Question

Consider an hypothetical six-coordinate complex SHe with the sulfur atom located at the center of a trigonal prism as shown below. 5. (a) |(b) prismatic SHg? (c) Please include the valence electrons in your diagram. (d) What is the point group symmetry of this complex? What are the symmetries of the ligand group orbitals of a trigonal Construct a molecular orbital energy diagram for trigonal prismatic SHs. Will the molecule be expected to be stable?

Answer 1

SH₆ :

(a) This molecule have Trigonal Prismatic geometry, as Sulfur is located at the center of trigonal prism (it is like 2-trigonal planar geometry attached to a point) ;

on using various symmetry operations it has : E;  2C₃ (z) ; 3C'_{2 ; h} (xy) ; 2S_{3 ;} 3_v symmetry elements , thus belongs to D_3h point group.

D3h 2С3 3C2 дh Е 2S3 30v A1" 1 1 1 -1 1 1 1 1 1 Rz A2" 1 -1 2 -1 0 2 1 1 -2 1 1 1 1 0 1 1 x,y A" 1 1 A21 2 1 1 -1 0 X,yz LLUJ

(b) Six H 1s orbitals in H₆ framework in this molecule can be seen that how these are affected by each symmetry operations of D_3h point group, to get symmetry of L.G.O.s.

D3h	E	2C3 (z)	3C'2	h (xy)	2S3	3v
$\Gamma$6H(1s)	6	0	0	0	0	2

This representation can be reduced to irreducible representation :

A₁’:1/12 [ (6x1x1) + (0x1x2) + (0x1x3) + (0x1x1) + (0x1x2) + (2x1x3) ] = 1/12[ 12 ] = 1

A₂’: 1/12 [ (6x1x1) + (0x1x2) + (0x-1x3) + (0x1x1) + (0x1x2) +(2x-1x3) ] =1/12 [ 0 ]= 0

E’ : 1/12 [ (6x2x1) + (0x-1x2) + (0x0x3) + (0x2x1) + (0x-1x2) + (2x0x3) ] = 1/12 [ 12 ] = 1

A₁”:1/12 [ (6x1x1) + (0x1x2) + (0x1x3) + (0x-1x1) + (0x-1x2) + (2x-1x3) ] = 1/12 [0 ]= 0

A₂”: 1/12 [(6x1x1) +(0x1x2) +(0x-1x3) + (0x-1x1) + (0x-1x2) + (2x1x3) ] = 1/12 [ 12 ] = 1

E” : 1/12 [ (6x2x1) + (0x-1x2) + (0x0x3) + (0x-2x1) + (0x1x2) + (2x0x3) ] = 1/12 [ 12 ] = 1

$\Gamma$6H(1s) = A₁’ + E’ + A₂” + E”

Thus symmetries of LGOs =  a₁’ + e’ +a₂” + e”

(c) MO diagram for this can be constructed using valence orbitals of sulfur (3s and 3p) ; from character table symmetries : 3s ( a₁’), 3px and 3py ( e’ ) and 3pz (a₂” ).

3d (3p) tk a C3s) S evalence aitals Но SHE 342-3py (Dah) Triganal friah'c M.D-Diagsam 1s

Non-bonding orbitals are shown higher in energy to account for possible interaction with 3d obitals.

(d) This molecule have 8 electrons in bonding orbital and 4 in non-bonding orbitals , thus overall bond order is 4 : it is for 6 S-H . Since it has bond order more than zero , thus this molecule can exist or occur, but its stabiilty will be less. For better explanation we shall include 3d orbitals into picture.There is greater ligand-ligand interaction :net repulsive, in this eclipsed geometry, thus making it less stable than O_h counterpart.