Carbon-13 Chemical Shifts Research Articles

Studies on the Termination Behavior of Styrenic Free‐Radicals

AbstractIn order to provide more evidence to understand the termination mechanism in styrene free‐radical polymerization, (1‐bromoethyl) benzene and polystyrene with bromide end group (PSt‐Br) synthesized by atom transfer radical polymerization (ATRP) were used as the model compound and model polymer to study the termination behavior of styrenic radical by atom transfer radical coupling (ATRC), and then the NMR chemical shifts of the head‐to‐head enchainment from coupling termination were obtained. SEC and different NMR measurement methods were used to analyze and characterize the products. It is confirmed that there is no bimolecular disproportionation termination between styrenic free radicals, but only coupling termination to form the head‐to‐head enchainment. The proton and carbon chemical shifts of the head‐to‐head enchainment from coupling termination for (1‐bromoethyl) benzene are 2.7–2.86 ppm and ~47.3 ppm. As for the polystyrene through ATRC from PSt‐Br, the corresponding chemical shifts are 2.61–3.29 ppm and ~46.4 ppm, respectively, they are almost the same as the data in our previous paper (~3.05 ppm, ~46.6 ppm) for polystyrene initiated by BPO, proving that the chain termination in free‐radical polymerization of styrene initiated by BPO occurs through primary termination between chain radical and primary radical rather than bimolecular termination between chain radicals.

Can Graph Machines Accurately Estimate 13C NMR Chemical Shifts of Benzenic Compounds?

In the organic laboratory, the 13C nuclear magnetic resonance (NMR) spectrum of a newly synthesized compound remains an essential step in elucidating its structure. For the chemist, the interpretation of such a spectrum, which is a set of chemical-shift values, is made easier if he/she has a tool capable of predicting with sufficient accuracy the carbon-shift values from the structure he/she intends to prepare. As there are few open-source methods for accurately estimating this property, we applied our graph-machine approach to build models capable of predicting the chemical shifts of carbons. For this study, we focused on benzene compounds, building an optimized model derived from training a database of 10,577 chemical shifts originating from 2026 structures that contain up to ten types of non-carbon atoms, namely H, O, N, S, P, Si, and halogens. It provides a training root-mean-squared relative error (RMSRE) of 0.5%, i.e., a root-mean-squared error (RMSE) of 0.6 ppm, and a mean absolute error (MAE) of 0.4 ppm for estimating the chemical shifts of the 10k carbons. The predictive capability of the graph-machine model is also compared with that of three commercial packages on a dataset of 171 original benzenic structures (1012 chemical shifts). The graph-machine model proves to be very efficient in predicting chemical shifts, with an RMSE of 0.9 ppm, and compares favorably with the RMSEs of 3.4, 1.8, and 1.9 ppm computed with the ChemDraw v. 23.1.1.3, ACD v. 11.01, and MestReNova v. 15.0.1-35756 packages respectively. Finally, a Docker-based tool is proposed to predict the carbon chemical shifts of benzenic compounds solely from their SMILES codes.

Java Script Programs for Calculation of Dihedral Angles with Manifold Equations

Java Script programs for calculation dihedral angles from NMR data with manifold equations of 3-Sphere approach: rectangle, Villarceau circles of cyclide (Torus – Dupin Cyclide), polar equations, Euler-Conic. Manifolds are curves or surface in higher dimension used for calculation of dihedral angles under wave character of NMR data, carbon and/or proton chemical shift δ<sub>Xn</sub>[ppm] and vicinal coupling constant <sup>3</sup><I>J</I><sub>HnHn+1</sub>[Hz]. 3-Sphere approach for calculation of the dihedral angles from NMR data in four steps: 1. Prediction, or more exactly calculation of the dihedral angles from vicinal coupling constant with trigonometric equations, 2. Calculation of the dihedral angles from manifold equations; 3. Building units from angle calculated with one of the manifold equations; 4. Calculation the vicinal coupling constant of the manifold dihedral angle. In this paper are presented Java Script programs of step 2 and from step 3 only the Java Script program for calculation of seven sets angles. The bond distances l<sub>CnCn+1</sub>[A<sup>0</sup>] between two atoms of carbon are under different polar equations (<i>i.e.</i> limaçons or cardioid, rose or lemniscale), our expectation was to find different manifold equations for calculation the best angle, differences are smaller but can be find sometimes a preferred one for a vicinal coupling constant. 3-Sphere approach has the advantages of calculation from vicinal angle or/and chemical shift the dihedral angle, tetrahedral angle and the bond distance l<sub>CnCn+1</sub>[A<sup>0</sup>], with application on conformational and configurational analysis.

