Domino Tunneling

Quantum Tunneling Instability in Pericyclic Reactions: The Cheletropic, Coarctate, and Ene Cases

Some retro-pericyclic reactions, as a result of their high exothermicity and short trajectories, are the perfect ground for heavy atom tunneling molecular decompositions, also known as "quantum tunneling instability" (QTI). Considering this effect, in our first installment [Frenklach, A.; Amlani, H.; Kozuch, S. Quantum Tunneling Instability in Pericyclic Reactions. J. Am. Chem. Soc. 2024, 146 (17), 11823-11834, DOI: 10.1021/jacs.4c00608], we computed several retro-Diels-Alder reactions, predicting that many studied reactants cannot be isolated. Herein, we will explore the QTI of retro-cheletropic, coarctate, and ene exemplars, where again we hypothesize the impossibility to detect their reactants.

Hydrogen Tunneling Exhibiting Unexpectedly Small Primary Kinetic Isotope Effects

Probing quantum mechanical tunneling (QMT) in chemical reactions is crucial to understanding and developing new transformations. Primary H/D kinetic isotopic effects (KIEs) beyond the semiclassical maximum values of 7-10 (room temperature) are commonly used to assess substantial QMT contributions in one-step hydrogen transfer reactions, because of the much greater QMT probability of protium vs. deuterium. Nevertheless, we report here the discovery of a reaction model occurring exclusively by H-atom QMT with residual primary H/D KIEs. 2-Hydroxyphenylnitrene, generated in N2 matrix, was found to isomerize to an imino-ketone via sequential (domino) QMT involving anti to syn OH-rotamerization (rate determining step) and [1,4]-H shift reactions. These sequential QMT transformations were also observed in the OD-deuterated sample, and unexpected primary H/D KIEs between 3 and 4 were measured at 3 to 20 K. Analogous residual primary H/D KIEs were found in the anti to syn OH-rotamerization QMT of 2-cyanophenol in a N2 matrix. Evidence strongly indicates that these intriguing isotope-insensitive QMT reactivities arise due to the solvation effects of the N2 matrix medium, putatively through coupling with the moving H/D tunneling particle. Should a similar scenario be extrapolated to conventional solution conditions, then QMT may have been overlooked in many chemical reactions.

A highly accurate full-dimensional ab initio potential surface for the rearrangement of methylhydroxycarbene (H3C-C-OH)

We report here a full-dimensional machine learning global potential surface (PES) for the rearrangement of methylhydroxycarbene (H₃C-C-OH, 1t). The PES is trained with the fundamental invariant neural network (FI-NN) method on 91 564 ab initio energies calculated at the UCCSD(T)-F12a/cc-pVTZ level of theory, covering three possible product channels. FI-NN PES has the correct symmetry properties with respect to permutation of four identical hydrogen atoms and is suitable for dynamics studies of the 1t rearrangement. The averaged root mean square error (RMSE) is 11.4 meV. Six important reaction pathways, as well as the energies and vibrational frequencies at the stationary geometries on these pathways are accurately preproduced by our FI-NN PES. To demonstrate the capacity of the PES, we calculated the rate coefficient of hydrogen migration in -CH₃ (path A) and hydrogen migration of -OH (path B) with instanton theory on this PES. Our calculations predicted the half-life of 1t to be 95 min, which is excellent in agreement with experimental observations.

Equilibrating parent aminomercaptocarbene and CO2 with 2-amino-2-thioxoacetic acid via heavy-atom quantum tunneling

The search for methods to bind CO₂ and use it synthetically as a C₁-building block under mild conditions is an ongoing endeavor of great urgency. The formation of heterocyclic carbene-carbon dioxide adducts occurs rapidly when the carbene is generated in solution in the presence of CO₂. Here we demonstrate the reversible formation of a complex of the hitherto unreported aminomercaptocarbene (H₂N-C̈-SH) with CO₂ isolated in solid argon by photolysis of 2-amino-2-thioxoacetic acid. Remarkably, the complex disappears in the dark as deduced by time-dependent matrix infrared measurements, and equilibrates back to the covalently bound starting material. This kinetically excluded process below ca. 8 K is made possible through heavy-atom quantum mechanical tunneling, as also evident from density functional theory and ab initio computations at the CCSD(T)/cc-pVTZ level of theory. Our results provide insight into CO₂ activation using a carbene and emphasize the role of quantum mechanical tunneling in organic processes, even involving heavy atoms.

