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Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method

Ryley, Matthew S.; Withnall, Michael; Irons, Tom J. P.; Helgaker, Trygve; Teale, Andrew M.


Matthew S. Ryley

Michael Withnall

Trygve Helgaker

Professor of Computational and Theoretical Chemistry


We present a Gaussian-basis implementation of orbital-free density-functional theory (OF-DFT) in which the trust-region image method (TRIM) is used for optimization. This second-order optimization scheme has been constructed to provide benchmark all-electron results with very tight convergence of the particle-number constraint, associated chemical potential, and electron density. It is demonstrated that, by preserving the saddle-point nature of the optimization and simultaneously optimizing the density and chemical potential, an order of magnitude reduction in the number of iterations required for convergence is obtained. The approach is compared and contrasted with a new implementation of the nested optimization scheme put forward by Chan, Cohen, and Handy. Our implementation allows for semilocal kinetic-energy (and exchange-correlation) functionals to be handled self-consistently in all-electron calculations. The all-electron Gaussian-basis setting for these calculations will enable direct comparison with a wide range of standard high-accuracy quantum-chemical methods as well as with Kohn-Sham density-functional theory. We expect that the present implementation will provide a useful tool for analyzing the performance of approximate kinetic-energy functionals in finite systems.


Ryley, M. S., Withnall, M., Irons, T. J. P., Helgaker, T., & Teale, A. M. (2021). Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method. Journal of Physical Chemistry A, 125(1), 459-475.

Journal Article Type Article
Acceptance Date Dec 22, 2020
Online Publication Date Dec 24, 2020
Publication Date Jan 14, 2021
Deposit Date Jun 23, 2021
Publicly Available Date Dec 25, 2021
Journal Journal of Physical Chemistry A
Print ISSN 1089-5639
Electronic ISSN 1520-5215
Publisher American Chemical Society
Peer Reviewed Peer Reviewed
Volume 125
Issue 1
Pages 459-475
Keywords Physical and Theoretical Chemistry
Public URL
Publisher URL
Additional Information This document is the Accepted Manuscript version of a Published Work that appeared in final form in the Journal of Physical Chemistry A, copyright© American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see


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