Question

4. The molecule PtCl42- is an important square planar starting material in synthetic inorganic chemistry. Using the pz orbitals of Cl as your basis find the irreducible representation(s) of the pz orbtials. Additionally, use the projection operator method and show what one irreducible representation looks like. What orbitals if any match up with the orbitals on Pt (from a pure symmetry approach). (10)

Answer 1

[PtCl, 12-(D4h)

D4h E 204 02 202 2C"2 i 254 oh 20v=oxz 20d NOUA 0 Tred 5 3 15 1 1 5 -1 1 -5 3 -1 -3 1 -1 -1 1 -3 -3 1 5 -1 1 -1 5 3 1 3 1 1

Where NOUA is the number of unshifted atoms during symmetry operation and Ɵ =Γxyz corresponds to the character of each symmetry element and Γred is the total reducible representation.

From the character table, we know that the A2u representation corresponds to the Pz orbital and the irreducible representation is given as follows:

Applying Irreducible representation formula we have: C; = .Xred,j.X:,j) = 1/16 ( 1*1*15) +(2*1*1)+(1*1*-5)+ (2*-1*-3)+(2*-1*1)+ (1*-1*-3)+(2*-1*-1)+(1*-1*5)+(2*1*3)+(2*1*1) = 1/16(15+2-5+6-2+3+2-5+6+2) = 1/16(26) = 1.65