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.

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.

IR-induced and tunneling reactions in cryogenic matrices: the (incomplete) story of a successful endeavor

In this article, IR-induced and tunneling-driven reactions observed in cryogenic matrices are described in a historical perspective, the entangling of the two types of processes being highlighted. The story of this still ongoing fascinating scientific endeavor is presented here following closely our own involvement in the field for more than 30 years, and thus focuses mostly on our work. It is, because of this reason, also an incomplete story. Nevertheless, it considers a large range of examples, from very selective IR-induced conformational isomerizations to IR-induced bond-breaking/bond-forming reactions and successful observations of rare heavy atom tunneling processes. As a whole, this article provides a rather general overview of the major progress achieved in the field.

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.

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).

Characterization of the Simplest Thiolimine: The Higher Energy Tautomer of Thioformamide

As sulfur‐containing organic molecules thioamides and their isomers are conceivable intermediates in prebiotic chemistry, for example, in the formation of amino acids and thiazoles and resemble viable candidates for detection in interstellar media. Here, we report the characterization of parent thioformamide in the solid state via single‐crystal X‐ray diffraction and its photochemical interconversion to its hitherto unreported higher energy tautomer thiolimine in inert argon and dinitrogen matrices. Upon photogeneration, four conformers of thiolimine form, whose ratio depends on the employed wavelength. One of these conformers interconverts due to quantum mechanical tunneling with a half‐life of 30–45 min in both matrix materials at 3 and 20 K. A spontaneous reverse reaction from thiolimine to thioformamide is not observed. To support our experimental findings, we explored the potential energy surface of the system at the AE‐CCSD(T)/aug‐cc‐pCVTZ level of theory and computed tunneling half‐lives with the CVT/SCT approach applying DFT methods.

Identification and Reactivity of s-cis,s-cis-Dihydroxycarbene, a New [CH2O2] Intermediate

We report the first preparation of the s-cis,s-cis conformer of dihydroxycarbene (1cc) by means of pyrolysis of oxalic acid, isolation of the lower-energy s-trans,s-trans (1tt) and s-cis,s-trans (1ct) product conformers at cryogenic temperatures in a N₂ matrix, and subsequent narrow-band near-infrared (NIR) laser excitation to give 1cc. Carbene 1cc converts quickly to 1ct via quantum-mechanical tunneling with an effective half-life of 22 min at 3 K. The potential energy surface features around 1 were pinpointed by convergent focal point analysis targeting the AE-CCSDT(Q)/CBS level of electronic structure theory. Computations of the tunneling kinetics confirm the time scale of the 1cc → 1ct rotamerization and suggest that direct 1cc → H₂ + CO₂ decomposition may also be a minor pathway. The intriguing latter possibility cannot be confirmed spectroscopically, but hints of it may be present in the measured kinetic profiles.

Biological concepts for catalysis and reactivity: empowering bioinspiration

Biological systems provide attractive reactivity blueprints for the design of challenging chemical transformations. Emulating the operating mode of natural systems may however not be so easy and direct translation of structural observations does not always afford the anticipated efficiency. Metalloenzymes rely on earth-abundant metals to perform an incredibly wide range of chemical transformations. To do so, enzymes in general have evolved tools and tricks to enable control of such reactivity. The underlying concepts related to these tools are usually well-known to enzymologists and bio(inorganic) chemists but may be a little less familiar to organometallic chemists. So far, the field of bioinspired catalysis has greatly focused on the coordination sphere and electronic effects for the design of functional enzyme models but might benefit from a paradigm shift related to recent findings in biological systems. The goal of this review is to bring these fields closer together as this could likely result in the development of a new generation of highly efficient bioinspired systems. This contribution covers the fields of redox-active ligands, entatic state reactivity, energy conservation through electron bifurcation, and quantum tunneling for C-H activation.

