Cyclooctatetraene computational photo- and thermal chemistry: a reactivity model for conjugated hydrocarbons

Restriction on molecular fluxionality by substitution: A case study for the 1,10-dicyanobullvalene

We show herein that 1,10-dicyano substitution restricts the paragon fluxionality of bullvalene to just 14 isomers which isomerize along a single cycle. The restricted fluxionality of 1,10-dicyanobullvalene (DCB) is investigated by means of: (i) Bonding analyses of the isomer structures using the adaptive natural density partitioning (AdNDP). (ii) Quantum dynamical simulations of the isomerizations along the cyclic intrinsic reaction coordinate of the potential energy surface (PES). The PES possesses 14 equivalent potential wells supporting 14 isomers which are separated by 14 equivalent potential barriers supporting 14 transition states. Accordingly, at low temperatures, DCB appears as a hindered molecular rotor, without any delocalization of the wavefunction in the 14 potential wells, without any nuclear spin isomers, and with completely negligible tunneling. These results are compared and found to differ from those for molecular boron rotors. (iii) Born-Oppenheimer molecular dynamics (BOMD) simulations of thermally activated isomerizations. (iv) Calculations of the rate constants in the frame of transition state theory (TST) with reasonable agreement achieved with the BOMD results. (v) Simulations of the equilibration dynamics using rate equations for the isomerizations with TST rate coefficients. Accordingly, in the long-time limit, isomerizations of the 14 isomers, each with Cs symmetry, approach the "14 Cs → C7v" thermally averaged structure. This is a superposition of the 14 equally populated isomer structures with an overall C7v symmetry. By extrapolation, the results for DCB yield working hypotheses for so far un-explored properties e.g. for the equilibration dynamics of C10H10.

Modulating Escape Channels of Cycloheptatrienyl Rhodium Carbenes To Form Semibullvalene

We describe the various escape channels available to dirhodium carbene intermediates from cycloheptatrienyl diazo compounds located with density functional theory. An intramolecular cyclopropanation would, in principle, provide a new route to semibullvalenes (SBVs). A detailed exploration of the potential energy surface reveals that methylating carbon-7 suppresses a competing β-hydride migration pathway to heptafulvene products, giving SBV formation a reasonable chance. During our explorations, we additionally discovered unusual spirononatriene, spironorcaradiene, and metal-stabilized 9-barbaralyl cation structures as local minima.

Monitoring vibronic coherences and molecular aromaticity in photoexcited cyclooctatetraene with an X-ray probe: a simulation study

Understanding conical intersection (CI) dynamics and subsequent conformational changes is key for exploring and controlling photo-reactions in aromatic molecules. Monitoring of their time-resolved dynamics remains a formidable experimental challenge. In this study, we simulate the photoinduced S3 to S1 non-adiabatic dynamics of cyclooctatetraene (COT), involving multiple CIs with relaxation times in good agreement with experiment. We further investigate the possibility to directly probe the CI passages in COT by off-resonant X-ray Raman spectroscopy (TRUECARS) and time-resolved X-ray diffraction (TRXD). We find that these signals sensitively monitor key chemical features during the ultrafast dynamics. First, we distinguish two CIs by using TRUECARS signals with their appearances at different Raman shifts. Second, we demonstrate that TRXD, where X-ray photons scatter off electron densities, can resolve ultrafast changes in the aromaticity of COT. It can further distinguish between planar and non-planar geometries explored during the dynamics, as e.g. two different tetraradical-type CIs. The knowledge gained from these measurements can give unique insight into fundamental chemical properties that dynamically change during non-adiabatic passages.

Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network

The Zagreb connection indices are the known topological descriptors of the graphs that are constructed from the connection cardinality (degree of given nodes lying at a distance 2) presented in 1972 to determine the total electron energy of the alternate hydrocarbons. For a long time, these connection indices did not receive much research attention. Ali and Trinajstić [Mol. Inform. 37, Art. No. 1800008, 2018] examined the Zagreb connection indices and found that they compared to basic Zagreb indices and that they provide a finer value for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers. This article acquires the formulae of expected values of the first Zagreb connection index of a random cyclooctatetraene chain, a random polyphenyls chain, and a random chain network with l number of octagons, hexagons, and pentagons, respectively. The article presents extreme and average values of all the above random chains concerning a set of special chains, including the meta-chain, the ortho-chain, and the para-chain.

Gas-Phase Formation of 1,3,5,7-Cyclooctatetraene (C8H8) through Ring Expansion via the Aromatic 1,3,5-Cyclooctatrien-7-yl Radical (C8H9•) Transient

Gas-phase 1,3,5,7-cyclooctatetraene (C₈H₈) and triplet aromatic 1,3,5,7-cyclooctatetraene (C₈H₈) were formed for the first time through bimolecular methylidyne radical (CH)-1,3,5-cycloheptatriene (C₇H₈) reactions under single-collision conditions on a doublet surface. The reaction involves methylidyne radical addition to the olefinic π electron system of 1,3,5-cycloheptatriene followed by isomerization and ring expansion to an aromatic 1,3,5-cyclooctatrien-7-yl radical (C₈H₉^•). The chemically activated doublet radical intermediate undergoes unimolecular decomposition to 1,3,5,7-cyclooctatetraene. Substituted 1,3,5,7-cyclooctatetraene molecules can be prepared in the gas phase with hydrogen atom(s) in the 1,3,5-cycloheptatriene reactant being replaced by organic side groups. These findings are also of potential interest to organometallic chemists by expanding the synthesis of exotic transition-metal complexes incorporating substituted 1,3,5,7-cyclooctatetraene dianion (C₈H₈^2-) ligands and to untangle the unimolecular decomposition of chemically activated and substituted 1,3,5-cyclooctatrien-7-yl radical, eventually gaining a fundamental insight of their bonding chemistry, electronic structures, and stabilities.

Enumeration of the Gutman and Schultz indices in the random polygonal chains

The Gutman index and Schultz index of a connected graph are degree-distance-based topological indices. In this paper, we devoted to establish the explicit analytical expressions for the simple formulae of the expected values of the Gutman and Schultz indices in a random polygonal. Based on these results above, we get the extremal values and average values of Gunman and Schultz indices of all polygonal chains.

Aromaticity reversals and their effect on bonding in the low-lying electronic states of cyclooctatetraene

Aromaticity reversals and their effect on chemical bonding in the low-lying electronic states of cyclooctatetraene (COT) are investigated through a visual approach which examines the variations in isotropic magnetic shielding in the space surrounding the molecule. The ground state (S₀) of COT is shown to be strongly antiaromatic at the π-bond-shifting transition state (TS), a regular octagon of D_8h symmetry; S₀ antiaromaticity decreases at the D_4h planar bond-alternating tub-to-tub ring-inversion TS but traces of it are shown to persist even at the tub-shaped D_2d local minimum geometry. The lowest triplet (T₁) and first singlet excited (S₁) states of COT are found to have very similar D_8h geometries and visually indistinguishable shielding distributions closely resembling that in benzene and indicating similarly high levels of aromaticity. Unexpectedly, COT diverges from its antiaromatic predecessor, cyclobutadiene, in the properties of the second singlet excited state (S₂): In cyclobutadiene S₂ is antiaromatic but in COT this state turns out to be strongly aromatic, with a shielding distribution closely following that around S₂ benzene.

