Results for Point Group O



Characters of representations for molecular motions
Motion E 8C3 6C2 6C4 3C2
Cartesian 3N 156 0 -2 0 0
Translation (x,y,z) 3 0 -1 1 -1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 150 0 0 -2 2


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 6 7 13 20 19 65
Translation (x,y,z) 0 0 0 1 0 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 6 7 13 18 19 63



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 6
Number of vibrational modes 63


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 6 7 13 18 19 18 / 45
Quadratic (Raman) 6 7 13 18 19 38 / 25
IR + Raman - - - - 7 - - - - - - - - - - - - 0 / 7


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 6C2 6C4 3C2
linear 150 0 0 -2 2
quadratic 11.325 0 75 3 77
cubic 573.800 50 0 -4 152
quartic 21.947.850 0 2.850 42 3.002
quintic 675.993.780 0 0 -80 5.852
sextic 17.463.172.650 1.275 73.150 118 79.002


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 6 7 13 18 19
quadratic 501 462 963 1.388 1.424
cubic 23.943 23.945 47.838 71.705 71.707
quartic 915.592 914.146 1.829.738 2.742.404 2.743.808
quintic 28.167.119 28.167.159 56.334.278 84.498.471 84.498.511
sextic 727.660.811 727.624.177 1.455.283.713 2.182.868.448 2.182.904.964


Further Reading



Contributions to nonvanishing force field constants


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

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)
..21. A1A1...28. A2A2...91. EE...171. T1T1...190. T2T2.
Subtotal: 501 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 501 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..56. A1A1A1...455. EEE...816. T1T1T1...1.330. T2T2T2.
Subtotal: 2.657 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..3.249. T1T1T2...168. A1A2A2...546. A1EE...1.026. A1T1T1...1.140. A1T2T2...546. A2EE...2.223. ET1T1...2.470. ET2T2...3.078. T1T2T2.
Subtotal: 14.446 / 9 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..2.394. A2T1T2...4.446. ET1T2.
Subtotal: 6.840 / 2 / 10
Total: 23.943 / 15 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..126. A1A1A1A1...210. A2A2A2A2...4.186. EEEE...20.691. T1T1T1T1...25.460. T2T2T2T2.
Subtotal: 50.673 / 5 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..58.482. T1T1T1T2...2.730. A1EEE...4.896. A1T1T1T1...7.980. A1T2T2T2...3.185. A2EEE...7.980. A2T1T1T1...6.783. A2T2T2T2...25.194. ET1T1T1...29.640. ET2T2T2...64.980. T1T2T2T2.
Subtotal: 211.850 / 10 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..588. A1A1A2A2...1.911. A1A1EE...3.591. A1A1T1T1...3.990. A1A1T2T2...2.548. A2A2EE...4.788. A2A2T1T1...5.320. A2A2T2T2...31.122. EET1T1...34.580. EET2T2...123.633. T1T1T2T2.
Subtotal: 212.071 / 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)
..57.798. EET1T2...19.494. A1T1T1T2...20.349. A2T1T1T2...80.028. ET1T1T2...3.276. A1A2EE...13.338. A1ET1T1...14.820. A1ET2T2...18.468. A1T1T2T2...15.561. A2ET1T1...17.290. A2ET2T2.
..23.940. A2T1T2T2...84.474. ET1T2T2.
Subtotal: 368.836 / 12 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..14.364. A1A2T1T2...26.676. A1ET1T2...31.122. A2ET1T2.
Subtotal: 72.162 / 3 / 5
Total: 915.592 / 40 / 70


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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement