A general harmonic potential function for water isThe second line contains off-diagonal force constants, while the first three terms are diagonal. In matrix form, this can be expressed as is the vector whose elements are the internal coordinates. Find the symmetry coordinates S₁, S₂, and S₃ for water, and the block diagonal force constant matrix f which permits the potential energy to be written as S^T f S.

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V: v ==k (Δη)* + =k (Δη) - + =ko(rΔΘ) + Κ„Δr_rz + Kar∆η Δθ + KarΔr Δθ