96
4 Representations
Fig. 4.10 (a) molecular graph of triphenylmethyl, (b) correspondence between ortho and meta
sites and octahedral C 4v positions, and (c) Hückel spectrum
extension along the threefold direction of the trigonal axis of the molecular frame
permute the atoms as follows:
ˆ
C 4 → (o)(a)(d)(p)(x)(q)(e)(b, c)(y, z)(f, h, g, i)(r, t, s, u)
ˆ
S 6 → (o)(a,c,b)(x,z,y)(d,i,f,e,h,g)(p,u,r,q,t,s)
(4.151)
A horizontal coordinate plane, ˆ
σ h , of the octahedron has the effect of flipping one
single phenyl group around. We can at once determine the irreps of the different
orbits by induction:
{a,b,c}:Γ(a 1g D 4h ↑ O h ) = A 1g + E g
{x,y,z}:Γ(a 1g D 4h ↑ O h ) = A 1g + E g
{d,e,f,g,h,i}:Γ(a 1 C 4v ↑ O h ) = A 1g + E g + T 1u
{p, q, r, s, t, u}:Γ(a 1 C 4v ↑ O h ) = A 1g + E g + T 1u
(4.152)
4 Representations
Fig. 4.10 (a) molecular graph of triphenylmethyl, (b) correspondence between ortho and meta
sites and octahedral C 4v positions, and (c) Hückel spectrum
extension along the threefold direction of the trigonal axis of the molecular frame
permute the atoms as follows:
ˆ
C 4 → (o)(a)(d)(p)(x)(q)(e)(b, c)(y, z)(f, h, g, i)(r, t, s, u)
ˆ
S 6 → (o)(a,c,b)(x,z,y)(d,i,f,e,h,g)(p,u,r,q,t,s)
(4.151)
A horizontal coordinate plane, ˆ
σ h , of the octahedron has the effect of flipping one
single phenyl group around. We can at once determine the irreps of the different
orbits by induction:
{a,b,c}:Γ(a 1g D 4h ↑ O h ) = A 1g + E g
{x,y,z}:Γ(a 1g D 4h ↑ O h ) = A 1g + E g
{d,e,f,g,h,i}:Γ(a 1 C 4v ↑ O h ) = A 1g + E g + T 1u
{p, q, r, s, t, u}:Γ(a 1 C 4v ↑ O h ) = A 1g + E g + T 1u
(4.152)