Tunneling by 16 Carbons: Planar Bond Shifting in [16]Annulene

Unveiling Möbius/Hückel Topology and Aromaticity in A Core-Expanded [10]Annulene at Different Oxidation States

The exploration of annulene's conformation, electronic properties and aromaticity has generated enduring interest over the years, yet it continues to present formidable challenges for annulenes with more than ten carbon atoms. In this study, we present the synthesis of a stable [10]cyclo-para-phenylmethine derivative (1), which bears a resemblance to [10]annulene. 1 can be readily oxidized into its respective cations, wherein electrons are effectively delocalized along the backbone, resulting in different conformations and aromaticity. Both 1 and its tetracation (14+  ⋅ 4SbF6 - ) exhibit a nearly planar conformation with a rectangular shape, akin to the E,Z,E,Z,Z-[10]annulene. In contrast, the radical cation (1⋅+  ⋅ SbCl6 - ) possesses a doubly twisted Hückel topology. Furthermore, the dication (12+  ⋅ 2SbCl6 - ) displays conformational flexibility in solution and crystalizes with the simultaneous presence of Möbius-twisted (1a2+  ⋅ 2SbCl6 - ) and Hückel-planar (1b2+  ⋅ 2SbCl6 - ) isomers in its unit cell. Detailed experimental measurements and theoretical calculations reveal that: (1) 1 demonstrates localized aromaticity with an alternating benzenoid/quinoid structure; (2) 1a2+  ⋅ 2SbCl6 - and 1b2+  ⋅ 2SbCl6 - with 48π electrons are weakly Möbius aromatic and Hückel antiaromatic, respectively; (3) 14+  ⋅ 4SbF6 - exhibits Hückel aromaticity (46π) and open-shell diradical character.

Synthesis and Characterization of Dibenzothieno[a,f]pentalenes Enabling Large Antiaromaticity and Moderate Open-Shell Character through a Small Energy Barrier for Bond-Shift Valence Tautomerization

Experimental and theoretical rationalization of bond-shift valence tautomerization, characterized by double-well potential surfaces, is one of the most challenging topics of study among the rich electronic properties of antiaromatic molecules. Although the pseudo-Jahn-Teller effect (PJTE) is an essential effect to provide attractive characteristics of 4nπ systems, an understanding of the structure-property relationship derived from the PJTE for planar 4nπ electron systems is still in its infancy. Herein, we describe the synthesis and characterization of two regioisomers of the thiophene-fused diareno[a,f]pentalenes 6 and 7. The magnetic and optoelectronic properties characterize these sulfur-doped diareno[a,f]pentalenes as open-shell antiaromatic molecules, in sharp contrast to the closed-shell antiaromatic systems of 3 and 5, in which these main cores consist of the same number of π electrons as 6 and 7. Notably, thiophene-fused 6b and 7b showed pronounced antiaromaticity, the strongest among the previous systems, as well as moderate open-shell characteristics. Our experimental and theoretical investigations concluded that these properties of 6b and 7b are derived from the small energy barrier Ea‡ for the bond-shift valence tautomerization. The energy profile of the single crystal of 6b showed the temperature-dependent structural variations assigned to the dynamic mutual exchange between the two Cs-symmetric structures, which was also supported by changes in the chemical shifts of variable-temperature 1H NMR spectra in the solution phase. Both experimental and computational results revealed the importance of introducing heteroaromatic rings into 4nπ systems for controlling the PJTE and manifesting the antiaromatic and open-shell natures originating from the high-symmetric structure. The findings of this study advance the understanding of antiaromaticity characterized by the PJTE by controlling the energy barrier for bond-shift valence tautomerizations, potentially leading to the rational design of optoelectronic devices based on novel antiaromatic molecules possessing the strong contributions of their high-symmetric geometries.

Quantum Tunneling in Reactions Modulated by External Electric Fields: Reactivity and Selectivity

Quantum tunneling and external electric fields (EEFs) can promote some reactions. However, the synergetic effect of an EEF on a tunneling-involving reaction and its temperature-dependence is not very clear. In this study, we extensively investigated how EEFs affect three reactions that involve hydrogen- or (ground- and excited-state) carbon-tunneling using reliable DFT, DLPNO-CCSD(T1), and variational transition-state theory methods. Our study revealed that oriented EEFs can significantly reduce the barrier and corresponding barrier width (and vice versa) through more electrostatic stabilization in transition states. These EEF effects enhance the nontunneling and tunneling-involving rates. Such EEF effects also decrease the crossover temperatures and quantum tunneling contribution, albeit with lower and thinner barriers. Moreover, EEFs can modulate and switch on/off the tunneling-driven 1,2-H migration of hydroxycarbenes under cryogenic conditions. Furthermore, our study predicts for the first time that EEF/tunneling synergy can control the chemo- or site-selectivity of one molecule bearing two similar/same reactive sites.

Simultaneous Tunneling Control in Conformer-Specific Reactions

We present here a new example of chemical reactivity governed by quantum tunneling, which also highlights the limitations of the classical theories. The syn and anti conformers of a triplet 2-formylphenylnitrene, generated in a nitrogen matrix, were found to spontaneously rearrange to the corresponding 2,1-benzisoxazole and imino-ketene, respectively. The kinetics of both transformations were measured at 10 and 20 K and found to be temperature-independent, providing clear evidence of concomitant tunneling reactions (heavy-atom and H-atom). Computations confirm the existence of these tunneling reaction pathways. Although the energy barrier between the nitrene conformers is lower than any of the observed reactions, no conformational interconversion was observed. These results demonstrate an unprecedented case of simultaneous tunneling control in conformer-specific reactions of the same chemical species. The product outcome is impossible to be rationalized by the conventional kinetic or thermodynamic control.

Difficulty of the evaluation of the barrier height of an open-shell transition state between closed shell minima: The case of small C4n rings

C_4n cyclacenes exhibit strong bond-alternation in their equilibrium geometry. In the two equivalent geometries, the system keeps an essentially closed-shell character. The two energy minima are separated by a transition state suppressing the bond-alternation, where the wave function is strongly diradical. This paper discusses the physical factors involved in this energy difference and possible evaluations of the barrier height. The barrier given as the energy difference between the restricted density functional theory (DFT)/B3LYP for the equilibrium and the broken symmetry DFT/B3LYP of the transition state is either negative or small, in contradiction with the most reliable Wave Function Theory calculations. The minimal (two electrons in two molecular orbitals) Complete Active Space self-consistent field (CASSCF) overestimates the barrier, and the subsequent second-order perturbation cancels it. Due to the collective character of the spin-polarization effect, it is necessary to perform a full π CASSCF + second-order perturbation to reach a reasonable value of the barrier, but this type of treatment cannot be applied to large molecules. DFT procedures treating on an equal foot the closed-shell and open-shell geometries have been explored, such as Mixed-Reference Spin-Flip Time-dependent-DFT and a new spin-decontamination proposal, namely, DFT-dressed configuration interaction, but the results still depend on the density functional. M06-2X without or with spin-decontamination gives the best agreement with the accurate wave function results.

Computational Evidence for Tunneling and a Hidden Intermediate in the Biosynthesis of Tetrahydrocannabinol

Quantum tunneling is computed for a reaction sequence that models the conversion of the ortho-quinone methide of cannabigerolic acid 1 to the decarboxylated product (-)-trans-Δ⁹-tetrahydrocannabinol (THC, 3). This calculation is the first to evaluate multidimensional tunneling in this sequence. Computations were carried out with POLYRATE and GAUSSRATE using B3LYP/6-31G(d,p) to examine the mechanism of THC 3 formation. The pentyl chain on THC 3 and its precursors were replaced with a methyl group to compute tunneling contributions to the rates of four separate steps: (i) initial Diels-Alder reaction of the quinone methide with the trisubstituted alkene end-group of the geranyl 1Z-CH₃ to give 2Z-CH₃, (ii) acid-catalyzed keto-enol tautomerization, which converts 2rZ-CH₃ to 4rZ-CH₃, (iii) carboxyl rotamerization converting 4rZ-CH₃ to 4E-CH₃, and (iv) decarboxylation that converts 4E-CH₃ to 3-CH₃. Tunneling contributions to the rate constants of steps (i)-(iv) are between 19 and 76% at 293 K. In step (ii), nonuniform changes in the zero-point vibrational energy along the reaction path created a shallow minimum in the 0 K free energy. It is a hidden intermediate because it is not a minimum on the potential energy surface and is detectable only when zero-point energy is taken into account along the reaction path. Predicted kinetic isotope effects would be experimentally observable at temperatures that are convenient to use. This is particularly relevant in the decarboxylation stage of the reaction sequence and has important implications because of its role in THC 3 formation.

Cyclic polyacetylene

Here we demonstrate the synthesis of cyclic polyacetylene (c-PA), or [∞]annulene, via homogeneous tungsten-catalysed polymerization of acetylene. Unique to the cyclic structure and evidence for its topology, the c-PA contains >99% trans double bonds, even when synthesized at -94 °C. High activity with low catalyst loadings allows for the synthesis of temporarily soluble c-PA, thus opening the opportunity to derivatize the polymer in solution. Absolute evidence for the cyclic topology comes from atomic force microscopy images of bottlebrush derivatives generated from soluble c-PA. Now available in its cyclic form, initial characterization studies are presented to elucidate the topological differences compared with traditionally synthesized linear polyacetylene. One advantage to the synthesis of c-PA is the direct synthesis of the trans-transoid isomer. Low defect concentrations, low soliton concentration, and relatively high conjugation lengths are characteristics of c-PA. Efficient catalysis permits the rapid synthesis of lustrous flexible thin films of c-PA, and when doped with I₂, they are highly conductive (398 (±76) Ω^-1 cm^-1).

Quantum mechanical tunnelling: the missing term to achieve sub-kJ mol-1 barrier heights

To predict barrier heights at low temperatures, it is not enough to employ highly accurate electronic structure methods. We discuss the influence of quantum tunnelling on the comparison of experimental and theoretical activation parameters (E_a, ΔH^‡, ΔG^‡, or ΔS^‡), since the slope-based experimental techniques to obtain them completely neglect the tunnelling component. The intramolecular degenerate rearrangement of four fluxional molecules (bullvalene, barbaralane, semibullvalene, and norbornadienylidene) were considered, systems that cover the range between fast deep tunneling and small but significant shallow tunnelling correction. The barriers were computed with the composite W3lite-F12 method at the CCSDT(Q)/CBS level, and the tunnelling contribution with small curvature tunnelling. While at room temperature the effect is small (∼1 kJ mol^-1), at low temperatures it can be considerable (in the order of tens of kJ mol^-1 at ∼80 K).

Hopping Conductance in Molecular Wires Exhibits a Large Heavy-Atom Kinetic Isotope Effect

We report a large kinetic isotope effect (KIE) for intramolecular charge transport in π-conjugated oligophenyleneimine (OPI) molecules connected to Au electrodes. ¹³C and ¹⁵N substitution on the imine bonds produces a conductance KIE of ∼2.7 per labeled atom in long OPI wires >4 nm in length, far larger than typical heavy-atom KIEs for chemical reactions. In contrast, isotopic labeling in shorter OPI wires <4 nm does not produce a conductance KIE, consistent with a direct tunneling mechanism. Temperature-dependent measurements reveal that conductance for a long ¹⁵N-substituted OPI wire is activated, and we propose that the exceptionally large conductance KIEs imply a thermally assisted, through-barrier polaron tunneling mechanism. In general, observation of large conductance KIEs opens up considerable opportunities for understanding microscopic conduction mechanisms in π-conjugated molecules.

Nunes C, Fausto R. Spin-forbidden heavy-atom tunneling in the ring-closure of triplet cyclopentane-1,3-diyl

The putative spin-forbidden heavy-atom tunneling process for the ring closure of cyclopentane-1,3-diyl at cryogenic temperatures is confirmed with calculations employing the weak-coupling formulation of nonadiabatic transition state theory.

Switch chemistry at cryogenic conditions: quantum tunnelling under electric fields

While the influence of intramolecular electric fields is a known feature in enzymes, the use of oriented external electric fields (EEF) to enhance or inhibit molecular reactivity is a promising topic still in its infancy. Herein we will explore computationally the effects that EEF can provoke in simple molecules close to the absolute zero, where quantum tunnelling (QT) is the sole mechanistic option. We studied three exemplary systems, each one with different reactivity features and known QT kinetics: π bond-shifting in pentalene, Cope rearrangement in semibullvalene, and cycloreversion of diazabicyclohexadiene. The kinetics of these cases depend both on the field strength and its direction, usually giving subtle but remarkable changes. However, for the cycloreversion, which suffers large changes on the dipole through the reaction, we also observed striking results. Between the effects caused by the EEF on the QT we observed an inversion of the Arrhenius equation, deactivation of the molecular fluxionality, and stabilization or instantaneous decomposition of the system. All these effects may well be achieved, literally, at the flick of a switch.

Bent Bond/Antiperiplanar Hypothesis and the Chemical Reactivity of Annulenes

The properties and stereochemical reactivity of cyclobutadiene, benzene, cyclooctatetraene, and the [10]- to [14]annulenes can be uniformly rationalized through the bent bond/antiperiplanar hypothesis (BBAH). This new orbital model considers electronic delocalization between pyramidal diradical resonance structures and associated bent bonds, as it applies to aromatic, nonaromatic, and antiaromatic molecules.

Heavy atom tunnelling on XeF6 pseudorotation

XeF₆ has multiple C_3v equivalent minima due to the Jahn–Teller effect. Through computational means we prove that the rearrangement between isomers occurs through fluorine quantum mechanical tunnelling.

Carbon Tunneling in the Automerization of Cyclo[18]carbon

Cyclo[18]carbon (C₁₈ ), a recently synthesized carbon allotrope, was found to have a polyynic ground-state structure with D_9h symmetry and formally alternating single and triple bonds. Yet, under less influencing experimental conditions this molecule might undergo an automerization reaction between its two degenerate geometries through a cumulenic (non-alternating, adjacent double bonds) D_18h transition state. Herein, we discuss the role of quantum mechanical tunneling (QMT) in this degenerate reaction. Our computations predict that at the experimental temperature (5 K) the reaction in the gas phase is completely driven by an extremely rapid heavy atom tunneling (k=2.1×10⁸  s^-1 ). Even when approaching room temperature, the QMT rate is still an order of magnitude faster than the semi-classical one. We propose an experimental test to support our prediction, by measuring a characteristic tunneling energy splitting within the radio wave region. Additionally, we examine the role of QMT in other hypothetical C_4n+2 carbon clusters.

Calculations Predict That Heavy-Atom Tunneling Dominates Möbius Bond Shifting in [12]- and [16]Annulene

The contribution of heavy-atom tunneling to reactions of [12]- and [16]annulene was probed using small-curvature tunneling rate calculations. At the CCSD(T)/cc-pVDZ//M06-2X/cc-pVDZ level, tunneling is predicted to account for more than 50% of the rate for Möbius bond shifting and ca. 35% of the rate for electrocyclization in [12]annulene, and over 80% of the rate for Möbius bond shifting in [16]annulene, at temperatures at which these reactions have been observed experimentally.