4-Component relativistic calculation of the magnetically induced current density in the group 15 heteroaromatic compounds
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Diamagnetism
Relativistic quantum chemistry
Ring current
Diamagnetism
Inductive coupling
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The electronic g-tensor calculations are carried out for various paramagnetic defects introduced into hydrogenated diamond nanocrystal C35H36, showing that such a system can be successfully used to model magnetic properties of nanodiamonds (NDs) with paramagnetic centers containing no vacancies. In addition, it is revealed that, depending on the geometric positions in ND, paramagnetic centers of the same type produce noticeable variations of the g-tensor values. A side-by-side comparison of the performance of effective nuclear charge and spin-orbit mean field (SOMF) approaches indicates that the latter is more sensitive to the quality of basis sets, especially concerning diffuse functions, the inclusion of which is found to be nonbeneficial. What is more, the SOMF method also exhibits a much more pronounced gauge-origin dependence. Compared to electronic charge centroid, spin centers (SCs) demonstrate a superior suitability as gauge origins, providing a better agreement with diamagnetic and paramagnetic contributions of g-tensor obtained employing gauge-including atomic orbitals (GIAOs). Therefore, SCs can be recommended for the g-tensor calculations of NDs whenever GIAOs are not available.
Diamagnetism
Magnetism
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A new formulation of the current within the London approximation allows the calculation of ring currents in topologically complex molecules. Application of this theory to C(60) demonstrates the existence of remarkable pi electron ring currents. Paramagnetic currents, in size comparable to the ones in benzene, flow within the pentagons, whereas weaker diamagnetic currents flow all around the C.(60) molecule. The overall vanishing ring-current magnetic susceptibility results from a cancellation of diamagnetic and paramagnetic contributions. The presence of ring currents significantly affects chemical shifts as measured in nuclear magnetic resonance experiments. In contrast to the magnetic susceptibility, which is a property of the molecule as a whole, chemical shifts are sensitive to the local magnetic field and the effect of ring currents does not vanish.
Diamagnetism
Ring current
Chemical shift
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Current-density maps at the coupled Hartree-Fock level calculated in the CTOCD (continuous transformation of origin of current density) approach demonstrate the magnetic response of the hypothetical planar hexacoordinate carbon species, CB(2-)(6). In contrast with the empty CB(2-)(6) framework, which supports paramagnetic currents, the carbon-containing species has a typical diamagnetic pi-ring current that circulates undisturbed by the central atom. In spite of the unconventional nature of the species, the properties of 6pi CB(2-)(6) and 4pi CB(2-)(6) can be rationalised with the same orbital model that accounts for the diamagnetic pi current of benzene and the paramagnetic pi current of planar cyclooctatetraene.
Diamagnetism
Hexacoordinate
Ring current
Cyclooctatetraene
Carbon fibers
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Diamagnetism
Ring current
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Diamagnetism
Ring current
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Diamagnetism
Ring current
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Magnetically induced current densities, calculated at the M06-2X/def2-TZVP level using the diamagnetic-zero version of the continuous transformation of origin of current density (CTOCD-DZ) method, were employed to study the aromaticity in Li3B2− and Li4B2. It was found that the Li3/Li4 rings in Li3B2− and Li4B2 remarkably resemble the monocyclic Li3+ and Li42+ clusters. Unlike the parent Li3+ and Li42+ systems that sustain negligibly weak global current density circulation, the Li3B2− and Li4B2 clusters exhibit a strong diatropic current density. The present work demonstrates how structural modifications introduced by the B2 unit can be used for modulating the current density in cyclic Li-based clusters.
Diamagnetism
Ring current
Spin density
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Diamagnetism
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We use the well-established functionals LDA, BLYP, BP86, BP91 and B3LYP as well as the more recent HCTH, PBE and PBE0 functionals to investigate the density functional theory (DFT) metal nuclear magnetic shieldings in ten transition-metal complexes ([Co(CN)6]3−, [Co(NH3)6]3+, Cr(CO)6, [CrO4]2−, Fe(CO)5 , Fe(C5H5)2, [MnO4]−, [Mn(CO)6]+, VOCl3, VF5). We also investigate the 13C and 17O ligand shielding parameters in three first-row transition-metal carbonyl complexes [Cr(CO)6 , Ni(CO)4 and Fe(CO)5] as well as the 17O shielding parameters in three first-row transition-metal oxo complexes ([CrO4]2−, [MnO4]−, FeO4). We apply Malkin's sum-over-states density functional perturbation theory (SOS-DFPT) to our own HCTH functional and discuss the effect of the level shift correction to the DFT orbital energies on the calculated metal and ligand shieldings. For the metal chemical shifts the hybrid functionals are superior in quality to the non-hybrid functionals. Amongst this latter group HCTH and LDA provide the least errors. The large discrepancy between hybrid and non-hybrid functional paramagnetic shieldings is rationalised in terms of differences in the magnitude of their matrix element terms and eigenvalue differences. Our analysis of the dominant paramagnetic shielding contributions from the occupied-virtual MO excitations indicates that the poor performance of the non-hybrid functionals originates from their underestimation of the numerator (b∣lα∣j)(j∣lAβrA−3∣b) term rather than any deficiency in their description of the eigenvalue differences εb–εj. The relative increase in the magnitude of εb–εj following inclusion of a fraction of exact Hartree-Fock exchange is less than the corresponding increase in the (b∣lα∣j)(j∣lAβrA−3∣b) term. The net effect is a significant increase in the paramagnetic shielding terms for hybrid functionals. For the metal carbonyls the GGA functional 13C and 17O shielding parameters are superior in quality compared to the non-hybrid functionals with HCTH providing the best agreement with experiment. For the metal-oxo complexes, the 17O shieldings produced by the hybrid and non-hybrid functionals were found to be too deshielded and too shielded respectively, where the latter lie closer to the experimental values.
Diamagnetism
Shielding effect
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