Results for Point Group I



Characters of representations for molecular motions
Motion E 12C5 12(C5)2 20C3 15C2
Cartesian 3N 420 0.000 -0.000 0 0
Translation (x,y,z) 3 1.618 -0.618 0 -1
Rotation (Rx,Ry,Rz) 3 1.618 -0.618 0 -1
Vibration 414 -3.236 1.236 0 2


Decomposition to irreducible representations
Motion A T1 T2 G H Total
Cartesian 3N 7 21 21 28 35 112
Translation (x,y,z) 0 1 0 0 0 1
Rotation (Rx,Ry,Rz) 0 1 0 0 0 1
Vibration 7 19 21 28 35 110



Molecular parameter
Number of Atoms (N) 140
Number of internal coordinates 414
Number of independant internal coordinates 7
Number of vibrational modes 110

Force field analysis


Allowed / forbidden vibronational transitions
Operator A T1 T2 G H Total
Linear (IR) 7 19 21 28 35 19 / 91
Quadratic (Raman) 7 19 21 28 35 42 / 68
IR + Raman - - - - - - - - 21 28 - - - - 0 / 49


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 12C5 12(C5)2 20C3 15C2
linear 414 -3.236 1.236 0 2
quadratic 85.905 5.854 -0.854 0 209
cubic 11.912.160 -7.236 -2.764 138 416
quartic 1.241.842.680 5.854 -0.854 0 21.944
quintic 103.818.048.048 80.764 85.236 0 43.472
sextic 7.249.960.355.352 -270.830 104.830 9.591 1.543.256


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A T1 T2 G H
linear 7 19 21 28 35
quadratic 1.485 4.245 4.242 5.726 7.211
cubic 198.684 595.502 595.504 794.192 992.738
quartic 20.702.865 62.086.650 62.086.647 82.789.511 103.492.376
quintic 1.730.311.702 5.190.891.550 5.190.891.552 6.921.203.170 8.651.514.872
sextic 120.833.061.567 362.497.631.853 362.497.632.021 483.330.693.587 604.163.745.563


Further Reading


Contributions to nonvanishing force field constants


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

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(A) ≤ i ≤ pos(H)
..28. AA...190. T1T1...231. T2T2...406. GG...630. HH.
Subtotal: 1.485 / 5 / 5
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(H)
Subtotal: 0 / 0 / 10
Total: 1.485 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(H)
..84. AAA...969. T1T1T1...1.330. T2T2T2...4.060. GGG...15.540. HHH.
Subtotal: 21.983 / 5 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(H)
..6.650. T1T1H...8.085. T2T2H...14.210. GGH...1.330. AT1T1...1.617. AT2T2...2.842. AGG...4.410. AHH...7.182. T1GG...11.305. T1HH...7.938. T2GG.
..12.495. T2HH...34.300. GHH.
Subtotal: 112.364 / 12 / 20
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(H)
..11.172. T1T2G...13.965. T1T2H...18.620. T1GH...20.580. T2GH.
Subtotal: 64.337 / 4 / 10
Total: 198.684 / 21 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(H)
..210. AAAA...18.145. T1T1T1T1...26.796. T2T2T2T2...134.561. GGGG...720.615. HHHH.
Subtotal: 900.327 / 5 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(H)
..27.930. T1T1T1T2...37.240. T1T1T1G...79.800. T1T1T1H...49.588. T2T2T2G...107.800. T2T2T2H...653.660. GGGH...6.783. AT1T1T1...9.310. AT2T2T2...28.420. AGGG...108.780. AHHH.
..33.649. T1T2T2T2...215.992. T1GGG...814.625. T1HHH...238.728. T2GGG...900.375. T2HHH...1.635.620. GHHH.
Subtotal: 4.948.300 / 16 / 20
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(H)
..5.320. AAT1T1...6.468. AAT2T2...11.368. AAGG...17.640. AAHH...87.780. T1T1T2T2...218.918. T1T1GG...460.845. T1T1HH...266.952. T2T2GG...561.540. T2T2HH...1.714.510. GGHH.
Subtotal: 3.351.341 / 10 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(H)
..212.268. T1T1T2G...265.335. T1T1T2H...539.980. T1T1GH...658.560. T2T2GH...46.550. AT1T1H...56.595. AT2T2H...99.470. AGGH...234.612. T1T2T2G...293.265. T1T2T2H...1.042.720. T1GGH.
..1.152.480. T2GGH...50.274. AT1GG...79.135. AT1HH...55.566. AT2GG...87.465. AT2HH...240.100. AGHH...323.988. T1T2GG...991.515. T1T2HH...1.638.560. T1GHH...1.811.040. T2GHH.
Subtotal: 9.879.478 / 20 / 30
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(H)
..78.204. AT1T2G...97.755. AT1T2H...130.340. AT1GH...144.060. AT2GH...1.173.060. T1T2GH.
Subtotal: 1.623.419 / 5 / 5
Total: 20.702.865 / 56 / 70


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A T1 T2 G H
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement