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Linear combinations of spherical harmonics are derived that are adapted to the molecular symmetry group Td(M) and its isomorphic point groups Td and O. The alternating group T(M), consisting of even permutations, is the semi-direct product where C 3 = {E, (123), (132)} is a cyclic group and V4 ≡ {E, (12)(34), (13)(24), (14)(23)}. Further This structure of the group enables one to write down simple closed expressions for basis functions. Using the program Maple, tables up to and including ℓ = 10 are generated.
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Paul E. S. Wormer (2001) studied this question.
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