Results for Point Group D5h



Characters of representations for molecular motions
Motion E 2C5 2(C5)2 5C'2 σh 2S5 2(S5)3 v
Cartesian 3N 210 0.000 -0.000 0 10 -0.000 -0.000 4
Translation (x,y,z) 3 1.618 -0.618 -1 1 -0.382 -2.618 1
Rotation (Rx,Ry,Rz) 3 1.618 -0.618 -1 -1 0.382 2.618 -1
Vibration 204 -3.236 1.236 2 10 -0.000 -0.000 4


Decomposition to irreducible representations
Motion A'1 A'2 E'1 E'2 A''1 A''2 E''1 E''2 Total
Cartesian 3N 12 10 22 22 9 11 20 20 126
Translation (x,y,z) 0 0 1 0 0 1 0 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 0 1 0 2
Vibration 12 9 21 22 9 10 19 20 122



Molecular parameter
Number of Atoms (N) 70
Number of internal coordinates 204
Number of independant internal coordinates 12
Number of vibrational modes 122


Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E'1 E'2 A''1 A''2 E''1 E''2 Total
Linear (IR) 12 9 21 22 9 10 19 20 31 / 91
Quadratic (Raman) 12 9 21 22 9 10 19 20 53 / 69
IR + Raman - - - - 9 - - - - - - - - 9 - - - - - - - - 20 0 / 38


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C5 2(C5)2 5C'2 σh 2S5 2(S5)3 v
linear 204 -3.236 1.236 2 10 -0.000 -0.000 4
quadratic 20.910 5.854 -0.854 104 152 0.618 -1.618 110
cubic 1.435.820 -7.236 -2.764 206 1.190 -0.000 0.000 420
quartic 74.303.685 5.854 -0.854 5.459 10.803 -0.618 1.618 6.085
quintic 3.091.033.296 38.764 43.236 10.712 70.872 2.000 2.000 22.256
sextic 107.670.993.144 -134.915 52.915 192.816 492.624 -1.000 -1.000 225.784


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A'1 A'2 E'1 E'2 A''1 A''2 E''1 E''2
linear 12 9 21 22 9 10 19 20
quadratic 1.107 1.000 2.107 2.105 1.037 1.040 2.076 2.075
cubic 72.006 71.693 143.701 143.702 71.677 71.784 143.463 143.464
quartic 3.718.611 3.712.839 7.431.449 7.431.448 3.714.488 3.714.801 7.429.289 7.429.287
quintic 154.563.459 154.546.975 309.110.412 309.110.413 154.545.243 154.551.015 309.096.238 309.096.239
sextic 5.383.678.930 5.383.469.630 10.767.148.560 10.767.148.602 5.383.516.776 5.383.533.260 10.767.050.035 10.767.050.077


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D5h

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'1) ≤ i ≤ pos(E''2)
..78. A'1A'1...45. A'2A'2...231. E'1E'1...253. E'2E'2...45. A''1A''1...55. A''2A''2...190. E''1E''1...210. E''2E''2.
Subtotal: 1.107 / 8 / 8
Irrep combinations (i,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''2)
Subtotal: 0 / 0 / 28
Total: 1.107 / 8 / 36


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E''2)
..364. A'1A'1A'1.
Subtotal: 364 / 1 / 8
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''2)
..5.082. E'1E'1E'2...540. A'1A'2A'2...2.772. A'1E'1E'1...3.036. A'1E'2E'2...540. A'1A''1A''1...660. A'1A''2A''2...2.280. A'1E''1E''1...2.520. A'1E''2E''2...1.890. A'2E'1E'1...2.079. A'2E'2E'2.
..1.539. A'2E''1E''1...1.710. A'2E''2E''2...5.313. E'1E'2E'2...4.410. E'1E''2E''2...4.180. E'2E''1E''1.
Subtotal: 38.551 / 15 / 56
Irrep combinations (i,j,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E''2)
..810. A'2A''1A''2...3.591. E'1A''1E''1...3.990. E'1A''2E''1...7.980. E'1E''1E''2...3.960. E'2A''1E''2...4.400. E'2A''2E''2...8.360. E'2E''1E''2.
Subtotal: 33.091 / 7 / 56
Total: 72.006 / 23 / 120


