Highly excited vibrational levels of ‘‘floppy’’ triatomic molecules: A discrete variable representation—Distributed Gaussian basis approach

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Abstract
A novel, efficient, and accurate quantum method for the calculation of highly excited vibrational levels of triatomic molecules is presented. The method is particularly well suited for applications to ‘‘floppy’’ molecules, having large amplitude motion, on potential surfaces which may have more than one local minimum. The discrete variable representation (DVR) for the angular, bend coordinate is combined with the distributed (real) Gaussian basis (DGB) for the expansion of other, radial coordinates. The DGB is tailored to the potential, covering only those regions where V(r)<EMAX. The DVR permits a contraction of the primitive Gaussian basis to a small eigenfunction basis at each of the discretized values of the angular coordinate. It is shown for the floppy two-mode LiCN/LiNC system (fixed CN distance) that N lowest vibrational levels (N=131) can be converged to within 1 cm−1 (the lowest 117 to 0.1 cm−1) using only 3N basis functions. This appears to reduce the computational effort by a factor of 10–40 over standard methods. Moreover, only a very low order Gauss–Hermite quadrature, 3–5 points, is needed to evaluate each potential matrix element.