Download Lecture 13: Octahedral ML6 π Complexes and more Lecture notes Inorganic Chemistry in PDF only on Docsity!
5.04, Principles of Inorganic Chemistry II Prof. Daniel G. Nocera Lecture 13: Octahedral ML 6 π Complexes
The basis set needs to be expanded for metal complexes with ligands containing π- orbitals. An appropriate basis for ligands with two orthogonal π orbitals, e.g. CO, CN–, O2–, X–, to the σ bond is shown below,
The arrow is indicative of the directional phase of the pπ orbitals. Owing to their ungerade symmetry, in constructing the pπ representation
a p orbital, i.e. arrow, that transforms into itself contributes + a p orbital that transforms into minus itself contributes – a p orbital that moves, contributes 0
Oh E 8C 3 6C 2 6C 4 3C 2 i 6S 4 8S 6 3 σh 6 σd
Γσ 6 0 0 2 2 0 0 0 4 2 → a1g + t1u + eg Γπ 12 0 0 0 –4 0 0 0 0 0 → t1g + t1u + t2g + t2u
There is a second method to derive the pπ basis. The Cartesian coordinate systems
on each ligand contains the σ and π basis sets. Thus the Γx,y,z irreducible
representation (which is the sum of Γx + Γy + Γz or Γz + Γx,y for irreducible
representations for which x,y,z are not triply degenerate) defines the 1σ and 2pπ bonds of each ligand. Since the bond is coincident with the ligand, an unmoved
atom is approximated by Γσ. On the basis of geometrical considerations, the
following is true,
Γunmoved = Γ σ atoms
Γσ+π = Γx,y,z • Γσ
5.04, Principles of Inorganic Chemistry II Lecture 13
Oh Γσ T (^) 1u = Γx,y,z Γσ+π
E
8C 3 6C 2
Γσ+π =
6C 4 3C 2 i 6S 4 8S 6 3 σh 2 2 0 0 0 4 1 –1 –3 –1 0 1 2 –2 0 0 0 4
a (^) 1g + eg + t1g + 2t1u + t2g + t2u
6 σd 2 → a1g + t (^) 1u + e (^) g 1 2 → a^ 1g^ + eg^ + t1g^ + 2t1u + t2g + t2u
Γσ = a (^) 1g + t1u + e (^) g
Γ π = Γσ+π – Γσ = t 1g + t1u + t2g + t2u
The σ SALCs have already been derived in Lecture 12. Methods 1-3 of Lecture 12 can be employed to determine the pπ SALCs. For the orbitals that transform as t1u and t2g , Method 3 (mirror the metal atomic orbital symmetry) is convenient. For the t1u SALC,
and 2 others (in the xz and yz planes as defined by the symmetries of the py and px orbitals)
pz ψ t^ ( 11 u^ )^ =
L π 3 + L π 4 + L π 5 + L π 6 )
The t2g SALCs have the mirrored symmetry of the (d (^) xy,dxz,dyz) orbital set,
and 2 others (in the xy and xz planes as defined by the symmetries of the dxy and dxz orbitals)
dyz ψ t^ ( 21 g^ )^ = 1
( L π 1 − L π 2 − L π 4 + L π 6 )
Non-bonding SALCs must be ascertained from projection operators and Schmidt orthogonalization methods.
5.04, Principles of Inorganic Chemistry II Lecture 13
For a π-accepting ligand set, orbitals have the same form (or symmetry) as π donors,
t1u t2g (^1) ⎛ 1 ⎜ ⎝
L π 3 ⎞⎟
L π ⎞⎟
ψ(1)^ = *^ + L π *^ + Lπ *^ + Lπ *^ (1)= *^ − L π *^ − Lπ *^ +Lπ *
t1u 2 4 5 6 t2g 2 1 2 4 6
The only difference between the π-donor and π-acceptor MO diagrams is the relative placement of the π* orbitals relative to the metal atomic orbitals; for Co(CN) 6 3–,
t1u M–L and M–L
3.7 eV (^) 4p see VOIE
7.3 eV
a1g
eg
M–L (dxz
t1u
eg
a1g
t2g
M–L
M–L
M–L (dx (^2) –y 2 , dz 2 )
n.b t1g, t2u (M-L ) t1u
(M-L *) t2g
Co3+^ 6 CN^ – Co(CN) 6 3–
increased energy gap (relative to -only case) owing to participation 9.4 eV (^) 3d of t2g orbitals in M-L see VOIE (^) bond
4s^ 12L * see VOIE
, dyz, dxy) the lone pair HOMO of 6L CO, PES spectrum setsthe energies of these orbitals at 14 eV
5.04, Principles of Inorganic Chemistry II Lecture 13
