=(8*s1^1.5*s2^1.5)/(s1+s2)^3;S21=S12; %Hamiltonian terasH11=1/2*s1^2-2*s1H22=1/2*s2^2-2*s2H12=(-1/2*s2^2*S12)+((4*(s2-2)*s1^1.5*s2^1.5)/(s1+s2)^2) %Interaksi antar elektronb1111=5/8*s1;b2222=5/8*s2;b1122=(s1^4*s2+4*s1^3*s2^2+s1*s2^4+4*s1^2*s2^3)/(s1+s2)^4;b2211=b1122;b1212=(20*s1^3*s2^3)/(s1+s2)^5;b2112=b1212; b1221=b1212; b2121=b1212;b1112=(16*s1^4.5*s2^1.5)/(((3*s1)+s2)^4)*(((12*s1)+(8*s2))/((s1+s2)^2)+((9*s1)+s2)/(2*s1^2));b1121=b1112; b1211=b1112; b111=b1112;b1222=(16*s2^4.5*s1^1.5)/(((3*s2)+s1)^4)*(((12*s2)+(8*s1))/((s1+s2)^2)+((9*s2)+s1)/(2*s2^2));b2212=b1222; b2122=b1222;b2221=b1222; %tebakan awal orbital atom keadaan dasar%psi1=c11X1+c12X2%k=c11/c12; %tebakan awalk=2; %mencari nilai c12c12=(1+k^2+2*k*S12)^-(0.5);c11=k*c12;c21=c12; %nilai-nilai elemen matriks kerapatan elektronrho11=2*c11*c11; rho12=2*c11*c12; rho21=rho12; rho22=2*c21*c21; %nilai-nilai matriks FF11=H11+(0.5)*rho11*b1111+rho12*b1112+rho22*(b1122-0.5*b1221);F12=H12+(0.5)*rho11*b1211+rho12*((3/2)*b1212-(1/2)*b1122)+(1/2)*rho22*b1222;F21=F12;F22=H22+rho11*(b2211-(1/2)*b2112)+rho12*b2212+(1/2)*rho22*b2222;

%penyelesaian persamaan sekuler (mencari nilai eigen)a=1-S12^2;b=-(F11+F22-S12*(F12+F21));c=F11*F22-F12*F21; e1=(-b-sqrt(b^2-4*a*c))/(2*a);e2=(-b+sqrt(b^2-4*a*c))/(2*a); %pengecekan%(F21-e1*S21)*c11+(F22-e1*S22)*c12=0kA=-(F22-e1*S22)/(F21-e1*S21); c12A=(1+kA^2+2*kA*S12)^-(0.5);c11A=kA*c12A;c21A=c12A; %nilai-nilai elemen matriks kerapatan elektronArho11A=2*c11A*c11A; rho12A=2*c11A*c12A; rho21A=rho12A; rho22A=2*c21A*c21A; %nilai-nilai matriks FAF11A=H11+(0.5)*rho11A*b1111+rho12A*b1112+rho22A*(b1122-0.5*b1221);F12A=H12+(0.5)*rho11A*b1211+rho12A*((3/2)*b1212-(1/2)*b1122)+(1/2)*rho22A*b1222;F21A=F12A;F22A=H22+rho11A*(b2211-(1/2)*b2112)+rho12A*b2212+(1/2)*rho22A*b2222; %penyelesaian persamaan sekuler (mencari nilai eigen)AaA=1-S12^2;bA=-(F11A+F22A-S12*(F12A+F21A));cA=F11A*F22A-F12A*F21A; e1A=(-bA-sqrt(bA^2-4*aA*cA))/(2*aA);e2A=(-bA+sqrt(bA^2-4*aA*cA))/(2*aA); %pengecekan A%(F21-e1*S21)*c11+(F22-e1*S22)*c12=0kB=-(F22A-e1A*S22)/(F21A-e1A*S21); c12B=(1+kB^2+2*kB*S12)^-(0.5);c11B=kB*c12B;c21B=c12B; %nilai-nilai elemen matriks kerapatan elektron Brho11B=2*c11B*c11B; rho12B=2*c11B*c12B; rho21B=rho12B; rho22B=2*c21B*c21B; %nilai-nilai matriks FBF11B=H11+(0.5)*rho11B*b1111+rho12B*b1112+rho22B*(b1122-0.5*b1221);F12B=H12+(0.5)*rho11B*b1211+rho12B*((3/2)*b1212-(1/2)*b1122)+(1/2)*rho22B*b1222;F21B=F12B;F22B=H22+rho11B*(b2211-(1/2)*b2112)+rho12B*b2212+(1/2)*rho22B*b2222; %penyelesaian persamaan sekuler (mencari nilai eigen)BaB=1-S12^2;bB=-(F11B+F22B-S12*(F12B+F21B));cB=F11B*F22B-F12B*F21B;

e1B=(-bB-sqrt(bB^2-4*aB*cB))/(2*aB);e2B=(-bB+sqrt(bB^2-4*aB*cB))/(2*aB); %pengecekan%(F21-e1*S21)*c11+(F22-e1*S22)*c12=0kC=-(F22B-e1B*S22)/(F21B-e1B*S21); c12C=(1+kC^2+2*kC*S12)^-(0.5);c11C=kC*c12C;c21C=c12C; %maka nilai psi1=0.842X1 + 0.183X2 %Energi Total sistem = 1/2(rho11(H11+F11)+ rho12 (H12+F12) + rho22 (H22+F22)) Ea=rho11B*(H11+F11B)Eb=rho12B*(H12+F12B)Ec=rho22B*(H22+F22B) EHT= 0.5*(rho11B*(H11+F11B)+ 2*rho12B*(H12+F12B) + rho22B*(H22+F22B)) %1 Hartree= 27.211395966 eV E=EHT*27.211395966

Hasil run program

EHT =

-2.861669258370659

E =

-77.870015313253575