Results for Point Group O



Characters of representations for molecular motions
Motion E 8C3 6C2 6C4 3C2
Cartesian 3N 21 0 -1 3 -3
Translation (x,y,z) 3 0 -1 1 -1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 15 0 1 1 -1


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 1 0 1 4 2 8
Translation (x,y,z) 0 0 0 1 0 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 1 0 1 2 2 6



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 1
Number of vibrational modes 6

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 1 0 1 2 2 2 / 4
Quadratic (Raman) 1 0 1 2 2 4 / 2
IR + Raman - - - - 0 - - - - - - - - - - - - 0 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 6C2 6C4 3C2
linear 15 0 1 1 -1
quadratic 120 0 8 0 8
cubic 680 5 8 0 -8
quartic 3.060 0 36 4 36
quintic 11.628 0 36 4 -36
sextic 38.760 15 120 0 120


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 1 0 1 2 2
quadratic 8 4 12 12 16
cubic 31 27 53 84 88
quartic 142 122 264 370 386
quintic 490 470 960 1.450 1.466
sextic 1.665 1.605 3.255 4.800 4.860


Further Reading


Contributions to nonvanishing force field constants


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

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(T2)
..1. A1A1...1. EE...3. T1T1...3. T2T2.
Subtotal: 8 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 8 / 4 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..1. A1A1A1...1. EEE...4. T2T2T2.
Subtotal: 6 / 3 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..6. T1T1T2...1. A1EE...3. A1T1T1...3. A1T2T2...3. ET1T1...3. ET2T2...2. T1T2T2.
Subtotal: 21 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..4. ET1T2.
Subtotal: 4 / 1 / 10
Total: 31 / 11 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..1. A1A1A1A1...1. EEEE...11. T1T1T1T1...11. T2T2T2T2.
Subtotal: 24 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..12. T1T1T1T2...1. A1EEE...4. A1T2T2T2...2. ET1T1T1...2. ET2T2T2...12. T1T2T2T2.
Subtotal: 33 / 6 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..1. A1A1EE...3. A1A1T1T1...3. A1A1T2T2...6. EET1T1...6. EET2T2...28. T1T1T2T2.
Subtotal: 47 / 6 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..4. EET1T2...6. A1T1T1T2...8. ET1T1T2...3. A1ET1T1...3. A1ET2T2...2. A1T1T2T2...8. ET1T2T2.
Subtotal: 34 / 7 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..4. A1ET1T2.
Subtotal: 4 / 1 / 5
Total: 142 / 24 / 70


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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement