Coarctate and Möbius: The Helical Orbitals of Allene and Other Cumulenes

The Antiaromatic Nucleophilic Substitution Reaction (SNAAr) in Cycloheptatrienyl-Anion Containing Zwitterions with a Möbius-Aromatic Intermediate

Antiaromatic nucleophilic substitution reactions in cycloheptatrienide pyridinium and phosphonium zwitterions with initial formation of a cycloheptatetraene intermediate are explored. The mechanism was supported by quantum chemical calculations, first-order reaction kinetics, and high-resolution mass spectrometry. The pyridinium zwitterion exhibited weak antiaromaticity, whereas the intermediate displayed Möbius aromaticity, as evidenced by nuclear independent chemical shift values and the shape of its HOMO. This study represents the eighth confirmed instance of a Möbius-aromatic organic species in its ground state.

Bending a Cumulene with Electrons: Stepwise Chemical Reduction and Structural Study of a Tetraaryl[4]Cumulene

Chemical reduction of a [4]cumulene with cesium metal was explored, and the structural changes stemming from electron acquisition are detailed using X-ray crystallography. It is found that the [4]cumulene undergoes dramatic geometric changes upon stepwise reduction, including bending of the cumulenic core and twisting of the endgroups from orthogonal to planar. The structural deformation is consistent with early theoretical reports that suggest that the twisting should occur upon reduction of both even and odd [n]cumulenes. The current results, on the other hand, are inconsistent with a previous experimental study of a [3]cumulene in which the predicted twisting is not observed upon reduction. DFT calculations reveal that the barrier to deformation is an order of magnitude lower in a [3]cumulene than a [4]cumulene, allowing the barrier to be overcome in the solid-state.

Chiral Jahn-Teller Distortion in Quasi-Planar Boron Clusters

In this work, we have observed that some chiral boron clusters (B16-, B20-, B24-, and B28-) can simultaneously have helical molecular orbitals and helical spin densities; these seem to be the first compounds discovered to have this intriguing property. We show that chiral Jahn-Teller distortion of quasi-planar boron clusters drives the formation of the helical molecular spin densities in these clusters and show that elongation/enhancement in helical molecular orbitals can be achieved by simply adding more building blocks via a linker. Aromaticity of these boron clusters is discussed. Chiral boron clusters may find potential applications in spintronics, such as molecular magnets.

Organometallic Allene [(μ-C)(Fe(CO)4 )2 ]: Bridging Carbon Showing Transformation from Classical Electron-Sharing Bonding to Double σ-Donor and Double π-Acceptor Ligation

Allenes (R2 C=C=CR2 ) have been traditionally perceived to feature localized orthogonal π-bonds between the carbon centres. We have carried out quantum-mechanical studies of the organometallic allenes envisioned by the isolobal replacement of the terminal CH2 groups by the d8 Fe(CO)4 fragment. Our studies have identified two organometallic allenes viz. D2d symmetric [(μ-C)(Fe(CO)4 )2 ] (2) and D3 symmetric [(μ-C)(Fe(CO)4 )2 ] (3) with trigonal bipyramidal coordination at the Fe atoms. Compound 2 features the bridging carbon atom in an equatorial position with respect to the ligands on the TM centre, while 3 features the central carbon atom in an axial position. The bis-pseudoallylic anionic delocalisation proposed in the C2-C1-C3 spine of organic allene is retained in the organometallic allene 2, and is transformed to a typical three-centre bis-allylic anionic delocalisation in the organometallic allene 3. The topological analysis of electron density also indicates a bis-allylic anionic type delocalisation in the organometallic allenes. The quantitative bonding analysis using the EDA-NOCV method suggests a transition from classical electron-sharing bonding between the central carbon atom and the terminal groups in 1 to donor-acceptor bonding in 3. Meanwhile, both electron-sharing and donor-acceptor bonding models are found to be probable heuristic bonding representations in the organometallic allene 2.

Understanding Current Density in Molecules Using Molecular Orbitals

While the use of molecular orbitals (MOs) and their isosurfaces to explain physical phenomena in chemical systems is a time-honored tool, we show that the nodes are an equally important component for understanding the current density through single-molecule junctions. We investigate three different model systems consisting of an alkane, alkene, and even [n]cumulene and show that we can explain the form of the current density using the MOs of the molecule. Essentially, the MOs define the region in which current can flow and their gradients define the direction in which current flows within that region. We also show that it is possible to simplify the current density for improved understanding by either partitioning the current density into more chemically intuitive parts, such as σ- and π-systems, or by filtering out MOs with negligible contributions to the overall current density. Our work highlights that it is possible to infer a non-equilibrium property (current density) given only equilibrium properties (MOs and their gradients), and this, in turn, grants deeper insight into coherent electron transport.

Riemannian Trust Region Method for Minimization of the Fourth Central Moment for Localized Molecular Orbitals

The importance of localized molecular orbitals (MOs) in correlation treatments beyond mean-field calculation and in the illustration of chemical bonding (and antibonding) can hardly be overstated. However, the generation of orthonormal localized occupied MOs is significantly more straightforward than obtaining orthonormal localized virtual MOs. Orthonormal MOs allow facile use of highly efficient group theoretical methods (e.g., graphical unitary group approach) for calculation of Hamiltonian matrix elements in multireference configuration interaction calculations (such as MRCISD) and in quasi-degenerate perturbation treatments, such as the Generalized Van Vleck Perturbation Theory. Moreover, localized MOs can elucidate qualitative understanding of bonding in molecules, in addition to high-accuracy quantitative descriptions. We adopt the powers of the fourth moment cost function introduced by Jørgensen and coworkers. Because the fourth moment cost functions are prone to having multiple negative Hessian eigenvalues when starting from easily available canonical (or near-canonical) MOs, standard optimization algorithms can fail to obtain the orbitals of the virtual or partially occupied spaces. To overcome this drawback, we applied a trust region algorithm on an orthonormal Riemannian manifold with an approximate retraction from the tangent space built into the first and second derivatives of the cost function. Moreover, the Riemannian trust region outer iterations were coupled to truncated Conjugate Gradient inner loops, which avoided any costly solutions of simultaneous linear equations or eigenvector/eigenvalue solutions. Numerical examples are provided on model systems, including the high-connectivity H₁₀ set in 1-, 2-, and 3-dimensional arrangements, and on a chemically realistic description of cyclobutadiene (c-C₄H₄) and the propargyl radical (C₃H₃). In addition to demonstrating the algorithm on occupied and virtual blocks of orbitals, the method is also shown to work on the active space at the MCSCF level of theory.

1,3-Butadiynamides the Ethynylogous Ynamides: Synthesis, Properties and Applications in Heterocyclic Chemistry

1,3-butadiynamides-the ethynylogous variants of ynamides-receive considerable attention as precursors of complex molecular scaffolds for organic and heterocyclic chemistry. The synthetic potential of these C4-building blocks reveals itself in sophisticated transition-metal catalyzed annulation reactions and in metal-free or silver-mediated HDDA (Hexa-dehydro-Diels-Alder) cycloadditions. 1,3-Butadiynamides also gain significance as optoelectronic materials and in less explored views on their unique helical twisted frontier molecular orbitals (Hel-FMOs). The present account summarizes different methodologies for the synthesis of 1,3-butadiynamides followed by the description of their molecular structure and electronic properties. Finally, the surprisingly rich chemistry of 1,3-butadiynamides as versatile C4-building blocks in heterocyclic chemistry is reviewed by compiling their exciting reactivity, specificity and opportunities for organic synthesis. Besides chemical transformations and use in synthesis, a focus is set on the mechanistic understanding of the chemistry of 1,3-butadiynamides-suggesting that 1,3-butadiynamides are not just simple alkynes. These ethynylogous variants of ynamides have their own molecular character and chemical reactivity and reflect a new class of remarkably useful compounds.

Jahn-Teller effects in initial and final states: high-resolution X-ray absorption, photoelectron and Auger spectroscopy of allene

Carbon K-edge resonant Auger spectra of gas-phase allene following excitation of the pre-edge 1s → π* transitions are presented and analysed with the support of EOM-CCSD/cc-pVTZ calculations. X-Ray absorption (XAS), X-ray photoelectron (XPS), valence band and non-resonant Auger spectra are also reanalysed with a series of computational approaches. The results presented demonstrate the importance of including nuclear ensemble effects for simulating X-ray observables and as an effective strategy for capturing Jahn-Teller effects in spectra.

Anatomy of Classical Boron-Boron Bonding: Overlap and sp Dissonance

Classical bonding is predominantly understood using the insipid spⁿ hybridization for σ-bonds as well as π bonds and their delocalized variants. Because hybridization ignores intricate differences in the energy and size of valence atomic orbitals, its naïve application to classically bonded boron atoms leads to numerous surprises in bond strengths, frontier MOs/bands, and even geometry. Here we show that the sp dissonance caused by size mismatch between the valence s and p orbitals of boron plays a crucial role in its bonding, subtly distinct from that of carbon and silicon. Unlike the heavier p block elements, boron prefers to actively engage its compact 2s orbitals in bonding. This leads to the overreach of p-p σ-type overlap that reduces its magnitude in the entire B─B bonding range. Consequently, the π-type overlap remains substantial, making its electronic structure visibly distinct in saturated and unsaturated regimes. The deltahedral frameworks offer a compromise by breaking this symmetry-enforced dichotomy of classical σ- and π-type bonding and following alternate electron counts that suit the electron deficiency of the boron. The pathological anatomy of classical B─B σ-bonding also explains the origins of puzzling metallic character and disorder in their classical boride networks even with ideal electron count, unlike deltahedral borides. The implications of sp dissonance are illustrated in classical boron networks of various hybridizations, explaining the unusual preference for unique sp³ lattice with strained four-membered rings in CrB₄, origins of observed σ holes in MgB₂ that lead to its superconducting nature, and the absence of Peierls distortion in LiB.

Single photon double and triple ionization of allene

Double and triple ionization of allene are investigated using electron-electron, ion-ion, electron-electron-ion and electron-electron-ion-ion (ee, ii, eei, eeii) coincidence spectroscopies at selected photon energies. The results provide supporting evidence for a previously proposed roaming mechanism in H₃⁺ formation by double ionization. The lowest vertical double ionization energy is found to be 27.9 eV, while adiabatic double ionization is not accessed by vertical ionization at the neutral geometry. The triple ionization energy is found to be close to 50 eV in agreement with theoretical predictions. The doubly charged parent ion is stable up to about 2 eV above the threshold, after which dissociations by charge separation and by double charge retention occur with comparable intensities. Fragmentation to H⁺ + C₃H₃⁺ starts immediately above the threshold as a slow (metastable) decay with 130.5 ± 9.9 ns mean lifetime.

Helical versus linear Jahn–Teller distortions in allene and spiropentadiene radical cations

The allene radical cation can be stabilized both by Jahn–Teller distortion of the bond lengths and by torsion of the end-groups.

Syntheses and Structures of trans-bis(Alkenylacetylide) Ruthenium Complexes

A series of ruthenium alkenylacetylide complexes trans-[Ru{C≡CC(=CH₂ )R}Cl(dppe)₂ ] (R=Ph (1 a), ^c C₄ H₃ S (1 b), 4-MeS-C₆ H₄ (1 c), 3,3-dimethyl-2,3-dihydrobenzo[b]thiophene (DMBT) (1 d)) or trans-[Ru{C≡C-^c C₆ H₉ }Cl(dppe)₂ ] (1 e) were allowed to react with the corresponding propargylic alcohol HC≡CC(Me)R(OH) (R=Ph (A), ^c C₄ H₃ S (B), 4-MeS-C₆ H₄ (C), DMBT (D) or HC≡C-^c C₆ H₁₀ (OH) (E) in the presence of TlBF₄ and DBU to presumably give alkenylacetylide/allenylidene intermediates trans-[Ru{C≡CC(=CH₂ )R}{C=C=C(Me)}(dppe)₂ ]PF₆ ([2]PF₆ ). These complexes were not isolated but deprotonated to give the isolable bis(alkenylacetylide) complexes trans-[Ru{C≡CC(=CH₂ )R}₂ (dppe)₂ ] (R=Ph (3 a), ^c C₄ H₃ S (3 b), 4-MeS-C₆ H₄ (3 c), DMBT (3 d)) and trans-[Ru{C≡C-^c C₆ H₉ }₂ (dppe)₂ ] (3 e). Analogous reactions of trans-[Ru(CH₃ )₂ (dmpe)₂ ], featuring the more electron-donating 1,2-bis(dimethylphosphino)ethane (dmpe) ancillary ligands, with the propargylic alcohols A or C and NH₄ PF₆ in methanol allowed isolation of the intermediate mixed alkenylacetylide/allenylidene complexes trans-[Ru{C≡CC(=CH₂ )R}{C=C=C(Me)}(dmpe)₂ ]PF₆ (R=Ph ([4 a]PF₆ ), 4-MeS-C₆ H₄ ([4 c]PF₆ ). Deprotonation of [4 a]PF₆ or [4 c]PF₆ gave the symmetric bis(alkenylacetylide) complexes trans-[Ru{C≡CC(=CH₂ )R}₂ (dmpe)₂ ] (R=Ph (5 a), 4-MeS-C₆ H₄ (5 c)), the first of their kind containing the dmpe ancillary ligand sphere. Attempts to isolate bis(allenylidene) complexes [Ru{C=C=C(Me)R}₂ (PP)₂ ]²⁺ (PP=dppe, dmpe) from treatment of the bis(alkenylacetylide) species 3 or 5 with HBF₄  ⋅ Et₂ O were ultimately unsuccessful.

Quantification of the Helicality of Helical Molecular Orbitals

The frontier molecular orbital (MO) topology of linear carbon molecules, such as polyynes, can be visually identified as helices. However, there is no clear way to quantify the helical curvature of these π-MOs, and it is thus challenging to quantify correlations between the helical curvature and molecular properties. In this paper, we develop a method that enables us to compute the helical curvature of MOs based on their nodal planes. Using this method, we define a robust way of quantifying the helical nature of MOs (helicality) by their deviation from a perfect helix. We explore several limiting cases, including polyynes, metallacumulenes, cyclic allenes, and spiroconjugated systems, where the change in helical curvature is subtle yet clearly highlighted with this method. For example, we show that strain only has a minor effect on the helicality of the frontier orbitals of cycloallenes and that the MOs of spiroconjugated systems are close to perfect helices around the spiro-carbon. Our work provides a well-defined method for assessing orbital helicality beyond visual inspection of MO isosurfaces, thus paving the way for future studies of how the helicality of π-MOs affects molecular properties.

Construction of an iminoketenylidene

The new isonitrile-μ-carbido complexes [WPt(μ-C)Br(CNR)(PPh₃)(CO)₂(Tp*)] (R = C₆H₂Me₃-2,4,6, C₆H₃Me₂-2,6; Tp* = hydrotris(dimethylpyrazolyl)borate) rearrange irreversibly in polar solvents to provide the first examples of iminoketenylidene (CCNR) complexes.

Helical Molecular Orbitals to Induce Spin-Orbit Coupling in Oligoyne-Bridged Bifluorenes

Singlet-Triplet energy exchange is an area of active research due to its role in optoelectronic devices and photodynamic therapy. Large spin-orbit coupling (SOC) is difficult to achieve in simple hydrocarbon structures limiting the intersystem crossing (ISC) rates. A new approach to enhance the spin-orbit coupling via helical molecular orbitals is investigated in oligoyne-bridged bifluorenes. Transient absorption studies showed a singlet-to-triplet ISC rate of up to 6 ns^-1 resulting in 0.84 triplet yield. Density functional calculations revealed a direct relation between high ISC and large SOC values mediated by helical molecular orbitals. Calculations and spectroscopic data also suggested that El-Sayed forbidden ISC occurs as a direct transition between ¹ππ* and ³ππ*, which becomes allowed due to a symmetry-breaking interaction leading to mixing between orthogonal π-systems in the oligoyne fragment.

Magnetic Modulation in Heteroallene and Heterocumulene Based tert-butyl Nitroxide Diradicals: Spin Delocalization and Conformation Play Crucial Roles

We have theoretically investigated the magnetic properties of heteroallene (>C=C=X-) and heterocumulene (>C=C=C=X-) based tert-butyl nitroxide diradicals (X is P/As). Calculation of magnetic exchange coupling constant (J) shows ferromagnetic interaction in heteroallene based diradicals. Whereas, in heterocumulene based diradicals, tuning of J value from antiferro- to ferro-magnetic state is observed from Z- to E- isomer. Delocalization of spin density from radical site to the coupler (in planar arrangement) is observed in spin distribution analysis which is also advocated by molecular orbital analysis. The typical feature of tert-butyl nitroxide radical creates spin delocalization along with spin polarization within the coupler. The J values of all the diradicals strongly depend on the dihedral angle between radical center and coupler. Magneto-structural correlation shows that the change in dihedral angle tunes the magnetic property for both the Z- and E- isomers of heterocumulenes depending on the spin accumulation on two nearby magnetic centers. The extent of spin delocalization and conformation of spin centers on the molecular axis are important for the different J values observed in our designed systems.

Origins of Endo Selectivity in Diels-Alder Reactions of Cyclic Allene Dienophiles

Strained cyclic allenes, first discovered in 1966 by Wittig and co-workers, have recently emerged as valuable synthetic building blocks. Previous experimental investigations, and computations reported here, demonstrate that the Diels-Alder reactions of furans and pyrroles with 1,2-cyclohexadiene and oxa- and azaheterocyclic analogs proceed with endo selectivity. This endo selectivity gives the adduct with the allylic saturated carbon of the cyclic allene endo to the diene carbons. The selectivity is very general and useful in synthetic applications. Our computational study establishes the origins of this endo selectivity. We analyze the helical frontier molecular orbitals of strained cyclic allenes and show how secondary orbital and electrostatic effects influence stereoselectivity. The LUMO of carbon-3 of the allene (C-3 is not involved in primary orbital interactions) interacts in a stabilizing fashion with the HOMO of the diene in such a way that the carbon of the cyclic allene attached to C-1 favors the endo position in the transition state. The furan LUMO, allene HOMO interaction reinforces this preference. These mechanistic studies are expected to prompt the further use of long-avoided strained cyclic allenes in chemical synthesis.

Helical electronic transitions of spiroconjugated molecules

The π–π* transitions of disubstituted spiropentadiene become helical due to mixing of its two perpendicular π-systems. The helicity is symmetry-protected and gives rise to experimentally observable effects, such as optical activity.

Mean-field density matrix decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.

Excited-State Aromaticity Reversals in Möbius Annulenes

It is suggested that Möbius annulenes follow a rule similar to Baird's rule such that the 4n and 4n + 2 criteria for Möbius electronic ground-state aromaticity and antiaromaticity are reversed in the lowest triplet and first singlet excited electronic states. Support comes from an investigation of aromaticity in the ground (S₀), lowest triplet (T₁), and first singlet excited (S₁) electronic states of the Möbius-aromatic cyclononatetraenyl cation, C₉H₉⁺, using isotropic magnetic shielding isosurfaces calculated with state-optimized complete-active-space self-consistent field wave functions constructed from gauge-including atomic orbitals. Examination of these isosurfaces demonstrates that while the S₀ state of C₉H₉⁺ is aromatic, the T₁ and S₁ states are antiaromatic.

Simulation vs. Understanding: A Tension, in Quantum Chemistry and Beyond. Part B. The March of Simulation, for Better or Worse

In the second part of this Essay, we leave philosophy, and begin by describing Roald's being trashed by simulation. This leads us to a general sketch of artificial intelligence (AI), Searle's Chinese room, and Strevens' account of what a go-playing program knows. Back to our terrain-we ask "Quantum Chemistry, † ca. 2020?" Then we move to examples of Big Data, machine learning and neural networks in action, first in chemistry and then affecting social matters, trivial to scary. We argue that moral decisions are hardly to be left to a computer. And that posited causes, even if recognized as provisional, represent a much deeper level of understanding than correlations. At this point, we try to pull the reader up, giving voice to the opposing view of an optimistic, limitless future. But we don't do justice to that view-how could we, older mammals on the way to extinction that we are? We try. But then we return to fuss, questioning the ascetic dimension of scientists, their romance with black boxes. And argue for a science of many tongues.

Understanding the singlet–triplet energy splittings in transition metal-capped carbon chains

Density functional theory and molecular orbital analysis suggest that the odd–even alternation of singlet–triplet energy separations is a general feature of transition metal-capped carbon chains, determined primarily by the carbon chains.

Hybrid light emitting diodes based on stable, high brightness all-inorganic CsPbI3 perovskite nanocrystals and InGaN

Despite important advances in the synthesis of inorganic perovskite nanocrystals (NCs), the long-term instability and degradation of their quantum yield (QY) over time need to be addressed to enable the further development and exploitation of these nanomaterials. Here we report stable CsPbI3 perovskite NCs and their use in hybrid light emitting diodes (LEDs), which combine in one system the NCs and a blue GaN-based LED. Nanocrystals with improved morphological and optical properties are obtained by optimizing the post-synthesis replacement of oleic acid ligands with iminodibenzoic acid: the NCs have a long shelf-life (>2 months), stability under different environmental conditions, and a high QY, of up to 90%, in the visible spectral range. Ligand replacement enables the engineering of the morphological and optical properties of the NCs. Furthermore, the NCs can be used to coat the surface of a GaN-LED to realize a stable diode where they are excited by blue light from the LED under low current injection conditions, resulting in emissions at distinct wavelengths in the visible range. The high QY and fluorescence lifetime in the nanosecond range are key parameters for visible light communication, an emerging technology that requires high-performance visible light sources for secure, fast energy-efficient wireless transmission.

