6.5.6 - CARBON ORBITALS EXPANDED IN STOs with variable exponents (A)

NSTO[l_,ζ_]:=((((2ζ))^(3/2))/(Sqrt[(2l+2)!]))(((2ζ))^l)
RSTO[l_,ζ_,r_]:=NSTO[l,ζ](r^l)Exp[-ζ r]

R1sA[r_]:=RSTO[0,5.58,r]
R2sA[r_]:=RSTO[1,1.57,r]
R2pA[r_]:=RSTO[1,1.46,r]

ϕ1sA[r_]:=0.998R1sA[r]+0.009R2sA[r]
ϕ2sA[r_]:=-0.231R1sA[r]+1.024R2sA[r]
ϕ2pA[r_]:=R2pA[r]

Plot[(r ϕ1sA[r])^2,{r,0,5},PlotRange-> All]

Integrate[(r ϕ1sA[r])^2,{r,0,Infinity}]

Plot[(r ϕ2sA[r])^2,{r,0,5},PlotRange-> All]

Integrate[(r ϕ2sA[r])^2,{r,0,Infinity}]

Plot[(r ϕ2pA[r])^2,{r,0,5},PlotRange-> All]

Integrate[(r ϕ2pA[r])^2,{r,0,Infinity}]

6.5.7 - CARBON ORBITALS EXPANDED IN STOs with variable exponents (B)

ζ1s1=9.2863;
ζ1s2=5.4125;
ζ2s1=4.2595;
ζ2s2=2.5897;
ζ2s3=1.5020;
ζ2s4=1.0311;
C1s1s1=0.07657;
C1s1s2=0.92604;
C1s2s1=0.00210;
C1s2s2=0.00638;
C1s2s3=0.00167;
C1s2s4=-0.00073;

ϕ1sB[r_]:=C1s1s1 RSTO[0,ζ1s1,r]+C1s1s2 RSTO[0,ζ1s2,r]+C1s2s1 RSTO[1,ζ2s1,r]+C1s2s2 RSTO[1,ζ2s2,r]+C1s2s3 RSTO[1,ζ2s3,r]+C1s2s4 RSTO[1,ζ2s4,r]

Plot[{(r ϕ1sA[r])^2,(r ϕ1sB[r])^2},{r,0,4},PlotRange-> All]

Integrate[(r ϕ1sB[r])^2,{r,0,Infinity}]

C2s1s1=-0.01196;
C2s1s2=-0.21041;
C2s2s1=-0.13209;
C2s2s2=0.34624;
C2s2s3=0.74108;
C2s2s4=0.06495;

ϕ2sB[r_]:=C2s1s1 RSTO[0,ζ1s1,r]+C2s1s2 RSTO[0,ζ1s2,r]+C2s2s1 RSTO[1,ζ2s1,r]+C2s2s2 RSTO[1,ζ2s2,r]+C2s2s3 RSTO[1,ζ2s3,r]+C2s2s4 RSTO[1,ζ2s4,r]

Plot[{(r ϕ2sA[r])^2,(r ϕ2sB[r])^2},{r,0,4},PlotRange-> All]

Integrate[(r ϕ2sB[r])^2,{r,0,Infinity}]

ζ2p1=6.3438;
ζ2p2=2.5873;
ζ2p3=1.4209;
ζ2p4=0.9554;
C2p2p1=0.01090;
C2p2p2=0.23563;
C2p2p3=0.57774;
C2p2p4=0.24756;

ϕ2pB[r_]:=C2p2p1 RSTO[1,ζ2p1,r]+C2p2p2 RSTO[1,ζ2p2,r]+C2p2p3 RSTO[1,ζ2p3,r]+C2p2p4 RSTO[1,ζ2p4,r]

Plot[{(r ϕ2pA[r])^2,(r ϕ2pB[r])^2},{r,0,4},PlotRange-> All]

Integrate[(r ϕ2pB[r])^2,{r,0,Infinity}]

6.6.5 - CARBON ORBITALS EXPANDED IN SPHERICAL-HARMONIC GTOs with variable exponents

RGTO[αnl_,l_,r_]:=((2(((2αnl))^(3/4)))/(π^(1/4)))(Sqrt[((2^l)/((2l+1)!!))])((((Sqrt[2αnl])r))^l)Exp[-αnl (r^2)]

