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A method for the calculation of divergenceless, magnetically induced quantum mechanical current densities in molecules that approximates the exact current is presented. This was achieved by adding to the calculated conventional current density, i.e., a current that typically has a non-zero divergence, a corrective term that is the negative of the irrotational field of its Helmholtz decomposition. The solenoidal field of the decomposition is the divergence-free current density, which is still an approximation of the exact current but which now satisfies the continuity requirement regardless of the quality of the basis set. Based on calculations performed on several simple molecules (LiH, H2O, benzene, and zethrene), adopting different kinds of low-level theoretical approaches, clear improvements are observed in the correspondence of vortices, sources, and sinks for which the conventional current density shows a lack of continuity. A little improvement is also observed for the calculated diagonal components of the magnetizability tensor., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Quantum chemical topology addresses the study of the chemical structure by applying the tools of differential topology to scalar and vector fields obtained by quantum mechanics. Here, the magnetically induced isotropically averaged Lorentz force density was computed and topologically analyzed for 11 small molecules. Critical points (attractors, repellers, and saddles) were determined and trajectories connecting the attractors computed. It is shown that kinds and numbers of the critical points are to some extent transferable in similar molecules. CC bonds of different orders are endowed with critical points of different kinds close to their center. The sum of topological indices of the isolated critical points is influenced by the presence of repellers on the outer part of the molecules.

Some years ago, Jishan Wu reported the synthesis of 8MC and 10MC, two homologues of the cyclopenta-ring-fused oligo(m-phenylene) macrocycles mMC, each behaving as an annulene-within-an-annulene (AWA). This was a surprising result as the AWA behavior is rare. Both molecules have a partial polyradical character, enforced by the quest for restoring some aromatic character of benzene rings. However, that restoration brings back some coupling between the two annulenes. Indeed, we found that the geometry and the magnetically induced currents indicate that, while 8MC does have an AWA character, this is not the case of the larger 10MC. Limitations of the design strategy of AWA molecules should be taken into account in future attempts to prepare novel large coronenes., (© 2024 Wiley-VCH GmbH.)

A time-dependent method has been developed to solve the standard response equation for the calculation of dynamic molecular property densities, endowed with the characteristic of being origin-invariant, entirely in the atomic orbital basis at both HF and DFT level of theory. The method has been tuned in particular for the calculation of origin-independent electric dipole polarizability density and specific rotation power density. Some demonstrations are given for the hexabenzocoronene molecule and the Tröger's base., (© 2024 Wiley-VCH GmbH.)

Some planar and non-planar clarenes have been studied using maps of magnetically induced quantum-mechanical current density and tools from differential topology to assess their magnetic response in connection with recent results by Du and Wang. Bond current strengths have been computed to estimate quantitative measures. Isosurfaces of the divergence of induced Lorentz force density have been shown to provide useful additional criteria, especially in the case of non-planar clarenes., (© 2024 Wiley-VCH GmbH.)

The calculation of the origin-independent density of the dynamic electric dipole polarizability, previously presented for uncorrelated and density functional theory (DFT)-based methods, has been developed and implemented at the coupled cluster singles and doubles (CCSD) level of theory. A pointwise analysis of polarizability densities calculated for a number of molecules at Hartree-Fock (HF) and CCSD clearly shows that the electron correlation effect is much larger than one would argue considering the integrated dipole electric polarizability alone. Large error compensations occur during the integration process, which hide fairly large deviations mainly located in the internuclear regions. The same is observed when calculated CCSD and B3LYP polarizability densities are compared, with the remarkable feature that positive/negative deviations between CCSD and HF reverse sign, becoming negative/positive when comparing CCSD to B3LYP.

