Results for Point Group Td



Characters of representations for molecular motions
Motion E 8C3 3C2 6S4 d
Cartesian 3N 156 0 0 0 14
Translation (x,y,z) 3 0 -1 -1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 150 0 2 0 14


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 10 3 13 16 23 65
Translation (x,y,z) 0 0 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 10 3 13 15 22 63



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 10
Number of vibrational modes 63


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 10 3 13 15 22 22 / 41
Quadratic (Raman) 10 3 13 15 22 45 / 18
IR + Raman - - - - 3 - - - - 15 22 22 / 18


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 3C2 6S4 d
linear 150 0 2 0 14
quadratic 11.325 0 77 1 173
cubic 573.800 50 152 0 1.512
quartic 21.947.850 0 3.002 38 11.866
quintic 675.993.780 0 5.852 0 79.492
sextic 17.463.172.650 1.275 79.002 38 490.042


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 10 3 13 15 22
quadratic 525 438 963 1.363 1.449
cubic 24.322 23.566 47.838 71.328 72.084
quartic 917.845 911.893 1.829.738 2.740.149 2.746.063
quintic 28.187.012 28.147.266 56.334.278 84.478.618 84.518.364
sextic 727.765.014 727.519.974 1.455.283.713 2.182.764.205 2.183.009.207


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of Td

Subtotal: <Number of nonvanishing force constants in subsection> / <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Number of nonvanishing force constants in force field> / <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>


Contributions to nonvanishing quadratic force field constants
Irrep combinations (i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..55. A1A1...6. A2A2...91. EE...120. T1T1...253. T2T2.
Subtotal: 525 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 525 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..220. A1A1A1...455. EEE...455. T1T1T1...2.024. T2T2T2.
Subtotal: 3.154 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..2.640. T1T1T2...60. A1A2A2...910. A1EE...1.200. A1T1T1...2.530. A1T2T2...234. A2EE...1.560. ET1T1...3.289. ET2T2...3.465. T1T2T2.
Subtotal: 15.888 / 9 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..990. A2T1T2...4.290. ET1T2.
Subtotal: 5.280 / 2 / 10
Total: 24.322 / 15 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..715. A1A1A1A1...15. A2A2A2A2...4.186. EEEE...10.320. T1T1T1T1...44.781. T2T2T2T2.
Subtotal: 60.017 / 5 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..39.600. T1T1T1T2...4.550. A1EEE...4.550. A1T1T1T1...20.240. A1T2T2T2...1.365. A2EEE...2.040. A2T1T1T1...4.620. A2T2T2T2...14.560. ET1T1T1...46.046. ET2T2T2...83.490. T1T2T2T2.
Subtotal: 221.061 / 10 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..330. A1A1A2A2...5.005. A1A1EE...6.600. A1A1T1T1...13.915. A1A1T2T2...546. A2A2EE...720. A2A2T1T1...1.518. A2A2T2T2...21.840. EET1T1...46.046. EET2T2...115.335. T1T1T2T2.
Subtotal: 211.855 / 10 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..55.770. EET1T2...26.400. A1T1T1T2...6.930. A2T1T1T2...64.350. ET1T1T2...2.340. A1A2EE...15.600. A1ET1T1...32.890. A1ET2T2...34.650. A1T1T2T2...4.680. A2ET1T1...9.867. A2ET2T2.
..11.385. A2T1T2T2...94.380. ET1T2T2.
Subtotal: 359.242 / 12 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..9.900. A1A2T1T2...42.900. A1ET1T2...12.870. A2ET1T2.
Subtotal: 65.670 / 3 / 5
Total: 917.845 / 40 / 70


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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement