Ring-current models from the differential Biot-Savart law

The differential Biot-Savart law provides simple models for the pi ring currents induced in diatropic and paratropic planar conjugated molecules by a perpendicular magnetic field. The model predictions are confirmed by ab initio maps of nuclear magnetic shielding density. The effects on the protons and on the ring carbon atoms from the closest and furthest segments of the current loop are easily interpreted. [structure: see text]     

Understanding the ring current effects on magnetic shielding of hydrogen and carbon nuclei in naphthalene and anthracene

The local response to an external magnetic field normal to the molecular plane of naphthalene and anthracene was investigated via current density and magnetic shielding density maps. The Biot-Savart law shows that the deshielding caused by pi-ring currents in naphthalene is stronger for alpha- than for beta-protons due to geometrical factors. The shielding tensor of the carbon nuclei in both molecules is strongly anisotropic and its out-of-plane component determines the up-field chemical shift of (13)C in nuclear magnetic resonance spectra. The pi-ring currents flowing beyond the C-skeleton in front of a probe carbon nucleus, and on remote parts of the molecular perimeter, yield positive contributions to the out-of-plane component of carbon shielding as big as approximately 10-15% of the total values. Near Hartree-Fock estimates of magnetizability and magnetic shielding at the nuclei fully consistent with the current model are reported.     

Topology of magnetic-field induced electron current density in the cubane molecule

A spatial model of the electronic current density induced in the cubane molecule by applying an external magnetic-field has been constructed employing quantum mechanical methods at the Hartree-Fock level of accuracy. The topological features of the current density vector field are described via a stagnation graph that shows the isolated points and the lines at which the current vanishes. Shielding density maps based on the differential Biot-Savart law, along with a collection of current density maps, explain magnetic shielding at hydrogen and carbon nuclei, and virtual shielding at ring and cage centers.     

Spatial ring current model for the prismane molecule

Spatial models of magnetic-field induced electronic ring currents have been constructed for the prismane molecule via stagnation graphs and current density maps. These tools provide an insight into the complicated phenomenology resulting from competition of diatropic and paratropic regimes that determine the magnitude of various components of magnetic susceptibility and magnetic shielding of hydrogen and carbon nuclei. Shielding density maps show that the differential Biot-Savart law, along with an atlas of the current density field, explains magnetic shielding at hydrogen and carbon nuclei and virtual shielding at ring and cage centers.     

Assessment of sigma-diatropicity of the cyclopropane molecule

Spatial models of the current density field induced in the cyclopropane molecule by stationary, homogeneous magnetic fields, parallel to either the C3 or the C2 symmetry axis, have been constructed. A compact, abridged representation of the models is given via stagnation graphs that convey essential information. Maps of streamlines and moduli are also reported to complete current models that have proven useful to rationalize magnetic tensor properties, that is, magnetizability, 1H and 13C nuclear shieldings, and magnetic shielding along the C3 symmetry axis. Plots of Biot-Savart magnetic shielding density combined with current density visualization yield an accurate, detailed account of the shielding mechanisms. The magnetropicity of the system described by the current density model is fully consistent with the magnitude of magnetic tensors calculated at near Hartree-Fock level. In a field perpendicular to the molecular plane, cyclopropane sustains a diatropic sigma-ring current with the following peculiar features: (i) it follows the molecular periphery rather than the CC framework; (ii) it bifurcates in the proximity of the methylene moieties flowing along the CH bonds, both above and below the sigma(h) plane; (iii) it has an effect on the values of response properties, although it is not as large as expected from naive arguments (e.g., the center-of-mass value of the magnetic shielding constant is dominated by in-plane components rather than the out-of-plane component, which is in contrast to pi-aromatic systems such as benzene); (iv) it has a negligible effect on the strong anisotropy of carbon magnetic shielding, which is shown to arise from local currents. No evidence for strong diatropism, and therefore sigma-aromaticity of the cyclopropane molecule, was found on the magnetic criterion.     

The validity of Musher's model for the magnetic properties of aromatic molecules

Plots of proton magnetic shielding density in the benzene molecule, obtained via accurate coupled Hartree-Fock calculations, are reported. They unequivocally show that proton deshielding is due to local effects arising in the adjacent carbon atom and C H bond. Therefore downfield chemical shifts observed in proton magnetic resonance spectroscopy can be entirely explained in terms of magnetic anisotropy of the carbon environment. This shows the unphysical character of the ring current model and the reliability of Musher's model.     

Ring currents in a proposed system containing planar hexacoordinate carbon, CB(2-)(6)

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.     

Sigma and pi contributions to the induced magnetic field: indicators for the mobility of electrons in molecules

The authors discuss the role of the sigma and pi contributions to the induced magnetic field for simple hydrocarbons containing a double or a triple bond, as well as for benzene and cyclobutadiene. While the magnetic field induced by the sigma electrons is short-ranged, the pi system is responsible for the formation of long-range cones. These cones influence the chemical shift of atoms by additional shielding (for aromatic) or deshielding (for antiaromatic molecules) contributions. While the hydrogen atoms of benzene are found to lie within the deshielded region of the magnetic field induced by the pi electrons, they are shielded by the total induced magnetic field. The induced magnetic field of the pi electrons support Pople's model on the basis of first-principles calculations.     

