Question

4. The planar molecule SO3 shown below has Dzh symmetry. Oos- a) Determine the irreducible representations of the oxygen o orbital combinations. b) Construct a qualitative MO diagram for SO3 using the oxygen o orbitals and the 3s and 3p valence orbitals on the sulphur. c) Which sulphur orbital is not involved in o bonding with the oxygens? d) Determine the irreducible representations of the six oxygen a orbital combinations. e) Which d orbitals on sulphur can undergo i bonding with oxygen?

Answer 1

Sol. (a) and (d). Consider the triangular planer SO₃ molecule.Its point group is D₃h.The operation associated with D₃h are E,C₃,C₂,S₃,$\sigma$_h and $\sigma$ _v . During the operation of E,all the three vectors retain position and hence the character is 3.During C₃ all the vectores shift $\chi$ (C₃₎=0. Each of the C₂ axis pass through one of the vectors and hence $\chi$ (C₂) =1.The S₃ axis coincide with the  C₃ and hence $\chi$ (S₃₎=0.As the $\sigma$ _h passes through all the vectors, $\chi$ ($\sigma$_h) =3.Each $\sigma$ ​​​​​​​_v passes through one vector and so $\chi$ ($\sigma$​​​​​​​_v) =1. and so on.

The irreducable representation below are labelled for the oxygen orbitals,

DonE 213 3C2 on 25 30r. Texoll FPgsd 3 3 0 0 - - 3 -3 0 0 - - - - - til 43" NN - - - - 1 1 - - 1 -1 0 0 1 -1 2 -2 1 -1 -1 | oo - I (X,Y T - 99 o 1 I TS = Ait E [Py) = A'TE FPx) = A₂ +E' (P₂) = tu+E" Salphur 8, Px, Py Sulphur si pxiPg Sulphur Px Py Sulphur P₂

The possible atomic orbitals are listed below.

Symmetry species	A1'	E'
Atomic orbitals	s	px,py
	$d_{z^{2}}$	$d_{x^{2}-y^{2}}$, dxy

(b) (d) p_z orbital

Energy 1. DVD: Napg? A2 (20) A 2 E(BR13 py) A B 192_ 16th 11th I == A2/2px) Airpy) **PP3) E (2px? Elapy E (203) ERP3) A las E299 (35) E 12px LAS AQs) EQs)

(e) In SO3, 2 p$\pi$−d$\pi$ bonds are present.The answer is $d_{x^{2}-y^{2}}$ , d_xy orbitals.