The Cope Rearrangement of 1,5-Dimethylsemibullvalene-2(4)-d1 : Experimental Evidence for Heavy-Atom Tunneling

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.

Hydrogen Bonding Shuts Down Tunneling in Hydroxycarbenes: A Gas-Phase Study by Tandem-Mass Spectrometry, Infrared Ion Spectroscopy, and Theory

Hydroxycarbenes can be generated and structurally characterized in the gas phase by collision-induced decarboxylation of α-keto carboxylic acids, followed by infrared ion spectroscopy. Using this approach, we have shown earlier that quantum-mechanical hydrogen tunneling (QMHT) accounts for the isomerization of a charge-tagged phenylhydroxycarbene to the corresponding aldehyde in the gas phase and above room temperature. Herein, we report the results of our current study on aliphatic trialkylammonio-tagged systems. Quite unexpectedly, the flexible 3-(trimethylammonio)propylhydroxycarbene turned out to be stable─no H-shift to either aldehyde or enol occurred. As supported by density functional theory calculations, this novel QMHT inhibition is due to intramolecular H-bonding of a mildly acidic α-ammonio C-H bonds to the hydroxyl carbene's C-atom (C:···H-C). To further support this hypothesis, (4-quinuclidinyl)hydroxycarbenes were synthesized, whose rigid structure prevents this intramolecular H-bonding. The latter hydroxycarbenes underwent "regular" QMHT to the aldehyde at rates comparable to, e.g., methylhydroxycarbene studied by Schreiner et al. While QMHT has been shown for a number of biological H-shift processes, its inhibition by H-bonding disclosed here may serve for the stabilization of highly reactive intermediates such as carbenes, even as a mechanism for biasing intrinsic selectivity patterns.

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.

Transformations of Strained Three-Membered Rings a Common, Yet Overlooked, Motif in Heavy-Atom Tunneling Reactions

Quantum mechanical tunneling has long been recognized as an important phenomenon when considering transformations dominated by a lightweight hydrogen atom. Tunneling of heavier atoms like carbon, initially dismissed as negligible, has seen a quickly increasing number of computationally predicted and/or experimentally confirmed examples over the last decade, thus highlighting its importance for a wide variety of reactions. However, no common structural motif has been pointed out within these seemingly unconnected examples, strongly limiting the predictability of the impact of heavy-atom tunneling on a given reaction. This Concept article will provide this perspective and showcase how the recognition of the formation and cleavage of three-membered rings as common motif can inform the prediction of and research into heavy-atom tunneling reactions.

Solvation Effects on Quantum Tunneling Reactions

A decisive factor for obtaining high yields and selectivities in organic synthesis is the choice of the proper solvent. Solvent selection is often guided by the intuitive understanding of transition state-solvent interactions. However, quantum-mechanical tunneling can significantly contribute to chemical reactions, circumventing the transition state and thus depriving chemists of their intuitive handle on the reaction kinetics. In this Account, we aim to provide rationales for the effects of solvation on tunneling reactions derived from experiments performed in cryogenic matrices.The tunneling reactions analyzed here cover a broad range of prototypical organic transformations that are subject to strong solvation effects. Examples are the hydrogen tunneling probability for the cis-trans isomerization of formic acid which is strongly reduced upon formation of hydrogen-bonded complexes and the [1,2]H-shift in methylhydroxycarbene where a change in product selectivity is predicted upon interaction with hydrogen bond acceptors.Not only hydrogen but also heavy atom tunneling can exhibit strong solvent effects. The direction of the nearly degenerate valence tautomerization between benzene oxide and oxepin was found to reverse upon formation of a halogen or hydrogen bond with ICF₃ or H₂O. But even in the absence of strong noncovalent interactions such as hydrogen or halogen bonding, solvation can have a decisive effect on tunneling as evidenced by the Cope rearrangement of semibullvalenes via heavy-atom tunneling. Can quantum tunneling be catalyzed? The acceleration of the ring expansion of 1H-bicyclo[3.1.0.]-hexa-3,5-dien-2-one by complexation with Lewis acids provides a proof-of-concept for tunneling catalysis.Two concepts are central for the explanation and prediction of solvation effects on tunneling phenomena: a simple approach expands the Born-Oppenheimer approximation by separating nuclear degrees of freedom into intra- and intermolecular degrees. Intermolecular movements represent the slowest motions within molecular aggregates, thus effectively freezing the position of the solvent in relation to the reactant during the tunneling process. Another useful approach is to treat reactants and products by separate single-well potentials, where the intersection represents the transition state. Thus, stabilization of the reactants via solvation should result in an increase in barrier heights and widths which in turn lowers tunneling probabilities. These simple models can predict trends in tunneling kinetics and provide a rational basis for controlling tunneling reactions via solvation.

