Charge delocalization and aromaticity of doubly reduced double-walled carbon nanohoops.

Cycloparaphenylenes (CPPs) exhibit selective host capabilities, featuring the ability to incorporate smaller CPPs to form double-walled host-guest complexes. Moreover, CPPs can also be stabilized by global aromaticity under twofold oxidation or reduction, involving electronic conjugation along with the overall structural backbone. Herein we explore the structural modifications, bonding, electron delocalization and magnetic properties of doubly reduced double-walled CPP complexes with DFT methods, in the isolated and aggregate [n + 5]CPP⊃[n]CPP2- (n = 5-8) species. Our results show that the hosts undergo structural, bonding and delocalization deformations towards quinoidal configurations and exhibit global long-ranged shielding cones similar to global aromatic free dianionic CPPs, accounting for charge delocalization on the outer nanohoops, whereas the guests preserve local aromatic benzenoid configurations, resulting in global and local aromatic circuits within the host-guest aggregate. This observation suggests that in multi-layered related species electronic delocalization will be retained at the outer structural surface. The aromaticity of the hosts is manifested in the strong upfield shifts of the guests 1H-NMR signals. Hence, CPP complexes can be extended to doubly reduced species stabilized by global host aromaticity expanding our understanding of doubled-walled nanotubes at the nanoscale regime.

Local and global aromaticity under rotation: analysis of two- and three-dimensional representative carbon nanostructures.

Nanoscaled 2D and 3D carbon structures with closed curved π-surfaces are of relevance in the development of desirable building units for materials science. Such species are able to sustain local and global aromatic circuits involving isolated regions or the overall structural backbone, respectively. Here we account for local and global aromaticity under rotation of representative two- and three-dimensional species involving para-connected and fused edge-sharing phenyl rings ([8]CPP, [10]CPP, CNB), and C60 fullerene at different charge states. Our results denote that nanoscaled 2D global aromatics mimic the behaviour of the most prototypical aromatic 6π-circuit, given by benzene, where the shielding cone properties vary along the rotation motion. In contrast, 3D spherical aromatics remain almost invariant under rotation, given the distinctive characteristics of such species, differing from 2D global aromatics. Dissection of orbital contributions reveals that π-orbitals are determinants for shifting from non-aromatic to spherical aromatic species. Under rotation, the variation of the anisotropic effect inherent to such nanoscaled structures is accounted for, which is relevant to rationalize variation in NMR signal shifts upon the formation of host-guest aggregates.

Core-electron contributions to the molecular magnetic response.

Orbital contributions to the magnetic response depend on the method used to compute them. Here, we show that dissecting nuclear magnetic shielding tensors using natural localized molecular orbitals (NLMOs) leads to anomalous core contributions. The arbitrariness of the assignment might significantly affect the interpretation of the magnetic response of nonplanar molecules such as C60 or [14]helicene and the assessment of their aromatic character. We solve this problem by computing the core- and σ-components of the induced magnetic field (and NICS) and the magnetically induced current density by removing the valence electrons (RVE). We estimate the core contributions to the magnetic response by performing calculations on the corresponding highly charged molecules, such as C6H630+ for benzene, using gauge-including atomic orbitals and canonical molecular orbitals (CMOs). The orbital contributions to nuclear magnetic shielding tensors are usually estimated by employing a natural chemical shielding (NCS) analysis in NLMO or CMO bases. The RVE approach shows that the core contribution to the magnetic response is small and localized at the nuclei, contrary to what NCS calculations suggest. This may lead to a completely incorrect interpretation of the magnetic σ-orbital response of nonplanar structures, which may play a major role in the overall magnetic shielding of the system. The RVE approach is thus a simple and inexpensive way to determine the magnetic response of the core- and σ-electrons.

Aromaticity of ortho and meta 8-Cycloparaphenylene and Their Dications: Induced Magnetic Field Analysis with Localized and Delocalized Orbitals in Strained Nanohoops.

