Results for Point Group C30



Characters of representations for molecular motions
Motion E C30 C15 C10 (C15)2 C6 C5 (C30)7 (C15)4 (C10)3 C3 (C30)11 (C5)2 (C30)13 (C15)7 C2 (C15)8 (C30)17 (C5)3 (C30)19 (C3)2 (C10)7 (C15)11 (C30)23 (C5)4 (C6)5 (C15)13 (C10)9 (C15)14 (C30)29
Cartesian 3N 0 0.000 0.000 0.000 0.000 0 0.000 0.000 0.000 0.000 0 0.000 0.000 0.000 0.000 0 0.000 0.000 0.000 0.000 0 0.000 0.000 0.000 0.000 0 0.000 0.000 0.000 0.000
Translation (x,y,z) 3 2.956 2.827 2.618 2.338 2 1.618 1.209 0.791 0.382 0 -0.338 -0.618 -0.827 -0.956 -1 -0.956 -0.827 -0.618 -0.338 0 0.382 0.791 1.209 1.618 2 2.338 2.618 2.827 2.956
Rotation (Rx,Ry,Rz) 3 2.956 2.827 2.618 2.338 2 1.618 1.209 0.791 0.382 0 -0.338 -0.618 -0.827 -0.956 -1 -0.956 -0.827 -0.618 -0.338 0 0.382 0.791 1.209 1.618 2 2.338 2.618 2.827 2.956
Vibration -6 -5.913 -5.654 -5.236 -4.677 -4 -3.236 -2.418 -1.582 -0.764 0 0.677 1.236 1.654 1.913 2 1.913 1.654 1.236 0.677 0 -0.764 -1.582 -2.418 -3.236 -4 -4.677 -5.236 -5.654 -5.913


Decomposition to irreducible representations
Motion A B E1* E2* E3* E4* E5* E6* E7* E8* E9* E10* E11* E12* E13* E14* Total
Cartesian 3N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Translation (x,y,z) 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
Rotation (Rx,Ry,Rz) 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
Vibration -2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 -4



Molecular parameter
Number of Atoms (N) 0
Number of internal coordinates -6
Number of independant internal coordinates -2
Number of vibrational modes -4


Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E1* E2* E3* E4* E5* E6* E7* E8* E9* E10* E11* E12* E13* E14* Total
Linear (IR) -2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 / 0
Quadratic (Raman) -2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 / 0
IR + Raman -2 0 -2 - - - - 0 0 0 0 0 0 0 0 0 0 0 0 -4 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C30 C15 C10 (C15)2 C6 C5 (C30)7 (C15)4 (C10)3 C3 (C30)11 (C5)2 (C30)13 (C15)7 C2 (C15)8 (C30)17 (C5)3 (C30)19 (C3)2 (C10)7 (C15)11 (C30)23 (C5)4 (C6)5 (C15)13 (C10)9 (C15)14 (C30)29
linear -6 -5.913 -5.654 -5.236 -4.677 -4 -3.236 -2.418 -1.582 -0.764 0 0.677 1.236 1.654 1.913 2 1.913 1.654 1.236 0.677 0 -0.764 -1.582 -2.418 -3.236 -4 -4.677 -5.236 -5.654 -5.913
quadratic 15 14.652 13.647 12.090 10.144 8 5.854 3.880 2.207 0.910 0 -0.562 -0.854 -0.970 -0.998 -1 -0.998 -0.970 -0.854 -0.562 0 0.910 2.207 3.880 5.854 8 10.144 12.090 13.647 14.652
cubic -20 -19.479 -17.985 -15.708 -12.935 -10 -7.236 -4.924 -3.251 -2.292 -2 -2.229 -2.764 -3.368 -3.829 -4 -3.829 -3.368 -2.764 -2.229 -2 -2.292 -3.251 -4.924 -7.236 -10 -12.935 -15.708 -17.985 -19.479
quartic 15 14.652 13.647 12.090 10.144 8 5.854 3.880 2.207 0.910 0 -0.562 -0.854 -0.970 -0.998 -1 -0.998 -0.970 -0.854 -0.562 0 0.910 2.207 3.880 5.854 8 10.144 12.090 13.647 14.652
quintic -6 -5.913 -5.654 -5.236 -4.677 -4 -3.236 -2.418 -1.582 -0.764 0 0.677 1.236 1.654 1.913 2 1.913 1.654 1.236 0.677 0 -0.764 -1.582 -2.418 -3.236 -4 -4.677 -5.236 -5.654 -5.913
sextic 1 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A B E1* E2* E3* E4* E5* E6* E7* E8* E9* E10* E11* E12* E13* E14*
linear -2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0
quadratic 5 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0
cubic -8 0 -4 -2 0 0 0 0 0 0 0 0 0 0 0 0
quartic 5 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0
quintic -2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0
sextic 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C30

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(E14)
..1. AA...4. E1E1.
Subtotal: 5 / 2 / 16
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E14)
Subtotal: 0 / 0 / 120
Total: 5 / 2 / 136


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(E14)
Subtotal: 0 / 0 / 16
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E14)
Subtotal: -8 / 0 / 240
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E14)
Subtotal: 0 / 0 / 560
Total: -8 / 0 / 816


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(E14)
..1. E1E1E1E1.
Subtotal: 1 / 1 / 16
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E14)
Subtotal: 0 / 0 / 240
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E14)
..4. AAE1E1.
Subtotal: 4 / 1 / 120
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E14)
Subtotal: 0 / 0 / 1.680
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(E14)
Subtotal: 0 / 0 / 1.820
Total: 5 / 2 / 3.876


Calculate contributions to

A B E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14
Show only nonzero contributions Show all contributions






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