On the advantages of a rectangular matrix collocation equation for computing vibrational spectra from small basis sets

► Vibrational Schrödinger equation (SE) solved with a small adaptable basis. ► Energies, wavefunctions found from a rectangular collocation matrix equation. ► Performance of rectangular and squared matrix methods compared. ► Rectangular approach outperforms square with small, incomplete bases. ► Rectangular approach enables fitting of energy, basis parameters to SE.