Results for Point Group Ih



Characters of representations for molecular motions
Motion E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
Cartesian 3N 240 0.000 -0.000 0 0 0 0.000 -0.000 0 8
Translation (x,y,z) 3 1.618 -0.618 0 -1 -3 0.618 -1.618 0 1
Rotation (Rx,Ry,Rz) 3 1.618 -0.618 0 -1 3 -0.618 1.618 0 -1
Vibration 234 -3.236 1.236 0 2 0 0.000 0.000 0 8


Decomposition to irreducible representations
Motion Ag T1g T2g Gg Hg Au T1u T2u Gu Hu Total
Cartesian 3N 3 5 5 8 11 1 7 7 8 9 64
Translation (x,y,z) 0 0 0 0 0 0 1 0 0 0 1
Rotation (Rx,Ry,Rz) 0 1 0 0 0 0 0 0 0 0 1
Vibration 3 4 5 8 11 1 6 7 8 9 62



Molecular parameter
Number of Atoms (N) 80
Number of internal coordinates 234
Number of independant internal coordinates 3
Number of vibrational modes 62


Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag T1g T2g Gg Hg Au T1u T2u Gu Hu Total
Linear (IR) 3 4 5 8 11 1 6 7 8 9 6 / 56
Quadratic (Raman) 3 4 5 8 11 1 6 7 8 9 14 / 48
IR + Raman - - - - 4 5 8 - - - - 1 - - - - 7 8 9 0* / 42
* Parity Mutual Exclusion Principle


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
linear 234 -3.236 1.236 0 2 0 0.000 0.000 0 8
quadratic 27.495 5.854 -0.854 0 119 117 -1.618 0.618 0 149
cubic 2.162.940 -7.236 -2.764 78 236 0 0.000 0.000 0 1.024
quartic 128.154.195 5.854 -0.854 0 7.139 6.903 1.618 -0.618 0 10.839
quintic 6.100.139.682 44.764 49.236 0 14.042 0 0.000 0.000 0 65.880
sextic 242.988.897.333 -154.331 60.331 3.081 287.861 273.819 -1.000 -1.000 39 517.787


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
linear 3 4 5 8 11 1 6 7 8 9
quadratic 264 658 656 920 1.184 225 689 688 912 1.137
cubic 18.194 53.915 53.916 72.112 90.267 17.938 54.171 54.172 72.112 90.011
quartic 1.070.257 3.201.781 3.201.780 4.272.036 5.342.293 1.067.432 3.204.146 3.204.144 4.271.576 5.339.008
quintic 50.844.497 152.493.506 152.493.507 203.337.980 254.182.477 50.828.027 152.509.976 152.509.977 203.337.980 254.166.007
sextic 2.025.010.976 6.074.628.544 6.074.628.592 8.099.639.568 10.124.648.984 2.024.876.953 6.074.744.300 6.074.744.348 8.099.621.300 10.124.496.732


Further Reading



Contributions to nonvanishing force field constants


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

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(Ag) ≤ i ≤ pos(Hu)
..6. AgAg...10. T1gT1g...15. T2gT2g...36. GgGg...66. HgHg...1. AuAu...21. T1uT1u...28. T2uT2u...36. GuGu...45. HuHu.
Subtotal: 264 / 10 / 10
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Hu)
Subtotal: 0 / 0 / 45
Total: 264 / 10 / 55