Inconsistency of the ring-current model for the cyclopropenyl cation

We present results of a quantum-mechanical calculation of electron current density, magnetic susceptibility and proton magnetic shielding in the cyclopropenyl cation, reflecting on the ring-current model. The current density induced in and out of the molecular plane by a perpendicular magnetic field is plotted, showing the existence of localized distributions and paramagnetic circulations around the centre of the molecule.     

Diatropicity of tetraazanaphthalenes

Tetraazanaphthalenes are diatropic molecules, whose magnetic response to a magnetic field perpendicular to the molecular plane closely resembles that of naphthalene. The out-of-plane component of the magnetic susceptibility tensor and its strong anisotropy can be used as quantifiers of magnetic aromaticity. Maps showing streamlines and modulus of the current density field provide clear evidence for diatropicity of these systems. They also explain the strong anisotropy of carbon and nitrogen magnetic shielding, which is determined by the big out-of-plane component of the nuclear shielding tensor. The electronic ring currents observed in the map deshield the nuclei of ring hydrogens by enforcing the local magnetic field and diminishing the out-of-plane component of proton shielding.     

The ring current model of the pentaprismane molecule

Three-dimensional models of the quantum-mechanical current density J(B) , induced in the electron cloud of the C(10)H(10) pentaprismane molecule by a magnetic field B applied along the C(5) (a C(2)) symmetry axis, orthogonal to the pentagonal (a rectangular) face, and denoted by B(‖) (B(⊥)), have been constructed. Predictions of near Hartree-Fock quality are reported for the diagonal components of magnetic tensors, magnetizability (ξ), nuclear shielding of carbon (σ(C)) and hydrogen (σ(H)), and virtual shielding at the center of mass (σ(CM)). The complicated spatial features of the induced electronic current-density field have been rationalized and compactly described via stagnation graphs that elucidate the details of its topological structure. A representation of J(B) is obtained by three-dimensional perspective plots and by planar maps visualizing phase portraits of electron flow in a series of molecular domains. Both streamline J(B) /|J(B) | and modulus |J(B) | are analyzed. These graphic tools illustrate the competition between diatropic and paratropic regimes which determine the magnitude of various components of magnetizability and magnetic shielding of hydrogen and carbon nuclei. Shielding density maps show that the differential Biot-Savart law explains magnetic shielding at hydrogen and carbon nuclei, and virtual shielding at ring and cage centers. Similarities and/or contrasting ring current effects on magnetotropicity are discussed by a comparison with triprismane C(6)H(6) and cubane C(8)H(8) .     

The leap-frog effect of ring currents in benzene

Symmetry arguments show that the ring-current model proposed by Pauling, Lonsdale, and London to explain the enhanced diamagnetism of benzene is flawed by an intrinsic drawback. The minimal basis set of six atomic 2p orbitals taken into account to develop such a model is inherently insufficient to predict a paramagnetic contribution to the perpendicular component of magnetic susceptibility in planar ring systems such as benzene. Analogous considerations can be made for the hypothetical H(6) cyclic molecule. A model allowing for extended basis sets is necessary to rationalize the magnetism of aromatics. According to high-quality coupled Hartree-Fock calculations, the trajectories of the current density vector field induced by a magnetic field perpendicular to the skeletal plane of benzene in the pi electrons are noticeably different from those typical of a Larmor diamagnetic circulation, in that (i) significant deformation of the orbits from circular to hexagonal symmetry occurs, which is responsible for a paramagnetic contribution of pi electrons to the out-of-plane component of susceptibility, and (ii) a sizable component of the pi current density vector parallel to the inducing field is predicted. This causes a waving motion of pi electrons; streamlines are characterized by a "leap-frog effect".     

Beyond NICS: estimation of the magnetotropicity of inorganic unsaturated planar rings

A simple classical model of magnetic-field induced electron flow is used to evaluate the ring current strength for a few inorganic monocyclic compounds: B(3)H(3)N(3), B(3)H(3)O(3), P(6), N(6), Si(6)H(6), N, Al and H(6). It is shown that, for these neutral and charged systems, sustaining delocalized electron currents in the presence of a magnetic field B(ext) orthogonal to the σ(h) plane, the out-of-plane component of the nuclear magnetic shielding along the central axis is connected to the out-of-plane magnetizability by a simple equation, involving the radius of an average loop of current. A novel estimate of this effective radius is provided. Reliable ring current susceptibilities (that is, current strengths) can be evaluated by a simple relationship, using the out-of-plane components of nuclear shielding and magnetizability tensors. The accuracy of the current susceptibilities calculated by the classical model is established by comparison with corresponding ab initio estimates obtained by integrating the quantum mechanical current-density vector field. The out-of-plane components of nuclear shielding and magnetizability are both strongly biased by the molecular geometry. Their combined use to estimate the ring current susceptibility offers a quantifier of magnetotropicity more reliable than (i) the ξ(∥) out-of-plane component of magnetizability, (ii) the σ(∥)(CM) out-of-plane component of the magnetic shielding at the center of mass, widely reported as NICS(∥)(0) = -σ(∥)(CM). The inadequacy of these commonly adopted magnetotropicity measures is demonstrated by comparing a set of related molecules, C(6)H(6) and Si(6)H(6), N(6) and P(6).     

