Structure and Bonding in π-Stacked Perylenes: The Impact of Charge on Pancake Bonding.

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 ([(C20H12)2]•+ or PER2+), crucial for stabilizing aggregation and crystal formation. We discovered energetically feasible sliding and rotation pathways within the [(C20H12)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 (PER2+), 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.

Aggregation of One-Dimensional Wires: The Case of Long Oligoynes.

We show an unexpected aggregation phenomenon of a long oligoyne (Py[16]) with 16 contiguous triple bonds and endcapped with bulky 3,5-bi(3,5-bis-tert-butylphenyl)pyridine groups. Aggregation of 1D p-conjugated oligoyne chains is rare, given the minimal p-p intermolecular interactions of the weakly polarizable polyyne chain, as well as its flexibility that works against self assembly. In dilute solutions, the reversible aggregation of Py[16] initiates at low temperature in the range of 140-180 K, and is not observed for shorter oligoynes in this series. Cryogenic UV-Vis electronic absorption spectra and vibrational Raman spectra with different laser wavelength lines tuning from in-resonance to off-resonance conditions have been used to extract the vibrational features characterizing the Monomer and aggregate species. Theoretical calculations complement the spectroscopic findings.

Functional trait trade-offs define plant population stability across different biomes.

Ecological theory posits that temporal stability patterns in plant populations are associated with differences in species' ecological strategies. However, empirical evidence is lacking about which traits, or trade-offs, underlie species stability, especially across different biomes. We compiled a worldwide collection of long-term permanent vegetation records (greater than 7000 plots from 78 datasets) from a large range of habitats which we combined with existing trait databases. We tested whether the observed inter-annual variability in species abundance (coefficient of variation) was related to multiple individual traits. We found that populations with greater leaf dry matter content and seed mass were more stable over time. Despite the variability explained by these traits being low, their effect was consistent across different datasets. Other traits played a significant, albeit weaker, role in species stability, and the inclusion of multi-variate axes or phylogeny did not substantially modify nor improve predictions. These results provide empirical evidence and highlight the relevance of specific ecological trade-offs, i.e. in different resource-use and dispersal strategies, for plant populations stability across multiple biomes. Further research is, however, necessary to integrate and evaluate the role of other specific traits, often not available in databases, and intraspecific trait variability in modulating species stability.

Polyradical character assessment using multireference calculations and comparison with density-functional derived fractional occupation number weighted density analysis.

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties. In this work, the unpaired electron densities and numbers of unpaired electrons (NU values) calculated at the high-level multireference averaged quadratic coupled-cluster (MR-AQCC) method are used to develop a test set to assess the capabilities of different biradical descriptors based on density functional theory. A benchmark collection of 29 different compounds has been selected. The DFT descriptors contain primarily the fractional occupation number weighted electron density (FOD) based on simplified thermally-assisted-occupation density functional theory (TAO-DFT) calculations, but the singlet-triplet energy difference and other descriptors denoted as y0 and nLUNO have been considered as well. After adjustment of the literature-recommended finite temperatures, a very good, detailed agreement between unpaired density and FOD analysis is observed which is also manifested in excellent statistical correlations. The other two descriptors also show good correlations even though the absolute scaling is not satisfactory. A new linear fit of FOD data to the MR-AQCC reference values leads to an improved regression relation for determining the recommended finite temperature value in dependence of the Hartree-Fock exchange. This provides the basis for fast and reliable assessment of the biradical character of many classes of PAHs without the need for performing computationally extended MR calculations.

Extremely Long C-C Bonds Predicted beyond 2.0 Å.

A number of conjugated molecules are designed with extremely long single C-C bonds beyond 2.0 Å. Some of the investigated molecules are based on analogues to the recently discovered molecule by Kubo et al. These bonds are analyzed by a variety of indices in addition to their equilibrium bond length including the Wiberg bond index, bond dissociation energy (BDE), and measures of diradicaloid character. All unrestricted DFT calculations indicate no diradical character supported by high-level multireference calculations. Finally, NFOD was computed through fractional orbital density (FOD) calculations and used to compare relative differences of diradicaloid character across twisted molecules without central C-C bonding and those with extremely elongated C-C bonds using a comparison with the C-C bond breaking in ethane. No example of direct C-C bonds beyond 2.4 Å are seen in the computational modeling; however, extremely stretched C-C bonds in the vicinity of 2.2 Å are predicted to be achievable with a BDE of 15-25 kcal mol-1.

Synchrony matters more than species richness in plant community stability at a global scale.

The stability of ecological communities is critical for the stable provisioning of ecosystem services, such as food and forage production, carbon sequestration, and soil fertility. Greater biodiversity is expected to enhance stability across years by decreasing synchrony among species, but the drivers of stability in nature remain poorly resolved. Our analysis of time series from 79 datasets across the world showed that stability was associated more strongly with the degree of synchrony among dominant species than with species richness. The relatively weak influence of species richness is consistent with theory predicting that the effect of richness on stability weakens when synchrony is higher than expected under random fluctuations, which was the case in most communities. Land management, nutrient addition, and climate change treatments had relatively weak and varying effects on stability, modifying how species richness, synchrony, and stability interact. Our results demonstrate the prevalence of biotic drivers on ecosystem stability, with the potential for environmental drivers to alter the intricate relationship among richness, synchrony, and stability.

