Analysis of Stabilization and Extrapolation Methods for Determining Energies and Lifetimes of Metastable Electronic...

Two methods that make use of standard electronic structure tools, the stabilization and extrapolation methods, are discussed with an eye toward pointing out their relative strengths and weaknesses and for improving their applications. In the former, whether to utilize energy data from only one or from both branches of an avoided crossing between the quasi-bound and pseudo-continuum states is one issue that is focused on. Another is the decision of where along the stabilization plot's branches (i.e., far from or close to the avoided crossing) to create data points for optimal performance given a reasonable (10^-5-10^-7 eV) precision in the electronic energy. A third issue is how many parameters to use in fitting energy data to the (one or two) branches of the stabilization plot. In extrapolation methods, one uses energy data computed when the metastable state's energy has been rendered stable by the application of an external potential, which thus produces a one-branch function. The main issues in implementing this method are the functional form for how the energy E depends on the strength of the external potential especially as the energy evolves from the bound-state region toward the unbound region and how to choose data points so that energy values of a reasonable precision are capable of determining the parameters in the formula that produces the metastable state's energy E and half-width Γ/2 (inversely related to the state's lifetime). In addition to explaining, critiquing, and comparing these two methods, several suggestions are offered for their further testing and improvements.