Exploring long-range fluorine–carbon J-coupling for conformational analysis of deoxyfluorinated disaccharides: A combined computational and NMR study

In this study, we investigated the potential of long-range fluorine–carbon J-coupling for determining the structures of deoxyfluorinated disaccharides. Three disaccharides, previously synthesized as potential galectin inhibitors, exhibited through-space fluorine–carbon J-couplings. In our independent conformational analysis of these disaccharide derivatives, we employed a combination of density functional theory (DFT) calculations and nuclear magnetic resonance (NMR) experiments. By comparing the calculated nuclear shieldings with the experimental carbon chemical shifts, we were able to identify the most probable conformers for each compound. A model comprising fluoromethane and methane molecules was used to study the relationship between molecular arrangements and intermolecular through-space J-coupling. Our study demonstrates the important effect of internuclear distance and molecular orientation on the magnitude of fluorine–carbon coupling. The experimental values for the fluorine–carbon through-space couplings (TSCs) of the disaccharides corresponded with values calculated for the most probable conformers identified by the conformational analysis. These results unlock the broader application of fluorine–carbon TSCs as powerful tools for conformational analysis of flexible molecules, offering valuable insights for future structural investigations.

Carbon-13 chemical shift tensor measurements for nitrogen-dense compounds.

This paper reports the principal values of the 13 C chemical shift tensors for five nitrogen-dense compounds (i.e., cytosine, uracil, imidazole, guanidine hydrochloride, and aminoguanidine hydrochloride). Although these are all fundamentally important compounds, the majority do not have 13 C chemical shift tensors reported in the literature. The chemical shift tensors are obtained from 1 H→13 C cross-polarization magic-angle spinning (CP/MAS) experiments that were conducted at a high field of 18.8T to suppress the effects of 14 N-13 C residual dipolar coupling. Quantum chemical calculations using density functional theory are used to obtain the 13 C magnetic shielding tensors for these compounds. The best agreement with experiment arises from calculations using the hybrid functional PBE0 or the double-hybrid functional PBE0-DH, along with the triple-zeta basis sets TZ2P or pc-3, respectively, and intermolecular effects modeled using large clusters of molecules with electrostatic embedding through the COSMO approach. These measurements are part of an ongoing effort to expand the catalog of accurate 13 C chemical shift tensor measurements, with the aim of creating a database that may be useful for benchmarking the accuracy of quantum chemical calculations, developing nuclear magnetic resonance (NMR) crystallography protocols, or aiding in applications involving machine learning or data mining. This work was conducted at the National High Magnetic Field Laboratory as part of a 2-week school for introducing undergraduate students to practical laboratory experience that will prepare them for scientific careers or postgraduate studies.

A stable rhodium-coordinated carbene with a σ0π2 electronic configuration.

Isolable singlet carbenes have universally adopted a σ2π0 electronic state, making them σ-donors and π-acceptors. We present a rhodium-coordinated, cationic cyclic diphosphinocarbene with a σ0π2 ground state configuration. Nuclear magnetic resonance spectroscopy studies show a carbene carbon chemical shift below -30.0 parts per million. X-ray crystallography reveals a planar RhP2C configuration. Quantum chemical calculations rationalize how σ-electron delocalization/donation and π-electron negative hyperconjugation together stabilize the formally vacant σ orbital and the filled π orbital at the carbene center. In contrast to traditional carbene counterparts this carbene can undergo synthetic transformations with both a Lewis base and a silver salt, producing a Lewis acid/base adduct and a silver π-complex, respectively. Exhibiting ambiphilic reactivity, it can also form a ketenimine through reaction with an isocyanide.

Crystal structure validation of verinurad via proton-detected ultra-fast MAS NMR and machine learning.

The recent development of ultra-fast magic-angle spinning (MAS) (>100 kHz) provides new opportunities for structural characterization in solids. Here, we use NMR crystallography to validate the structure of verinurad, a microcrystalline active pharmaceutical ingredient. To do this, we take advantage of 1H resolution improvement at ultra-fast MAS and use solely 1H-detected experiments and machine learning methods to assign all the experimental proton and carbon chemical shifts. This framework provides a new tool for elucidating chemical information from crystalline samples with limited sample volume and yields remarkably faster acquisition times compared to 13C-detected experiments, without the need to employ dynamic nuclear polarization.

Supramolecular structure of bis(1-methyl-1,3,5,7-tetraazatricyclo[3.3.1.13,7]decan-1-ium)2,5-dicarboxybenzene-1,4-dicarboxylate: Synthesis, spectral, structural and third-order nonlinear optical properties

Single crystals of bis(1-methyl-1,3,5,7-tetraazatricyclo[3.3.1.13,7]decan-1-ium)2,5-dicarboxybenzene-1,4-dicarboxylate (I) were grown from an aqueous solution containing benzene-1,2,4,5-tetracarboxylic acid (BTCA) and hexamethylenetetramine (HMT) (1:4) under mild hydrothermal conditions. It was characterized by IR, 1H, 13C NMR, mass, DRS, PL, TG-DTA, powder and single crystal XRD. The characteristic peaks in HMT cation CN stretching mode appear at 1018 cm−1. 13C NMR shows the carboxylic acid carbon chemical shift is observed at 167.64 ppm. The compound is thermally stable up to ∼176 °C. Single crystal X-ray crystallography shows it crystallizes in the triclinic system with centric space group Pī. Powder X-ray diffraction scrutinizes, experimental and simulated from single-crystal diffractogram data have been matched. The existence of intramolecular (O–H•••O) and intermolecular (C–H•••O, C–H•••N) interactions helps to achieve crystal cohesion. The third-order nonlinear optical susceptibility (χ(3)) for the compound is found to be 7.67 × 10−7 esu. Hirshfeld surface analysis exposes the molecular interactions and their relative contributions.

On the Efficiency of the Density Functional Theory (DFT)-Based Computational Protocol for 1H and 13C Nuclear Magnetic Resonance (NMR) Chemical Shifts of Natural Products: Studying the Accuracy of the pecS-n (n = 1, 2) Basis Sets.

The basis set issue has always been one of the most important factors of accuracy in the quantum chemical calculations of NMR chemical shifts. In a previous paper, we developed new pecS-n (n = 1, 2) basis sets purposed for the calculations of the NMR chemical shifts of the nuclei of the most popular NMR-active isotopes of 1-2 row elements and successfully approbated these on the DFT calculations of chemical shifts in a limited series of small molecules. In this paper, we demonstrate the performance of the pecS-n (n = 1, 2) basis sets on the calculations of as much as 713 1H and 767 13C chemical shifts of 23 biologically active natural products with complicated stereochemical structures, carried out using the GIAO-DFT(PBE0) approach. We also proposed new alternative contraction schemes for our basis sets characterized by less contraction depth of the p-shell. New contraction coefficients have been optimized with the property-energy consistent (PEC) method. The accuracies of the pecS-n (n = 1, 2) basis sets of both the original and newly contracted forms were assessed on massive benchmark calculations of proton and carbon chemical shifts of a vast variety of natural products. It was found that less contracted pecS-n (n = 1, 2) basis sets provide no noticeable improvement in accuracy. These calculations represent the most austere test of our basis sets as applied to routine calculations of the NMR chemical shifts of real-life compounds.

Cyclic Tetrapeptide Natural Product Asperterrestide A: Total Synthesis and Structural Revision