Heavy‐Atom Quantum Tunnelling in Spin Crossovers of Nitrenes**

We simulate two recent matrix‐isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak‐coupling method (based on a linear approximation of the potentials) in describing these deep‐tunnelling reactions. The more rigorous approach of semiclassical golden‐rule instanton theory in conjunction with double‐hybrid density‐functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy‐atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.

Heavy-Atom Tunneling in the Covalent/Dative Bond Complexation of Cyclo[18]carbon-Piperidine

Recent quantum chemical computations demonstrated the electron-acceptance behavior of this highly reactive cyclo[18]carbon (C₁₈) ring with piperidine (pip). The C₁₈–pip complexation exhibited a double-well potential along the N–C reaction coordinate, forming a van der Waals (vdW) adduct and a more stable, strong covalent/dative bond (DB) complex by overcoming a low activation barrier. By means of direct dynamical computations using canonical variational transition state theory (CVT), including the small-curvature tunneling (SCT), we show the conspicuous role of heavy atom quantum mechanical tunneling (QMT) in the transformation of vdW to DB complex in the solvent phase near absolute zero. Below 50 K, the reaction is entirely driven by QMT, while at 30 K, the QMT rate is too rapid (k_T ∼ 0.02 s^–1), corresponding to a half-life time of 38 s, indicating that the vdW adduct will have a fleeting existence. We also explored the QMT rates of other cyclo[n]carbon–pip systems. This study sheds light on the decisive role of QMT in the covalent/DB formation of the C₁₈–pip complex at cryogenic temperatures.

Sequential Hydrogen Tunneling in o-Tolylmethylene

o‐Tolylmethylene 1 is a metastable triplet carbene that rearranges to o‐xylylene 2 even at temperatures as low as 2.7 K via [1,4] H atom tunneling. Electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) spectroscopical techniques were used to identify two conformers of 1 (anti and syn) in noble gas matrices and in frozen organic solutions. Conformer‐specific kinetic measurements revealed that the rate constants for the rearrangements of the anti and syn conformers of 1 are very similar. However, the orbital alignment in the syn conformer is less favorable for the hydrogen transfer reaction than the orbital configuration in the anti conformer. Our spectroscopic and quantum chemical investigations indicate that anti1 and syn1 rapidly interconvert via efficient quantum tunneling forming a rotational pre‐equilibrium. The subsequent second tunneling reaction, the [1,4] H migration from anti1 to 2, is rate‐limiting for the formation of 2. We here present an efficient strategy for the study of such tunneling equilibria.

Fluxionality by quantum tunnelling: nonclassical 21-homododecahedryl cation rearrangement re-revisited

The 21-homododecahedryl cation is a unique system in terms of its complete fluxionality based on two different rearrangements. In this work, we report the quantum tunneling effects that drive the reactions at temperatures where the semi-classical kinetics are impossible. We postulate that the tunnel effect in this system can serve to create a refrigerator that may operate at arbitrarily low temperatures.

Lewis acid catalyzed heavy atom tunneling - the case of 1H-bicyclo[3.1.0]-hexa-3,5-dien-2-one

For many thermal reactions, the effects of catalysis or the influence of solvents on reaction rates can be rationalized by simple transition state models. This is not the case for reactions controlled by quantum tunneling, which do not proceed via transition states, and therefore lack the simple concept of transition state stabilization. 1H-Bicyclo[3.1.0]-hexa-3,5-dien-2-one is a highly strained cyclopropene that rearranges to 4-oxocyclohexa-2,5-dienylidene via heavy-atom tunneling. H₂O, CF₃I, or BF₃ form Lewis acid–base complexes with both reactant and product, and the influence of these intermolecular complexes on the tunneling rates for this rearrangement was studied. The tunneling rate increases by a factor of 11 for the H₂O complex, by 23 for the CF₃I complex, and is too fast to be measured for the BF₃ complex. These observations agree with quantum chemical calculations predicting a decrease in both barrier height and barrier width upon complexation with Lewis acids, resulting in the observed Lewis acid catalysis of the tunneling rearrangement.

