Using Weighted and Chopped Rectangular Collocation Methods with Tensor-Product Contracted Bases To Compute Vibrational Spectra: Avoiding Quadrature

Product contracted (PC) bases are efficient for computing (ro-)vibrational spectra of molecules. However, to account for coupling between subsystems, all previous PC methods require computing integrals by quadrature. The cost of the quadrature is significant and increases with the dimensionality of the molecule. In this paper, we propose a weighted and chopped rectangular collocation (WC-RC) method that obviates quadrature. We use Christoffel weights and Christoffel-Fekete (CF) collocation points. They are known to be near-optimal for weighted least-squares fitting. Matrix chopping increases the accuracy of energy levels. An additional chopping makes it possible to symmetry adapt (SA) the calculation. With the WC-RC method, we achieve sub-0.1 cm-1 accuracy for both 9-D CH2NH and 6-D HF dimer using many fewer points than required when quadrature is used.