Results for Point Group D6d



Characters of representations for molecular motions
Motion E 2S12 2C6 2S4 2C3 2(S12)5 C2 6C'2 d
Cartesian 3N 216 0.000 0 0 0 -0.000 0 0 4
Translation (x,y,z) 3 0.732 2 -1 0 -2.732 -1 -1 1
Rotation (Rx,Ry,Rz) 3 -0.732 2 1 0 2.732 -1 -1 -1
Vibration 210 0.000 -4 0 0 -0.000 2 2 4


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E1 E2 E3 E4 E5 Total
Cartesian 3N 10 8 8 10 18 18 18 18 18 126
Translation (x,y,z) 0 0 0 1 1 0 0 0 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 0 0 0 1 2
Vibration 10 7 8 9 17 18 18 18 17 122



Molecular parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 10
Number of vibrational modes 122


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E1 E2 E3 E4 E5 Total
Linear (IR) 10 7 8 9 17 18 18 18 17 26 / 96
Quadratic (Raman) 10 7 8 9 17 18 18 18 17 45 / 77
IR + Raman - - - - 7 8 - - - - - - - - - - - - 18 18 - - - - 0 / 51


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2S12 2C6 2S4 2C3 2(S12)5 C2 6C'2 d
linear 210 0.000 -4 0 0 -0.000 2 2 4
quadratic 22.155 -2.000 8 1 0 -2.000 107 107 113
cubic 1.565.620 0.000 -10 0 70 0.000 212 212 432
quartic 83.369.265 2.000 8 53 0 2.000 5.777 5.777 6.421
quintic 3.568.204.542 -0.000 -4 0 0 -0.000 11.342 11.342 23.540
sextic 127.860.662.755 -1.000 37 53 2.485 -1.000 209.827 209.827 244.709


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E1 E2 E3 E4 E5
linear 10 7 8 9 17 18 18 18 17
quadratic 983 873 927 930 1.838 1.854 1.836 1.855 1.838
cubic 65.409 65.087 65.193 65.303 130.444 130.481 130.464 130.481 130.444
quartic 3.477.015 3.470.916 3.473.795 3.474.117 6.946.958 6.947.911 6.946.956 6.947.928 6.946.958
quintic 148.684.382 148.666.941 148.672.612 148.678.711 297.349.433 297.351.324 297.349.434 297.351.324 297.349.433
sextic 5.327.650.206 5.327.422.938 5.327.527.843 5.327.545.284 10.655.037.540 10.655.072.496 10.655.038.152 10.655.072.514 10.655.037.540


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D6d

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(E5)
..55. A1A1...28. A2A2...36. B1B1...45. B2B2...153. E1E1...171. E2E2...171. E3E3...171. E4E4...153. E5E5.
Subtotal: 983 / 9 / 9
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E5)
Subtotal: 0 / 0 / 36
Total: 983 / 9 / 45


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E5)
..220. A1A1A1...1.140. E4E4E4.
Subtotal: 1.360 / 2 / 9
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E5)
..2.754. E1E1E2...3.078. E2E2E4...280. A1A2A2...360. A1B1B1...450. A1B2B2...1.530. A1E1E1...1.710. A1E2E2...1.710. A1E3E3...1.710. A1E4E4...1.530. A1E5E5.
..952. A2E1E1...1.071. A2E2E2...1.071. A2E3E3...1.071. A2E4E4...952. A2E5E5...1.368. B1E3E3...1.539. B2E3E3...2.754. E2E5E5.
Subtotal: 25.890 / 18 / 72
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E5)
..504. A2B1B2...2.312. B1E1E5...2.592. B1E2E4...2.601. B2E1E5...2.916. B2E2E4...5.508. E1E2E3...5.508. E1E3E4...5.202. E1E4E5...5.508. E2E3E5...5.508. E3E4E5.
Subtotal: 38.159 / 10 / 84
Total: 65.409 / 30 / 165