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Hu)
..10. AgAgAg...4. T1gT1gT1g...10. T2gT2gT2g...120. GgGgGg...572. HgHgHg.
Subtotal: 716 / 5 / 10
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Hu)
..110. T1gT1gHg...165. T2gT2gHg...396. GgGgHg...30. AgT1gT1g...45. AgT2gT2g...108. AgGgGg...198. AgHgHg...3. AgAuAu...63. AgT1uT1u...84. AgT2uT2u.
..108. AgGuGu...135. AgHuHu...112. T1gGgGg...220. T1gHgHg...60. T1gT1uT1u...112. T1gGuGu...144. T1gHuHu...140. T2gGgGg...275. T2gHgHg...105. T2gT2uT2u.
..140. T2gGuGu...180. T2gHuHu...968. GgHgHg...288. GgGuGu...648. GgHuHu...231. HgT1uT1u...308. HgT2uT2u...396. HgGuGu...990. HgHuHu.
Subtotal: 6.762 / 29 / 90
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Hu)
..160. T1gT2gGg...220. T1gT2gHg...352. T1gGgHg...24. T1gAuT1u...216. T1gT1uHu...224. T1gT2uGu...252. T1gT2uHu...288. T1gGuHu...440. T2gGgHg...35. T2gAuT2u.
..240. T2gT1uGu...270. T2gT1uHu...315. T2gT2uHu...360. T2gGuHu...64. GgAuGu...336. GgT1uT2u...384. GgT1uGu...432. GgT1uHu...448. GgT2uGu...504. GgT2uHu.
..576. GgGuHu...99. HgAuHu...462. HgT1uT2u...528. HgT1uGu...594. HgT1uHu...616. HgT2uGu...693. HgT2uHu...1.584. HgGuHu.
Subtotal: 10.716 / 28 / 120
Total: 18.194 / 62 / 220


