The H3 molecular ion, which plays an important role in chemical reactions occurring in interstellar clouds, is

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The H3 molecular ion, which plays an important role in chemical reactions occurring in interstellar clouds, is known to be equilateral triangular.
(a) Identify the symmetry elements and determine the point group of this molecule.
(b) Take as a basis for a representation of this molecule the three H1s orbitals and set up the matrices that group in this basis.
(c) Obtain the group multiplication table by explicit multiplication of the matrices.
(d) Determine if the representation is reducible and, if so, give the irreducible representations obtained.
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