Theory of electronic resonances: Fundamental aspects and recent advances

TL;DR

This paper reviews complex-variable methods for studying electronic resonances, highlighting their theoretical foundations, recent advancements, and applications in molecular electronic-structure calculations.

Contribution

It provides a comprehensive overview of complex scaling and absorbing potential techniques, including recent developments like gradient theory and embedding methods for electronic resonances.

Findings

Development of analytic gradient theory for resonances

Application of rank-reduction and quantum embedding techniques

Methods for evaluating partial decay widths

Abstract

Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under ambient conditions that involve unbound electrons. This feature article focuses on complex-variable techniques such as complex scaling and complex absorbing potentials that afford a treatment of electronic resonances in terms of discrete square-integrable eigenstates of non-Hermitian Hamiltonians with complex energy. Fundamental aspects of these techniques as well their integration into molecular electronic-structure theory are discussed and an overview of some recent developments is given: analytic gradient theory for electronic resonances, the application of rank-reduction techniques and quantum embedding to them, as well as approaches for evaluating partial decay widths.