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. 2020 Mar 18;10:4938. doi: 10.1038/s41598-020-61675-y

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© The Author(s) 2020

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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CTL based on combined DFT and GW formalism. (a) Schematic description for calculating CTL in the combined DFT and GW formalism, where E_relax is obatined from DFT total energy calculations, and E_QP is calculated from GW calculation. The formation energy is a state function, so that the CTL values calcualted following path 1 (P1) or path 2 (P2) result in the same ε(q/q⁻1). (b) Calculated CTL of N-substituted MoS₂ from neutral state to negatively charged state as following P1 shown in a.