RGTO1s[r_]:=RGTO[8.80,0,r]
RGTO2s[r_]:=RGTO[0.252,0,r]
RGTO2p[r_]:=RGTO[0.385,1,r]

ϕGTO1s[r_]:=0.982RGTO1s[r]+0.077RGTO2s[r]

Plot[{(((ϕ1sB[r]r))^2),(((ϕGTO1s[r]r))^2)},{r,0,4},PlotRange->All]

Integrate[(((ϕGTO1s[r]r))^2),{r,0,Infinity}]

ϕGTO2s[r_]:=-0.266RGTO1s[r]+1.016RGTO2s[r]

Plot[{(((ϕ2sB[r]r))^2),(((ϕGTO2s[r]r))^2)},{r,0,4},PlotRange->All]

Integrate[(((ϕGTO2s[r]r))^2),{r,0,Infinity}]

ϕGTO2p[r_]:=RGTO2p[r]

Plot[{(((ϕ2pB[r]r))^2),(((ϕGTO2p[r]r))^2)},{r,0,4},PlotRange->All]

Integrate[(((ϕGTO2p[r]r))^2),{r,0,Infinity}]

8.2.2 - CARBON ORBITALS EXPANDED IN (9s5p) GTOs basis set

α11=4232.61;
α12=634.882;
α13=146.097;
α14=42.4974;
α15=14.1892;
α16=5.1477;
α17=1.9666;
α18=0.4962;
α19=0.1533;
C1s1=0.00122;
C1s2=0.00934;
C1s3=0.04534;
C1s4=0.15459;
C1s5=0.35867;
C1s6=0.43809;
C1s7=0.14581;
C1s8=0.00199;
C1s9=0.00041;

ϕGTO1s9s5p[r_]:=C1s1 RGTO[α11,0,r]+C1s2 RGTO[α12,0,r]+C1s3 RGTO[α13,0,r]+C1s4 RGTO[α14,0,r]+C1s5 RGTO[α15,0,r]+C1s6 RGTO[α16,0,r]+C1s7 RGTO[α17,0,r]+C1s8 RGTO[α18,0,r]+C1s9 RGTO[α19,0,r]

Plot[{(((ϕ1sB[r]r))^2),(((ϕGTO1s9s5p[r]r))^2)},{r,0,1},PlotRange->All]

Integrate[(((ϕGTO1s9s5p[r]r))^2),{r,0,Infinity}]

C2s1=-0.00026;
C2s2=-0.00202;
C2s3=-0.00974;
C2s4=-0.03606;
C2s5=-0.08938;
C2s6=-0.17699;
C2s7=-0.05267;
C2s8=0.57408;
C2s9=0.54768;

ϕGTO2s9s5p[r_]:=C2s1 RGTO[α11,0,r]+C2s2 RGTO[α12,0,r]+C2s3 RGTO[α13,0,r]+C2s4 RGTO[α14,0,r]+C2s5 RGTO[α15,0,r]+C2s6 RGTO[α16,0,r]+C2s7 RGTO[α17,0,r]+C2s8 RGTO[α18,0,r]+C2s9 RGTO[α19,0,r]

Plot[{(((ϕ2sB[r]r))^2),(((ϕGTO2s9s5p[r]r))^2)},{r,0,4},PlotRange->All]

Integrate[(((ϕGTO2s9s5p[r]r))^2),{r,0,Infinity}]

α21=18.1557;
α22=3.9864;
α23=1.1429;
α24=0.3594;
α25=0.1146;
C2p1=0.01469;
C2p2=0.09150;
C2p3=0.30611;
C2p4=0.50734;
C2p5=0.31735;

ϕGTO2p9s5p[r_]:=C2p1 RGTO[α21,1,r]+C2p2 RGTO[α22,1,r]+C2p3 RGTO[α23,1,r]+C2p4 RGTO[α24,1,r]+C2p5 RGTO[α25,1,r]

Plot[{(((ϕ2pB[r]r))^2),(((ϕGTO2p9s5p[r]r))^2)},{r,0,5},PlotRange->All]

Integrate[(((ϕGTO2p9s5p[r]r))^2),{r,0,Infinity}]

8.2.5 - CARBON ORBITALS EXPANDED IN (9s5p) GTOs basis set with segmented contractions

α31=4232.61;
α32=634.882;
α33=146.097;
α34=42.4974;
α35=14.1892;
α36=1.9666;
α37=5.1477;
α38=0.4962;
α39=0.1533;

