V-22
D. p – systems and Huckel theory
4 H’s – identical, consider 1s
GH1s = 4 0 0 0 0 4 0 0
= Ag + B1g + B2u + B3u
GC2s = 2 0 0 2 0 2 2 0
= Ag + B3u
GC2px = 2 0 0 2 0 2 2 0
= Ag + B3u
G2pz = 2 0 0 -2 0 2 -2 0
= B1g + B2u
G2pz = 2 0 0 -2 0 -2 2 0
= B2g + B1u « note do not interact with any other
CH bonds ® fC + fH same symmetry
come from Ag – 2s, 2px
B1g – 2py
B2u – 2py
B3u – 2s, 2px
C–C bonds ® fC - fC all as listed
Ethylene
Minimal basis set: 4–H-1s: G1s = 4 0 0 0 0 4 0 0
Þ ag + b1g + b2u + b3u
2–C2s: G2s = 2 0 0 2 0 2 2 0
Þ ag + b3u
2–C2px: G2px = 2 0 0 2 0 2 2 0
Þ ag + b3u
2–C2py: G2py = 2 0 0 -2 0 -2 2 0
Þ b1g + b2u
2–C2pz: G2pz = 2 0 0 -2 0 -2 2 0
Þ b2g + b1u
basis – 12 orbitals, 12 x 12 determinants, but block by symmetry
see that b1u + b2g effectively non-bond – i.e.
no interaction with H’s and C’s but credited as LCAO so not equal energy ® Hückel
basis – 12 orbitals (neglect C1S) 12 x 12 determinant
HHH2s
H2px
Ethylene ® used minimal valence basis
C–2s, 2p, H–1s
took 12 x 12 ® 2 3 x 3 (ag + b3u) – CH + CC
2 2 x 2 (b1g + b2u) – CH
2 1 x 1 (b2g + b1u) ® Õ matrix with s
Mixing ® makes up and down balance
lowest configuration – 12e-
(1ag)2 (1b3u) ( )2 ( )2 ( )2 (b1u)2 = 1Ag
turns out b1u – HOMO
b2g – LUMO
1st excited state ® 1B3u or 3B3u
1A1g ® 1B3u E1 allowed
by m selection rule
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