Reduction formula for point group D2d



Characters for molecular motions
Motion E 2S4 C2 (z) 2C'2 2d
Cartesian 3N 21 -1 -3 -1 5
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 15 -1 -1 1 5



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 3 1 1 4 6 15
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 3 0 1 3 4 11



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 3
Number of vibrational modes 11





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 3 0 1 3 4 7 / 4
Quadratic (Raman) 3 0 1 3 4 11 / 0
IR + Raman - 0 - 3 4 7 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2S4 C2 (z) 2C'2 2d
linear 1 15 -1 -1 1 5
quadratic 2 120 0 8 8 20
cubic 3 680 0 -8 8 60
quartic 4 3.060 4 36 36 160
quintic 5 11.628 -4 -36 36 376
sextic 6 38.760 0 120 120 820


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 3 0 1 3 4
quadratic 2 23 9 13 19 28
cubic 3 101 67 71 97 172
quartic 4 437 339 355 417 756
quintic 5 1.551 1.345 1.365 1.535 2.916
sextic 6 5.095 4.625 4.685 5.035 9.660


Literature




Character tables for chemically important point groups Character table for point group D2d Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement