[qrt388]

Hi, could somebody please explain to me how to reduce C4V for vector transformations?

I'm looking at the molecule [TlCl5]-. I know E will be 5, and I thought C4 would be 1, C2 would be 1, sigma v would be 3, and sigma d would be 1. But when I work out the table, it doesn't work (I don't get integers). Could somebody please help me with this?

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In response to the previous answer, I did mean [TlCl5]2-, I just forgot the 2. PCl5 is D3h, not C4v (which is what the [TlCl5]2- is drawn as for my particular example). Could somebody please still help me figure this out? I'm trying to deduce the atomic orbitals on the central Tl attom that have the appropriate symmetry to form valence bond hybrid orbitals towards the Cl. So I applied vectors to the molecule as described above. Clearly it's incorrect.

[shelanachium]

[TlCl5]- is not possible. Do you mean [TlCl5]2-? Then consider isoelectronic species such as PCl5, and look up their symmetry properties.

[Dolphinsiu]

For ML₅ that belongs to D_3h

D3h      E     2 C3       3 C2      sigma h       2 S3      3 sigma v
Irr.       5        2           1           3               0            3

A1'       1        1           1           1               1            1
A2'       1        1          -1          1               1           -1
E'         2      -1           0           2              -1            0
A1''      1       1           1          -1              -1           -1
A2''      1        1          -1         - 1             -1            1
E''        2      -1           0          -2               1            0

Irr. = 2A1'      +        E'                         +    A2''
      s or dz       (px,py) or (dx²-y²,dxy)       (pz)

Irr. = irreducible representation of 5 M - L sigma bonds

Hence, the possible hybridization state: sp³d and spd³