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Hu)
..15. AgAgAgAg...55. T1gT1gT1gT1g...120. T2gT2gT2gT2g...1.066. GgGgGgGg...7.777. HgHgHgHg...1. AuAuAuAu...231. T1uT1uT1uT1u...406. T2uT2uT2uT2u...1.066. GuGuGuGu...3.600. HuHuHuHu.
Subtotal: 14.337 / 10 / 10
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Hu)
..100. T1gT1gT1gT2g...160. T1gT1gT1gGg...220. T1gT1gT1gHg...280. T2gT2gT2gGg...440. T2gT2gT2gHg...5.016. GgGgGgHg...392. T1uT1uT1uT2u...448. T1uT1uT1uGu...630. T1uT1uT1uHu...672. T2uT2uT2uGu.
..1.008. T2uT2uT2uHu...4.104. GuGuGuHu...12. AgT1gT1gT1g...30. AgT2gT2gT2g...360. AgGgGgGg...1.716. AgHgHgHg...140. T1gT2gT2gT2g...1.152. T1gGgGgGg...5.324. T1gHgHgHg...1.440. T2gGgGgGg.
..6.655. T2gHgHgHg...15.224. GgHgHgHg...20. AuT1uT1uT1u...35. AuT2uT2uT2u...120. AuGuGuGu...330. AuHuHuHu...504. T1uT2uT2uT2u...1.728. T1uGuGuGu...4.374. T1uHuHuHu...2.016. T2uGuGuGu.
..5.103. T2uHuHuHu...8.472. GuHuHuHu.
Subtotal: 68.225 / 32 / 90
Irrep combinations (i,i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Hu)
..60. AgAgT1gT1g...90. AgAgT2gT2g...216. AgAgGgGg...396. AgAgHgHg...6. AgAgAuAu...126. AgAgT1uT1u...168. AgAgT2uT2u...216. AgAgGuGu...270. AgAgHuHu...300. T1gT1gT2gT2g.
..888. T1gT1gGgGg...2.310. T1gT1gHgHg...10. T1gT1gAuAu...510. T1gT1gT1uT1u...560. T1gT1gT2uT2u...888. T1gT1gGuGu...1.566. T1gT1gHuHu...1.360. T2gT2gGgGg...3.520. T2gT2gHgHg...15. T2gT2gAuAu.
..630. T2gT2gT1uT1u...1.050. T2gT2gT2uT2u...1.360. T2gT2gGuGu...2.385. T2gT2gHuHu...14.564. GgGgHgHg...36. GgGgAuAu...1.932. GgGgT1uT1u...2.604. GgGgT2uT2u...5.456. GgGgGuGu...9.792. GgGgHuHu.
..66. HgHgAuAu...4.983. HgHgT1uT1u...6.699. HgHgT2uT2u...14.564. HgHgGuGu...28.611. HgHgHuHu...21. AuAuT1uT1u...28. AuAuT2uT2u...36. AuAuGuGu...45. AuAuHuHu...1.176. T1uT1uT2uT2u.
..1.932. T1uT1uGuGu...3.375. T1uT1uHuHu...2.604. T2uT2uGuGu...4.536. T2uT2uHuHu...9.792. GuGuHuHu.
Subtotal: 131.752 / 45 / 45
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Hu)
..640. T1gT1gT2gGg...880. T1gT1gT2gHg...2.288. T1gT1gGgHg...36. T1gT1gAuT1u...90. T1gT1gAuHu...420. T1gT1gT1uT2u...480. T1gT1gT1uGu...864. T1gT1gT1uHu...896. T1gT1gT2uGu...1.008. T1gT1gT2uHu.
..1.872. T1gT1gGuHu...3.520. T2gT2gGgHg...70. T2gT2gAuT2u...135. T2gT2gAuHu...630. T2gT2gT1uT2u...1.200. T2gT2gT1uGu...1.350. T2gT2gT1uHu...840. T2gT2gT2uGu...1.575. T2gT2gT2uHu...2.880. T2gT2gGuHu.
..168. GgGgAuT1u...196. GgGgAuT2u...288. GgGgAuGu...324. GgGgAuHu...3.024. GgGgT1uT2u...4.800. GgGgT1uGu...6.912. GgGgT1uHu...5.600. GgGgT2uGu...8.064. GgGgT2uHu...11.808. GgGgGuHu.
..330. HgHgAuT1u...385. HgHgAuT2u...968. HgHgAuGu...1.188. HgHgAuHu...10.626. HgHgT1uT2u...14.784. HgHgT1uGu...19.602. HgHgT1uHu...17.248. HgHgT2uGu...22.869. HgHgT2uHu...35.640. HgHgGuHu.
..2.016. T1uT1uT2uGu...2.268. T1uT1uT2uHu...4.104. T1uT1uGuHu...5.544. T2uT2uGuHu...330. AgT1gT1gHg...495. AgT2gT2gHg...1.188. AgGgGgHg...800. T1gT2gT2gGg...1.100. T1gT2gT2gHg...5.632. T1gGgGgHg.
..7.040. T2gGgGgHg...189. AuT1uT1uHu...252. AuT2uT2uHu...324. AuGuGuHu...2.352. T1uT2uT2uGu...2.646. T1uT2uT2uHu...6.912. T1uGuGuHu...8.064. T2uGuGuHu...336. AgT1gGgGg...660. AgT1gHgHg.
