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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.)

Optical chirality sensing has gained significant attention in recent years. Within this field, the quest for stereodynamic chiroptical probes capable of detecting cryptochiral guests presents a formidable challenge. Macrocycles exhibiting planar chirality have emerged as promising candidates for amplifying the chirality of cryptochiral guests. In this study, we demonstrate that the formation of host-guest complexes between cryptochiral molecules and planar chiral prismarenes triggers electronic circular dichroism (ECD) signals via host-guest complexation-induced chirality amplification. The absolute configuration of the most stable chiral macrocyclic host-guest complex has been established by resorting to both exciton model and DFT computations. Furthermore, we demonstrated that this supramolecular chirality sensing system can be employed to determine the enantiomeric composition of scalemic mixtures by measuring the ECD bands intensity. The information described here opens the way for the use of prismarenes as stereodynamic probes for sensing of cryptochiral guests., (© 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.)

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH 3 radical and the superoctazethrene molecule are also illustrated.

New naphthocorrole ligands, display both the cavity size of corroles and the dianionic character of porphyrins. Nonaromatic and yet flaunting deceptively porphyrin-like optical spectra, they are readily accessible via a simple protocol.

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 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.)

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.

Enantiomorphic right- and left-handed polyproline type I helices in four cyclic dodecapeptoids with methoxyethyl and propargyl side chains are observed for the first time by single crystal X-ray diffraction. The peculiar absence of NH⋯OC hydrogen bonds in peptoids unveils the role of intramolecular backbone-to-backbone CO⋯CO interactions and CH⋯OC hydrogen bonds in the stabilization of the macrocycle conformation. Moreover, intramolecular backbone-side chain C5 CH⋯OC hydrogen bonds emerge as a stabilizing factor.

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.

1,4-Conjugate addition of ((chloromethyl)sulfonyl)benzenes to arylideneisoxazol-5-ones, followed by one-pot, N-selective trapping in the presence of electrophiles, was investigated. This strategy led to the synthesis of new, stable N-protected isoxazol-5-ones in good yields and high diastereolectivity. The study of the reactivity of obtained products in the presence of the Mo(CO) 6 /H 2 O system allowed the development of a cascade reaction leading to novel methyl ketones in high yields and unchanged dr bearing an uncommon chloromethinearylsulfonyl end group., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

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.

The properties of mixtures of two polysaccharides, arabinogalactan (AG) and hyaluronic acid (HA), were investigated in solution by the measurement of diffusion coefficients D of water protons by DOSY (Diffusion Ordered SpectroscopY), by the determination of viscosity and by the investigation of the affinity of a small molecule molecular probe versus AG/HA mixtures in the presence of bovine submaxillary mucin (BSM) by 1 HNMR spectroscopy. Enhanced mucoadhesive properties, decreased mobility of water and decreased viscosity were observed at the increase of AG/HA ratio and of total concentration of AG. This unusual combination of properties can lead to more effective and long-lasting hydration of certain tissues (inflamed skin, dry eye corneal surface, etc.) and can be useful in the preparation of new formulations of cosmetics and of drug release systems, with the advantage of reducing the viscosity of the solutions.

Cascade reactions of ortho -carbonyl-substituted benzonitriles with ((chloromethyl)sulfonyl)benzenes as pronucleophiles led to new isoindolin-1-ones with a tetrasubstituted C-3 position or to ( Z )-3-(sulfonyl-methylene)isoindolin-1-ones. The reactions start from readily available materials, are carried out under mild conditions, and do not require metal catalysis. Promoted only by the cheap and environmentally benign K 2 CO 3 as the base, up to six elemental steps can be combined in a single pot. Hence, a sequential one-pot cascade/β-elimination/alkylation furnished useful intermediates for the synthesis of aristolactam natural products. The observed selectivity and the mechanism were investigated by DFT studies.

The notion of the electric dipole polarizability density function of atoms and molecules has been considered. The current density induced by the time derivative of the electric field of monochromatic light allows for a new definition of the electric dipole polarizability density, which is translationally invariant. This translational invariance provides the physical meaning that was lacking in previous defined polarizability densities. The new polarizability density has been implemented at the TD-DFT level of theory. The origin independence has been proven in silico to hold regardless of the basis set size. Two emblematic molecules, i.e., CO and N 2 , which in many respects display similar electric response, have been studied in detail. The substantial differences, which have been highlighted in the topology of the parallel and perpendicular polarizability density tensor components of CO and N 2 , are grossly hidden by compensation, when integration is carried out to get the molecular properties.

Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way to test electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relationships were recast into absolute deviations from zero, which have been used to assess the performance of some popular DFT functionals. Extended TD-DFT calculations have been carried out for a pool of molecules chosen for this purpose, adopting a large basis set to ensure high quality results. A partial agreement with previous benchmarks is observed.

The electric dipole-magnetic dipole polarizability tensor κ', introduced to interpret the optical activity of chiral molecules, has been expressed in terms of a series of density functions kαβ', which can be integrated all over the three-dimensional space to evaluate components καβ' and trace καα'. A computational approach to kαβ', based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of kαβ' on the origin of the coordinate system has been investigated in connection with the corresponding change of καβ'. It is shown that only the trace kαα' of the density function defined via dynamic current density evaluated using the continuous translation of the origin of the coordinate system is invariant of the origin. Accordingly, this function is recommended as a tool that is quite useful for determining the molecular domains that determine optical activity to a major extent. A series of computations on the hydrogen peroxide molecule, for a number of different HO-OH dihedral angles, is shown to provide a pictorial documentation of the proposed method.

We present SYSMOIC, a program package for the calculation of the origin-independent current density induced at first order by an external magnetic field in planar and nonplanar molecular systems. Origin independence is obtained adopting the continuous transformation of the origin of the current density method, implemented at both density functional theory (DFT) and Hartree-Fock (HF) levels. Expansion coefficients for perturbed and unperturbed molecular orbitals, over basis sets containing up to m-type Gaussian functions, can be calculated by the package itself or obtained from a Gaussian calculation. A number of different functionalities presented so far in the literature that are connected to the induced current, such as current density maps for any orientation of the inducing magnetic field, net bond current strengths, stagnation graphs, magnetic shielding densities, vorticities, and anisotropies, are now made available all together in a single multiplatform package installation.

The proton NMR magnetic shieldings of the recently synthesized D 3d isomers of methylene-bridged [6]cycloparaphenylene (MB[6]CPP) and [12]cyclophenacene hide in themselves the effect of a global paratropic current around the nanobelts, which is induced by a magnetic field parallel to the main symmetry axis of the molecules. The effect is particularly pronounced for the methylene protons of MB[6]CPP, especially for those facing inside the nanobelt. The small experimental chemical shift difference of only 0.2 ppm is incompatible with the separation of the signals caused by the belt curvature, which, by itself, is calculated to be larger than 1 ppm, with both signals shifted upfield with respect to the position detected for the nanobelt. A careful dissection of the proton magnetic shielding in terms of molecular orbital contributions, has permitted a quantitative assessment of the genuine effect on each different proton caused by a substantial paratropic belt-current, which brings all the signals in nice agreement with the experimental spectra.