Dications of cycloparaphenyles ([n]CPPs) are known to exhibit in-plane global aromaticity, contained in a nanobelt structure. Recently synthesized ortho and meta isomers of [n]CPPs break the radial symmetry of π structure incorporating perpendicular oriented π orbitals. Herein we set to explore the aromaticity of neutral and dicationic ortho and meta isomers of [8]CPP by dissecting the induced magnetic field to contributions of the twofold radial/perpendicular π system using delocalized canonical molecular orbitals (CMO), and introducing the natural localized molecular orbitals (NLMO) analysis with DFT methods. The dications sustain a reduced global aromatic character of the radial π system under a perpendicular orientation of the external field which declines from ortho to meta isomer and reinforces local aromaticity of ortho ring while it destroys aromaticity of meta ring. Aromaticity variations are determined by symmetry governed rotational excitations of frontier π orbitals. The parallel orientation reveals a substantial reduction of local aromaticity verified with NICSπ analysis and electron delocalization indices.

On the formation of spherical aromatic endohedral buckminsterfullerene. Evaluation of M@C60 (M = Cr, Mo, W) from relativistic DFT calculations.

Endohedral metallofullerenes are key species for expanding the range of viable fullerenes, their versatility, and applications. Here we report our computational evaluation on the formation of spherical aromatic counterparts of the C60 fullerene from relativistic DFT calculations, based on the inclusion of Cr, Mo and W endohedral atoms. The resulting M@C60 endohedral fullerenes are 66-π electron neutral species exhibiting bonding properties and electronic structure mimicking the aromaticity and diamagnetic insulator behavior of alkali-C606- phases. The resulting structures are interesting candidates for further experimental realization as novel neutral building blocks for more flexible nanostructured organic materials, highlighting truly spherical aromatic neutral species retaining the truncated icosahedral structure of the seminal Buckminster fullerene.

Induced magnetic field in sp-hybridized carbon rings: analysis of double aromaticity and antiaromaticity in cyclo[2N]carbon allotropes.

The induced magnetic field of C2N (N = 3-14) carbon rings was dissected to contributions from out-of-plane and in-plane π orbitals revealing two concurrent long range shielding or deshielding cones as a manifestation of the dual aromatic and antiaromatic character of C4n+2 and of C4n rings respectively. Aromaticity based on the magnetic criterion was evaluated with regard to the bonding pattern and geometrical characteristics that elucidate the influence of bond length and bond angle alteration on out-of-plane and in-plane magnetic responses. Ground state polyynic geometries of C4n+2 rings exhibit comparable shielding cones to annulenes, decreasing the magnetic response with regard to the ring size and similar πout and πin diatropicity. Transition state cumulenic rings display increased aromaticity expressed by a very strong constant magnetic response and augmented πout diatropicity with regard to πin. The variations of the induced magnetic field are explained on the basis of frontier orbital interactions through rotational excitations, which enable further rationalization of the aromatic/antiaromatic behavior.

Consequences of Curvature on Induced Magnetic Field: The Case of Helicenes.

Helicenes consist of several fused rings twisted around an axis, forming a cylindrical helix, with π-delocalized electrons in the non-planar rings. Induced magnetic fields dissecting the orbital contributions of [6]-, [7]-, and [14]helicene are discussed. Computations show a deshielding cone produced by the π-electrons along the helical axis. Unexpectedly, the response of the core electrons produces a shielding cone, which is cumulative and sensitive to the curvature of the systems owing to the overlap of the other ring responses. A warning is provided regarding the evaluation of the delocalization in curved systems in which the x- and y-components of the induced magnetic field become relevant.

Double aromaticity of the B40 fullerene: induced magnetic field analysis of π and σ delocalization in the boron cavernous structure.

The induced magnetic field of B40 was dissected into contributions from π, σ and core electrons revealing the origins for the formation of the strong long range shielding response characterizing the spherical aromatic nature of the cavernous D2d structure. Our analysis showed the complementary role of π and σ orbitals for the formation of the global shielding cone, with weak π contributions at a long range and strong σ contributions inside the cage, supporting the molecule as double aromatic with weak π and strong σ delocalization. Similar local variations of both π and σ magnetic responses were identified portraying peripheral diatropic and local paratropic currents. The weak π aromaticity is explained on the basis of symmetry rules pertaining to its electronic structure which forbid small gap paratropic rotational excitations.

The pseudo-π model of the induced magnetic field: fast and accurate visualization of shielding and deshielding cones in planar conjugated hydrocarbons and spherical fullerenes.

