Point Group D8d

Results for Point Group D_8d

**Characters of representations for molecular motions**
Motion	E	2S₁₆	2C₈	2(S₁₆)³	2C₄	2(S₁₆)⁵	2(C₈)³	2(S₁₆)⁷	C₂	8C'₂	8σ_d
Cartesian 3N	99	0.848	2.414	-0.235	1	-1.765	-0.414	-2.848	-1	-1	5
Translation (x,y,z)	3	0.848	2.414	-0.235	1	-1.765	-0.414	-2.848	-1	-1	1
Rotation (R_x,R_y,R_z)	3	-0.848	2.414	0.235	1	1.765	-0.414	2.848	-1	-1	-1
Vibration	93	0.848	-2.414	-0.235	-1	-1.765	0.414	-2.848	1	1	5

**Decomposition to irreducible representations**
Motion	A₁	A₂	B₁	B₂	E₁	E₂	E₃	E₄	E₅	E₆	E₇	Total
Cartesian 3N	4	2	2	5	7	6	6	6	6	6	6	56
Translation (x,y,z)	0	0	0	1	1	0	0	0	0	0	0	2
Rotation (R_x,R_y,R_z)	0	1	0	0	0	0	0	0	0	0	1	2
Vibration	4	1	2	4	6	6	6	6	6	6	5	52

**Molecular parameter**
Number of Atoms (N)	33
Number of internal coordinates	93
Number of independant internal coordinates	4
Number of vibrational modes	52

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A₁	A₂	B₁	B₂	E₁	E₂	E₃	E₄	E₅	E₆	E₇	Total
Linear (IR)	4	1	2	4	6	6	6	6	6	6	5	10 / 42
Quadratic (Raman)	4	1	2	4	6	6	6	6	6	6	5	15 / 37
IR + Raman	- - - -	1	2	- - - -	- - - -	- - - -	6	6	6	6	- - - -	0 / 27

Characters of force fields
(Symmetric powers of vibration representation)
Force field	E	2S₁₆	2C₈	2(S₁₆)³	2C₄	2(S₁₆)⁵	2(C₈)³	2(S₁₆)⁷	C₂	8C'₂	8σ_d
linear	93	0.848	-2.414	-0.235	-1	-1.765	0.414	-2.848	1	1	5
quadratic	4.371	-0.848	2.414	0.235	1	1.765	-0.414	2.848	47	47	59
cubic	138.415	-1.000	-1.000	-1.000	-1	-1.000	-1.000	-1.000	47	47	255
quartic	3.321.960	-0.000	0.000	-0.000	24	-0.000	0.000	-0.000	1.128	1.128	1.720
quintic	64.446.024	-0.000	-0.000	0.000	-24	0.000	0.000	-0.000	1.128	1.128	6.616
sextic	1.052.618.392	-0.000	0.000	-0.000	24	-0.000	0.000	0.000	18.424	18.424	33.320

Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field	A₁	A₂	B₁	B₂	E₁	E₂	E₃	E₄	E₅	E₆	E₇
linear	4	1	2	4	6	6	6	6	6	6	5
quadratic	165	112	135	141	270	276	270	276	270	276	271
cubic	4.402	4.251	4.275	4.379	8.648	8.654	8.648	8.654	8.648	8.654	8.648
quartic	104.560	103.136	103.700	103.996	207.552	207.690	207.552	207.696	207.552	207.690	207.552
quintic	2.015.908	2.012.036	2.012.600	2.015.344	4.027.806	4.027.950	4.027.806	4.027.944	4.027.806	4.027.950	4.027.806
sextic	32.907.838	32.881.966	32.891.178	32.898.626	65.787.498	65.789.798	65.787.498	65.789.804	65.787.498	65.789.798	65.787.498

Contributions to nonvanishing force field constants

pos(X) : Position of irreducible representation (irrep) X in character table of D_8d

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(E₇)
..10.	A₁A₁.	..1.	A₂A₂.	..3.	B₁B₁.	..10.	B₂B₂.	..21.	E₁E₁.	..21.	E₂E₂.	..21.	E₃E₃.	..21.	E₄E₄.	..21.	E₅E₅.	..21.	E₆E₆.
..15.	E₇E₇.
Subtotal: 165 / 11 / 11
Irrep combinations (i,j) with indices: pos(A₁) ≤ i ≤ j ≤ pos(E₇)
Subtotal: 0 / 0 / 55
Total: 165 / 11 / 66

