RESUMEN
We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as resonances and provide the energies and inverse lifetimes of the system under study (e.g., molecules) in metastable states. This approach allows incorporating finite grid methods in the study of resonance phenomena in chemistry. Possible applications include the calculation of electronic autoionization resonances which occur when ionization takes place as the bond lengths of the molecule are varied. Alternatively, the method can be applied to calculate nuclear predissociation resonances which are associated with activated complexes with finite lifetimes.
RESUMEN
Custom tokenization dictionary (CUSTODI) is introduced as a novel way for tackling the problem of molecular representations, and especially the challenge of molecular property prediction. Herein, the motivational theory and the actual representation and model are presented and shown to have performance that is in line with benchmark methodologies. The uniqueness of CUSTODI is its applicability on small training sets and the developed theory suggests its possible use for a-priori estimation of future fit quality on any given dataset, regardless of the method used for fitting.