Answered: Consider the character table given…

Introductory Chemistry: A Foundation

8th Edition

ISBN:9781285199030

Author:Steven S. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Donald J. DeCoste

Chapter2: Measurements And Calculations

Section: Chapter Questions

Problem 104AP: Convert 45 mi/h to m/s, showing how the units cancel appropriately.

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Question

Consider the character table given below for the point group D_3h, which includes molecules like cyclopropane and BF₃. Suppose has been already determined a reducible representation for the collective motions of one such molecule, Γ^(3N). What combination of irreps should we remove from it to account for translations & rotations, thereby yielding the purely vibrational representation, Γ^vib?

E' O A
D3h E 2C3 3C, ơn 2S3 30y
h = 12
A,
1
1
1
1
1
1
x² + y²,z?
A O E"
A
1
1
-1
1
1
-1
R2
2A, O E' O E"
E'
2
-1
2
-1
(х, у)
(ху, х2 — у?)
-
1
1
1
-1
-1
-1
A, O E' Ð A Ð E"
1
1
-1
-1
-1
1
A, O 2E' O A O 2E"
0 (Rx, Ry)
(xz, yz)
E"
2
-1
0 -2
1

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