Uniform vs Partial Scaling within Resonances via Padé Based on the Similarities to Other Non-Hermitian Methods: Illustration for the Beryllium 1s22p3s State

Fano–Feshbach formalism applied to the calculation of autoionization widths through analytic continuation

A method to calculate the autoionization width from a discretized pseudo-spectrum is proposed. This method relies on an analytic continuation of Green’s function within the Fano–Feshbach formalism. The pseudo-spectrum is obtained at the multireference configuration interaction level in a square-integrable basis set, commonly found in quantum chemistry software. Few states around the desired resonance are needed to perform the analytic continuation. This method was applied to atomic (He and Ne) and molecular (HF and benzene) systems, and the results for the autoionization width show good agreement with the available theoretical and experimental values.

Complex energies and transition dipoles for shape-type resonances of uracil anion from stabilization curves via Padé

Absorption of slow moving electrons by neutral ground state nucleobases has been known to produce resonance metastable states. There are indications that such metastable states may play a key role in DNA/RNA damage. Therefore, herein, we present an ab initio non-Hermitian investigation of the resonance positions and decay rates for the low lying shape-type states of the uracil anion. In addition, we calculate the complex transition dipoles between these resonance states. We employ the resonance via Padé (RVP) method to calculate these complex properties from real stabilization curves by analytical dilation into the complex plane. This method has already been successfully applied to many small molecular systems, and herein, we present the first application of RVP to a medium-sized system. The presented resonance energies are optimized with respect to the size of the basis set and compared with previous theoretical studies and experimental findings. Complex transition dipoles between the shape-type resonances are computed using the optimal basis set. The ability to calculate ab initio energies and lifetimes of biologically relevant systems paves the way for studying reactions of such systems in which autoionization takes place, while the ability to also calculate their complex transition dipoles opens the door for studying photo-induced dynamics of such biological molecules.

Variational Solutions for Resonances by a Finite-Difference Grid Method

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.