Symmetry Adapted Linear Combinations (SALCs)

Determine the symmetry labels for the SALCs and draw a picture of each SALC
1. SF6 (octahedral, Oh) [Solution]
2. NiCl4 (tetrahedral, Td) [Solution]
3. AsF5 (trigonal bipyramidal, D3h) [Solution]
4. PdCl42− (square planar, D4h) [Solution]
5. [Ni(CN)5]3− (square pyramidal, C4v) [Solution]

 

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Solutions

  
1.

SF6:

Oh E 8C3 6C2 6C4 3C2 i 6S4 8S6 3σh 6σd
Γtotal 6 0 0 2 2 0 0 0 4 2

Reduces to: A1g + Eg + T1u

a1g eg
t1u
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2.

NiCl4:

Td E 8C3 3C2 6S4 6σd
Γtotal 4 1 0 0 2

Reduces to: A1 + T2

a1
t2
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3.

AsF5:

D3h E 2C3 3C2 σh 2S3 3σv
Γtotal 5 2 1 3 0 3

Reduces to: 2A1′ + E′ + A2″

a1′(s) a1′(dz2) a2″
 
e′  
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4.

PdCl42− (square planar):

D4h E 2C4 C2 2C2′ 2C2″ i 2S4 σh 2σv 2σd
Γtotal 4 0 0 2 0 0 0 4 2 0

Reduces to: A1g + B1g + Eu

a1g b1g
eu
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5.

[Ni(CN)5]3−:

C4v E 2C4 C2 2σv 2σd
Γtotal 5 1 1 3 1

Reduces to: 2A1 + B1 + E

a1(s) a1(pz) b1
e
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