The point group to which the water molecule, H₂O, belongs is C2v. The four associated symmetry operations (SOs) are represented by the following set of four matrices: --~--:¦ C2(z) [100] E= 0 0 0 -1 0 = 0 -1 0 σ₂(x, 2) = 0 0 1 Define the R=R₂(π/2) matrix. 0 0 -1 0 0 -1 (y, z)= 0 1 0 0 1

The point group to which the water molecule, H₂O, belongs is C2v. The four associated symmetry operations (SOs) are represented by the following set of four matrices: --~--:¦ C2(z) [100] E= 0 0 0 -1 0 = 0 -1 0 σ₂(x, 2) = 0 0 1 Define the R=R₂(π/2) matrix. 0 0 -1 0 0 -1 (y, z)= 0 1 0 0 1

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 13.56E

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Question

The point group to which the water molecule, H₂O, belongs is C2v. The four associated
symmetry operations (SOs) are represented by the following set of four matrices:
E
=
1
0 0
0 1 0
0 0 1
C₂(z) =
0
0
Define the R=R₂(π/2) matrix.
0
-1
0
0
0
1
ov(x, z) =
=
[1 0 0
[9]
-1 0
0
1
1
(y, z)= 0
0
0
0
1 0
0
1

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