Using the relationships imposed by the orthogonality theorem, predict the characters, XK(R), that have been omitted from this table, and match each with its correct value. All symmetry elements and irreducible representations (labelled with subscripts k = 1, 2, 3, 4, and 5) are included in this table.

Using the relationships imposed by the orthogonality theorem, predict the characters, XK(R), that have been omitted from this table, and match each with its correct value. All symmetry elements and irreducible representations (labelled with subscripts k = 1, 2, 3, 4, and 5) are included in this table.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter13: Introduction To Symmetry In Quantum Mechanics

Section: Chapter Questions

Problem 13.3E: Identify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to...

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Question

Using the relationships imposed by the orthogonality theorem, predict the characters, XK(R), that have been omitted from this table, and
match each with its correct value. All symmetry elements and irreducible representations (labelled with subscripts k = 1, 2, 3, 4, and
5) are included in this table.
+ X2(C3)
◆ X3(C₂)
+ X4(0d)
X5(E)
-
₁₁
[₂
[3
T4
[5
E
1
3
1
3
_?___
6 S4 8 C3
1
1
1
-1
T
-1
0
?
1
0
-1
A. 1
B.-2
C. 2
D.-1
E. 3
F. 0
3 C₂
1
-1
?
어
-1
2
60d
1
-1
-1
?
O

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Step 2: Calculation of characters applying orthogonality theorem

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Step 3: Calculation of characters by orthogonality theorem

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