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. 2021 Dec 10;12:7230. doi: 10.1038/s41467-021-27576-y

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — Natural orbitals derived from state-specific scalar-relativistic CAS(1,7) and CAS(8,7) for Ce1 and Bk1. a For both complexes, there is an f-orbital similar to the f_±3 orbital that shows a preferential orbital interaction between the metal center, terpy*, and the water molecule. This orbital is crucial to define the plane of covalency. b Orbital mixing between the 5p/6p orbitals with 2p-ligand orbitals showing the participation of the core in chemical bonding.