Nonadiabatic Molecular Dynamics Study of the Relaxation Pathways of Photoexcited Cyclooctatetraene

In the current study, we present nonadiabatic (NAMD) and adiabatic molecular dynamics simulations of the transition-state dynamics of photoexcited cyclooctatetraene (COT). The equilibrium-state structure and absorption spectra are analyzed using the semiempirical Austin Model 1 potential. The NAMD simulations are obtained by a surface-hopping algorithm. We analyzed in detail an active excited to ground state relaxation pathway accompanied by an S₂/S₃(D_2d) → S₁(D_8h) → S₀(D_4h) → S₀(D_2d) double-bond shifting mechanism. The simulated excitation lifetime is in good agreement with experiment. The first excited singlet state S₁ plays a crucial role in the photochemistry. The obtained critical molecular conformations, energy barrier, and transition-state lifetime results will provide a basis for further investigations of the bond-order inversion and photoswitching process of COT.

Is Excited-State Aromaticity a Driving Force for Planarization of Dibenzannelated 8π-Electron Heterocycles?

Compounds with dibenzannelated heterocycles with eight π-electrons are found in a range of applications. These molecules often adopt a bent structure in the ground state (S₀ ) but can become planar in the first excited states (S₁ and T₁ ) because of the cyclically conjugated 4nπ central ring, which fulfils the requirements for excited state aromaticity. We report on a quantum chemical investigation of the aromatic character in the S₁ and T₁ states of dibenzannelated seven- and six-membered heterocycles with one, two, or three heteroatoms in the 8π-electron ring. These states could have ππ* or nπ* character. We find that compounds with one or two heteroatoms in the central ring have ππ* states as their S₁ and T₁ states. They are to a significant degree influenced by excited state aromaticity, and their optimal structures are planar or nearly planar. Among the heteroatoms, nitrogen provides for the strongest excited state aromaticity whereas oxygen provides for the weakest, following the established trend of the S₀ state. Yet, dibenzannelated seven-membered-ring compounds with N=N bonds have non-aromatic nπ* states with strongly puckered structures as their S₁ and T₁ states.

Discovery of conical intersection mediated photochemistry with growing string methods

Conical intersections (CIs) are important features of photochemistry that determine yields and selectivity. Traditional CI optimizers require significant human effort and chemical intuition, which typically restricts searching to only a small region of the CI space. Herein, a systematic approach utilizing the growing string method is introduced to locate multiple CIs. Unintuitive MECI are found using driving coordinates that can be generated using a combinatorial search, and subsequent optimization allows reaction pathways, transition states, products, and seam-space pathways to be located. These capabilities are demonstrated by application to two prototypical photoisomerization reactions and the dimerization of butadiene. In total, many reaction pathways were uncovered, including the elusive stilbene hula-twist mechanism, and a previously unidentified product in butadiene dimerization. Overall, these results suggest that growing string methods provide a predictive strategy for exploring photochemistry.

Molecular Photoswitching Aided by Excited-State Aromaticity

Central to the development of optoelectronic devices is the availability of efficient synthetic molecular photoswitches, the design of which is an arena where the evolving concept of excited-state aromaticity (ESA) is yet to make a big impact. The aim of this minireview is to illustrate the potential of this concept to become a key tool for the future design of photoswitches. The paper starts with a discussion of challenges facing the use of photoswitches for applications and continues with an account of how the ESA concept has progressed since its inception. Then, following some brief remarks on computational modeling of photoswitches and ESA, the paper describes two different approaches to improve the quantum yields and response times of switches driven by E/Z photoisomerization or photoinduced H-atom/proton transfer reactions through simple ESA considerations. It is our hope that these approaches, verified by quantum chemical calculations and molecular dynamics simulations, will help stimulate the application of the ESA concept as a general tool for designing more efficient photoswitches and other functional molecules used in optoelectronic devices.

