Calculations of vibrational spectra with rectangular collocation: suitability for catalytic systems, tests of PES representations and selection of important regions of space

We present the latest developments in the rectangular collocation method to compute vibrational spectra. Rectangular collocation allows using a small number of fixed-shape or tuned basis functions of various forms to compute anharmonic spectra from a relatively small number of potential energy surface (PES) samples. It is well suited for calculations of anharmonic spectra when an analytic PES is unavailable and when underlying ab initio calculations are costly, such as molecules on surfaces. We show that collocation points can be placed in important regions of space further reducing computational cost. Accurate anharmonic spectra for a four-atomic molecules are computable on a desktop. We compare spectra on PESs fitted with neural networks and Gaussian process regression and show that the method also permits to get a clearer understanding of how errors due to PES representation translate into errors in the spectrum.