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration.

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C96 H24 Ar6 )2 (Ar=2,6-dimethylphenyl) (12 ) was transformed to a triply negatively charged species 12 3.- , which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 12 3.- features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp2 carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 12 3.- , which indicates graphene upon reduction doping may behave as a quantum spin liquid.

Splitting the Ring: Impact of Ortho and Meta Pi Conjugation Pathways through Disjointed [8]Cycloparaphenylene Electronic Materials.

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 (C2 symmetry) and anti (C1 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.

Molecular tetrominoes: selective masking of the donor π-face to control the configuration of donor-acceptor complexes.

Understanding the doping mechanism in organic semiconductors and generating molecular design rules to control the doping process are crucial for improving the performance of organic electronics. Even though controlling the location and orientation of the dopant along the semiconductor backbone is an important step in the doping mechanism, studies in this direction are scarce as it is a challenging task. To address this, herein, we incorporated π-face masked (strapped) units in 1,4-bis(phenylethynylene)benzene (donor) to control the acceptor (dopant) location along the trimer, donor-acceptor binding strength, and acceptor ionization. Two strapped trimers, PCP and CPC, are synthesized with control over the location of the strapped repeat unit in the trimer. The trimers are complexed with the 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) acceptor in solution. DFT calculations show that DDQ residing on the non-strapped repeat unit (the percentage of this configuration is at least ca. 73%) has the highest binding energy for both PCP and CPC. The percentage of dopant ionization is higher in the case of strapped trimers (PCP and CPC) compared to that of linear control trimers (PLP and LPL) and the completely non-strapped (PPP) trimer. The percentage of dopant ionization increased by 15 and 59% in the case of PCP and CPC respectively compared to that of PPP.

Polycyclic Hydrocarbons from [4n]Annulenes: Correlation versus Hybridization Forces in the Formation of Diradicaloids.

The conceptual connections between [4n] Hückel antiaromaticity, disjoint orbitals, correlation energy, pro-aromaticity and diradical character for a variety of extended π-conjugated systems, including some salient recent examples of nanographenes and polycyclic aromatic radicals, are provided based on their [4n]annulene peripheries. The realization of such structure-property relationships has led to a beneficial pedagogic exercise establishing design guidelines for diradicaloids. The antiaromatic fingerprint of the [4n]annulene peripheries upon orbital interactions due to internal covalent connectors gives insights into the diradicaloid property of a diversity of π-conjugated molecules that have fascinated chemists recently.

NMR spectral fingerprint patterns as diagnostics for the unambiguous configurational analysis of the classic organo-gelator 1,3:2,4-dibenzylidene-d-sorbitol (DBS) and its derivatives.

On the basis of experimental data and density functional theory (DFT) chemical shift and scalar coupling predictions, simple spectral nuclear magnetic resonance (NMR) fingerprint patterns have been established for the determination of the configuration in 1,3:2,4-dibenzylidene-d-sorbitol (DBS), a classic low molecular weight gelator, and its derivatives. The results rigorously prove the orientation of the phenyl rings in DBS that had been previously assumed in the literature on the basis of thermodynamic arguments.

Linear and Radial Conjugation in Extended π-Electron Systems.

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.

Quinonoid vs. aromatic structures of heteroconjugated polymers from oligomer calculations.

Conjugated polymers with quinonoid ground states can display low optical band gaps. The design of novel conjugated polymers with quinonoid ground states offers insights into the relative stabilities of aromatic vs. quinonoid structures. In this work, we present parameters such as the quinonoid (Q)/aromatic (A) energy difference, the band gap, and the C-C distances between the repeat units. This study reveals eight new polymers which exist in quinonoid ground state among twenty-nine polymers of varying structural composition that were subject to analysis. We expect that copolymerizing such quinonoid ground state monomers with aromatic ground state monomers will modulate the bandgap of the resulting polymers.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry.

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

Pancake Bonding: An Unusual Pi-Stacking Interaction.

A category of parallel π-stacking interaction, termed pancake bonding, is surveyed. The main characteristics are: the interaction occurs among radicals with highly delocalized π-electrons in their singly occupied molecular orbitals (SOMOs), the contact distances in the π-stacking direction are shorter than the typical van der Waals distances, and the stabilization obtained by the bonding combination of the SOMO orbitals leads to direct atom-to-atom overlap with strong orientational preferences. These atypical intermolecular interactions contain a component of electron sharing between the radicals that can be viewed as covalent-like. Pancake bonded dimers characteristically have low-lying singlet and triplet states and show characteristic interlayer vibrational modes. Pancake bonded aggregates serve as molecular components in many conducting and other functional organic materials. The role of van der Waals (vdW) interactions in pancake bonded dimers, chains, and other aggregates is different from closed shell vdW aggregates: here the Pauli repulsions reduce the attractive dispersion interaction significantly. Fluxionality between π- and σ-bonded aggregates often occur in the context of pancake bonding. Both experimental and computational aspects are reviewed.