We have studied for the total synthesis of asperterrestide A, which is a cyclic tetrapeptide natural product reported to be composed of D-alanine, anthranilic acid, (2R,3S)-3-hydroxy-N-methylphenylalanine, and D-isoleucine or D-allo-isoleucine. We initially performed the total synthesis of the reported structure of asperterrestide A via solid-phase peptide synthesis and macrocyclization in solution. However, the spectral data of the synthetic (9R,25R)-derivative did not match those of the natural product. Then, we considered the true structure should be the (9S,25S)-stereoisomer because all NOE correlations predicted from its three-dimensional structures obtained by theoretical calculations were consistent with those observed in the natural product. Thus, the (9S,25S)-stereoisomer was synthesized through solution-phase synthesis because N-acylation of a polymer-supported (2S,3S)-3-hydroxy-N-methylphenylalanine derivative resulted in low yield. The (9S,25S)-stereoisomer was successfully synthesized and was found to be identical to the natural product. Therefore, the stereochemical configuration of asperterrestide A was corrected from (9R,25R) to (9S,25S). We also tested whether the DFT calculation of carbon chemical shifts can discriminate stereoisomers of cyclic tetrapeptides. After conformational analysis of four possible stereoisomers of asperterrestide A, Boltzmann-weighted carbon chemical shifts based on DFT calculations using Spartan’20 revealed a DP4 accuracy of 96%, which is sufficient to determine the stereochemical configuration among the stereoisomers. In addition, three 9-deoxy derivatives were synthesized and the cell growth inhibitory activity of the five synthetic compounds against human cancer cells (U937, MOLT-4, and A549) was evaluated. The results showed that the (9S,25S)-stereoisomer is as potent as asperterrestide A, whereas the (9R,25R)-derivative is not. The (9S,25S)-3-deoxy analogs were found to be equipotent to the natural product although the activity of the (9S,25R)-deoxy analog was lost.

Tetrahedral angles of six membered ring calculated from NMR data with 3-sphere approach

Hypersphere equations enable calculation tetrahedral angles φCn[deg] of six membered ring from carbon chemical shift δCn[deg]. The tetrahedral angles calculated directly from eq. 2a,b are confirmed by the dihedral angles found in close relationship on the five sets unit (Ci and Ti, i = 1-5, C, T = U or S) having ϕ2X, ϕ2Y equal with θZ1, θZ2 were Z is A or B and X, Y are D, E or F,G, angle of seven sets unit, or on two units with six sets. A method which is expected in case of six membered ring to ensure calculation of the tetrahedral angles for all conformations, chair – boat – skew.

Relationship between tetrahedral and dihedral on hypersphere coordinates

The wave character of the NMR data (chemical shift ΔδCn[ppm] – vicinal coupling constant 3JHH[Hz]) enable calculation the tandem dihedral-vicinal or tetrahedral-internal angles with 3-sphere approach. Golden ratio, invers of Fibonacci number, and manifold inversion torus to Dupin cyclide under 3-sphere units ensure the calculation of the tetrahedral angles of five membered ring in opposite with dihedral angles sin versus tan functions. The transformation from space/time to space under electric and magnetic rule gives dodecahedron and icosahedron values for calculation tetrahedral angles from polyhedron and hypersphere equations. Tetrahedral angles of five membered ring can be calculated from carbon chemical shift ΔδCn[ppm] with Java Script program and hypersphere equations.

Hypersphere and Antiviral Activity of Three Alkyl Chain Iminocyclitols with D and L Ribitol Stereochemistry

<I>N</I>-Alkyl-C₁-dialkyl chains iminocyclitols with D or L-ribitol stereochemistry are synthesized with high diastereoselectivity after Grignard reagents addition to <I>N</I>-quaternary pyrrolines salts, and tested for antiviral activity in bovine viral diarrhea virus (BVDV), surrogate for hepatitis C virus (HCV). Dihedral angles are calculated from carbon chemical shift (δ_Cn[ppm]) with 3-sphere method without building units. 3-Sphere, a hypersphere in 4D, under Hopf fibration and Lie algebra mathematics theories enable calculation of the dihedral angles from the NMR data (vicinal coupling constant ³<I>J</I>_HnHn+1[Hz], chemical shift δ_Cn[ppm]). Instead of 3D manifold equations on seven sets unit or six sets units are proposed equations between 4D – 2D, in function of the curvature. The relationship between the antiviral activity and the iminocyclitol structure reveals that monoalkyl chain, <I>N</I>-n-C₁-dodecyl β-L-ribitol trifloroacetate salt 30 (IC₅₀ 1.5 uM) has higher antiviral activity in tangential space, relative to three alkyl chain, <I>N</I>-Methyl-C₁-butil, nonyl-L-ribitol. HCl 26 (IC₅₀ < 2 uM) with torus and Dupin cyclide coordinate, both with coordinates in 2D. Three alkyl chain isopropylidene protected pyrrolidine 25 has in 4D with all equations for calculation of the dihedral angles, and in protected pyrroline 19b double bond moves the coordinates in 2D.