Spectroscopic Diagnosis of Excited-State Aromaticity: Capturing Electronic Structures and Conformations upon Aromaticity Reversal

Aromaticity, the special energetic stability derived from cyclic [4 n + 2]π-conjugated electronic structures, has been the topic of intense interest in chemistry because it plays a critical role in rationalizing molecular stability, reactivity, and physical/chemical properties. Recently, the pioneering work by Colin Baird on aromaticity reversal, postulating that aromatic (antiaromatic) character in the ground state reverses to antiaromatic (aromatic) character in the lowest excited triplet state, has attracted much scientific attention. The completely reversed aromaticity in the excited state provides direct insight into understanding the photophysical/chemical properties of photoactive materials. In turn, the application of aromatic molecules to photoactive materials has led to numerous studies revealing this aromaticity reversal. However, most studies of excited-state aromaticity have been based on the theoretical point of view. The experimental evaluation of aromaticity in the excited state is still challenging and strenuous because the assessment of (anti)aromaticity with conventional magnetic, energetic, and geometric indices is difficult in the excited state, which practically restricts the extension and application of the concept of excited-state aromaticity. Time-resolved optical spectroscopies can provide a new and alternative avenue to evaluate excited-state aromaticity experimentally while observing changes in the molecular features in the excited states. Time-resolved optical spectroscopies take advantage of ultrafast laser pulses to achieve high time resolution, making them suitable for monitoring ultrafast changes in the excited states of molecular systems. This can provide valuable information for understanding the aromaticity reversal. This Account presents recent breakthroughs in the experimental assessment of excited-state aromaticity and the verification of aromaticity reversal with time-resolved optical spectroscopic measurements. To scrutinize this intriguing and challenging scientific issue, expanded porphyrins have been utilized as the ideal testing platform for investigating aromaticity because they show distinct aromatic and antiaromatic characters with aromaticity-specific spectroscopic features. Expanded porphyrins exhibit perfect aromatic and antiaromatic congener pairs having the same molecular framework but different numbers of π electrons, which facilitates the study of the pure effect of aromaticity by comparative analyses. On the basis of the characteristics of expanded porphyrins, time-resolved electronic and vibrational absorption spectroscopies capture the changes in electronic structure and molecular conformations driven by the change in aromaticity and provide clear evidence for aromaticity reversal in the excited states. The approaches described in this Account pave the way for the development of new and alternative experimental indices for the evaluation of excited-state aromaticity, which will enable overarching and fundamental comprehension of the role of (anti)aromaticity in the stability, dynamics, and reactivity in the excited states with possible implications for practical applications.

Bent Bonds (τ) and the Antiperiplanar Hypothesis-The Chemistry of Cyclooctatetraene and Other C8H8 Isomers

The bent bond/antiperiplanar hypothesis (BBAH) has been applied to the thermal rearrangements of cyclooctatetraene and related C₈H₈ isomers. This novel orbital model shows that pyramidal singlet diradical intermediates produced from thermal vibrational states of C₈H₈ isomers account for their chemical reactivity.

Structural Monitoring of the Onset of Excited-State Aromaticity in a Liquid Crystal Phase

Aromaticity of photoexcited molecules is an important concept in organic chemistry. Its theory, Baird's rule for triplet aromaticity since 1972 gives the rationale of photoinduced conformational changes and photochemical reactivities of cyclic π-conjugated systems. However, it is still challenging to monitor the dynamic structural change induced by the excited-state aromaticity, particularly in condensed materials. Here we report direct structural observation of a molecular motion and a subsequent packing deformation accompanied by the excited-state aromaticity. Photoactive liquid crystal (LC) molecules featuring a π-expanded cyclooctatetraene core unit are orientationally ordered but loosely packed in a columnar LC phase, and therefore a photoinduced conformational planarization by the excited-state aromaticity has been successfully observed by time-resolved electron diffractometry and vibrational spectroscopy. The structural change took place in the vicinity of excited molecules, producing a twisted stacking structure. A nanoscale torque driven by the excited-state aromaticity can be used as the working mechanism of new photoresponsive materials.

Cyclopropyl Group: An Excited-State Aromaticity Indicator?