**Contributions to nonvanishing cubic force field constants**
Irrep combinations (i,i,i) with indices: pos(A₁) ≤ i ≤ pos(E₇)
..20.	A₁A₁A₁.
Subtotal: 20 / 1 / 11
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A₁) ≤ i ≤ j ≤ pos(E₇)
..126.	E₁E₁E₂.	..126.	E₂E₂E₄.	..126.	E₃E₃E₆.	..126.	E₅E₅E₆.	..4.	A₁A₂A₂.	..12.	A₁B₁B₁.	..40.	A₁B₂B₂.	..84.	A₁E₁E₁.	..84.	A₁E₂E₂.	..84.	A₁E₃E₃.
..84.	A₁E₄E₄.	..84.	A₁E₅E₅.	..84.	A₁E₆E₆.	..60.	A₁E₇E₇.	..15.	A₂E₁E₁.	..15.	A₂E₂E₂.	..15.	A₂E₃E₃.	..15.	A₂E₄E₄.	..15.	A₂E₅E₅.	..15.	A₂E₆E₆.
..10.	A₂E₇E₇.	..42.	B₁E₄E₄.	..84.	B₂E₄E₄.	..90.	E₂E₇E₇.	..126.	E₄E₆E₆.
Subtotal: 1.566 / 25 / 110
Irrep combinations (i,j,k) with indices: pos(A₁) ≤ i ≤ j ≤ k ≤ pos(E₇)
..8.	A₂B₁B₂.	..60.	B₁E₁E₇.	..72.	B₁E₂E₆.	..72.	B₁E₃E₅.	..120.	B₂E₁E₇.	..144.	B₂E₂E₆.	..144.	B₂E₃E₅.	..216.	E₁E₂E₃.	..216.	E₁E₃E₄.	..216.	E₁E₄E₅.
..216.	E₁E₅E₆.	..180.	E₁E₆E₇.	..216.	E₂E₃E₅.	..216.	E₂E₄E₆.	..180.	E₂E₅E₇.	..180.	E₃E₄E₇.	..180.	E₃E₆E₇.	..180.	E₄E₅E₇.
Subtotal: 2.816 / 18 / 165
Total: 4.402 / 44 / 286