The induced magnetic fields originating from the π system of planar conjugated polycyclic hydrocarbons and spherical fullerenes are accurately reproduced by their corresponding hydrogen skeletal models (HSMs). Moreover, the individual contribution per molecular orbital is also reproduced unraveling simple symmetry rules related to canonical molecular orbitals. Hence, fast, handy and accurate 3D visualization of shielding and deshielding cones is realized, enabling the interpretation of global and local π aromaticity and antiaromaticity of PAHs and spherical species in a simple and concise manner to facilitate further interpretations of large sized hydrocarbon systems.

Canonical orbital contributions to the magnetic fields induced by global and local diatropic and paratropic ring currents.

The induced magnetic field (IMF) of naphthalene, biphenyl, biphenylene, benzocyclobutadiene, and pentalene is dissected to contributions from the total π system, canonical π-molecular orbitals (CMO), and HOMO→π* excitations, to evaluate and interpret relative global and local diatropicity and paratropicity. Maps of the IMF of the total π system reveal its relative strength and topology that corresponds to global and local diatropic and paratropic ring currents. The total π magnetic response is determined by this of canonical HOMOs and particularly by paratropic contributions of rotational excitations from HOMOs to unoccupied π* orbitals. Low energy excitations and similar nodal structure of HOMO and π* induce strong paratropic fields that dominate on antiaromatic rings. High energy excitations and different nodal structures lead to weak paratropic contributions of canonical HOMOs, which are overwhelmed by diatropic response of lower energy canonical orbitals in aromatic rings. CMO-IMF analysis is found in agreement with ring current analysis. © 2017 Wiley Periodicals, Inc.

Study of Electron Delocalization in 1,2-, 1,3-, and 1,4-Azaborines Based on the Canonical Molecular Orbital Contributions to the Induced Magnetic Field and Polyelectron Population Analysis.

The electron delocalization in 1,2-azaborine, 1,3-azaborine, and 1,4-azaborine is studied using canonical molecular orbital contributions to the induced magnetic field (CMO-IMF) method and polyelectron population analysis (PEPA). Contour maps of the out-of-plane component of the induced magnetic field (Bz(ind)) of the π system show that the three azaborines, in contrast with borazine, sustain much of benzene's π-aromatic character. Among them, 1,3-azaborine exhibits the strongest π delocalization, while 1,4-azaborine is the weakest. Contour maps of Bz(ind) for individual π orbitals reveal that the differentiation of the magnetic response among the three isomers originates from the π-HOMO orbitals, whose magnetic response is governed by rotational allowed transitions to unoccupied orbitals. The low symmetry of azaborines enables a paratropic response from HOMO to unoccupied orbitals excitations, with their magnitude depending on the shape of interacting orbitals. 1,3-Azaborine presents negligible paratropic contributions to Bz(ind) from HOMO to unoccupied orbitals transitions, where 1,2- and 1,4-azaborine present substantial paratropic contributions, which lead to reduced diatropic response. Natural bond orbital (NBO) analysis employing PEPA shows that only the 1,3-azaborine contains π-electron fully delocalized resonance structures.

Interpretation of electron delocalization in benzene, cyclobutadiene, and borazine based on visualization of individual molecular orbital contributions to the induced magnetic field.

The magnetic response of the valence molecular orbitals (MOs) of benzene, cyclobutadiene, and borazine to an external magnetic field has been visualized by calculating the chemical shielding in two-dimensional grids of points on the molecular plane and on a plane perpendicular to it, using gauge-including atomic orbitals (GIAOs). The visualizations of canonical MO contributions to the induced magnetic field (CMO-IMF) provide a clear view of the spatial extension, the shape, and the magnitude of shielding and deshielding areas within the vicinity of the molecule, originating from the induced currents of each valence orbital. The results are used to investigate the delocalization of each valence MO and to evaluate its contribution to the aromatic character of systems under study. The differentiation of the total magnetic response among the three molecules originates exclusively from π-HOMO orbitals because the magnetic response of the subsets of the remaining MOs is found to be almost identical. Borazine is classified as nonaromatic as the four electrons that occupy the π-HOMO are found to be strongly localized on nitrogen centers. CMO-IMF can clarify the interpretation of various NICS indexes and can be applied for the investigation of various types of electron delocalization.