Force field analysis for point group Dh


Number of atoms: 3


Your 3N representation

E 2C v i 2S C'2
9 3+ 6cos() 3 -3 -1+2cos() -1

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
1 0 1 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
1 0 0 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 4 4 1
quadratic 16 10 3
cubic 64 20 3
quartic 256 35 6
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 1 0 0 0 0 0 1 0 1 0 0 0
quadratic 3 0 1 1 0 0 1 0 1 0 0 0
cubic 3 0 3 1 1 0 3 0 1 1 0 0
quartic 6 0 3 3 1 1 3 0 3 1 1 0

Number of independant internal coordinates 1

Literature




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