The cyclopropyl (cPr) group, which is a well-known probe for detecting radical character at atoms to which it is connected, is tested as an indicator for aromaticity in the first ππ* triplet and singlet excited states (T₁ and S₁ ). Baird's rule says that the π-electron counts for aromaticity and antiaromaticity in the T₁ and S₁ states are opposite to Hückel's rule in the ground state (S₀ ). Our hypothesis is that the cPr group, as a result of Baird's rule, will remain closed when attached to an excited-state aromatic ring, enabling it to be used as an indicator to distinguish excited-state aromatic rings from excited-state antiaromatic and nonaromatic rings. Quantum chemical calculations and photoreactivity experiments support our hypothesis; calculated aromaticity indices reveal that openings of cPr substituents on [4n]annulenes ruin the excited-state aromaticity in energetically unfavorable processes. Yet, polycyclic compounds influenced by excited-state aromaticity (e.g., biphenylene), as well as 4nπ-electron heterocycles with two or more heteroatoms represent limitations.

Stabilizing a different cyclooctatetraene stereoisomer

An unconventional cis-cis-cis-trans or (Z,Z,Z,E) structure B of cyclooctatetraene (COT) is calculated to lie only 23 kcal/mol above the well-known tub-shaped (Z,Z,Z,Z) isomer A; one example of this type of structure is known. The barrier for B returning to A is small, 3 kcal/mol. However, by suitable choice of substituents, the (Z,Z,Z,E) isomer can be made to lie in energy below the tub-shaped structure. Steric, clamping, and electronic strategies are proposed for achieving this. In the steric strategy, the C₈H₄(CH₃)₂(C( ^t Bu)₃)₂ structure B is predicted to lie 21 kcal/mol below structure A, which is separated from form B only by a small barrier. A simple clamping strategy, effective for COT planarization, does not influence the A/B isomerization much. But, if the clamping group is aromatic (a fused benzene, pyrrole, thiophene, furan), the subtle interplay of potential aromaticity with clamping can be used to confer persistence if not stability on the (Z,Z,Z,E) isomer. An electronic strategy of a different kind, push-pull substitution on the COT ring, was not very effective in stabilizing the B form. However, it led us to vicinal amine-borane-substituted normal COTs that proved to be quite good at activating H₂ in a frustrated Lewis pair scenario.

Energetics of Baird aromaticity supported by inversion of photoexcited chiral [4n]annulene derivatives

For the concept of aromaticity, energetic quantification is crucial. However, this has been elusive for excited-state (Baird) aromaticity. Here we report our serendipitous discovery of two nonplanar thiophene-fused chiral [4n]annulenes Th4 COT Saddle and Th6 CDH Screw , which by computational analysis turned out to be a pair of molecules suitable for energetic quantification of Baird aromaticity. Their enantiomers were separable chromatographically but racemized thermally, enabling investigation of the ring inversion kinetics. In contrast to Th6 CDH Screw , which inverts through a nonplanar transition state, the inversion of Th4 COT Saddle , progressing through a planar transition state, was remarkably accelerated upon photoexcitation. As predicted by Baird's theory, the planar conformation of Th4 COT Saddle is stabilized in the photoexcited state, thereby enabling lower activation enthalpy than that in the ground state. The lowering of the activation enthalpy, i.e., the energetic impact of excited-state aromaticity, was quantified experimentally to be as high as 21-22 kcal mol-1.Baird's rule applies to cyclic π-conjugated molecules in their excited state, yet a quantification of the involved energetics is elusive. Here, the authors show the ring inversion kinetics of two nonplanar and chiral [4n]annulenes to support Baird's rule from an energetic point of view.

Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials

The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.

