Question

please explain and answer both questions very confused and not sure where to start. Thank You!

1. E10C.5(b): Consider BF3 (point group D3h). There are SALCs from the F valence orbitals which transform as A" and E". Are there any valence orbitals of the central B atom that can have a non-zero overlap with the SALCs? How would your conclusion differ for AlF3, where 3d orbitals might be available? 2. E10C.6(b): The ClO2 molecule (which belongs to the group C2v) was trapped in a solid. Its ground state is know to be B. Light polarized parallel to the y-axis (parallel to the OO separation) excited the molecule to an upper state. What is the symmetry species of that state?

Answer 1

1. BF₃ (D_3h ) :

Given : SALCs of 3 F atoms transforms as : A"₂ + E"  

B have 2s and 3 -2p orbitals for bonding : to have non-zero overlap we must have orbitals of A₂" and E" symmetry, so we get integral overlap with totally symmetric part.

Using character table for D_3h :  

2s orbital has symmetry (totally symmetric) : A'₁

2pz orbital has symmetry : A"₂

2px and 2py orbital are degenerate and have symmetry : E'

With this we can say that only 2pz orbital ( symmetry : A"₂ ) can have non zero overlap.

If we consider 3d-orbitals for AlF₃ (D_3h ) : Using character table we can say that dxz and dyz (E" symmetry ) can have  non zero overlap with SALCs

: so AlF₃ , it can have    A"₂ (2pz )+ E" (dxz and dyz ).

2. ClO₂ (C_2v ) have B₁ ground state :

From character table , character of B₁ ground state :

B₁  = E :(1) ; C₂ :(-1) ;  _v(xz) : (1) ;  _v(yz) : (-1)

Light polarized to y-axis , so character of y-axis From character table :

y-axis = B₂  = E :(1) ; C₂ :(-1) ;  _v(xz) : (-1) ;  _v(yz) : (1)

So, symmetry of excited state = B_{1 *} B₂

we get = B_{1 *} B₂ = E :(1) ; C₂ :(1) ;  _v(xz) : (-1) ;  _v(yz) : (-1) = A₂

Since ,  B_{1 *} B₂ = A₂ (So, symmetry of excited state is A₂ ).