Hydrogen-Atom Tunneling in Metaphosphorous Acid

Metaphosphorous acid (HOPO), a key intermediate in phosphorus chemistry, has been generated in syn- and anti-conformations in the gas phase by high-vacuum flash pyrolysis (HVFP) of a molecular precursor ethoxyphosphinidene oxide (EtOPO→C₂ H₄ +HOPO) at ca. 1000 K and subsequently trapped in an N₂ -matrix at 2.8 K. Unlike the two conformers of the nitrogen analogue HONO, the anti-conformer of HOPO undergoes spontaneous rotamerization at 2.8 K via hydrogen-atom tunneling (HAT) with noticeable kinetic isotope effects for H/D (>10⁴ for DOPO) and ¹⁶ O/¹⁸ O (1.19 for H¹⁸ OPO and 1.06 for HOP¹⁸ O) in N₂ -matrices.

Riddles of the structure and vibrational dynamics of HO3 resolved near the ab initio limit

The hydridotrioxygen (HO₃) radical has been investigated in many previous theoretical and experimental studies over several decades, originally because of its possible relevance to the tropospheric HO_x cycle but more recently because of its fascinating chemical bonding, geometric structure, and vibrational dynamics. We have executed new, comprehensive research on this vexing molecule via focal point analyses (FPA) to approach the ab initio limit of optimized geometric structures, relative energies, complete quartic force fields, and the entire reaction path for cis-trans isomerization. High-order coupled cluster theory was applied through the CCSDT(Q) and even CCSDTQ(P) levels, and CBS extrapolations were performed using cc-pVXZ (X = 2-6) basis sets. The cis isomer proves to be higher than trans by 0.52 kcal mol^-1, but this energetic ordering is achieved only after the CCSDT(Q) milestone is reached; the barrier for cis → trans isomerization is a minute 0.27 kcal mol^-1. The FPA central r_e(O-O) bond length of trans-HO₃ is astonishingly long (1.670 Å), consistent with the semiexperimental r_e distance we extracted from microwave rotational constants of 10 isotopologues using FPA vibration-rotation interaction constants (α_i). The D₀(HO-O₂) dissociation energy converges to a mere 2.80 ± 0.25 kcal mol^-1. Contrary to expectation for such a weakly bound system, vibrational perturbation theory performs remarkably well with the FPA anharmonic force fields, even for the torsional fundamental near 130 cm^-1. Exact numerical procedures are applied to the potential energy function for the torsional reaction path to obtain energy levels, tunneling rates, and radiative lifetimes. The cis → trans isomerization occurs via tunneling with an inherent half-life of 1.4 × 10^-11 s and 8.6 × 10^-10 s for HO₃ and DO₃, respectively, thus resolving the mystery of why the cis species has not been observed in previous experiments executed in dissipative environments that allow collisional cooling of the trans-HO₃ product. In contrast, the pure ground eigenstate of the cis species in a vacuum is predicted to have a spontaneous radiative lifetime of about 1 h and 5 days for HO₃ and DO₃, respectively.

S–H rotamerizationviatunneling in a thiol form of thioacetamide

Rotamerization of the S–H groupviahydrogen tunneling is reported for the first time.

