Atomic and molecular complex resonances from real eigenvalues using standard (hermitian) electronic structure calculations

TL;DR

This paper presents a method to compute complex resonance eigenvalues, including positions and widths, using standard electronic structure calculations combined with analytical continuation techniques, enabling easier analysis of metastable states.

Contribution

The authors introduce a novel approach to calculate resonance eigenvalues using standard electronic structure packages and analytical continuation, avoiding complex modifications of existing codes.

Findings

Accurate resonance eigenvalues for helium, hydrogen anion, and hydrogen molecule.

Excellent agreement with other theoretical and experimental results.

Method leverages analytical passages from real to complex energies.

Abstract

Complex eigenvalues, resonances, play an important role in large variety of fields in physics and chemistry. For example, in cold molecular collision experiments and electron scattering experiments, autoionizing and pre-dissociative metastable resonances are generated. However, the computation of complex resonance eigenvalues is difficult, since it requires severe modifications of standard electronic structure codes and methods. Here we show how resonance eigenvalues, positions and widths, can be calculated using the standard, widely used, electronic-structure packages. Our method enables the calculations of the complex resonance eigenvalues by using analytical continuation procedures (such as Pad\'{e}). The key point in our approach is the existence of narrow analytical passages from the real axis to the complex energy plane. In fact, the existence of these analytical passages relies on using finite basis sets. These passages become narrower as the basis set becomes more complete, whereas in the exact limit, these passages to the complex plane are closed. As illustrative numerical examples we calculated the autoionization resonances of helium, hydrogen anion and hydrogen molecule. We show that our results are in an excellent agreement with the results obtained by other theoretical methods and with available experimental results.