The assignment of vibrational states is an integral part of quantum chemical calculations, which supports the analysis of experimental infrared spectra. In variational calculations, usually, it is the leading coefficient of the configuration interaction vector, which provides the state identity. However, this concept will possibly fail in case of special coordinate systems, such as, for example, localized normal coordinates, or within calculations for overtones of non-Abelian molecules, when a real valued configuration basis has been employed. A combination of both renders a proper assignment fairly tedious. We present a route to overcome this problem by using a highly efficient calculation of multidimensional overlap integrals based on the Smolyak quadrature. Beside this, a general protocol for the symmetry assignment of vibrational states will be discussed, which completes a general assignment. Extensive benchmark calculations are provided for the fundamental modes and overtones of chloromethane, CH3Cl, in canonical and localized normal coordinates based on accurate potential energy surfaces obtained from explicitly correlated coupled-cluster theory. In addition, the linear CNNC molecule has been studied, for which hardly any reference data do exist.
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