Results for Point Group D7h



Characters of representations for molecular motions
Motion E 2C7 2(C7)2 2(C7)3 7C'2 σh 2S7 2(S7)5 2(S7)3 v
Cartesian 3N 42 0.000 0.000 -0.000 -2 14 0.000 -0.000 -0.000 2
Translation (x,y,z) 3 2.247 0.555 -0.802 -1 1 0.247 -1.445 -2.802 1
Rotation (Rx,Ry,Rz) 3 2.247 0.555 -0.802 -1 -1 -0.247 1.445 2.802 -1
Vibration 36 -4.494 -1.110 1.604 0 14 0.000 -0.000 0.000 2


Decomposition to irreducible representations
Motion A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3 Total
Cartesian 3N 2 2 4 4 4 0 2 2 2 2 24
Translation (x,y,z) 0 0 1 0 0 0 1 0 0 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 0 0 1 0 0 2
Vibration 2 1 3 4 4 0 1 1 2 2 20



Molecular parameter
Number of Atoms (N) 14
Number of internal coordinates 36
Number of independant internal coordinates 2
Number of vibrational modes 20


Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3 Total
Linear (IR) 2 1 3 4 4 0 1 1 2 2 4 / 16
Quadratic (Raman) 2 1 3 4 4 0 1 1 2 2 7 / 13
IR + Raman - - - - 1 - - - - - - - - 4 0 - - - - - - - - 2 2 0 / 9


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C7 2(C7)2 2(C7)3 7C'2 σh 2S7 2(S7)5 2(S7)3 v
linear 36 -4.494 -1.110 1.604 0 14 0.000 -0.000 0.000 2
quadratic 666 9.543 1.418 -0.961 18 116 -0.555 0.802 -2.247 20
cubic 8.436 -12.098 -2.616 -3.286 0 714 -0.000 0.000 -0.000 38
quartic 82.251 9.543 1.418 -0.961 171 3.601 0.555 -0.802 2.247 209
quintic 658.008 -4.494 -1.110 1.604 0 15.652 0.000 0.000 0.000 380
sextic 4.496.388 1.000 1.000 1.000 1.140 60.528 -1.000 -1.000 -1.000 1.520


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3
linear 2 1 3 4 4 0 1 1 2 2
quadratic 38 19 57 55 55 20 21 40 39 38
cubic 335 316 653 654 655 265 284 551 552 553
quartic 3.162 2.972 6.133 6.132 6.131 2.800 2.819 5.619 5.617 5.617
quintic 24.154 23.964 48.118 48.119 48.119 22.846 23.036 45.882 45.883 45.883
sextic 163.412 162.082 325.494 325.494 325.494 158.329 158.519 316.847 316.847 316.847


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D7h

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''3)
..3. A'1A'1...1. A'2A'2...6. E'1E'1...10. E'2E'2...10. E'3E'3...1. A''2A''2...1. E''1E''1...3. E''2E''2...3. E''3E''3.
Subtotal: 38 / 9 / 10
Irrep combinations (i,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
Subtotal: 0 / 0 / 45
Total: 38 / 9 / 55


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E''3)
..4. A'1A'1A'1.
Subtotal: 4 / 1 / 10
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
..24. E'1E'1E'2...40. E'2E'2E'3...2. A'1A'2A'2...12. A'1E'1E'1...20. A'1E'2E'2...20. A'1E'3E'3...2. A'1A''2A''2...2. A'1E''1E''1...6. A'1E''2E''2...6. A'1E''3E''3.
..3. A'2E'1E'1...6. A'2E'2E'2...6. A'2E'3E'3...1. A'2E''2E''2...1. A'2E''3E''3...30. E'1E'3E'3...9. E'1E''3E''3...4. E'2E''1E''1...12. E'3E''2E''2.
Subtotal: 206 / 19 / 90
Irrep combinations (i,j,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E''3)
..48. E'1E'2E'3...3. E'1A''2E''1...6. E'1E''1E''2...12. E'1E''2E''3...8. E'2A''2E''2...8. E'2E''1E''3...16. E'2E''2E''3...8. E'3A''2E''3...8. E'3E''1E''2...8. E'3E''1E''3.
Subtotal: 125 / 10 / 120
Total: 335 / 30 / 220