Configurational and Conformational Analysis of 5-deoxy-5-iodo-α,β-D-ribose with 3-Sphere Approach

Configurational and conformational analysis with 3-Sphere approach on selective iodination of α, β-methyl D-ribofuranose (2-α:2-β) with iodotriphenilphosphonium iodide complex [Ph₃P⁺I]I^- generated in situ, under RT, reflux, microwave and sonochemistry. Introduction of the unit and hypersphere trigonometric equations, under Hopf fibration and Lie algebra theories, on Lambert-Wu methods enable calculation of the dihedral angles from NMR data (¹³C chemical shift, vicinal coupling constant ³<I>J</I><SUB>HH</SUB>[Hz]) and the ratio of anomers. The conformation/configuration at anomeric position is <i>cis</i>: <i>trans</i> with <i>axial</i>:<i>axial</i> 3-α:3-β<i> </i>(³<I>J</I><SUB>H1H2</SUB> 3 or 4.5:0[Hz])<i> </i>or <i>equatorial</i>:<i>axial</i> 3-α:3-β (³<I>J</I><SUB>H1H2</SUB> 6 or 4.5:0[Hz]) as state based on dihedral angles θ<SUB>H1H2</SUB>[deg], recorded carbon chemical shift δ_Cn[deg] and VISION molecular models. The conformation of 3-β anomer is ³E, and in case of 3-α anomer ₃E on Altona’s map, the last having the succession of sign (+, -, -) with θ<SUB>H3H4</SUB>^α <i>trans-ee</i>, or alternatively ³₂T conformation having the succession of sign (-, +, -) with θ<SUB>H3H4</SUB>^α <i>trans-aa</i>. An equilibrium between ₃E^α and ³₂T^α was confirmed by ³<I>J</I><SUB>H1H2</SUB> of 4.5[Hz], <i>i.e.</i> negative θ<SUB>H1H2</SUB>^α with ³₂T and <i>equatorial</i> OCH₃, or positive θ<SUB>H1H2</SUB>^α with ₃E and axial OCH₃. The APT experiment (attached proton test) demonstrated the formation of tetrahydro 2H-pyran-2-ol as side product after selective iodination of methyl 5-deoxy-<i>β</i>-D-ribofuranoside 2-β.

Determination of the molecular structure and spectroscopic properties of capsaicin

In this study, the ground state molecular structure and spectroscopic features of cis- and trans-forms of capsaicin were investigated using DFT (B3LYP) invoking 6–311++G(d,p) basis set. The optimized geometry of capsaicin was determined for the isolated molecule in a vacuum, and then the vibrational spectra –IR and Raman-were obtained, and the assignments of fundamental vibrational modes were done. By applying the GIAO method, proton and carbon chemical shifts were computed for the gas and solvated phases. Besides using the TD-DFT, the Hirshfeld surface and Molecular Electrostatic Potential surfaces were obtained and evaluated to understand the electronic properties. The Total and partial density of state (TDOS and PDOS) spectra were also examined. All obtained computational results were compared with the previously reported experimental data. A high accuracy was obtained for the ground state geometrical structure, and thus, the vibrational frequencies especially lie on the finger print region are predicted also with a high correlation. Similarly, the optimization of chemical shift values calculated by considering solvent effects with experimental data were found as high R2 values of 0.9953 and 0.9455 for C and H atoms, respectively. This comparison shows that the DFT method precisely predicts capsaicin's molecular and spectroscopic characteristics.