The interaction of a molecule with optical fields is customarily interpreted by means of induced time-dependent electric polarizabilities, magnetizabilities and mixed electric-magnetic polarizabilities. In general, these properties can be rationalized by integrals of density functions formulated in terms of induced charge and current densities. In this perspective, we focus on what has been done so far at the theoretical level, and on what can be expected to be unveiled from the topological study of suitable density functions, endowed with the fundamental requirement of origin invariance. Densities characterized by such a property can be integrated all over the configuration space to obtain electric dipole polarizability and optical rotatory power. Corresponding maps visualize domains mainly involved in the molecular response. The diagonal components of origin-independent density tensor functions that, on integration, yield corresponding electric dipole polarizability tensor of benzene, naphthalene, phenanthrene and ovalene, have been computed, confirming the ubiquitous presence of counter-polarization regions in the proximity of the atomic nuclei. They are associated with toroidal electron currents, induced by time derivative of the electric field of impinging radiation. Electron (de)localization in these systems is readily observed and estimated. The optical rotation density of the carbonyl chromophore is studied in detail. Its essential feature is the separation in quadrants of alternating sign of density about the CO bond. The presence of an extrachromophoric perturbation determines asymmetry in the extension of the quadrant distribution, thus causing optical rotation.

In the computation of molecular dynamic magnetizabilities and magnetic dipole moments, three different reference points are required: (i) origin of coordinate system, (ii) origin of vector potential A , and (iii) origin of multipole expansion. This study shows that methods relying on continuous translation of origin of the current density I B r ω t induced by optical magnetic fields provide an effective solution to the problem of choices (i) and (ii), in that they yield origin independent I B within the algebraic approximation, for any basis set. Frequency-dependent magnetizabilities are also invariant with respect to (iii), as a consequence of symmetry, for a number of molecular point groups. In molecules of lower symmetries, computed magnetizabilities depend on origin of the multipole expansion. Large basis set computations carried out for water, ammonia, methane, ethane, ethylene, boranylborane, and hydroxilamine, at the DFT level, have been reported to document these statements. A comparison is made for results obtained within the conventional common origin approach for static magnetic field. Sum rules for invariance of computed properties are discussed. Representations of streamlines and stagnation graphs of dynamical current density vector field induced in the water molecule by monochromatic waves of four frequencies are displayed., (© 2023 The Authors. Journal of Computational Chemistry published by Wiley Periodicals LLC.)

Cycloparaphenylenes (CPPs) and carbon nanobelts (CNBs) represent some of the most iconic cyclic molecular nanocarbons in recent chemistry owing to their unique properties derived from rigid, strained, and cyclic π-conjugated systems. In the last decade, the synthesis of various sizes of CPPs and CNBs has been achieved that allowed not only for investigating their size-dependent properties and strategically using such properties in various applications but also understanding the fundamental features of cyclic π-conjugated systems and molecular nanocarbons in general. Herein, we report on the synthesis, size-dependent properties, and paratropic belt currents of methylene-bridged [ n ]cycloparaphenylenes ([ n ]MCPP, n = 6, 8, 10). [8]MCPP and [10]MCPP were synthesized by the same strategy we developed for [6]MCPP synthesis. With readily available ethoxy-substituted pillar[8]arene and pillar[10]arene as precursors, [8]MCPP and [10]MCPP were successfully synthesized in three steps consisting of de-ethylation, triflation, and nickel-mediated aryl-aryl coupling. The structural and electronic properties of MCPPs were investigated by nuclear magnetic resonance analyses, absorption/fluorescence measurements, X-ray crystallographic analyses, and computational studies, revealing their interesting size-dependent properties. The differences in the size dependency between MCPPs and CPPs reflect the belt-form features of MCPPs, namely, methylene-bridging effects on MCPPs. Moreover, an interesting paratropic belt current along the MCPP backbone has been uncovered both experimentally and theoretically. The 1 H NMR chemical shifts of MCPPs confirmed the presence of a paratropic belt current, whose strength rapidly decreases with increasing nanobelt size.

The origin-independent magnetically induced CTOCD-GRRO and -GPRO (after continuous transformation of the origin of the current density-gradient of ρ and gradient of a power of ρ) current densities are shown to vary linearly with respect to their own defining α and β parameters. The same is reflected in the connected magnetic properties, in particular the magnetic shielding. This is exploited to find values for α and β that, using small basis sets, provide isotropic nuclear magnetic shieldings matching an accurate prediction, chosen as the complete basis set limit. An application to the 20 naturally occurring amino acids shows that different nuclei require different values of the parameters, which have been determined at the BHandHLYP/6-31+G(d,p) level with or without consideration of diversified chemical environments. Using CTOCD-GRRO and -GPRO methods, equipped with the optimized parameters at this low-cost level of calculation, 1 H, 13 C, 15 N, and 17 O magnetic shielding constants in glutathione, ophthalmic acid, and thyrotropin-releasing hormone are predicted with nearly the same accuracy as that of much more expensive calculations.

