Results for Point Group D3h



Characters of representations for molecular motions
Motion E 2C3 3C'2 σh 2S3 v
Cartesian 3N 222 0 0 6 0 8
Translation (x,y,z) 3 0 -1 1 -2 1
Rotation (Rx,Ry,Rz) 3 0 -1 -1 2 -1
Vibration 216 0 2 6 0 8


Decomposition to irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 21 17 38 16 20 36 148
Translation (x,y,z) 0 0 1 0 1 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 1 2
Vibration 21 16 37 16 19 35 144



Molecular parameter
Number of Atoms (N) 74
Number of internal coordinates 216
Number of independant internal coordinates 21
Number of vibrational modes 144


Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 21 16 37 16 19 35 56 / 88
Quadratic (Raman) 21 16 37 16 19 35 93 / 51
IR + Raman - - - - 16 37 16 - - - - - - - - 37 / 32


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 3C'2 σh 2S3 v
linear 216 0 2 6 0 8
quadratic 23.436 0 110 126 0 140
cubic 1.703.016 72 218 686 2 952
quartic 93.240.126 0 6.104 7.896 0 9.534
quintic 4.102.565.544 0 11.990 39.522 0 56.952
sextic 151.111.164.204 2.628 227.810 329.042 38 425.516


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A'1 A'2 E' A''1 A''2 E''
linear 21 16 37 16 19 35
quadratic 2.026 1.901 3.927 1.935 1.950 3.885
cubic 142.280 141.695 283.938 141.689 142.056 283.710
quartic 7.774.578 7.766.759 15.541.337 7.768.495 7.770.210 15.538.705
quintic 341.900.991 341.866.520 683.767.511 341.865.928 341.888.409 683.754.337
sextic 12.592.788.213 12.592.461.550 25.185.248.430 12.592.520.602 12.592.619.455 25.185.138.762


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D3h

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'')
..231. A'1A'1...136. A'2A'2...703. E'E'...136. A''1A''1...190. A''2A''2...630. E''E''.
Subtotal: 2.026 / 6 / 6
Irrep combinations (i,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
Subtotal: 0 / 0 / 15
Total: 2.026 / 6 / 21


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E'')
..1.771. A'1A'1A'1...9.139. E'E'E'.
Subtotal: 10.910 / 2 / 6
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
..2.856. A'1A'2A'2...14.763. A'1E'E'...2.856. A'1A''1A''1...3.990. A'1A''2A''2...13.230. A'1E''E''...10.656. A'2E'E'...9.520. A'2E''E''...23.310. E'E''E''.
Subtotal: 81.181 / 8 / 30
Irrep combinations (i,j,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E'')
..4.864. A'2A''1A''2...20.720. E'A''1E''...24.605. E'A''2E''.
Subtotal: 50.189 / 3 / 20
Total: 142.280 / 13 / 56


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E'')
..10.626. A'1A'1A'1A'1...3.876. A'2A'2A'2A'2...247.456. E'E'E'E'...3.876. A''1A''1A''1A''1...7.315. A''2A''2A''2A''2...198.765. E''E''E''E''.
Subtotal: 471.914 / 6 / 6
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
..191.919. A'1E'E'E'...146.224. A'2E'E'E'...124.320. A''1E''E''E''...147.630. A''2E''E''E''.
Subtotal: 610.093 / 4 / 30
Irrep combinations (i,i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
..31.416. A'1A'1A'2A'2...162.393. A'1A'1E'E'...31.416. A'1A'1A''1A''1...43.890. A'1A'1A''2A''2...145.530. A'1A'1E''E''...95.608. A'2A'2E'E'...18.496. A'2A'2A''1A''1...25.840. A'2A'2A''2A''2...85.680. A'2A'2E''E''...95.608. E'E'A''1A''1.
..133.570. E'E'A''2A''2...1.282.050. E'E'E''E''...25.840. A''1A''1A''2A''2...85.680. A''1A''1E''E''...119.700. A''2A''2E''E''.
Subtotal: 2.382.717 / 15 / 15
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E'')
..202.464. E'E'A''1A''2...393.680. E'E'A''1E''...467.495. E'E'A''2E''...223.776. A'1A'2E'E'...199.920. A'1A'2E''E''...489.510. A'1E'E''E''...372.960. A'2E'E''E''...180.880. A''1A''2E''E''.
Subtotal: 2.530.685 / 8 / 60
Irrep combinations (i,j,k,l) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E'')
..102.144. A'1A'2A''1A''2...435.120. A'1E'A''1E''...516.705. A'1E'A''2E''...331.520. A'2E'A''1E''...393.680. A'2E'A''2E''.
Subtotal: 1.779.169 / 5 / 15
Total: 7.774.578 / 38 / 126


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