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E''3)
..5. A'1A'1A'1A'1...1. A'2A'2A'2A'2...21. E'1E'1E'1E'1...55. E'2E'2E'2E'2...55. E'3E'3E'3E'3...1. A''2A''2A''2A''2...1. E''1E''1E''1E''1...6. E''2E''2E''2E''2...6. E''3E''3E''3E''3.
Subtotal: 151 / 9 / 10
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
..40. E'1E'1E'1E'3...2. E''1E''1E''1E''3...60. E'1E'2E'2E'2...80. E'2E'3E'3E'3...4. E''1E''2E''2E''2...8. E''2E''3E''3E''3.
Subtotal: 194 / 6 / 90
Irrep combinations (i,i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E''3)
..3. A'1A'1A'2A'2...18. A'1A'1E'1E'1...30. A'1A'1E'2E'2...30. A'1A'1E'3E'3...3. A'1A'1A''2A''2...3. A'1A'1E''1E''1...9. A'1A'1E''2E''2...9. A'1A'1E''3E''3...6. A'2A'2E'1E'1...10. A'2A'2E'2E'2.
..10. A'2A'2E'3E'3...1. A'2A'2A''2A''2...1. A'2A'2E''1E''1...3. A'2A'2E''2E''2...3. A'2A'2E''3E''3...78. E'1E'1E'2E'2...78. E'1E'1E'3E'3...6. E'1E'1A''2A''2...12. E'1E'1E''1E''1...21. E'1E'1E''2E''2.
..21. E'1E'1E''3E''3...136. E'2E'2E'3E'3...10. E'2E'2A''2A''2...10. E'2E'2E''1E''1...66. E'2E'2E''2E''2...36. E'2E'2E''3E''3...10. E'3E'3A''2A''2...10. E'3E'3E''1E''1...36. E'3E'3E''2E''2...66. E'3E'3E''3E''3.
..1. A''2A''2E''1E''1...3. A''2A''2E''2E''2...3. A''2A''2E''3E''3...3. E''1E''1E''2E''2...3. E''1E''1E''3E''3...10. E''2E''2E''3E''3.
Subtotal: 758 / 36 / 45
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E''3)
..96. E'1E'1E'2E'3...12. E'1E'1A''2E''2...12. E'1E'1E''1E''3...24. E'1E'1E''2E''3...20. E'2E'2A''2E''3...20. E'2E'2E''1E''2...20. E'2E'2E''1E''3...10. E'3E'3A''2E''1...20. E'3E'3E''1E''2...40. E'3E'3E''2E''3.
..4. E''1E''1E''2E''3...48. A'1E'1E'1E'2...80. A'1E'2E'2E'3...24. A'2E'1E'1E'2...40. A'2E'2E'2E'3...120. E'1E'2E'2E'3...2. A''2E''1E''1E''2...6. A''2E''2E''2E''3...6. E''1E''2E''2E''3...6. A'1A'2E'1E'1.
..12. A'1A'2E'2E'2...12. A'1A'2E'3E'3...2. A'1A'2E''2E''2...2. A'1A'2E''3E''3...60. A'1E'1E'3E'3...18. A'1E'1E''3E''3...8. A'1E'2E''1E''1...24. A'1E'3E''2E''2...30. A'2E'1E'3E'3...9. A'2E'1E''3E''3.
..4. A'2E'2E''1E''1...12. A'2E'3E''2E''2...120. E'1E'2E'3E'3...36. E'1E'2E''2E''2...36. E'1E'2E''3E''3...12. E'1E'3E''1E''1...36. E'1E'3E''2E''2...16. E'2E'3E''1E''1...48. E'2E'3E''3E''3...3. A''2E''1E''3E''3.
..6. E''1E''2E''3E''3.
Subtotal: 1.116 / 41 / 360
Irrep combinations (i,j,k,l) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E''3)
..96. A'1E'1E'2E'3...6. A'1E'1A''2E''1...12. A'1E'1E''1E''2...24. A'1E'1E''2E''3...16. A'1E'2A''2E''2...16. A'1E'2E''1E''3...32. A'1E'2E''2E''3...16. A'1E'3A''2E''3...16. A'1E'3E''1E''2...16. A'1E'3E''1E''3.
..48. A'2E'1E'2E'3...3. A'2E'1A''2E''1...6. A'2E'1E''1E''2...12. A'2E'1E''2E''3...8. A'2E'2A''2E''2...8. A'2E'2E''1E''3...16. A'2E'2E''2E''3...8. A'2E'3A''2E''3...8. A'2E'3E''1E''2...8. A'2E'3E''1E''3.
..12. E'1E'2A''2E''1...24. E'1E'2A''2E''3...48. E'1E'2E''1E''2...24. E'1E'2E''1E''3...48. E'1E'2E''2E''3...24. E'1E'3A''2E''2...24. E'1E'3A''2E''3...24. E'1E'3E''1E''2...48. E'1E'3E''1E''3...48. E'1E'3E''2E''3.
..16. E'2E'3A''2E''1...32. E'2E'3A''2E''2...32. E'2E'3E''1E''2...32. E'2E'3E''1E''3...128. E'2E'3E''2E''3...4. A''2E''1E''2E''3.
Subtotal: 943 / 36 / 210
Total: 3.162 / 128 / 715


Calculate contributions to

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