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E''2)
..1.365. A'1A'1A'1A'1...495. A'2A'2A'2A'2...26.796. E'1E'1E'1E'1...32.131. E'2E'2E'2E'2...495. A''1A''1A''1A''1...715. A''2A''2A''2A''2...18.145. E''1E''1E''1E''1...22.155. E''2E''2E''2E''2.
Subtotal: 102.297 / 8 / 8
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''2)
..38.962. E'1E'1E'1E'2...26.600. E''1E''1E''1E''2...42.504. E'1E'2E'2E'2...29.260. E''1E''2E''2E''2.
Subtotal: 137.326 / 4 / 56
Irrep combinations (i,i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''2)
..3.510. A'1A'1A'2A'2...18.018. A'1A'1E'1E'1...19.734. A'1A'1E'2E'2...3.510. A'1A'1A''1A''1...4.290. A'1A'1A''2A''2...14.820. A'1A'1E''1E''1...16.380. A'1A'1E''2E''2...10.395. A'2A'2E'1E'1...11.385. A'2A'2E'2E'2...2.025. A'2A'2A''1A''1.
..2.475. A'2A'2A''2A''2...8.550. A'2A'2E''1E''1...9.450. A'2A'2E''2E''2...106.953. E'1E'1E'2E'2...10.395. E'1E'1A''1A''1...12.705. E'1E'1A''2A''2...123.690. E'1E'1E''1E''1...88.410. E'1E'1E''2E''2...11.385. E'2E'2A''1A''1...13.915. E'2E'2A''2A''2.
..87.571. E'2E'2E''1E''1...150.150. E'2E'2E''2E''2...2.475. A''1A''1A''2A''2...8.550. A''1A''1E''1E''1...9.450. A''1A''1E''2E''2...10.450. A''2A''2E''1E''1...11.550. A''2A''2E''2E''2...72.390. E''1E''1E''2E''2.
Subtotal: 844.581 / 28 / 28
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E''2)
..18.900. E'1E'1A''1A''2...41.580. E'1E'1A''1E''2...46.200. E'1E'1A''2E''2...87.780. E'1E'1E''1E''2...20.790. E'2E'2A''1A''2...43.263. E'2E'2A''1E''1...48.070. E'2E'2A''2E''1...96.140. E'2E'2E''1E''2...60.984. A'1E'1E'1E'2...45.738. A'2E'1E'1E'2.
..34.200. A''1E''1E''1E''2...38.000. A''2E''1E''1E''2...22.680. A'1A'2E'1E'1...24.948. A'1A'2E'2E'2...18.468. A'1A'2E''1E''1...20.520. A'1A'2E''2E''2...63.756. A'1E'1E'2E'2...52.920. A'1E'1E''2E''2...50.160. A'1E'2E''1E''1...47.817. A'2E'1E'2E'2.
..39.690. A'2E'1E''2E''2...37.620. A'2E'2E''1E''1...87.780. E'1E'2E''1E''1...97.020. E'1E'2E''2E''2...15.390. A''1A''2E''1E''1...17.100. A''1A''2E''2E''2...35.910. A''1E''1E''2E''2...39.900. A''2E''1E''2E''2.
Subtotal: 1.253.324 / 28 / 168
Irrep combinations (i,j,k,l) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E''2)
..9.720. A'1A'2A''1A''2...43.092. A'1E'1A''1E''1...47.880. A'1E'1A''2E''1...95.760. A'1E'1E''1E''2...47.520. A'1E'2A''1E''2...52.800. A'1E'2A''2E''2...100.320. A'1E'2E''1E''2...32.319. A'2E'1A''1E''1...35.910. A'2E'1A''2E''1...71.820. A'2E'1E''1E''2.
..35.640. A'2E'2A''1E''2...39.600. A'2E'2A''2E''2...75.240. A'2E'2E''1E''2...79.002. E'1E'2A''1E''1...83.160. E'1E'2A''1E''2...87.780. E'1E'2A''2E''1...92.400. E'1E'2A''2E''2...351.120. E'1E'2E''1E''2.
Subtotal: 1.381.083 / 18 / 70
Total: 3.718.611 / 86 / 330


Calculate contributions to

A'1 A'2 E'1 E'2 A''1 A''2 E''1 E''2
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement