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Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

Gidopoulos, N.I.; Lathiotakis, N.N.

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ” Thumbnail


Authors

N.N. Lathiotakis



Abstract

The Comment by Friedrich et al. does not dispute the central result of our paper [Phys. Rev. A 85, 052508 (2012)] that nonanalytic behavior is present in long-established mathematical pathologies arising in the solution of finite basis optimized effective potential (OEP) equations. In the Comment, the terms “balancing of basis sets” and “basis-set convergence” imply a particular order towards the limit of a large orbital basis sets where the large-orbital-base limit is always taken first, before the large-auxiliary-base limit, until overall convergence is achieved, at a high computational cost. The authors claim that, on physical grounds, this order of limits is not only sufficient, but also necessary in order to avoid the mathematical pathologies. In response to the Comment, we remark that it is already written in our paper that the nonanalyticity trivially disappears with large orbital basis sets. We point out that the authors of the Comment give an incorrect proof of this statement. We also show that the order of limits towards convergence of the potential is immaterial. A recent paper by the authors of the Comment proposes a partial correction for the incomplete orbital basis error in the full-potential linearized augmented-plane-wave method. Similar to the correction developed in our paper, this correction also benefits from an effectively complete orbital basis, even though only a finite orbital basis is employed in the calculation. This shows that it is unnecessary to take, in practice, the limit of an infinite orbital basis in order to avoid mathematical pathologies in the OEP. Our paper is a significant contribution in that direction with general applicability to any choice of basis sets. Finally, contrary to an allusion in the abstract and assertions in the main text of the Comment that unphysical oscillations of the OEP are supposedly attributed to the common energy denominator approximation, in fact, such anomalies arise with the full treatment of the small eigenvalues of the density response function. This characteristic of the finite basis OEP is well known in the literature but also is clearly demonstrated in our paper.

Citation

Gidopoulos, N., & Lathiotakis, N. (2013). Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”. Physical Review A, 88(4), Article 046502. https://doi.org/10.1103/physreva.88.046502

Journal Article Type Article
Publication Date Oct 1, 2013
Deposit Date Jan 15, 2014
Publicly Available Date Jul 11, 2014
Journal Physical Review A
Print ISSN 1050-2947
Electronic ISSN 1094-1622
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 88
Issue 4
Article Number 046502
DOI https://doi.org/10.1103/physreva.88.046502
Public URL https://durham-repository.worktribe.com/output/1445456

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Copyright Statement
Reprinted with permission from the American Physical Society: Phys. Rev. A 88, 046502 © (2013) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.






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