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Complex-scaled equation-of-motion coupled-cluster method with single and double substitutions for autoionizing excited states: Theory, implementation, and examples

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10.1063/1.4795750

### Abstract

Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H^{−}, and Be). The dependence of the results on one-electron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that one-electron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, θ. Standard basis sets that are optimized for not-complex-scaled calculations (θ = 0) are not sufficiently flexible to describe the θ-dependence of the wave functions even when heavily augmented by additional sets.

© 2013 American Institute of Physics

Received 10 November 2012
Accepted 05 March 2013
Published online 26 March 2013

Acknowledgments: The authors are grateful to Professor Heinz Seidentop, Professor Nimrod Moiseyev, and Professor C. William McCurdy for stimulating discussions. K.B.B. also thanks Dr. Arie Landau and Dr. Tomasz Kus for valuable discussions. This work is supported by the Army Research Office through Grant No. W911NF-12-1-0543. A.I.K. is a grateful recipient of the Bessel Research Award from the Humboldt Foundation supporting her sabbatical stay at the University of Heidelberg.

Article outline:

I. INTRODUCTION

II. COMPLEX-SCALING FORMALISM: GENERAL THEORY AND EOM-EE-CCSD IMPLEMENTATION

A. C-product versus scalar product

B. One- and many-electron basis sets

C. Complex-scaled EOM-EE-CCSD

III. RESULTS AND DISCUSSION

A. Two-electron systems: 2s^{2} resonances in He and H^{−}

1. Resonance energies and lifetimes convergence to the exact limit: An even-tempered 30s15p10d basis

2. Standard basis sets and the effect of diffuse basis functions

3. The effect of the valence basis set

4. The character of the resonance wave function

B. Many-electrons systems: Be atom

IV. CONCLUSIONS

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2013-03-26

2014-04-16

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