Exploration of Quenching Pathways of Multiluminescent Acenes Using the GRRM Method with the SF-TDDFT Method

The quenching pathways were investigated for three types of multiluminescent acene derivatives, which show environment-dependent fluorescence. Spin-flip time dependent density functional theory (SF-TDDFT) combined with the Global Reaction Route mapping (GRRM) strategy is employed to locate minimum-energy conical intersections (MECIs). The energies and geometries of the MECIs relative to the Franck-Condon (FC) state control the difference in fluorescence behavior among the three derivatives. For the molecule with a phenyamide moiety, a MECI with energy lower than the FC state with large geometrical change from V-type to flat structure provides an efficient internal conversion (quenching) pathway in solution. For the same molecule, in a solid, this large geometrical change is inhibited, and the second MECI, with an energy lower than FC but higher than the first MECI requiring only a small geometry change of CH out-of-plane bending, contributes to the quenching. The molecule with the napthaleneimide moiety has only one low-energy MECI that requires large geometrical change from the V-type to flat structure. Although this MECI provides the quenching pathway in solution, in the solid, this large motion is inhibited, and the molecule will stay in the excited state and emit. The molecule with an anthraceneimide moiety has no conical intersection lower than the FC state, and no quenching pathway is available in solution or solid. In addition, in this molecule, at the local minimum of the excited state, the dipole transition to the ground state is allowed, and this molecule prefers emission rather than internal conversion.

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Example of concerted electronic (right) and nuclear (left) fluxes: isomerization of B₄.

Aromaticity changes along the lowest-triplet-state path for C=C bond rotation of annulenyl-substituted olefins probed by the electron localization function

The pi-contribution to the electron localization function (ELF(pi)) was used to analyze changes in the aromaticity of annulenyl-substituted olefins in their lowest triplet state (T1) when the structure around the olefin C=C bond is twisted from planar to a structure (3p*) at which the planes of the two RR'C units are perpendicular. The ring closure bifurcation value and the range in the bifurcation values of the ELF(pi) basins serve as (anti)aromaticity indicators directly linked to the electronic structure. Both Hückel's 4n + 2 pi-electron rule for aromaticity in the singlet ground state (S0) and Baird's 4n pi-electron rule for aromaticity in the lowest pipi* triplet state are applied. Three olefins with S0 aromatic (T1 antiaromatic) substituents and four olefins with T1 aromatic (S0 antiaromatic) substituents were studied using the ELF(pi) topology at the OLYP/6-311G(d,p) density functional theory level. The changes in the substituent ELF(pi) bifurcation values upon rotation about the olefin bond in the T1 state reveal that aromatic character is recovered for the first three olefins and that it is reduced for the latter ones. These changes in aromatic character are reflected in the shapes of the T1 potential energy surfaces as a twist away from planar structures in olefins with T1 antiaromatic substituents is energetically favorable, but that in olefins with T1 aromatic substituents is unfavorable. Hence, aromaticity change is a driver for a photochemical reaction as for many ground-state reactions.

Aromaticity and antiaromaticity in the low-lying electronic states of cyclooctatetraene

The levels of aromaticity of the most important geometries on the ground-state (S(0)), lowest triplet-state (T(1)), and first singlet excited-state (S(1)) potential energy surfaces (PESs) for cycloocta-1,3,5,7-tetraene (COT) are assessed using a wide range of magnetic criteria including nucleus-independent chemical shifts (NICSs), proton shieldings, and magnetic susceptibilities calculated using complete-active-space self-consistent-field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). It is shown that the ground state of D(8h) COT (transition state for the pi-bond-shift process on the S(0) PES) is markedly antiaromatic, even more so than the classical example of an antiaromatic system, the ground state of square cyclobutadiene. The CASSCF-GIAO magnetic properties of the ground state of D(4h) COT (transition state for the ring-inversion process on the S(0) PES) strongly suggest that it is much less antiaromatic than the ground state of D(8h) COT, whereas those of the ground state of D(2d) COT (local minimum on the S(0) PES) indicate that it is decidedly nonaromatic. The lowest triplet state and the first singlet excited state of D(8h) COT (local minima on the T(1) PES and the S(1) PES, respectively) exhibit surprisingly similar magnetic properties. These, in turn, are very close to the magnetic properties of benzene, which is a strong indication of a high degree of aromaticity.