Shaping and controlling stabilisation graphs for calculating stable complex resonance energies

ABSTRACT

Stabilisation technique is a traditional approach for studying resonances, such as the metastable autoionisation states. Stabilisation graphs are usually calculated by scaling the employed basis functions. Over the years, many methods for extracting the resonance complex energies from these graphs have been developed, nowadays, they are usually evaluated via analytical continuation schemes. However, many times it is difficult to obtain a well-behaved stabilisation graphs upon basis-set scaling. Herein, we illustrate that it is possible to shape stabilisation graphs to behave physically by adjusting the relevant Gaussian basis function exponents. We illustrate this for the excited Li–He${}^{\ast }$ ${}^2\mathrm{\Sigma }$ and ${}^2\mathrm{\Pi }$ states [with He${}^{\ast }(1s2p;{}^{1}P$)], which serve as an excellent example since generating well-behaved graphs in this case is challenging. We show that by controlling and shaping the stabilisation graphs we can obtain converged complex energies, which are calculated by the resonances via Padé approach (a recently proposed analytical continuation scheme). Nevertheless, the concepts presented here are general to any stabilisation-graph based method.

GRAPHICAL ABSTRACT

Keywords:

• Stabilization-graph
• coupled-cluster
• resonance states
• autoionisation

Acknowledgments

The author wish to thank Nimrod Moiseyev for his support and for many discussions, and Anael Ben-Asher for her input and for reading the manuscript. This work is dedicated to Nimrod Moiseyev (the non-Hermitian Peter Pan) on his 70th birthday.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 See supplemental material at [URL will be inserted by AIP] for additional computational details of the hydrogen atomic anion, and all the basis set exponents used in this paper

Additional information

Funding

This research was supported by the I-Core: the Israeli Excellence Center ‘Circle of Light’ by the Israel Science Foundation [grants No. 298/11 and No. 1530/15].