Mechanism of the electronic stabilization of the 3MR and divalent carbon of bis(diisopropylamino)cyclopropenylidene

Analysis of the topology of the electron density of bis(dimethylamino)cyclopropenylidene as a model of the recently synthesized, stable bis(diisopropylamino)cyclopropenylidene with the quantum theory of atoms in molecules is used to investigate the stabilizing electronic effects at the reactive carbene site by amino substitution. This work demonstrates that the plane perpendicular lone pairs of nitrogen utilize in-plane sigma-aromaticity as a conduit to delocalize charge to the carbene carbon C2, where it is transferred preferentially back into the pi-plane at the site through sigma-pi polarization. C2 is thus stabilized relative to the parent cyclopropenylidene, c-C(3)H(2), by a very different mechanism than that suggested in the orbital view of n(pi)(N) and pi(C=C) conjugation and n(pi)(N) --> p(pi)*(C2) hyperconjugation. Validation of this premise is also found in properties of asymmetric atomic quadrupole tensors, bond path ellipticities, and diamagnetic/paramagnetic components of NMR shielding tensors.     

Spatial ring current model of the [2.2]paracyclophane molecule

A representation of the current density induced in the [2.2]paracyclophane molecule by a homogeneous magnetic field parallel to the line joining the centers of the phenylene rings is given in compact form by a stagnation graph that conveys essential information. Analogous graphs were obtained for two perpendicular directions. Plots of streamlines are also reported to complete a ring current model that has been proved useful to understand the magnetropicity of the system. Stagnation graphs, maps of streamlines and moduli of the current density, and plots of Biot-Savart magnetic shielding density provide a basic tool kit for rationalizing magnetic response of complex systems.     

Control of the diatropic pi ring current in strained benzenes: effects of annelation with cyclopropa,cyclobuta, and cyclobutadieno clamping groups

Direct visualization of the pi current density maps of highly strained annelated benzenes containing cyclopropa, cyclobuta, and cyclobutadieno clamps, alone and in combination, using a reliable distributed-origin, coupled Hartree-Fock method, shows the robustness of the classical benzene diatropic pi ring current. When only saturated clamps are used, the benzene ring current is essentially unchanged. In contrast, annelation with one or more cyclobutadieno clamps disrupts the benzene ring current. Analysis of orbital contributions to the current density maps gives a unified account of these observations in terms of the nature of the HOMO-LUMO transition.     

填充碳纳米管/石墨的复合型电磁波屏蔽膜

介绍一种填充碳纳米管/石墨的复合型电磁波屏蔽膜的组成、制备及其耐老化性能,实验发现：当碳纳米管/石墨的配比为1/7～1/2、有机聚合物/导电填料的配比为29.6/70.4～32.4/67.6时,该屏蔽膜具有最佳的电性能、屏蔽性能和加工性能,且在一定条件下具有负的温度系数。用多层结构模型讨论了该屏蔽膜的导电性,并与铜、镍蒸发膜的屏蔽特性进行了比较。     

Ring currents in the porphyrins: pi shielding, delocalisation pathways and the central cation

It is shown that the ipsocentric orbital-based model explains how the charge of the central cation drives the delocalisation pathway in metalloporphyrins. A positive charge +Ze at the centre of the porphin ring gives rise to a two-way radial transfer of charge within the pi structure of the porphin macrocycle. This manifests itself in a change of pathway of the global pi current, as Z increases from Z = 0, from an inner- through a bifurcated- to an outer-pathway. Changes of pathway can be interpreted in terms of a specific pi shielding effect whereby electrons in high-lying pi orbitals are screened from the central charge by the electrons in lower-lying orbitals of the same symmetry. These changes in pi structure are essentially independent of accompanying changes in the sigma structure.     

Counterintuitive deshielding on the 13C NMR chemical shift for the trifluoromethyl anion

The trifluoromethyl anion (CF₃⁻) displays ¹³C NMR chemical shift (175.0 ppm) surprisingly larger than neutral (CHF₃, 122.2 ppm) and cation (CF₃⁺, 150.7 ppm) compounds. This unexpected deshielding effect for a carbanion is investigated by density functional theory calculations and decomposition analyses of the ¹³C shielding tensor into localized molecular orbital contributions. The present work determines the shielding mechanisms involved in the observed behaviour of the fluorinated anion species, shedding light on the experimental NMR data and demystify the classical correlation between electron density and NMR chemical shift. The presence of fluorine atoms induces the carbon lone pair to create a paramagnetic shielding on the carbon nucleus.