The RVP Method—From Real Ab-Initio Calculations to Complex Energies and Transition Dipoles

Abstract

The purpose of this review is to describe the rationale behind the RVP (resonance via Padé) approach for calculating energies and widths of resonances, while emphasizing a solid mathematical ground. The method takes real input data from stabilization graphs, where quasi-discrete continuum energy levels are plotted as a function of a parameter, which gradually makes the employed basis functions more diffuse. Thus, input data is obtained from standard quantum chemistry packages, which are routinely used for calculating molecular bound electronic states. The method simultaneously provides the resonance positions (energies) and widths (decay rates) via analytical continuations of real input data into the complex plane (via the Padé approximant). RVP holds for isolated resonances (in which the energy-gap between resonance states is smaller than their decay rates). We focus also on the ability to use an open-source “black-box” code to calculate the resonance positions and widths as well as other complex electronic properties, such as transition dipoles.