Force field analysis for point group Dh


Number of atoms: 4


Your 3N representation

E 2C v i 2S C'2
12 4+ 8cos() 4 0 0 0

can be reduced to

A1g=+g A2g=-g E1g=g E2g=g E3g=g E4g=g A1u=+u A2u=-u E1u=u E2u=u E3u=u E4u=u
2 0 2 0 0 0 2 0 2 0 0 0

Substraction of translational and rotational contributions results in

A1g=+g A2g=-g E1g=g E2g=g E3g=g E4g=g A1u=+u A2u=-u E1u=u E2u=u E3u=u E4u=u
2 0 1 0 0 0 1 0 1 0 0 0



Infrared and Raman activities (harmonic approximation)
Method A1g=+g A2g=-g E1g=g E2g=g E3g=g E4g=g A1u=+u A2u=-u E1u=u E2u=u E3u=u E4u=u
Infrared - - - - - - + - + - - -
Raman + - + + - - - - - - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 7 7 2
quadratic 49 28 6
cubic 343 84 11
quartic 2401 210 23
No. 1 : Total number of force constants .
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.

Symmetry properties of force field parameters
Force field A1g=+g A2g=-g E1g=g E2g=g E3g=g E4g=g A1u=+u A2u=-u E1u=u E2u=u E3u=u E4u=u
linear 2 0 1 0 0 0 1 0 1 0 0 0
quadratic 6 0 3 2 0 0 3 1 3 1 0 0
cubic 11 1 9 5 2 0 8 2 9 4 2 0
quartic 23 3 19 14 6 3 16 6 19 12 6 2

Number of independant internal coordinates 2

Literature




Character tables for chemically important point groups Computational Laboratory for Analysis, Modeling and Visualization Jacobs University Bremen