The following character table (accompanied by a molecule of the corresponding point group) has some missing information. 2 C3 3 C2 2 S3 3 ov X1 1 1 1 1 1 1 x2+ y?, z2 1 1 -1 1 1 -1 Rz E' 2 -1 2 -1 (x, y) (x2- y?, xy) A;" 1 X2 1 -1 -1 -1 Az" 1 1 -1 -1 -1 1 X3 BH; E" -1 -2 1 (Rx, Ry) (2х, yz) а. Based on symmetry labels and Mulliken symbols, what is the missing symmetry element? b. Provide the missing information in the table: i. X1 = ii. X2 = iii. X3 = С. For this point group, what is the symmetry of the following orbitals for an atom located along the main C3 axis? i. A px orbital: ii. A d? orbital: iii. A dxy orbital:

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 13.26E: Determine the point groups of the following molecules. a Hydrogen peroxide, H2O2 it is not planar. b...
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7.
The following character table (accompanied by a molecule of the corresponding point
group) has some missing information.
E
2 C3
3 C2
?
2 S3
3 oy
X1
1
1
1
1
1
x2+ y?, z2
A2
1
1
-1
1
-1
Rz
E'
2
-1
2
-1
(х, у)
(x2- у?, ху)
A,"
1
X2
1
-1
-1
-1
A2"
1
1
-1
-1
-1
1
X3
BH3
E"
2
-1
-2
1
(Rx, Ry)
(zx, yz)
а.
Based on symmetry labels and Mulliken symbols, what is the missing symmetry element?
b. Provide the missing information in the table:
i. X1 =
ii. X2 =
iii. X3 =
С.
For this point group, what is the symmetry of the following orbitals for an atom located along
the main C3 axis?
i. А Рх
orbital:
ii. A d,? orbital:
iii. A dxy orbital:
Transcribed Image Text:7. The following character table (accompanied by a molecule of the corresponding point group) has some missing information. E 2 C3 3 C2 ? 2 S3 3 oy X1 1 1 1 1 1 x2+ y?, z2 A2 1 1 -1 1 -1 Rz E' 2 -1 2 -1 (х, у) (x2- у?, ху) A," 1 X2 1 -1 -1 -1 A2" 1 1 -1 -1 -1 1 X3 BH3 E" 2 -1 -2 1 (Rx, Ry) (zx, yz) а. Based on symmetry labels and Mulliken symbols, what is the missing symmetry element? b. Provide the missing information in the table: i. X1 = ii. X2 = iii. X3 = С. For this point group, what is the symmetry of the following orbitals for an atom located along the main C3 axis? i. А Рх orbital: ii. A d,? orbital: iii. A dxy orbital:
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