Benchmarking computational chemistry approaches on iminodiacetic acid

In the present study, theoretical harmonic vibrational frequencies (IR and Raman), carbon and proton NMR chemical shifts, geometric parameters, atomic charges (only for heteroatoms), reactivity indices (eLUMO, eHOMO, electronegativity, and hardness), and thermodynamical data (inner energy, enthalpy, Gibbs free energy, and entropy) of iminodiacetic acid (IDA) molecule have been investigated. We utilized ORCA software for B3LYP and HF (combined with Pople and Karlsruhe basis sets) calculations and MOPAC2016 software for semi-empirical calculations (AM1, PM3, and PM6). Theoretical vibrational frequencies and carbon and proton NMR chemical shifts have been compared with the corresponding experimental data. Although there was a strong correlation between the experimental and computational vibrational frequencies at low frequencies (<2200 cm−1), the computational predictions of vibrational frequencies were unsuccessful at high frequencies (>2200 cm−1). Distinctly, the studied computational approaches appeared to perform better in the prediction of carbon and proton NMR chemical shifts. Theoretical vibrational frequencies were also compared to each other to understand the impact of method choice (HF vs B3LYP D3 vs semi-empirical methods), dispersion correction (B3LYP D3 vs B3LYP), water solvation (SMD supplemented vs non-supplemented calculations), the family of basis set (Pople vs Karlsruhe basis sets), numbers of zeta (double vs triple zeta), polarization function (polarized vs nonpolarized basis sets), and diffusion function (diffusion supplemented vs non-supplemented basis sets). Moreover, geometric parameters, heteroatom charges, reactivity indices, and thermodynamical data produced by distinct computational approaches, as well, were compared to each other. Based on these comparisons, we detected critical factors (such as water solvation) acting on the computation of geometries, energies, and charges.

Theoretical study on the origins of sildenafil tautomers’ relative stability

Abstract Tautomers of sildenafil (5-{2-Ethoxy-5-[(4-methylpiperazin-1-yl)sulfonyl]phenyl}-1-methyl-3-propyl-1,6-dihydro-7H-pyrazolo[4,3-d]pyrimidin-7-one), a drug commonly used for treating the erectile dysfunction and pulmonary arterial hypertension were studied computationally at the DFT (B3LYP/6-311++G**) level. Four possible structures of sildenafil tautomers structures were considered. The geometries and chemical shifts of carbon and nitrogen nuclei were calculated and compared with available experimental data. The theoretical calculations proved to be consistent with experimental data and indicate the same lowest energy sildenafil structure. The energies of the all considered sildenafil tautomers were determined and ranked according to their energy values. This article presents calculations of several properties (aromaticity, atomic charges, atomic energies, intramolecular hydrogen bonding) and discusses their influence on the relative energies of sildenafil tautomers.

Structure Revision of the Sesquiterpene Nordine Based on NMR Spectroscopic Analysis and X-ray Crystallography.

Nordine was reported to be an unusual humulene-type macrocyclic sesquiterpenoid that contains an ether-bridged bicyclic ring between C-10 and C-6 with a hydroxy group at position 2. Here, we report the structure revision of nordine based on incongruities found for carbon chemical shifts in the originally proposed structure, in addition to formation of a diacetylated derivative. As expected, a single-crystal X-ray diffraction analysis unambiguously confirmed our proposal that the nordine (1) structure contains an ether-bridged bicyclic ring between C-10 and C-7 and hydroxy groups at C-2 and C-6. Furthermore, the absolute configuration was determined by ECD spectroscopic analysis.

Hydrogen Bonding Directed Reversal of 13C NMR Chemical Shielding

AbstractThe deshielding or downfield 13C NMR chemical shift of amide carbonyl carbon upon H‐bonding is a widely observed phenomenon. This downfield shift is commonly used as a spectroscopic ruler for H‐bonding. However, the very first observation of an upfield 13C NMR of thiocarbonyl carbon in thioamides upon H‐bonding encouraged us to explore the physical origin of the reversal of 13C NMR chemical shielding. Careful NMR analysis shows that sulfur and selenium‐centered H‐bonds (S/SeCHBs) induce a shielding effect on the 13CC=S(Se) while changing from amides to thioamides or selenoamides. In addition, natural chemical shielding (NCS) analysis shows that the σ11 and σ22 components of the isotropic shielding tensor (σ) have a crucial role in this unusual shielding.

Hydrogen Bonding Directed Reversal of 13 C NMR Chemical Shielding.

The deshielding or downfield 13 C NMR chemical shift of amide carbonyl carbon upon H-bonding is a widely observed phenomenon. This downfield shift is commonly used as a spectroscopic ruler for H-bonding. However, the very first observation of an upfield 13 C NMR of thiocarbonyl carbon in thioamides upon H-bonding encouraged us to explore the physical origin of the reversal of 13 C NMR chemical shielding. Careful NMR analysis shows that sulfur and selenium-centered H-bonds (S/SeCHBs) induce a shielding effect on the 13 CC=S(Se) while changing from amides to thioamides or selenoamides. In addition, natural chemical shielding (NCS) analysis shows that the σ11 and σ22 components of the isotropic shielding tensor (σ) have a crucial role in this unusual shielding.