Citation: Nizovtsev, A.; Pushkarchuk, A.; Kuten, S.; Michels, D.; Lyakhov, D.; Kargin, N.; Kilin, S. Simulation of Indirect 13 C– 13 C J-Coupling Tensors in Diamond Clusters Hosting the NV Center. Mater. Proc. 2022, 9, 4. https://doi.org/10.3390/ materproc2022009004 Academic Editor: Antonio Di Bartolomeo Published: 22 April 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Proceeding Paper Simulation of Indirect 13 C– 13 C J -Coupling Tensors in Diamond Clusters Hosting the NV Center † Alexander Nizovtsev 1,2, *, Aliaksandr Pushkarchuk 2,3 , Semen Kuten 4 , Dominik Michels 5 , Dmitry Lyakhov 5 , Nikolai Kargin 2 and Sergei Kilin 1 1 Institute of Physics, National Academy of Science, 220072 Minsk, Belarus; sergei_kilin@yahoo.com 2 National Research Nuclear University “MEPhI”, Moscow 115409, Russia; alexp51@bk.ru (A.P.); nikargin@mephi.ru (N.K.) 3 Institute of Physical and Organic Chemistry, National Academy of Science, 220072 Minsk, Belarus 4 Institute for Nuclear Problems, Belarusian State University, 220006 Minsk, Belarus; semen_kuten@list.ru 5 Computer, Electrical and Mathematical Science and Engineering Division, 4700 King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia; dominik.michels@kaust.edu.sa (D.M.); dmitry.lyakhov@kaust.edu.sa (D.L.) * Correspondence: apniz@dragon.bas-net.by † Presented at the 3rd International Online-Conference on Nanomaterials, 25 April–10 May 2022; Available online: https://iocn2022.sciforum.net/. Abstract: The full tensors n J KL (K,L = X,Y,Z), describing n-bond J-coupling of nuclear spins 13 C in H-terminated diamond-like clusters C 10 H 16 (adamantane) and C 35 H 36 , as well as in the cluster C 33 [NV − ]H 36 hosting the negatively charged NV − center, were simulated. We found that, in addition to the usually considered isotropic scalar n J-coupling constant, the anisotropic contributions to the n J-coupling tensor are essential. We also showed that the presence of the NV center affects the J-coupling characteristics, especially in the case of 13 C– 13 C pairs located near the vacancy of the NV center. Keywords: solid-state NMR; J C–C -coupling tensor; H-terminated diamond cluster; NV center; DFT simulation 1. Introduction In the past decade, there was rapid progress in the development of quantum mag- netic sensing technologies based on nitrogen-vacancy (NV) color centers in diamond (e.g., see [1,2] for recent reviews). A magnetometer based on a single NV center can have nanometer-scale spatial resolution and exceptional sensitivity (up to ~Hz) allowing the detection of target single 13 C nuclear spins or coupled 13 C– 13 C pairs located within the diamond, which can be used as long-lived quantum memory [3]. Moreover, an NV-based magnetometer allows to distinguish (by chemical shifts) inequivalent nuclear spins of molecules located at diamond surface [4]. This enables a new exciting application area of single-spin nuclear magnetic resonance (NMR) to investigate important issues ranging from determination of molecular structures of inorganic/biological compounds up to med- ical imaging for therapeutic matters. In these respects, predicting high-resolution NMR characteristics for studied spin systems is essential. Among them, the characteristics of indirect nuclear spin–spin coupling (J-coupling) that arise due to second-order hyperfine interactions with electrons from chemical bonds connecting nuclei are important. Generally, a second-rank tensor n J KL (K,L = X,Y,Z) is required to fully describe J-coupling between two nuclei [5]. However, until recently, most high-resolution NMR experiments were focused on measuring only isotropic scalar constant n J iso = Sp n J KL /3 because the anisotropic parts of the J-tensor were averaged out to zero by fast molecular motion in solution-state NMR or fast magic-angle spinning (MAS) in solid-state experiments [6–8]. Meanwhile, in the case of crystalline solids, the constituent atoms are located in a certain order determined by Mater. Proc. 2022, 9, 4. https://doi.org/10.3390/materproc2022009004 https://www.mdpi.com/journal/materproc