Investigations of transformed mass-scaled Jacobi coordinates for vibrations of polyatomic molecules with application to H2O

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Abstract
We present an investigation of orthogonal transformations of Delves coordinates, i.e., mass-scaled Jacobi coordinates, in applications to polyatomic molecule vibrations. First, we show for triatomic molecules with a stationary point of C2v symmetry that these coordinates can be transformed exactly to yield normal coordinates in the small displacement limit. A partial transformation to normal coordinates is also given for tetraatomic molecules with C2v symmetry. Second, we show that this transformation can be used to optimize a set of coordinates for use in variational calculations of vibrations of polyatomic molecules, and demonstrate its utility in variational calculations of vibrational energies for H2O.