Generating STO's for C, N and Si

1. Generate STO’s
2s&2p orbitals of C
2s&2p orbitals of N
3s&3p orbitals of Si

2. Slater Type Orbital Expression
𝝍ₙₙₙ (r,Ө,ф)= [ N r⁽ⁿ⁻¹⁾ (exp -Z*r/n)] [ (yₙₙ (Өф))]
● N is the normalization factor
● n’ is the effective principal quantum number
● l is the azimuthal quantum number
● m is the magnetic quantum number
● Z* is the effective nuclear charge
● yₗₗ (Өф) is the spherical harmonics

3. Effective Nuclear charge get expressed as
Z* = Z - S
● Z is the atomic number
● S is the screening constant
The value of screening constant is determined from slater rules.

4. C ( 1s22s22p2)
S = (3*0.35) + (2*0.85)= 2.75
Z* = Z - S = 6 - 2.75 = 3.25
STO for 2s : Ф2s = [R₂₀(r)] [ (yₙₙ (Өф) ]
= [ r exp ( -3.25r/2)] [1/√4ℼ]
STO for 2p : Ф2p = [ r exp ( -3.25r/2)] [½ . (√3/ℼ) cosӨ

5. N ( 1s22s22p3 )
S = (4*0.35) + (2*0.85) = 3.10
Z* = Z - S = 7 - 3.10 = 3.90
STO for 2s : Ф2s = [R₂₀(r)] [ (yₙₙ (Өф) ]
= [ r exp ( -3.90r/2)] [1/√4ℼ]
STO for 2p : Ф2p = [ r exp ( -3.25r/2)] [½ . (√3/ℼ) cosӨ

6. Si (1s22s22p63s23p2)
S = (0.35*3) + (0.85*8) + (1*2)= 9.85
Z* = Z - S = 14 - 9.85 = 4.15
STO for 3s : Ф3s = [R₃₀(r)] [ yₙₙ (Өф) ]
= [ r² exp ( -4.15r/3)] [1/√4ℼ]
STO for 3p : Ф3p = [ r² exp ( -4.15r/3)] [½ . (√3/ℼ) cosӨ