C3s1=0.002029;
C3s2=0.015535;
C3s3=0.075411;
C3s4=0.257121;
C3s5=0.596555;
C3s6=0.242517;
C3s7=1.000000;
C3s8=0.542048;
C3s9=0.517121;

χGTO1s9s5p[r_]:=C3s1 RGTO[α31,0,r]+C3s2 RGTO[α32,0,r]+C3s3 RGTO[α33,0,r]+C3s4 RGTO[α34,0,r]+C3s5 RGTO[α35,0,r]+C3s6 RGTO[α36,0,r]

Plot[{(((ϕ1sB[r]r))^2),(((χGTO1s9s5p[r]r))^2)},{r,0,4},PlotRange->All]

Integrate[(((χGTO1s9s5p[r]r))^2),{r,0,Infinity}]

C4s1=0.002029;
C4s2=0.015535;
C4s3=0.075411;
C4s4=0.257121;
C4s5=0.596555;
C4s6=0.242517;
C4s7=1.000000;
C4s8=1.000000;
C4s9=1.000000;

χGTO2s9s5p[r_]:=RGTO[α37,0,r]

Integrate[(((χGTO2s9s5p[r]r))^2),{r,0,Infinity}]

C5s1=0.006228;
C5s2=0.047676;
C5s3=0.231439;
C5s4=0.789108;
C5s5=0.791751;
C5s6=0.321870;
C5s7=1.000000;
C5s8=1.000000;
C5s9=1.000000;

χGTO3s9s5p[r_]:=RGTO[α38,0,r]

χGTO4s9s5p[r_]:=RGTO[α39,0,r]

Plot[{(((ϕ1sB[r]r))^2),(((χGTO1s9s5p[r]r))^2),(((χGTO2s9s5p[r]r))^2),(((χGTO3s9s5p[r]r))^2),(((χGTO4s9s5p[r]r))^2)},{r,0,4},PlotRange->All]

Integrate[(((χGTO3s9s5p[r]r))^2),{r,0,Infinity}]

ϕCGTO1s4s2p[r_]:=0.601χGTO1s9s5p[r]+0.438χGTO2s9s5p[r]+0.005χGTO3s9s5p[r]+0.001χGTO4s9s5p[r]

Plot[{(((ϕ1sB[r]r))^2),(((ϕCGTO1s4s2p[r]r))^2)},{r,0,1},PlotRange->All]

α21=18.1557;
α22=3.9864;
α23=1.1429;
α24=0.3594;
α25=0.1146;
C22p1=0.018534;
C22p2=0.115442;
C22p3=0.386206;
C22p4=0.640089;
C22p5=1.0;

C3p1=0.039196;
C3p2=0.244144;
C3p3=0.816775;
C3p4=1.0;
C3p5=1.0;

χGTO1p4s2p[r_]:=C22p1 RGTO[α21,1,r]+C22p2 RGTO[α22,1,r]+C22p3 RGTO[α23,1,r]+C22p4 RGTO[α24,1,r]

χGTO2p4s2p[r_]:=C22p5 RGTO[α25,1,r]

Plot[{(((ϕ2pB[r]r))^2),(((χGTO1p4s2p[r]r))^2),(((χGTO2p4s2p[r]r))^2)},{r,0,7},PlotRange->All]

χGTO2p4s2ptest[r_]:=1.0 RGTO[α24,1,r]

Plot[{(((ϕ2pB[r]r))^2),(((χGTO1p4s2p[r]r))^2),(((χGTO2p4s2p[r]r))^2),(((χGTO2p4s2ptest[r]r))^2)},{r,0,7},PlotRange->All]

ϕCGTO2p4s2p[r_]:=0.792χGTO1p4s2p[r]+0.318χGTO2p4s2p[r]

Plot[{(((ϕ2pB[r]r))^2),(((ϕCGTO2p4s2p[r]r))^2)},{r,0,7},PlotRange->All]

ϕCGTO2s4s2p[r_]:=-0.142χGTO1s9s5p[r]-0.195χGTO2s9s5p[r]+0.562χGTO3s9s5p[r]+0.553χGTO4s9s5p[r]

Plot[{(((ϕ2sB[r]r))^2),(((ϕCGTO2s4s2p[r]r))^2)},{r,0,7},PlotRange->All]