Question

A set of four group orbitals derived from four 3s atomic orbitals in necessary to examine the bonding in [PtCl4]-, a square planar complex. Deduce the wave function equations for these four SALCs using the 3s labeling scheme specified, starting with the irreducible representations for these group orbitals. Using sketches of the deduced orbitals, symmetry characteristics of the representation, and a coefficient table like in Section 5.4.4, deduce the SALCs not derived initially from the character table analysis. Provide normalized equation and sketch each group orbital.

 

Answer 1

group point = D4h

Table of group orbitals symmetry

Reduction affords

For deducing SALCs

Check 3s orbitals by every symmetry

simplification form

3s(A) + 3s(B) + 3s(C) + 3s(D)

Normalization constant

SALCs

multiply by B_1g

_{Simplification form}

_{3s(A) - 3s(B) + 3s(C) - 3s(D)}

_{Normalization constant}

_SALCs

multiply by E_u

Eu = 2(3s(A)) - 2(3s(C)) - 2(3s(C)) + 2(3s(A))

= 4(3s(A)) - 4(3s(C))

The Simplification form

3s (A ) - 3s (C )

Normalization constant

SALCs

Equation Eu SALCs

Sum of squares = 1

Normalization SALCs coefficients are

CA, CB, CC, CD

Squares of these coefficients are

CA², CB², CC², CD²

Values in the form of table

Without second Eu SALCs

CA² + CC² = 1

With second Eu SALCs

CA = CC = 0

With second Eu SALCs with equal contribution

CB = CD = 1/

Normalization equation for second Eu

Diagram of group orbitals has shown below