Sigma- versus Pi-Dimerization Modes of Triangulene.

We show that the diradicaloid triangulene, a graphene nano-flake molecule, can aggregate in a variety of dimerization modes. We found by density functional theory modeling a number of triangulene dimers including six doubly bonded σ-dimers in addition to the previously reported six pancake bonded π-dimer isomers. The σ-dimers display a wide range of stabilities: the interaction energy of the most stable σ-dimer is -25.17 kcal mol-1 . Besides the doubly bonded σ-dimers with closed shell ground states, we also found an open-shell singly σ-bonded diradicaloid dimer. We found an interesting isomerization route between a doubly bonded σ-dimer, a singly bonded σ-dimer with a low-lying triplet state and two π-bonded dimers with low-lying quintet states. Derivatives of triangulene, trioxo-triangulenes (TOTs) have been previously characterized experimentally. Here, we show the reasons why so far only the π-dimer but not the σ-dimer was experimentally observed for all TOTs.

Pancake Bonding in π-Stacked Trimers in a Salt of Tetrachloroquinone Anion.

The crystal structure of [4-damp])2 [Cl4 Q]3 (4-damp=4-dimethylamino-N-methylpyridinium, Cl4 Q=tetrachloroquinone) salt is built up from slipped columnar stacks of quinoid rings composed of closely bound trimers with the intra-trimer separation distance of 2.84 Šand total charge of -2 whereas the inter-trimer distance is 3.59 Å. The individual rings exhibit partial negative charges that are distributed unevenly among the three Cl4 Qs in the trimer. The strong interactions within a trimer (Cl4 Q)32- have a partially covalent character with two-electron/multicentered bonding, that is extended over three rings, plausibly termed as "pancake bonding". The electron pairing within this multicentre bond leads to the fact that the crystals are diamagnetic and act as insulators. The studies of the structure and nature of bonding are based on X-ray charge density analysis and density functional theory.

Mechanochemistry in [6]Cycloparaphenylene: A Combined Raman Spectroscopy and Density Functional Theory Study.

Raman spectroscopy under high pressures up to 10 GPa and density functional computations up to 30 GPa are combined to obtain insights into the behavior of a prototypical nanohoop conjugated molecule, [6]cycloparaphenylene ([6]CPP). Upon increasing pressure, the nanohoop undergoes deformations, first reversible ovalization and then at even higher pressures aggregates are formed. This irreversible aggregation is caused by the formation of new intermolecular σ-bonds. Frequencies and derivatives of the Raman frequency shifts as a function of pressure are well reproduced by the computations. The frequency behavior is tied to changes in aromatic/quinonoid character of the nanohoop. The modeling at moderate high pressures reveals the deformation of the [6]CPP molecules into oval-like and peanut-like shapes. Surprisingly the pressure derivatives of the observed Raman mode shifts undergo a sudden change around a pressure value that is common to all Raman modes, indicating an underlying geometrical change extended over the whole molecule that is interpreted by the computational modeling. Simulations predict that under even larger deformations caused by higher pressures, oligomerization reactions would be triggered. Our simulations demonstrate that these transformations would occur regardless of the solvent, however pressures at which they happen are influenced by solvent molecules encapsulated in the interior of the [6]CPP.

Cethrene: The Chameleon of Woodward-Hoffmann Rules.

We demonstrate that the electrocyclic (EC) ring-closure of cethrene in solution proceeds in a conrotatory mode both thermally and photochemically. The facile photochemical EC process promises that cethrene can serve as an efficient chiroptical switch operated solely by light. As for the thermally activated EC reaction, a low reaction barrier and a solvation effect on the EC rate indicate that the C2-symmetric pathway predicted by DFT calculations might not be the correct mechanism. Instead, we argue that the molecular symmetry decreases along the reaction coordinate as a consequence of the low-energy singlet excited state in this diradicaloid molecule, which might lead to a lower activation energy in accord with that determined through kinetic studies. Cethrene, therefore, represents a thought-provoking molecular chameleon of the Woodward-Hoffmann rules that puts our chemical concepts and intuition to test.

Intramolecular Pancake Bonding in Helical Structures.

We show that diradicaloid helical conjugated molecules can display strong through-space bonding interactions. These interactions are analogous to π-stacking pancake bonding widely observed for dimers and other aggregates of stable π-conjugated radicals. We show that these multicenter interactions can have a significant stabilizing effect, but they depend in subtle ways on the specific overlap and relative orientations of the radical carrying subunits. The specific through-space interactions between the radicaloid units occur at specific size ranges of the helical molecules.