Systematic experimental study of quantum interference effects in anthraquinoid molecular wires

In order to translate molecular properties in molecular-electronic devices, it is necessary to create design principles that can be used to achieve better structure-function control oriented toward device fabrication. In molecular tunneling junctions, cross-conjugation tends to give rise to destructive quantum interference effects that can be tuned by changing the electronic properties of the molecules. We performed a systematic study of the tunneling charge-transport properties of a series of compounds characterized by an identical cross-conjugated anthraquinoid molecular skeleton but bearing different substituents at the 9 and 10 positions that affect the energies and localization of their frontier orbitals. We compared the experimental results across three different experimental platforms in both single-molecule and large-area junctions and found a general agreement. Combined with theoretical models, these results separate the intrinsic properties of the molecules from platform-specific effects. This work is a step towards explicit synthetic control over tunneling charge transport targeted at specific functionality in (proto-)devices.

Helical orbitals and circular currents in linear carbon wires

Disubstituted odd-carbon cumulenes are linear carbon wires with helical π-orbitals, which results in circular current around the wire.

Disubstituted odd-carbon cumulenes are linear carbon wires with near-degenerate helical π-orbitals. Such cumulenes are chiral molecules but their electronic structure consists of helical orbitals of both chiralities. For these helical molecular orbitals to give rise to experimentally observable effects, the near-degenerate orbitals of opposite helicities must be split. Here we show how pyramidalized single-faced π-donors, such as the amine substituent, provide a strategy for splitting the helical molecular orbitals. The chirality induced by the amine substituents allow for systematic control of the helicity of the frontier orbitals. We examine how the helical orbitals in odd-carbon cumulenes control the coherent electron transport properties, and we explicitly predict two modes in the experimental single-molecule conductance for these molecules. We also show that the current density through these linear wires exhibits strong circular currents. The direction of the circular currents is systematically controlled by the helicity of the frontier molecular orbitals, and is therefore altered by changing between the conformations of the molecule. Furthermore, the circular currents are subject to a full ring-reversal around antiresonances in the Landauer transmission, emphasizing the relation to destructive quantum interference. With circular currents present around truly linear carbon wires, cumulenes are promising candidates for novel applications in molecular electronics.

Does the Electronic Structure of Möbius Annulenes Follow Heilbronner's Ideas?

It is shown, on the example of the monocyclic cyclononatetraenyl cation,C 9 H 9 + , that the fully-variational optimization of modern ab initio wavefunctions based on spin-coupled generalized valence bond (SCGVB) theory vindicates, in a surprising level of detail, essential features of Heilbronner's ideas for the electronic structure of Möbius annulenes such as the arrangement of overlapping carbon 2p atomic orbitals along a Möbius strip, leading to a phase inversion between the first and last orbitals. In the SCGVB description, the aromaticity of this Möbius system with eight π electrons follows from the extensive resonance between VB structures.

Unraveling Mechanisms of Chiral Induction in Double-Helical Metallopolymers

Self-assembled helical polymers hold great promise as new functional materials, where helical handedness controls useful properties such as circularly polarized light emission or electron spin. The technique of subcomponent self-assembly can generate helical polymers from readily prepared monomers. Here we present three distinct strategies for chiral induction in double-helical metallopolymers prepared via subcomponent self-assembly: (1) employing an enantiopure monomer, (2) polymerization in a chiral solvent, (3) using an enantiopure initiating group. Kinetic and thermodynamic models were developed to describe the polymer growth mechanisms and quantify the strength of chiral induction, respectively. We found the degree of chiral induction to vary as a function of polymer length. Ordered, rod-like aggregates more than 70 nm long were also observed in the solid state. Our findings provide a basis to choose the most suitable method of chiral induction based on length, regiochemical, and stereochemical requirements, allowing stereochemical control to be established in easily accessible ways.