..180. AgT1gT1uT1u...336. AgT1gGuGu...432. AgT1gHuHu...420. AgT2gGgGg...825. AgT2gHgHg...315. AgT2gT2uT2u...420. AgT2gGuGu...540. AgT2gHuHu...2.904. AgGgHgHg...864. AgGgGuGu.
..1.944. AgGgHuHu...693. AgHgT1uT1u...924. AgHgT2uT2u...1.188. AgHgGuGu...2.970. AgHgHuHu...1.440. T1gT2gGgGg...5.060. T1gT2gHgHg...420. T1gT2gT1uT1u...560. T1gT2gT2uT2u...1.440. T1gT2gGuGu.
..3.420. T1gT2gHuHu...9.856. T1gGgHgHg...672. T1gGgT1uT1u...1.568. T1gGgT2uT2u...3.200. T1gGgGuGu...6.624. T1gGgHuHu...1.584. T1gHgT1uT1u...2.156. T1gHgT2uT2u...5.632. T1gHgGuGu...10.692. T1gHgHuHu.
..12.320. T2gGgHgHg...1.440. T2gGgT1uT1u...1.120. T2gGgT2uT2u...4.000. T2gGgGuGu...8.280. T2gGgHuHu...1.980. T2gHgT1uT1u...2.695. T2gHgT2uT2u...7.040. T2gHgGuGu...13.365. T2gHgHuHu...5.016. GgHgT1uT1u.
..6.776. GgHgT2uT2u...14.432. GgHgGuGu...29.304. GgHgHuHu...168. AuT1uGuGu...216. AuT1uHuHu...196. AuT2uGuGu...252. AuT2uHuHu...648. AuGuHuHu...3.024. T1uT2uGuGu...7.182. T1uT2uHuHu.
..9.936. T1uGuHuHu...11.592. T2uGuHuHu.
Subtotal: 449.011 / 112 / 360
Irrep combinations (i,j,k,l) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ l ≤ pos(Hu)
..480. AgT1gT2gGg...660. AgT1gT2gHg...1.056. AgT1gGgHg...72. AgT1gAuT1u...648. AgT1gT1uHu...672. AgT1gT2uGu...756. AgT1gT2uHu...864. AgT1gGuHu...1.320. AgT2gGgHg...105. AgT2gAuT2u.
..720. AgT2gT1uGu...810. AgT2gT1uHu...945. AgT2gT2uHu...1.080. AgT2gGuHu...192. AgGgAuGu...1.008. AgGgT1uT2u...1.152. AgGgT1uGu...1.296. AgGgT1uHu...1.344. AgGgT2uGu...1.512. AgGgT2uHu.
..1.728. AgGgGuHu...297. AgHgAuHu...1.386. AgHgT1uT2u...1.584. AgHgT1uGu...1.782. AgHgT1uHu...1.848. AgHgT2uGu...2.079. AgHgT2uHu...4.752. AgHgGuHu...5.280. T1gT2gGgHg...160. T1gT2gAuGu.
..180. T1gT2gAuHu...1.680. T1gT2gT1uT2u...1.920. T1gT2gT1uGu...2.160. T1gT2gT1uHu...2.240. T1gT2gT2uGu...2.520. T1gT2gT2uHu...4.320. T1gT2gGuHu...224. T1gGgAuT2u...256. T1gGgAuGu...288. T1gGgAuHu.
..2.688. T1gGgT1uT2u...4.608. T1gGgT1uGu...5.184. T1gGgT1uHu...3.584. T1gGgT2uGu...6.048. T1gGgT2uHu...9.216. T1gGgGuHu...264. T1gHgAuT1u...308. T1gHgAuT2u...352. T1gHgAuGu...396. T1gHgAuHu.
..3.696. T1gHgT1uT2u...6.336. T1gHgT1uGu...9.504. T1gHgT1uHu...7.392. T1gHgT2uGu...11.088. T1gHgT2uHu...15.840. T1gHgGuHu...240. T2gGgAuT1u...320. T2gGgAuGu...360. T2gGgAuHu...3.360. T2gGgT1uT2u.
..3.840. T2gGgT1uGu...6.480. T2gGgT1uHu...6.720. T2gGgT2uGu...7.560. T2gGgT2uHu...11.520. T2gGgGuHu...330. T2gHgAuT1u...385. T2gHgAuT2u...440. T2gHgAuGu...495. T2gHgAuHu...4.620. T2gHgT1uT2u.
..7.920. T2gHgT1uGu...11.880. T2gHgT1uHu...9.240. T2gHgT2uGu...13.860. T2gHgT2uHu...19.800. T2gHgGuHu...528. GgHgAuT1u...616. GgHgAuT2u...704. GgHgAuGu...1.584. GgHgAuHu...11.088. GgHgT1uT2u.
..16.896. GgHgT1uGu...23.760. GgHgT1uHu...19.712. GgHgT2uGu...27.720. GgHgT2uHu...44.352. GgHgGuHu...336. AuT1uT2uGu...378. AuT1uT2uHu...432. AuT1uGuHu...504. AuT2uGuHu...9.072. T1uT2uGuHu.
Subtotal: 406.932 / 90 / 210
Total: 1.070.257 / 289 / 715


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Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement