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
63	1.6180	-0.6180	-1	-3	-1.6180	0.6180	5

can be reduced to

A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
4	2	6	6	2	5	7	6

Substraction of translational and rotational contributions results in

A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
4	1	5	6	2	4	6	6

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	57	57	4
quadratic	3249	1653	102
cubic	185193	32509	1669
quartic	10556001	487635	24721

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	4	1	5	6	2	4	6	6
quadratic	102	67	169	168	78	84	162	162
cubic	1669	1572	3242	3242	1596	1664	3260	3260
quartic	24721	24098	48819	48819	24260	24448	48708	48708

Number of independant internal coordinates	4

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