The ring-opening of a highly strained cyclopropene to a carbene proceeds via heavy-atom tunneling. This rearrangement is accelerated in the presence of H₂O, ICF₃ or BF₃, resulting in a novel Lewis-acid catalyzed tunneling reaction.

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).

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.

Adding an external electric field to reactions driven by quantum mechanical tunneling brings a whole new dimension to the idea of switch chemistry.

External Electric Fields Interrupt the Concerted Cope Rearrangement of Semibullvalene

The topic of this paper is whether the mechanism of the degenerate Cope rearrangement of semibullvalene can be affected by the presence of electrostatic fields. Herein, we report that the shape of the energy surface, as demonstrated by an "interrupted" (stepwise) mechanism, is altered in the presence of a copper cation, Cu⁺. Natural bond-orbital and block-localized wave-function energy decomposition analyses suggest that orbital and electrostatic interactions play a major role in altering the shape of the energy surface. Applying additional external electric fields (EEFs) induces a significant change to the energy surface with Cu⁺ present but negligible effects in the absence of Cu⁺. These findings are consistent with recent studies that demonstrate that EEFs more readily stabilize/destabilize systems with larger, more polarizable, dipole moments.

The Mystery of the Benzene-Oxide/Oxepin Equilibrium-Heavy-Atom Tunneling Reversed by Solvent Interactions

The equilibrium between benzene oxide (1) and oxepin (2) is of large importance for understanding the degradation of benzene in biological systems and in the troposphere. Our studies reveal that at cryogenic temperatures, this equilibration is governed by rare heavy-atom tunneling. In solid argon at 3 K, 1 rearranges to 2 via tunneling with a rate constant of approximately 5.3×10-5  s-1 . Thus, in a nonpolar environment, 2 is slightly more stable than 1, in agreement with calculations at the CCSD(T) level of theory. However, if the argon is doped with 1 % of H2 O or CF3 I as typical hydrogen or halogen bond donors, respectively, weak complexes of 1 and 2 are formed, and now 2 is tunneling back to form 1. Thus, by forming non-covalent complexes, 1 becomes slightly more stable than 2 and the direction of the heavy-atom tunneling is reversed.

Heavy-Atom Tunneling in Semibullvalenes: How Driving Force, Substituents, and Environment Influence the Tunneling Rates

The Cope rearrangement of selectively deuterated isotopomers of 1,5-dimethylsemibullvalene 2 a and 3,7-dicyano-1,5-dimethylsemibullvalene 2 b were studied in cryogenic matrices. In both semibullvalenes the Cope rearrangement is governed by heavy-atom tunneling. The driving force for the rearrangements is the small difference in the zero-point vibrational energies of the isotopomers. To evaluate the effect of the driving force on the tunneling probability in 2 a and 2 b, two different pairs of isotopomers were studied for each of the semibullvalenes. The reaction rates for the rearrangement of 2 b in cryogenic matrices were found to be smaller than the ones of 2 a under similar conditions, whereas differences in the driving force do not influence the rates. Small curvature tunneling (SCT) calculations suggest that the reduced tunneling rate of 2 b compared to that of 2 a results from a change in the shape of the potential energy barrier. The tunneling probability of the semibullvalenes strongly depends on the matrix environment; however, for 2 a in a qualitatively different way than for 2 b.

Heavy-atom tunnelling in Cu(ii)N6 complexes: theoretical predictions and experimental manifestation

The degenerate rearrangement on Jahn-Teller distorted metal complexes is a promising reaction for the observation of significant heavy atom quantum mechanical tunnelling. Herein, a family of Cu(ii)-N₆ complexes are theoretically proven to exhibit rapid dynamical Jahn-Teller tunneling even close to the absolute zero. The manifestation of our predictions apparently appeared in solid state EPR experimental measurements on [Cu(en)₃]SO₄ more than 40 years ago, without the authors realizing that it was a quantum outcome.

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.

Conformer-Specific Heavy-Atom Tunneling in the Rearrangement of Benzazirines to Ketenimines

5-Methoxy-2H-benzazirine was prepared via irradiation of the corresponding phenyl azide, isolated in an argon matrix at cryogenic temperatures. It undergoes ring expansion to the corresponding ketenimine in the dark at T < 30 K despite a calculated activation barrier of 4.9 kcal mol^-1 [B3LYP/6-311++G(d,p)]. Since this rearrangement proceeds with a rate constant in the order of 10^-4 s^-1, exhibiting only a shallow temperature dependence, the results are interpreted in terms of heavy-atom tunneling. Of the four isomeric benzazirines resulting from the initial photolysis, only one can be observed to rearrange; this conformer specificity is explained by the other potentially observable rearrangements being either too fast or too slow to be detected due to the differences in heights and widths of their respective activation barriers.

