Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 120 0 0 0 0 8 8 8
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 114 2 2 2 0 8 8 8



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 18 14 14 14 12 16 16 16 120
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 18 13 13 13 12 15 15 15 114



Molecule Parameter
Number of Atoms (N) 40
Number of internal coordinates 114
Number of independant internal coordinates 18
Number of vibrational modes 114





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 18 13 13 13 12 15 15 15 45 / 69
Quadratic (Raman) 18 13 13 13 12 15 15 15 57 / 57
IR + Raman - - - - 12 - - - 0* / 12
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
linear 1 114 2 2 2 0 8 8 8
quadratic 2 6.555 59 59 59 57 89 89 89
cubic 3 253.460 116 116 116 0 544 544 544
quartic 4 7.413.705 1.769 1.769 1.769 1.653 3.669 3.669 3.669
quintic 5 174.963.438 3.422 3.422 3.422 0 18.600 18.600 18.600
sextic 6 3.470.108.187 35.931 35.931 35.931 32.509 96.957 96.957 96.957


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 18 13 13 13 12 15 15 15
quadratic 2 882 808 808 808 801 816 816 816
cubic 3 31.930 31.600 31.600 31.600 31.522 31.736 31.736 31.736
quartic 4 928.959 926.240 926.240 926.240 925.794 926.744 926.744 926.744
quintic 5 21.878.688 21.867.677 21.867.677 21.867.677 21.864.738 21.872.327 21.872.327 21.872.327
sextic 6 433.817.420 433.750.976 433.750.976 433.750.976 433.736.575 433.767.088 433.767.088 433.767.088


Literature




Character tables for chemically important point groups Character table for point group D2h Jacobs University Bremen

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