Reduction formula for point group D5d

Reduction formula for point group D_5d

Your representation

E	2C₅	2(C₅)²	5C'₂	i	2(S₁₀)³	2S₁₀	5_d
36	3.2361	-1.2361	0	0	-0.0000	0.0000	4

can be reduced to

A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
3	1	4	3	1	3	4	3

Substraction of translational and rotational contributions results in

A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
3	0	3	3	1	2	3	3

Infrared and Raman activities (harmonic approximation)
Method	A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
Infrared	-	-	-	-	-	+	+	-
Raman	+	-	+	+	-	-	-	-

Number of force field parameters
Force field	No. 1	No. 2	No. 3
linear	30	30	3
quadratic	900	465	34
cubic	27000	4960	274
quartic	810000	40920	2154

No. 1 : Total number of force constants

.
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.

Symmetry properties of force field parameters
Force field	A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
linear	3	0	3	3	1	2	3	3
quadratic	34	14	48	48	21	24	45	45
cubic	274	222	496	496	238	258	496	496
quartic	2154	1950	4104	4104	2014	2066	4080	4080

Number of independant internal coordinates	3

J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules

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