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E5)
..715. A1A1A1A1...210. A2A2A2A2...330. B1B1B1B1...495. B2B2B2B2...11.781. E1E1E1E1...14.706. E2E2E2E2...20.691. E3E3E3E3...14.706. E4E4E4E4...11.781. E5E5E5E5.
Subtotal: 75.415 / 9 / 9
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E5)
..17.442. E1E1E1E3...11.400. A1E4E4E4...7.980. A2E4E4E4...9.120. B1E2E2E2...10.260. B2E2E2E2...17.442. E3E5E5E5.
Subtotal: 73.644 / 6 / 72
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E5)
..1.540. A1A1A2A2...1.980. A1A1B1B1...2.475. A1A1B2B2...8.415. A1A1E1E1...9.405. A1A1E2E2...9.405. A1A1E3E3...9.405. A1A1E4E4...8.415. A1A1E5E5...1.008. A2A2B1B1...1.260. A2A2B2B2.
..4.284. A2A2E1E1...4.788. A2A2E2E2...4.788. A2A2E3E3...4.788. A2A2E4E4...4.284. A2A2E5E5...1.620. B1B1B2B2...5.508. B1B1E1E1...6.156. B1B1E2E2...6.156. B1B1E3E3...6.156. B1B1E4E4.
..5.508. B1B1E5E5...6.885. B2B2E1E1...7.695. B2B2E2E2...7.695. B2B2E3E3...7.695. B2B2E4E4...6.885. B2B2E5E5...46.971. E1E1E2E2...46.971. E1E1E3E3...46.971. E1E1E4E4...65.314. E1E1E5E5.
..52.650. E2E2E3E3...81.891. E2E2E4E4...46.971. E2E2E5E5...52.650. E3E3E4E4...46.971. E3E3E5E5...46.971. E4E4E5E5.
Subtotal: 678.530 / 36 / 36
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E5)
..49.572. E1E1E2E4...46.818. E1E1E3E5...52.326. E2E2E3E5...27.540. A1E1E1E2...30.780. A1E2E2E4...19.278. A2E1E1E2...21.546. A2E2E2E4...22.032. B1E1E1E4...24.786. B2E1E1E4...52.326. E1E2E2E3.
..49.419. E1E2E2E5...98.838. E1E3E3E5...49.419. E1E4E4E5...110.808. E2E3E3E4...52.326. E3E4E4E5...9.520. A1A2E1E1...10.710. A1A2E2E2...10.710. A1A2E3E3...10.710. A1A2E4E4...9.520. A1A2E5E5.
..13.680. A1B1E3E3...15.390. A1B2E3E3...27.540. A1E2E5E5...9.576. A2B1E3E3...10.773. A2B2E3E3...19.278. A2E2E5E5...9.792. B1B2E1E1...11.016. B1B2E2E2...11.016. B1B2E3E3...11.016. B1B2E4E4.
..9.792. B1B2E5E5...24.624. B1E2E4E4...22.032. B1E4E5E5...27.702. B2E2E4E4...24.786. B2E4E5E5...52.326. E1E3E4E4...46.818. E1E3E5E5...49.572. E2E4E5E5.
Subtotal: 1.155.713 / 38 / 252
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E5)
..5.040. A1A2B1B2...23.120. A1B1E1E5...25.920. A1B1E2E4...26.010. A1B2E1E5...29.160. A1B2E2E4...55.080. A1E1E2E3...55.080. A1E1E3E4...52.020. A1E1E4E5...55.080. A1E2E3E5...55.080. A1E3E4E5.
..16.184. A2B1E1E5...18.144. A2B1E2E4...18.207. A2B2E1E5...20.412. A2B2E2E4...38.556. A2E1E2E3...38.556. A2E1E3E4...36.414. A2E1E4E5...38.556. A2E2E3E5...38.556. A2E3E4E5...44.064. B1E1E2E3.
..41.616. B1E1E2E5...44.064. B1E1E3E4...44.064. B1E2E3E5...44.064. B1E3E4E5...49.572. B2E1E2E3...46.818. B2E1E2E5...49.572. B2E1E3E4...49.572. B2E2E3E5...49.572. B2E3E4E5...99.144. E1E2E3E4.
..187.272. E1E2E4E5...99.144. E2E3E4E5.
Subtotal: 1.493.713 / 32 / 126
Total: 3.477.015 / 121 / 495


Calculate contributions to

A1 A2 B1 B2 E1 E2 E3 E4 E5
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement