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A topological quantum phase transition has been identified for the first time for 24 π-conjugated polymers as a function of external longitudinal strain due to a level crossing of the frontier orbitals at the topological phase transition. Topological phase is determined by the presence/absence of edge states. Out of the 24 polymers 15 are traditionally assigned an aromatic character, and 9 are traditionally assigned a quinonoid character. We find that all aromatic ones correspond to the trivial topological phase (Zak invariant, Z 2 = 0), while all of the quinonoid ones to the nontrivial topological phase ( Z 2 = 1) replacing the intuitive characterization of aromatic/quinonoid with the physically well-defined Zak invariant. Unique topological phase transition as a function of tensile strain can be achieved for four of the quinonoid ones. Tensile strain in these cases leads to a reduction of the bandgap. We introduced a figure of merit for indicating the efficiency of achievable very small bandgap upon the application of external strain.

Perylene (PER) is a prototype of polycyclic aromatic hydrocarbons (PAHs), which play a pivotal role in various functional and electronic materials due to favorable molecule-to-molecule overlaps, which enhance electronic transport. This study provides guidelines regarding the impact of molecular charge on pancake bonding, a form of strong π-stacking interaction. Pancake bonding significantly boosts interaction energies within the monopositive dimer ([(C 20 H 12 ) 2 ] •+ or PER 2 + ), crucial for stabilizing aggregation and crystal formation. We discovered energetically feasible sliding and rotation pathways within the [(C 20 H 12 ) 2 ] •+ dimer, connecting different configurations found in the Cambridge Structural Database (CSD). The dimer's charge profoundly influences the pancake bond order (PBO) and the strength and structural preferences of pancake bonding. The most stable configuration is found in the monocationic state (PER 2 + ), featuring a pancake bond order of 1/2 with one-electron multicenter bonding (1e/mc) with similar characteristics for charge -1. Increasing the total charge of the dimer to +2 or -2 leads to an unstable local minimum. Diverse distribution of pancake bonding types present in crystal structures is interpreted with modeling based on dimer computations with varying charges.

In this report, we describe the synthesis and electronic properties of small-molecule and polymeric [8]cycloparaphenylenes ([8]CPPs) with disjointed pi-conjugated substituents. Arylene-ethynylene linkers were installed on opposite sides of the [8]CPP nanohoop as separated by three phenyl units on either side such that the monomer systems have syn (C 2 symmetry) and anti (C 1 symmetry) conformers with a small energy gap (0.1-0.6 kcal/mol). This disjoined substitution pattern necessarily forces delocalization through and around the CPP radial structure. We demonstrate new electronic states from this radial/linear mixing in both the small molecules and the pi extended polymers. Quantum chemical calculations reveal that these electronic processes arise from multiple operative radial/linear conjugation pathways, as the disjoint pattern results in both ortho and meta connections to the CPP ring. These results affirm the unique nature of hybrid radial and linear pi electron delocalization operative in these new conjugation pathways.

We describe the synthesis and electronic properties of new π-conjugated small molecules and polymers that combine the linear intramolecular conjugation pathways commonly associated with organic electronic materials with the emerging properties of radial conjugation found in cycloparaphenylenes (CPPs) and other curved π-surfaces. Using arylene ethynylenes as prototypical linear segments and [6]/[8]CPP as the radial segments, we demonstrate the formation of new electronic states that are not simply additive responses from the individual components. Quantum chemical calculations of model oligomeric structures reveal these electronic processes to arise from the hybrid nature of wave function delocalization over the linear and radial contributors in the photophysically relevant electronic states.

Direct evidence for σ-bond fluxionality in a phenalenyl σ-dimer was successfully obtained by a detailed investigation of the solution-state dynamics of 2,5,8-trimethylphenalenyl (TMPLY) using both experimental and theoretical approaches. TMPLY formed three diamagnetic dimers, namely, the σ-dimer (RR/SS), σ-dimer (RS), and π-dimer, which were fully characterized by (1)H NMR spectroscopy and electronic absorption measurements. The experimental findings gave the first quantitative insights into the essential preference of these competitive and unusual dimerization modes. The spectroscopic analyses suggested that the σ-dimer (RR/SS) is the most stable in terms of energy, whereas the others are metastable; the energy differences between these three isomers are less than 1 kcal mol(-1). Furthermore, the intriguing dynamics of the TMPLY dimers in the solution state were fully revealed by means of (1)H-(1)H exchange spectroscopy (EXSY) measurements and variable-temperature (1)H NMR studies. Surprisingly, the σ-dimer (RR/SS) demonstrated a sixfold σ-bond shift between the six sets of α-carbon pairs. This unusual σ-bond fluxionality is ascribed to the presence of a direct interconversion pathway between the σ-dimer (RR/SS) and the π-dimer, which was unambiguously corroborated by the EXSY measurements. The proposed mechanism of the sixfold σ-bond shift based on the experimental findings was well-supported by theoretical calculations.

