Results for Point Group O



Characters of representations for molecular motions
Motion E 8C3 6C2 6C4 3C2
Cartesian 3N 240 0 0 0 0
Translation (x,y,z) 3 0 -1 1 -1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 234 0 2 -2 2


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 10 10 20 30 30 100
Translation (x,y,z) 0 0 0 1 0 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 10 10 20 28 30 98



Molecular parameter
Number of Atoms (N) 80
Number of internal coordinates 234
Number of independant internal coordinates 10
Number of vibrational modes 98


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 10 10 20 28 30 28 / 70
Quadratic (Raman) 10 10 20 28 30 60 / 38
IR + Raman - - - - 10 - - - - - - - - - - - - 0 / 10


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 6C2 6C4 3C2
linear 234 0 2 -2 2
quadratic 27.495 0 119 3 119
cubic 2.162.940 78 236 -4 236
quartic 128.154.195 0 7.139 63 7.139
quintic 6.100.139.682 0 14.042 -122 14.042
sextic 242.988.897.333 3.081 287.861 181 287.861


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 10 10 20 28 30
quadratic 1.191 1.130 2.321 3.393 3.451
cubic 90.236 90.120 180.278 270.278 270.398
quartic 5.342.451 5.338.850 10.681.301 16.016.613 16.020.151
quintic 254.177.722 254.170.762 508.348.484 762.512.164 762.519.246
sextic 10.124.646.409 10.124.502.388 20.249.145.716 30.373.504.264 30.373.648.104


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)
..55. A1A1...55. A2A2...210. EE...406. T1T1...465. T2T2.
Subtotal: 1.191 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 1.191 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..220. A1A1A1...1.540. EEE...3.276. T1T1T1...4.960. T2T2T2.
Subtotal: 9.996 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..12.180. T1T1T2...550. A1A2A2...2.100. A1EE...4.060. A1T1T1...4.650. A1T2T2...1.900. A2EE...8.120. ET1T1...9.300. ET2T2...12.180. T1T2T2.
Subtotal: 55.040 / 9 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..8.400. A2T1T2...16.800. ET1T2.
Subtotal: 25.200 / 2 / 10
Total: 90.236 / 15 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..715. A1A1A1A1...715. A2A2A2A2...22.155. EEEE...114.086. T1T1T1T1...149.265. T2T2T2T2.
Subtotal: 286.936 / 5 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..341.040. T1T1T1T2...15.400. A1EEE...32.760. A1T1T1T1...49.600. A1T2T2T2...15.400. A2EEE...40.600. A2T1T1T1...40.600. A2T2T2T2...146.160. ET1T1T1...179.800. ET2T2T2...390.600. T1T2T2T2.
Subtotal: 1.251.960 / 10 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..3.025. A1A1A2A2...11.550. A1A1EE...22.330. A1A1T1T1...25.575. A1A1T2T2...11.550. A2A2EE...22.330. A2A2T1T1...25.575. A2A2T2T2...170.520. EET1T1...195.300. EET2T2...730.800. T1T1T2T2.
Subtotal: 1.218.555 / 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)
..336.000. EET1T2...121.800. A1T1T1T2...113.400. A2T1T1T2...470.400. ET1T1T2...19.000. A1A2EE...81.200. A1ET1T1...93.000. A1ET2T2...121.800. A1T1T2T2...81.200. A2ET1T1...93.000. A2ET2T2.
..130.200. A2T1T2T2...504.000. ET1T2T2.
Subtotal: 2.165.000 / 12 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..84.000. A1A2T1T2...168.000. A1ET1T2...168.000. A2ET1T2.
Subtotal: 420.000 / 3 / 5
Total: 5.342.451 / 40 / 70


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