Molecular Spectra Calculations Using an Optimized Quasi-Regular Gaussian Basis and the Collocation Method

We revisit the collocation method of Manzhos and Carrington [ J. Chem. Phys., 2016, 145, 224110] in which a distributed localized (e.g., Gaussian) basis is used to set up generalized eigenvalue problem compute eigenenergies eigenfunctions molecular vibrational Hamiltonian. Although resulting linear algebra involves full matrices, provides number important advantages, namely, (i) it very simple both conceptually numerically, (ii) can be formulated using any internal coordinates, (iii) flexible with respect choice basis, (iv) no integrals need computed, (v) has potential significantly reduce size through optimizing placement shapes functions. In present paper, we explore latter aspect recently introduced, here further improved, quasi-regular grids (QRGs). By computing four-atom molecule formaldehyde, demonstrate that QRG-based Gaussian superior previously choices.