**Contributions to nonvanishing quartic force field constants**
Irrep combinations (i,i,i,i) with indices: pos(A₁) ≤ i ≤ pos(E₇)
..35.	A₁A₁A₁A₁.	..1.	A₂A₂A₂A₂.	..5.	B₁B₁B₁B₁.	..35.	B₂B₂B₂B₂.	..231.	E₁E₁E₁E₁.	..231.	E₂E₂E₂E₂.	..231.	E₃E₃E₃E₃.	..357.	E₄E₄E₄E₄.	..231.	E₅E₅E₅E₅.	..231.	E₆E₆E₆E₆.
..120.	E₇E₇E₇E₇.
Subtotal: 1.708 / 11 / 11
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A₁) ≤ i ≤ j ≤ pos(E₇)
..336.	E₁E₁E₁E₃.	..336.	E₂E₂E₂E₆.	..280.	E₃E₃E₃E₇.	..336.	E₁E₅E₅E₅.	..336.	E₂E₆E₆E₆.	..210.	E₅E₇E₇E₇.
Subtotal: 1.834 / 6 / 110
Irrep combinations (i,i,j,j) with indices: pos(A₁) ≤ i ≤ j ≤ pos(E₇)
..10.	A₁A₁A₂A₂.	..30.	A₁A₁B₁B₁.	..100.	A₁A₁B₂B₂.	..210.	A₁A₁E₁E₁.	..210.	A₁A₁E₂E₂.	..210.	A₁A₁E₃E₃.	..210.	A₁A₁E₄E₄.	..210.	A₁A₁E₅E₅.	..210.	A₁A₁E₆E₆.	..150.	A₁A₁E₇E₇.
..3.	A₂A₂B₁B₁.	..10.	A₂A₂B₂B₂.	..21.	A₂A₂E₁E₁.	..21.	A₂A₂E₂E₂.	..21.	A₂A₂E₃E₃.	..21.	A₂A₂E₄E₄.	..21.	A₂A₂E₅E₅.	..21.	A₂A₂E₆E₆.	..15.	A₂A₂E₇E₇.	..30.	B₁B₁B₂B₂.
..63.	B₁B₁E₁E₁.	..63.	B₁B₁E₂E₂.	..63.	B₁B₁E₃E₃.	..63.	B₁B₁E₄E₄.	..63.	B₁B₁E₅E₅.	..63.	B₁B₁E₆E₆.	..45.	B₁B₁E₇E₇.	..210.	B₂B₂E₁E₁.	..210.	B₂B₂E₂E₂.	..210.	B₂B₂E₃E₃.
..210.	B₂B₂E₄E₄.	..210.	B₂B₂E₅E₅.	..210.	B₂B₂E₆E₆.	..150.	B₂B₂E₇E₇.	..666.	E₁E₁E₂E₂.	..666.	E₁E₁E₃E₃.	..666.	E₁E₁E₄E₄.	..666.	E₁E₁E₅E₅.	..666.	E₁E₁E₆E₆.	..780.	E₁E₁E₇E₇.
..666.	E₂E₂E₃E₃.	..666.	E₂E₂E₄E₄.	..666.	E₂E₂E₅E₅.	..1.107.	E₂E₂E₆E₆.	..465.	E₂E₂E₇E₇.	..666.	E₃E₃E₄E₄.	..1.107.	E₃E₃E₅E₅.	..666.	E₃E₃E₆E₆.	..465.	E₃E₃E₇E₇.	..666.	E₄E₄E₅E₅.
..666.	E₄E₄E₆E₆.	..465.	E₄E₄E₇E₇.	..666.	E₅E₅E₆E₆.	..465.	E₅E₅E₇E₇.	..465.	E₆E₆E₇E₇.
Subtotal: 17.544 / 55 / 55
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A₁) ≤ i ≤ j ≤ k ≤ pos(E₇)
..756.	E₁E₁E₂E₄.	..756.	E₁E₁E₃E₅.	..756.	E₁E₁E₄E₆.	..630.	E₁E₁E₅E₇.	..630.	E₂E₂E₃E₇.	..630.	E₂E₂E₅E₇.	..756.	E₃E₃E₄E₆.	..504.	A₁E₁E₁E₂.	..504.	A₁E₂E₂E₄.	..504.	A₁E₃E₃E₆.
..504.	A₁E₅E₅E₆.	..126.	A₂E₁E₁E₂.	..126.	A₂E₂E₂E₄.	..126.	A₂E₃E₃E₆.	..126.	A₂E₅E₅E₆.	..252.	B₁E₁E₁E₆.	..252.	B₁E₂E₂E₄.	..504.	B₂E₁E₁E₆.	..504.	B₂E₂E₂E₄.	..756.	E₁E₂E₂E₃.
..756.	E₁E₂E₂E₅.	..756.	E₁E₃E₃E₅.	..630.	E₁E₃E₃E₇.	..1.260.	E₁E₄E₄E₇.	..630.	E₁E₅E₅E₇.	..756.	E₂E₃E₃E₄.	..1.512.	E₂E₄E₄E₆.	..1.512.	E₃E₄E₄E₅.	..630.	E₃E₅E₅E₇.	..630.	E₃E₆E₆E₇.
..756.	E₄E₅E₅E₆.	..630.	E₅E₆E₆E₇.	..60.	A₁A₂E₁E₁.	..60.	A₁A₂E₂E₂.	..60.	A₁A₂E₃E₃.	..60.	A₁A₂E₄E₄.	..60.	A₁A₂E₅E₅.	..60.	A₁A₂E₆E₆.	..40.	A₁A₂E₇E₇.	..168.	A₁B₁E₄E₄.
