Symmetry, Spectroscopy, and the Molecular Structure of XeF 4
The infrared spectrum of XeF4 has absorptions at 161, 291, and 586 cm-1 (two bends, one stretch), while the Raman
spectrum has peaks at 218, 524, and 554 cm-1 (one bend, two stretches). Is its molecular structure tetrahedral or
square planar? References: J. Am. Chem. Soc. 1963, 85, 1927; J. Phys. Chem. 1971, 54, 5247.
Tetrahedral Symmetry - Td
E C3 C2 S4 σ
C Td
1 1
1
1
1
A1: x2 + y2 + z 2
1
5
1 1
1
1
1
A2
8
2
1 2
0
0
E: 2z2 - x2 - y2, x2 - y2
3 0
1 1
1
T1: (Rx, Ry, Rz)
6
1
3 0
1
T2: (x, y, z), (xy, xz, yz)
6
3
2
A1
C Td
T2
C Td
i
T
T
1 1
<1 >
A2
<5 >
Γ tot
C Td
T
Td
<2 >
Γ uma. T 2
E
C Td
h
Td
T
Γ uma
3
1
<3 >
T1
C Td
T
Γ tot = ( 15 0
T
<4 >
1 1 3 )
1 .. 5
Γ vib
Γ tot
T1
T2
Vibi
T
Td. C Td
h
<i >
.Γ
vib
1
A1: x2 + y2 + z 2
0
A2
Vib = 1
E: 2z2 - x2 - y2, x2 - y2
0
T1: (Rx, Ry, Rz)
2
T2: (x, y, z), (xy, xz, yz)
This analysis predicts two IR active modes (2T2) and four Raman active modes (A1, E, 2T2). It also suggests that the IR
and Raman should have the two T2 modes in common. Thus, tetrahedral geometry is not consistent with the
spectroscopic data. Further detail can be obtained by noting that the stretching vibrations have the same symmetry
properties as the chemical bonds. This allows the vibrational modes to be decomposed further into the symmetry of the
stretches and bends.
Square Planar Symmetry - D4h
E C4 C2 C2' C2" i S4 σh σv σd
C D4h
1 1
1
1
1
1
1
1
1
1
1 1
1
1
1 1
1
1
1
1
1
1 1
1
1 1
1 1
1
1
1
1 1
1 1
1
1 1
1 1
A 1u
4
A2g: Rz
2
1
0
B1g: x2 - y2
1
1
0
B2g: xy
2
3
2
0
2
0
2 0
0
Eg: (Rx, Ry), (xz, yz)
1 1
1
1
1
1
1
1
1
1
A1u:
1 1
1
1
1
1
1
1 1
1
A2u: z
1
1 1
1
1
1 1
1
1
1 1
1 1
1 1
1 1
1
B2u
2 0
2
0
Eu: (x, y)
C D4h
2 0
T
T
Γ tot
0
1 1
0
<1 >
A 2g
C D4h
T
A 2u
C D4h
T
<6 >
Γ trans
D4h
Γ vib
Vibi
5
2 0
C D4h
h
1
2 0
2 0
A 1g
A1g: x2 + y2, z2
Γ trans
T
D4h. C D4h
A 2u
Γ rot
<i >
.Γ
vib
h
B 1g
C D4h
T
B 1u
C D4h
T
<7 >
Γ rot
Eu
Γ bonds
Vib =
5
4
2
3
2
2
1
0
T
B 2u
C D4h
T
Γ tot
.Γ
stretch
0
B2g: xy
0
Eg: (Rx, Ry), (xz, yz)
0
A1u:
1
1
Stretch =
Eg
C D4h
T
Eu
C D4h
T
<9 >
Γ stretch
i
Bendi
<10 >
<i >
.Γ
bend
h
A1g: x2 + y2, z2
0
A2g: Rz
0
B1g: x2 - y2
0
B2g: xy
0
Eg: (Rx, Ry), (xz, yz)
0
Bend =
A2g: Rz
B1g: x2 - y2
1
B2g: xy
0
Eg: (Rx, Ry), (xz, yz)
0
A1u
0
A1u
A2u: z
0
A2u: z
1
A2u: z
0
B1u
0
B1u
0
B1u
1
B2u
0
B2u
1
B2u
Eu: (x, y)
1
Eu: (x, y)
1
Eu: (x, y)
2
<5 >
1 .. 10
T
D4h. C D4h
A1g: x2 + y2, z2
B1g: x2 - y2
1
<4 >
Γ uma. Γ trans
1
A2g: Rz
0
1
C D4h
h
A1g: x2 + y2, z2
1
<i >
1
0
B 2g
Γ vib
0
Γ bonds
1
<8 >
Γ bend
1
2
<3 >
Eg
T
D4h. C D4h
Stretchi
1
0
A 2g
Γ uma
1
B1u
<2 >
Γ stretch
2
D4h
This analysis predicts three IR active modes (A2u, 2Eu) and three Raman active modes (A1g, B1g, B2g). It also indicates
that there are no coincidences between the IR and Raman spectra. Thus, square planar geometry is consistent with
the spectroscopic data. Examining the symmetry of the stretches and bends adds further support to this conclusion.
This analysis also predicts two Raman (A1g, B1g) and one IR (Eu) active stretches, and two IR (A2u, Eu) and one Raman
(B2g) active bends. This is also consistent with the experiemental data.