Intricate Conformational Tunneling in Carbonic Acid Monomethyl Ester

Disentangling internal and external effects is a key requirement for understanding conformational tunneling processes. Here we report the s- trans/ s- cis tunneling rotamerization of carbonic acid monomethyl ester (1) under matrix isolation conditions and make comparisons to its parent carbonic acid (3). The observed tunneling rate of 1 is temperature-independent in the 3-20 K range and accelerates when using argon instead of neon as the matrix material. The methyl group increases the effective half life (τ_eff) of the energetically disfavored s- trans-conformer from 3-5 h for 3 to 11-13 h for 1. Methyl group deuteration slows the rotamerization further (τ_eff ≈ 35 h). CCSD(T)/cc-pVQZ//MP2/aug-cc-pVTZ computations of the tunneling probability suggest that the rate should be almost unaffected by methyl substitution or its deuteration. Thus the observed relative rates are puzzling, and they disagree with previous explanations involving fast vibrational relaxation after the tunneling event facilitated by the alkyl rotor.

Hydrogen-atom tunneling through a very high barrier; spontaneous thiol → thione conversion in thiourea isolated in low-temperature Ar, Ne, H2and D2matrices

Hydrogen-atom tunneling in thiourea involves breaking of the S–H chemical bond and the formation of a new N–H bond.

Computational Chemistry: The Fate of Current Methods and Future Challenges

"Where do we go from here?" is the underlying question regarding the future (perhaps foreseeable) developments in computational chemistry. Although this young discipline has already permeated practically all of chemistry, it is likely to become even more powerful with the rapid development of computational hard- and software.

Computational Prediction of Excited-State Carbon Tunneling in the Two Steps of Triplet Zimmerman Di-π-Methane Rearrangement

The photoinduced Zimmerman di-π-methane (DPM) rearrangement of polycyclic molecules to form synthetically useful cyclopropane derivatives was found experimentally to proceed in a triplet excited state. We have applied state-of-the-art quantum mechanical methods, including M06-2X, DLPNO-CCSD(T) and variational transition-state theory with multidimensional tunneling corrections, to an investigation of the reaction rates of the two steps in the triplet DPM rearrangement of dibenzobarrelene, benzobarrelene and barrelene. This study predicts a high probability of carbon tunneling in regions around the two consecutive transition states at 200-300 K, and an enhancement in the rates by 104-276/35-67% with carbon tunneling at 200/300 K. The Arrhenius plots of the rate constants were found to be curved at low temperatures. Moreover, the computed ¹²C/¹³C kinetic isotope effects were affected significantly by carbon tunneling and temperature. Our predictions of electronically excited-state carbon tunneling and two consecutive carbon tunneling are unprecedented. Heavy-atom tunneling in some photoinduced reactions with reactive intermediates and narrow barriers can be potentially observed at relatively low temperature in experiments.

Contrasting Effects of Water on the Barriers to Decarboxylation of Two Oxalic Acid Monohydrates: A Combined Rotational Spectroscopic and Ab Initio Study

Using rotational spectroscopy, we have observed two isomers of the monohydrate of oxalic acid, the most abundant dicarboxylic acid in the atmosphere. In the lowest-energy isomer, water hydrogen-bonds to both carboxylic acid groups, and the barrier to decarboxylation decreases. In the second isomer, water bonds to only one carboxylic acid group, and the barrier increases. Though the lower barrier in the former is not unequivocal evidence that water acts as a photocatalyst, the higher barrier in the latter indicates that water acts as an inhibitor in this topology. Oxalic acid is unique among dicarboxylic acids: for the higher homologues calculated, the inhibiting topology of the monohydrate is lowest in energy and most abundant under atmospheric conditions. Consequently, oxalic acid is the only dicarboxylic acid for which single-water catalysis of overtone-induced decarboxylation in the atmosphere is plausible.

σ Bond activation through tunneling: formation of the boron hydride cations BHn+ (n = 2, 4, 6)

The network of H₂ additions to B⁺ and subsequent insertion reactions serve as a tractable model for hydrogen storage in elementary boron-containing compounds.

Tunnelling in carbonic acid

The cis,trans-conformer of carbonic acid (H₂CO₃), generated by near-infrared radiation, undergoes an unreported quantum mechanical tunnelling rotamerization with half-lives in cryogenic matrices of 4–20 h, depending on temperature and host material.

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.