The JAP model (after Jirásek, Anderson, and Peeks) to retrieve global current strengths from experimental 1 H chemical shifts has been tested with DFT computations. Both global and local tropicities are correctly predicted in most cases and the quantitative agreement is overall fair. An extension of the model is found to give improvement in an exemplary critical case, where the global delocalized current is negligible and the current density map is dominated by local currents., (© 2022 The Authors. ChemPhysChem published by Wiley-VCH GmbH.)

A novel α-tetrazole-substituted 1,1'-binaphthylazepine chiral catalyst has been synthesized and its absolute configuration has been determined by DFT computational analysis of the vibrational circular dichroism (VCD) spectrum of its precursor. The VCD analysis, carried out through the model averaging method, allowed to assign the absolute configuration of a benzylic stereocenter in the presence of a chiral binaphthyl moiety. The 1,1'-binaphthylazepine tetrazole and the nitrile its immediate synthetic precursor, have been preliminarily tested as chiral organocatalysts in the asymmetric intramolecular oxa-Michael cyclization of 2-hydroxy chalcones for the synthesis of chiral flavanones obtaining low enantioselectivity.

The origin-independent current density induced by a perpendicular magnetic field in the infinitene molecule has been calculated, confirming the recently presented result by Orozco-Ic et al. ( Phys. Chem. Chem. Phys. 2022, 24, 6404-6409) of two disjointed global current pathways along the edges formed by 24 carbon atoms having the form of the infinity symbol. The current strength has been assessed along the C-C bonds forming the two separate circuits, whose particular shape provides a diamagnetic exaltation which is only 73% of the expected value for this aromatic molecule. Through space currents have been found along the bond paths determined by the electron density gradient, whose strength is 10% that of the aromatic benzene ring current. It is shown that the pair of high-field 1 H NMR experimental signals carry the signature of the two global currents, which are counterrotating inside the fjord regions with respect to the rim of the coronene subunits.

The electronic current density, induced in a molecule by the optical magnetic field associated with a frequency-dependent monochromatic plane wave, assumed to be spatially uniform within the electric quadrupole approximation, has been studied by using a theoretical method based on a continuous translation of its origin. The induced electronic current density vector field designated by this procedure, invariant of the origin for any point of the molecular domain, is obtained via a computational scheme, formally annihilating the diamagnetic contribution of the conventional common-origin approach based on perturbation theory. In a preliminary application of the theoretical methods outlined in the present work, the simple molecule of lithium hydride has been investigated. Particular attention has been paid to the structure of induced electronic current density for several values of the magnetic field frequency by investigating equilibrium points of four different types, organized in stagnation lines, which constitute its stagnation graph, i.e., a topological fingerprint of the vector field conveying complete information in the condensed form, to verify the fulfillment of fundamental requirements, e.g., the continuity equation and the Poincaré-Hopf theorem on spherical and toroidal surfaces.

The continuous search for metamaterials with special properties, suitable for new technological applications, is presently being driven by a preceding theoretical development, which took place after the introduction of new physical entities, anapole and a family of toroidal multipoles, having a border in common with those considered in the more familiar electric and magnetic multipole expansions. The related concept of toroidization, i.e., toroidal moment per unit volume, has been advocated in analogy to electric polarization and magnetization operated by electromagnetic fields and should be considered on the same footing regarding its relevance and practicality for understanding certain properties, e.g., ferrotoroidicity in condensed matter physics, and for rationalizing the behavior of charge-current distributions that neither radiate nor interact with external fields in classical and quantum electrodynamics. Toroidizability, i.e., the ability of sustaining toroidal moments, can also be defined by an analogy with electric polarizability and magnetizability. The present study shows that such a property is general and characterizes atoms and molecules and that the optical electric field of a light beam induces an oscillating anapole moment, i.e., the superposition of toroidal moment with an electric dipole moment. However, values of anapole polarizabilities induced by monochromatic light, estimated by time-dependent perturbation theory for rare gas atoms and a few molecules, are quite small and possibly hard to detect experimentally.