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Simulation of Indirect 13C–13C J-Coupling Tensors in Diamond Clusters Hosting the NV Center
* 1, 2 , 1, 3 , 4 , 5 , 5 , 1 , 2
1  National Research Nuclear University “MEPhI”, 115409, Moscow, Russia.
2  Institute of Physics, Nat. Acad. Sci., 220072 Minsk, Belarus.
3  Institute of Physical and Organic Chemistry, Nat. Acad. Sci., 220072 Minsk, Belarus.
4  Institute for Nuclear Problems, Belarusian State University, 220006 Minsk, Belarus.
5  Computer, Electrical and Mathematical Science and Engineering Division, 4700 King Abdullah University of Science and Technology(KAUST),23955-6900,Thuwal, Saudi Arabia.
Academic Editor: Antonio Di Bartolomeo


In the past decade there was rapid progress in development of quantum magnetic sensing technology based on nitrogen-vacancy (NV) color centers in diamond (see, e.g. [1,2] for recent reviews). Magnetometer based on single NV center can have nanometer-scale spatial resolution and exceptional sensitivity (up to ~Hz) allowing to detect target single 13C nuclear spins or coupled 13C-13C pairs located within the diamond which can be used as long-lived quantum memory [3]. Moreover, NV-based magnetometer allows to distinguish (by their chemical shifts) inequivalent nulear spins of molecules located at diamond surface [4], thus enabling new exciting research area of single-spin nuclear magnetic resonance (NMR) for investigating important issues ranging from determination of molecular structures of inorganic/biological compounds up to medical imaging for therapeutic matters.

In these respects, predicting of high-resolution NMR characteristics for studied spin systems is essential. Among them, those of indirect nuclear spin–spin coupling (the J-coupling), that arise due to second-order hyperfine interactions, are important. Here we are presenting for a first time the results of simulation of full tensors JKL (K,L=X,Y,Z) describing the J-couplings of nucler spins 13C in H-terminated NV-hosting diamond clusters. We have optimized the cluster geometry using the ORCA 5.0.1 software package with the B3LYP/def2/J/RIJCOSX level of theory and then simulated the n-bond J-coupling tensors nJKL for all possible 13C-13C pairs in the clusters using B3LYP/TZVPP/AUTOAUX/decontract level of theory. We found that, in addition to usually considered isotropic Fermi-contact contribution to JKL, the anisotropic contributions resulted from dia- and paramagnetic, spin-dipolar and spin-dipolar/Fermi-contact cross terms are essential and can manifest in NMR spectra of 13C dimers recorded using the NV centers. Using simlated tensors nJKL we calculated the values of scalar J-constants nJ=Sp(nJKL)/3 for different 13Ci-13Cj pairs in the examplary C33[NV]-H36 cluster. The highest ones are those for neighboring 13C: one-bond constant 1J were 30-37 Hz depending on the position of the 13C dimer in the cluster with respect to the NV center. Moreover, using the same theory level we also simulated full tensors nJKL for the adamantane and found that for this molecule the calculated value 1J = Sp(1JKL)/3=29.9 Hz correlates well with the isotropic constant 1J=31.4 Hz obtained experimentally in [5].


[1] Schwartz I. et al. Blueprint for nanoscale NMR. Scientific Reports. 9 (2019) 6938.

[2] Barry J.F. et al. Sensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys. 92 (2020) 015004.

[3] Chen Q. et al. Steady-state preparation of long-lived nuclear spin singlet pairs at room temperature. Phys. Rev. B. 95 (2017) 224105.

[4] Glenn D.R. et al. High-resolution magnetic resonance spectroscopy using a solid-state spin sensor.

Nature.555 (2018) 351.

[5] Gay I.D. et al, INADEQUATE in the Solid State. HomonuclearCouplings in [(CH3)2SnE]3. J .Magn. Res. 91 (1991) 185.

Keywords: NV center in diamond; 13C-13C J-coupling tensor; DFT simulation.