Advantages of complex scaling only the most diffuse basis functions in simultaneous description of both resonances and bound states

Abstract

An accurate description of both bound and resonance states is desirable in the study of molecules. However, it is not a trivial task to accomplish, as theoretical and numerical formalisms developed for describing one do not always fit for describing the other. One such formalism, mainly designed to describe resonances, is the complex scaling method, in which the Hamiltonian internal coordinates are scaled by a complex factor of e^iθ. As Kaprálová-Žďánská and Šmydke recently showed in their study on helium, in order to well describe both bound and resonance states, one should use quasi-complete basis sets. Yet, the use of large and dense basis sets is ineffective and highly impractical. In addition, the above-mentioned complex scaling method is unsuitable for a molecular analysis. Not long ago, an evidence that a mixed complex-scaled basis set can serve as a solution to the problem was presented by White et al., however, the behaviour of the bound states was not investigated systematically. In this work, we demonstrate systematically that using such a mixed basis set, in which only diffuse functions are scaled, is an appropriate approach for simultaneous description. On the one hand, using this method, complex scaling can be applied on molecular systems in order to find resonance states. On the other hand, in this method, both the bound and the resonance states can be well described even in relatively small basis sets. In addition, we demonstrate the stability of the bound state in relation to the scaling parameter.

Keywords:

• resonance
• complex scaling
• non-Hermitian
• ab-initio

Acknowledgements

N. Moiseyev, I. Haritan, and A. Landau acknowledge ISF [grant number 298/11] and the ICore: the Israeli Excellence Center ‘Circle of Light’ for a partial support. In addition, P.R. Kaprálová-Žďánská acknowledges the institutional supports RVO:68378271 and RVO:61388955, and a financial support provided by the Czech Ministry of Education [grant LG13029].

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

Supplemental data for this article can be accessed at: http://dx.doi.org/10.1080/00268976.2015.1080872.