Results for Point Group D2



Characters of representations for molecular motions
Motion E C2.(z) C2.(y) C2.(x)
Cartesian 3N 39 -5 -1 -1
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 33 -3 1 1


Decomposition to irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 8 9 11 11 39
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 8 7 9 9 33



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 8
Number of vibrational modes 33


Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 8 7 9 9 25 / 8
Quadratic (Raman) 8 7 9 9 33 / 0
IR + Raman - - - - 7 9 9 25 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) C2.(y) C2.(x)
linear 33 -3 1 1
quadratic 561 21 17 17
cubic 6.545 -55 17 17
quartic 58.905 225 153 153
quintic 435.897 -531 153 153
sextic 2.760.681 1.653 969 969


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A B1 B2 B3
linear 8 7 9 9
quadratic 154 137 135 135
cubic 1.631 1.614 1.650 1.650
quartic 14.859 14.706 14.670 14.670
quintic 108.918 108.765 109.107 109.107
sextic 691.068 690.099 689.757 689.757


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D2

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) ≤ i ≤ pos(B3)
..36. AA...28. B1B1...45. B2B2...45. B3B3.
Subtotal: 154 / 4 / 4
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B3)
Subtotal: 0 / 0 / 6
Total: 154 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(B3)
..120. AAA.
Subtotal: 120 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B3)
..224. AB1B1...360. AB2B2...360. AB3B3.
Subtotal: 944 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(B3)
..567. B1B2B3.
Subtotal: 567 / 1 / 4
Total: 1.631 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(B3)
..330. AAAA...210. B1B1B1B1...495. B2B2B2B2...495. B3B3B3B3.
Subtotal: 1.530 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B3)
Subtotal: 0 / 0 / 12
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B3)
..1.008. AAB1B1...1.620. AAB2B2...1.620. AAB3B3...1.260. B1B1B2B2...1.260. B1B1B3B3...2.025. B2B2B3B3.
Subtotal: 8.793 / 6 / 6
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(B3)
Subtotal: 0 / 0 / 12
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(B3)
..4.536. AB1B2B3.
Subtotal: 4.536 / 1 / 1
Total: 14.859 / 11 / 35


Calculate contributions to

A B1 B2 B3
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement