Localized representations for large amplitude molecular vibrations

Two novel, closely related variational quantum approaches for efficient and accurate calculation of highly excited vibrational levels of triatomic molecules are presented. The two approaches employ, in slightly different ways, the discrete variable representation (DVR) and the distributed Gaussian basis (DGB) for representation of the internal degrees of freedom. The scope of their applicability is broad; they are particularly suitable for molecules having one or more large amplitude vibrations, on potential surfaces with several local minima. Although formulated in Jacobi and hyperspherical coordinates, respectively, both approaches can be implemented in any coordinate system for which suitable DVRs can be defined. The DVR allows us to define sequentially problems of lower dimensionality, whose truncated sets of eigenvectors serve as very compact, contracted basis sets for the higher dimensional problem. Other important advantages of the DVR-DGB approaches, as well as applications to molecules like LiCN/LiNC, HCN/HNC and H₂O, are discussed.