Parameterized Bases for Calculating Vibrational Spectra Directly from ab Initio Data Using Rectangular Collocation.

We compared different parametrized bases for computing anharmonic vibrational spectra using a new version of the rectangular collocation-optimization method of Manzhos and Carrington (Can. J. Chem. 2009, 87, 864; Chem. Phys. Lett. 2011, 511, 434). The method enables one to compute a small number of vibrational levels with an ultrasmall basis set without a potential function. To test the ideas, parametrized uncoupled and coupled Gaussian functions as well as direct-product and coupled Hermite basis sets are used to compute four low-lying vibrational energy levels of H2O on model harmonic and anharmonic uncoupled (polynomial) potential energy surfaces. In addition, we compute levels directly from ab initio points and thereby include all coupling and anharmonicity. We conclude that uncoupled parametrized Gaussian and Hermite functions are a good choice for anharmonic and coupled problems.