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.

Ping-pong tunneling reactions, part 2: boron and carbon bell-clapper rearrangement

Anthracene can be used as a scaffold for intramolecular SN2 degenerate reactions of the “bell clapper” type, where a central boron atom or its isoelectronic carbocation bonds alternatively towards one or the other lateral Lewis bases at the first and eight anthracene positions. This ping-pong bond-switching reaction possesses a symmetrical double-well potential with low activation barrier and relatively narrow barrier width. Herein we show by computational means the active role played by heavy atom quantum tunneling in this degenerate rearrangement reaction at cryogenic temperatures. At these conditions the thermal “over the barrier” reaction is forbidden, whereas the tunneling effect enhances the rate of reaction up to an experimentally measurable half-life. Kinetic isotope effects and cryogenic NMR spectroscopy can, in principle, experimentally demonstrate the tunneling mechanism.

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

Midsized annulenes are known to undergo rapid π-bond shifting. Given that heavy-atom tunneling plays a role in planar bond shifting of cyclobutadiene, we computationally explored the contribution of heavy-atom tunneling to planar π-bond shifting in the major (CTCTCTCT, 5a) and minor (CTCTTCTT, 6a) known isomers of [16]annulene. UM06-2X/cc-pVDZ calculations yield bond-shifting barriers of ca. 10 kcal/mol. The results also reveal extremely narrow barrier widths, suggesting a high probability of tunneling for these bond-shifting reactions. Rate constants were calculated using canonical variational transition state theory (CVT) as well as with small curvature tunneling (SCT) contributions, via direct dynamics. For the major isomer 5a, the computed SCT rate constant for bond shifting at 80 K is 0.16 s^-1, corresponding to a half-life of 4.3 s, and indicating that bond shifting is rapid at cryogenic temperatures despite a 10 kcal/mol barrier. This contrasts with the CVT rate constant of 8.0 × 10^-15 s^-1 at 80 K. The minor isomer 6a is predicted to undergo rapid bond shifting via tunneling even at 10 K. For both isomers, bond shifting is predicted to be much faster than competing conformation change despite lower barriers for the latter process. The preference for bond shifting represents cases of tunneling control in which the preferred reaction is dominated by heavy-atom motions. At all temperatures below -50 °C, tunneling is predicted to dominate the bond shifting process for both 5a and 6a. Thus, [16]annulene is predicted to be an example of tunneling by 16 carbons. Bond shifting in both isomers is predicted to be rapid at temperatures accessible by solution-phase NMR spectroscopy, and an experiment is proposed to verify these predictions.

Real-Space Observation of Quantum Tunneling by a Carbon Atom: Flipping Reaction of Formaldehyde on Cu(110)

We present a direct observation of carbon-atom tunneling in the flipping reaction of formaldehyde between its two mirror-reflected states on a Cu(110) surface using low-temperature scanning tunneling microscopy (STM). The flipping reaction was monitored in real time, and the reaction rate was found to be temperature independent below 10 K. This indicates that this reaction is governed by quantum mechanical tunneling, albeit involving a substantial motion of the carbon atom (∼1 Å). In addition, deuteration of the formaldehyde molecule resulted in a significant kinetic isotope effect ( R_CH2O/ R_CD2O ≈ 10). The adsorption structure, reaction pathway, and tunneling probability were examined by density functional theory calculations, which corroborate the experimental observations.

Dynamical Effects along the Bifurcation Pathway Control Semibullvalene Formation in Deazetization Reactions

Post-transition-state dynamics during the deazetization of 3 resulting in two degenerate semibullvalenes (4 and 5) have been investigated with density functional theory (DFT) and quasi-classical trajectory (QCT) calculations. Removal of N₂ from 3 occurs through a synchronous and concerted pathway through an ambimodal transition-state (TS1). In addition to TS2, the exclusively anticipated product from minimum energy pathway (MEP) calculations, trajectories initiated from TS1 produce 4, TS2, and 5 in 1:1:1 ratio. Isotopic substitutions (¹²C(¹³C/¹⁴C)-H(D) at 1-2 positions) result in purely Newtonian kinetic isotope effects (4:5 ≈ 1.4 for ¹³C₁-¹³C₂), an unequivocal evidence for dynamics controlled product formation.