Phenalenyl and a wide variety of its derivatives form stable radicals, which often associate in various aggregates with interesting properties that include magnetism and high electrical conductivity. The two main modes of aggregation involve π-stacking pancake multicenter bond formation and σ-bond formation. We explore the energetics of the various σ- and π-dimers for six phenalenyl derivatives with both computational and experimental methods. A modern density functional theory (M05-2X) is used to survey the potential energy surface revealing the mechanism of the aggregation. In order to enrich experimental data, the triphenyl and trimethyl derivatives are newly prepared and their aggregation behaviors are investigated by various analytical methods including ESR, (1)H NMR, UV-vis, and single-crystal X-ray diffraction. The agreement between computations and experiments are very good forming the basis of describing trends in this series. We find that π-dimer formation can proceed via an asynchronous concerted path from the monomers or in a stepwise process via σ-dimers. The strength of the π-stacking pancake interaction depends strongly on substituents and covers a wide range both in terms of binding energies and contact distances. The spin densities in the π-stacking dimers reflect these trends and display a wide range of diradicaloid characters. Many σ-dimer configurations compete some of which are separated by small barriers leading to fluxional structures between σ-bonded configurations or σ- and π-bonded configurations.

The concept of a double-bonded pancake bonding mechanism is introduced to explain the extremely short π-π stacking contacts in dimers of dithiatriazines. While ordinary single pancake bonds occur between radicals and already display significantly shorter interatomic distances in comparison to van der Waals (vdW) contacts, the double-bonded pancake dimer is based on diradicaloid or antiaromatic molecules and exhibits even shorter and stronger intermolecular bonds that breach into the range of extremely stretched single bonds in terms of bond distances and binding energies. These properties give rise to promising possibilities in the design of new materials with high electrical conductivity and for the field of spintronics. The analysis of the double pancake bond is based on cutting edge electron correlation theory combining multireference (nondynamical) effects and dispersion (dynamical) contributions in a balanced way providing accurate interaction energies and distributions of unpaired spins. It is also shown that the present examples do not stand isolated but that similar mechanisms operate in several analogous nonradical molecular systems to form double-bonded π-stacking pancake dimers. We report on the amazing properties of a new type of stacking interaction mechanism between π conjugated molecules in the form of a "double pancake bond" which breaks the record for short intermolecular distances and provides formidable strength for some π-π stacking interactions.

Pancake π-stacking produces shorter contacts than van der Waals bonding but it has strongly preferred configurations. By high-level multireference average quadratic coupled cluster theory for the singlet and triplet, we identify the specific orbital component and the nonspecific vdW contributions in the prototypical pancake-bonded dimer of phenalenyl thereby explaining the configurational preferences.

We show that the reaction path connecting the tethered bi(anthracene-9,10-dimethylene) and its photodimer proceeds stepwise via a diradicaloid transition state where one σ-bond is made before a second. The newly found transition state (TS) has a smaller molecular volume than either the reactant or the product giving an atomistic explanation to the recently found pressure catalyzed barrier lowering and rate enhancement. The density functional methods used include long-range contributions as required in a system where the dispersion interactions are significant. We discuss this transformation in the context of the diamond-to-graphite transition owing to the similarity of σ-bond breakage into a delocalized π-system. We also comment on the controversy surrounding the equilibrium geometries of photoisomerized cyclophanes, concluding that D2h symmetry in the photoisomer of the title molecule is a transition structure connecting a pair of degenerate ground state D2 geometries.

Two-electron multicenter (2e/mc) bonding of phenalenyl (PHYL) pi-dimers was found to be significantly affected by the electron density on the bonding active sites. The computational analysis shows that, upon appropriate beta-substitutions, the newly introduced dimers have the shortest and strongest covalent bonding interactions seen in any neutral pi-dimer. The unusual strengthening of the bonding was attributed to the reduced lone pair bond weakening effect, LPBWE, upon substitutions with electron-withdrawing groups.

Density-functional theory (DFT) calculations were performed for energy band structure and geometry optimizations on the stepped pi-chain, the isolated molecule and (di)cations of the chain, and various related molecules of a neutral biphenalenyl biradicaloid (BPBR) organic semiconductor 2. The dependence of the geometries on crystal packing provides indirect evidence for the intermolecular covalent pi-pi bonding interaction through space between neighboring pi-stacked phenalenyl units along the chain. The two phenalenyl electrons on each molecule, occupying the singly occupied molecular orbitals (SOMOs), are participating in the intermolecular covalent pi-pi bonding making them partially localized on the phenalenyl units and less available for intramolecular delocalization. The band structure shows a relatively large bandwidth and small band gap indicative of good pi-pi overlap and delocalization between neighboring pi-stacked phenalenyl units. A new interpretation is presented for the magnetism of the stepped pi-chain of 2 using an alternating Heisenberg chain model, which is consistent with DFT total energy calculations for 2 and prevails against the previous interpretation using a Bleaney-Bowers dimer model. The obtained transfer integrals and the magnetic exchange parameters fit well into the framework of a Hubbard model. All presented analyses on molecular geometries, energy bands, and magnetism provide a coherent picture for 2 pointing toward an alternating chain with significant intermolecular through-space covalent pi-pi bonding interactions in the molecular crystal. Surprisingly, both the intermolecular transfer integrals and exchange parameters are larger than the intramolecular through-bond values indicating the effectiveness of the intermolecular overlap of the phenalenyl SOMO electrons.