..336.	A₁B₂E₄E₄.	..360.	A₁E₂E₇E₇.	..504.	A₁E₄E₆E₆.	..42.	A₂B₁E₄E₄.	..84.	A₂B₂E₄E₄.	..90.	A₂E₂E₇E₇.	..126.	A₂E₄E₆E₆.	..120.	B₁B₂E₁E₁.	..120.	B₁B₂E₂E₂.	..120.	B₁B₂E₃E₃.
..120.	B₁B₂E₄E₄.	..120.	B₁B₂E₅E₅.	..120.	B₁B₂E₆E₆.	..80.	B₁B₂E₇E₇.	..252.	B₁E₂E₃E₃.	..252.	B₁E₂E₅E₅.	..252.	B₁E₄E₆E₆.	..180.	B₁E₆E₇E₇.	..504.	B₂E₂E₃E₃.	..504.	B₂E₂E₅E₅.
..504.	B₂E₄E₆E₆.	..360.	B₂E₆E₇E₇.	..756.	E₁E₃E₆E₆.	..540.	E₁E₃E₇E₇.	..756.	E₁E₅E₆E₆.	..756.	E₂E₄E₅E₅.	..540.	E₂E₄E₇E₇.	..540.	E₃E₅E₇E₇.	..540.	E₄E₆E₇E₇.
Subtotal: 30.306 / 69 / 495
Irrep combinations (i,j,k,l) with indices: pos(A₁) ≤ i ≤ j ≤ k ≤ l ≤ pos(E₇)
..32.	A₁A₂B₁B₂.	..240.	A₁B₁E₁E₇.	..288.	A₁B₁E₂E₆.	..288.	A₁B₁E₃E₅.	..480.	A₁B₂E₁E₇.	..576.	A₁B₂E₂E₆.	..576.	A₁B₂E₃E₅.	..864.	A₁E₁E₂E₃.	..864.	A₁E₁E₃E₄.	..864.	A₁E₁E₄E₅.
..864.	A₁E₁E₅E₆.	..720.	A₁E₁E₆E₇.	..864.	A₁E₂E₃E₅.	..864.	A₁E₂E₄E₆.	..720.	A₁E₂E₅E₇.	..720.	A₁E₃E₄E₇.	..720.	A₁E₃E₆E₇.	..720.	A₁E₄E₅E₇.	..60.	A₂B₁E₁E₇.	..72.	A₂B₁E₂E₆.
..72.	A₂B₁E₃E₅.	..120.	A₂B₂E₁E₇.	..144.	A₂B₂E₂E₆.	..144.	A₂B₂E₃E₅.	..216.	A₂E₁E₂E₃.	..216.	A₂E₁E₃E₄.	..216.	A₂E₁E₄E₅.	..216.	A₂E₁E₅E₆.	..180.	A₂E₁E₆E₇.	..216.	A₂E₂E₃E₅.
..216.	A₂E₂E₄E₆.	..180.	A₂E₂E₅E₇.	..180.	A₂E₃E₄E₇.	..180.	A₂E₃E₆E₇.	..180.	A₂E₄E₅E₇.	..432.	B₁E₁E₂E₅.	..360.	B₁E₁E₂E₇.	..432.	B₁E₁E₃E₄.	..432.	B₁E₁E₃E₆.	..432.	B₁E₁E₄E₅.
..360.	B₁E₂E₃E₇.	..432.	B₁E₂E₄E₆.	..360.	B₁E₃E₄E₇.	..432.	B₁E₃E₅E₆.	..360.	B₁E₄E₅E₇.	..360.	B₁E₅E₆E₇.	..864.	B₂E₁E₂E₅.	..720.	B₂E₁E₂E₇.	..864.	B₂E₁E₃E₄.	..864.	B₂E₁E₃E₆.
..864.	B₂E₁E₄E₅.	..720.	B₂E₂E₃E₇.	..864.	B₂E₂E₄E₆.	..720.	B₂E₃E₄E₇.	..864.	B₂E₃E₅E₆.	..720.	B₂E₄E₅E₇.	..720.	B₂E₅E₆E₇.	..1.296.	E₁E₂E₃E₄.	..1.296.	E₁E₂E₃E₆.	..1.296.	E₁E₂E₄E₅.
..1.080.	E₁E₂E₄E₇.	..1.296.	E₁E₂E₅E₆.	..2.160.	E₁E₂E₆E₇.	..1.296.	E₁E₃E₄E₆.	..2.160.	E₁E₃E₅E₇.	..1.296.	E₁E₄E₅E₆.	..1.080.	E₁E₄E₆E₇.	..1.296.	E₂E₃E₄E₅.	..1.080.	E₂E₃E₄E₇.	..2.592.	E₂E₃E₅E₆.
..1.080.	E₂E₃E₆E₇.	..1.080.	E₂E₄E₅E₇.	..1.080.	E₂E₅E₆E₇.	..1.296.	E₃E₄E₅E₆.	..1.080.	E₃E₄E₆E₇.	..1.080.	E₄E₅E₆E₇.
Subtotal: 53.168 / 76 / 330
Total: 104.560 / 217 / 1.001

Calculate contributions to

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

Results for Point Group D8d

Force field analysis

Further Reading

Contributions to nonvanishing force field constants

Calculate contributions to

Results for Point Group D_8d