We extend the periodic von Neumann basis to non-Cartesian coordinates. The bound states of two isomerizing triatomic molecules, LiCN/LiNC and HCN/HNC, are calculated using the vibrational Hamiltonian in Jacobi coordinates. The phase space localization of the basis functions leads to a flexible and accurate representation of the Hamiltonian. This results in significant savings compared to a basis localized just in coordinate space. The favorable scaling of the method with dimensionality makes it promising for applications to larger systems.

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