Results for Point Group D2



Characters of representations for molecular motions
Motion E C2.(z) C2.(y) C2.(x)
Cartesian 3N 156 0 -2 -2
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 150 2 0 0


Decomposition to irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 38 40 39 39 156
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 38 38 37 37 150



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 38
Number of vibrational modes 150

Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 38 38 37 37 112 / 38
Quadratic (Raman) 38 38 37 37 150 / 0
IR + Raman - - - - 38 37 37 112 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) C2.(y) C2.(x)
linear 150 2 0 0
quadratic 11.325 77 75 75
cubic 573.800 152 0 0
quartic 21.947.850 3.002 2.850 2.850
quintic 675.993.780 5.852 0 0
sextic 17.463.172.650 79.002 73.150 73.150


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A B1 B2 B3
linear 38 38 37 37
quadratic 2.888 2.813 2.812 2.812
cubic 143.488 143.488 143.412 143.412
quartic 5.489.138 5.486.288 5.486.212 5.486.212
quintic 168.999.908 168.999.908 168.996.982 168.996.982
sextic 4.365.849.488 4.365.776.338 4.365.773.412 4.365.773.412


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)
..741. AA...741. B1B1...703. B2B2...703. B3B3.
Subtotal: 2.888 / 4 / 4
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B3)
Subtotal: 0 / 0 / 6
Total: 2.888 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(B3)
..9.880. AAA.
Subtotal: 9.880 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B3)
..28.158. AB1B1...26.714. AB2B2...26.714. AB3B3.
Subtotal: 81.586 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(B3)
..52.022. B1B2B3.
Subtotal: 52.022 / 1 / 4
Total: 143.488 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(B3)
..101.270. AAAA...101.270. B1B1B1B1...91.390. B2B2B2B2...91.390. B3B3B3B3.
Subtotal: 385.320 / 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)
..549.081. AAB1B1...520.923. AAB2B2...520.923. AAB3B3...520.923. B1B1B2B2...520.923. B1B1B3B3...494.209. B2B2B3B3.
Subtotal: 3.126.982 / 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)
..1.976.836. AB1B2B3.
Subtotal: 1.976.836 / 1 / 1
Total: 5.489.138 / 11 / 35


Calculate contributions to

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