Reduction formula for point group D6h



Characters for molecular motions
Motion E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
Cartesian 3N 324 0 0 0 0 0 0 0 0 24 12 8
Translation 3 2 0 -1 -1 -1 -3 -2 0 1 1 1
Rotation 3 2 0 -1 -1 -1 3 2 0 -1 -1 -1
Vibration 318 -4 0 2 2 2 0 0 0 24 12 8



Decomposition into Irreducible representations
Motion A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u Total
Cartesian 3N 17 12 13 12 25 29 10 15 14 15 29 25 216
Translation 0 0 0 0 0 0 0 1 0 0 1 0 2
Rotation 0 1 0 0 1 0 0 0 0 0 0 0 2
Vibration 17 11 13 12 24 29 10 14 14 15 28 25 212



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 17
Number of vibrational modes 212





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u Total
Linear (IR) 17 11 13 12 24 29 10 14 14 15 28 25 42 / 170
Quadratic (Raman) 17 11 13 12 24 29 10 14 14 15 28 25 70 / 142
IR + Raman - 11 13 12 - - 10 - 14 15 - 25 0* / 100
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
linear 1 318 -4 0 2 2 2 0 0 0 24 12 8
quadratic 2 50.721 8 0 161 161 161 159 0 0 447 231 191
cubic 3 5.410.240 -10 106 320 320 320 0 8 0 6.128 2.200 1.360
quartic 4 434.171.760 8 0 13.040 13.040 13.040 12.720 0 0 72.528 25.080 18.000
quintic 5 27.960.661.344 -4 0 25.760 25.760 25.760 0 0 0 741.552 201.432 116.112
sextic 6 1.505.215.602.352 55 5.671 708.400 708.400 708.400 682.640 85 53 6.858.544 1.748.824 1.120.816


Decomposition into Irreducible representations
Force field Tensor
Order
A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
linear 1 17 11 13 12 24 29 10 14 14 15 28 25
quadratic 2 2.239 2.053 2.099 2.089 4.190 4.290 2.083 2.108 2.113 2.123 4.238 4.189
cubic 3 226.229 225.179 225.272 225.062 450.307 451.382 224.827 225.557 225.574 225.784 451.327 450.362
quartic 4 18.103.231 18.085.941 18.088.339 18.086.569 36.174.910 36.189.170 18.085.357 18.089.607 18.091.553 18.093.323 36.184.878 36.174.962
quintic 5 1.165.105.660 1.165.013.394 1.165.006.250 1.164.984.920 2.329.991.169 2.330.119.055 1.164.964.478 1.165.030.984 1.165.046.716 1.165.068.046 2.330.114.761 2.329.995.463
sextic 6 62.718.196.791 62.717.125.181 62.717.108.885 62.716.951.883 125.434.059.372 125.435.320.506 62.716.850.926 62.717.214.136 62.717.466.547 62.717.623.549 125.435.088.684 125.434.063.665


Literature




Character tables for chemically important point groups Character table for point group D6h Jacobs University Bremen

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