Multicenter covalent pi-bonding between pi-conjugated radicals has been recently recognized as a novel and important bonding interaction. The Cope rearrangement of cyclo-biphenalenyl 9 is studied by exploring its potential energy surface with density functional theory (DFT), and it is found that pi-bonding plays a critical role in the rearrangement process. Affected by this, the rearrangement of 9 takes place by a stepwise mechanism through an unusual pi-intermediate 10, of C2h symmetry, which can be characterized as a 2 x 13pi + 2 x 2pi system. The pi-intermediate has a long inter-phenalenyl distance of R approximately 2.8 angstroms, which is shorter than the sum of the van der Waals radii displaying multicenter covalent pi-bonding between the two phenalenyl units. The energy of the pi-intermediate 10 is higher than that of the sigma-bonded reactant 9 by approximately 2 kcal/mol according to the employed spin-restricted DFT. NMR chemical shift calculations support the sigma-bonded 9 as the global minimum. The calculated activation barrier of approximately 6 kcal/mol for the Cope rearrangement is consistent with the stepwise mechanism. A covalent pi-bonding effect in the pi-intermediate 10 is demonstrated indirectly by the shortening of inter-naphthalene distance of the dianion and dication of the cyclophane 14 compared to that of its neutral counterpart. The unusual pi-bonded structure with a long inter-phenalenyl distance becomes the most stable structure for the ethano-bridged derivative 13, which should have observable paramagnetism according to the calculated paramagnetic susceptibility.

The unprecedented metallic character of the cyclohexyl-substituted spiro-biphenalenyl neutral radical molecular crystal (5) suggested by its Pauli paramagnetism [Science 2005, 309, 281] is contradicted by the thermally activated conduction measured along the needle axis of crystal 5 and by an optical gap of Eg = 0.34 eV. Herein we provide the first high quality ab initio electronic structure calculations using density functional theory to reconcile these properties. The calculations point toward 5 being a quasi one-dimensional (1-D) material, with a 1-D conducting pathway along the [101] pi-chain direction. Along any directions other than the pi-chain, conduction is impeded by the small interchain overlap. 5 has a quarter-filled band structure with a density of states of N(Ef) = 7.5 states eV-1 at the Fermi level, leading to a metallic character along the pi-chain.

We present ab initio molecular and solid-state calculations at the level of density functional theory (DFT) for the ethyl-substituted spiro-biphenalenyl neutral radical organic conductor. We find that the phase transition of this material is accompanied by a spin crossover (low-spin, LS, to high-spin, HS), and consequently a different band becomes the conduction band. The energy gap (Eg) increases from 0.12 eV of the low-temperature polymorph to 0.23 eV of the high-temperature polymorph corresponding to a different occupancy causing a change in the number of the available charge carriers, explaining the change of conductivity by 2 orders of magnitude at the phase transition. These gap values are also consistent with structural, IR, electrical conductivity, and magnetic susceptibility data of Itkis et al. The proximity of the monomers in the stacking dimers is closely related to the spin crossover in this material.

Motivated by the central importance of charge-induced dimensional changes for carbon nanotube electromechanical actuators, we here predict changes in nanotube length and diameter as a function of charge injection for armchair and zigzag nanotubes having different diameters. Density functional theory with periodic boundary conditions is used, which we show provides results consistent with experimental observations for intercalated graphites. Strain-versus-charge relationships are predicted from dimensional changes calculated with a uniform background charge ("jellium") for representing the counterions. These jellium calculations are consistent with presented calculations that include specific counterions for intercalated graphite, showing that hybridization between the ions and the graphite sheets is unimportant. The charge-strain relationships calculated with the jellium approximation for graphite and isolated single-walled nanotubes are asymmetric with respect to the sign of charge transfer. The dependence of nanotube strain on charge approaches that for a graphite sheet for intermediate-sized metallic nanotubes and for larger diameter semiconducting nanotubes. However, the strain-charge curves strongly depend on nanotube type when the nanotube diameter is small. This reflects both the dependence of the frontier orbitals for the semiconducting nanotubes on the nanotube type and the pi-sigma mixing when the nanotube diameter is small.