The H 2 O molecule belongs to the point group C 2v , which contains the symmetry
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The H2O molecule belongs to the point group C2v, which contains the symmetry operators Ê, Ĉ2, σ̂a, and σ̂b, where the C2 axis passes through the oxygen nucleus and midway between the two hydrogen nuclei, and where the σa mirror plane contains the three nuclei and the σb mirror plane is perpendicular to the σa mirror plane.
(a) Find the 3 by 3 matrix that is equivalent to each symmetry operator.
(b) Show that the matrices obtained in part (a) have the same multiplication table as the symmetry operators, and that they form a group. The multiplication table for the group was to be obtained in Problem 8.23.
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