Theory and simulation of atom tunneling in chemical reactions

Direct Observation of HOON Intermediate in the Photochemistry of HONO

The photochemistry of nitrous acid (HONO), encompassing dissociation into OH and NO as well as the reverse association reaction, plays a pivotal role in atmospheric chemistry. Here, we report the direct observation of nitrosyl-O-hydroxide (HOON) in the photochemistry of HONO, employing matrix-isolation IR and UV-vis spectroscopy. Despite a barrier of approximately 30 kJ/mol, HOON undergoes spontaneous rearrangement to the more stable HONO isomer through quantum mechanical tunneling, with a half-life of 28 min at 4 K. Kinetic isotope effects and instanton theory calculations reveal that the tunneling process involves the concerted motion of the NO moiety (65.2%) and the hydrogen atom (32.3%). Our findings underscore the significance of HOON as a key intermediate in the photolytic dissociation-association cycle of HONO at low temperatures.

Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.

Mechanisms of glycine formation in cold interstellar media: a theoretical study

The possibility of the formation of glycine (Gly) from fundamental gas molecules in cold interstellar media was studied using quantum chemical methods, transition state theory and microcanonical molecular dynamics simulations with surface hopping dynamics (NVE-MDSH). This theoretical study emphasized five photochemical pathways in the lowest singlet-excited (S 1) state, thermochemical processes after non-radiative S 1→S 0 relaxations, and photo-to-thermal energy conversion in the NVE ensemble. The optimized reaction pathways suggested that to generate a reactive singlet dihydroxy carbene (HOCOH) intermediate, photochemical pathways involving the H2O…CO van der Waals and H2O-OC hydrogen bond precursors (Ch (1)_Step (1)) possess considerably lower energy barriers than the S 0 state pathways. The Gibbs free energy barriers (∆G ǂ ) calculated after the non-radiative S 1 →S 0 relaxations indicated higher spontaneous temperatures (T s) for the formation of the HOCOH intermediate (Ch (1)_Step (1)) than for Gly formation (Ch (1)_Step (2) and Ch (4)). Although the termolecular reaction in Ch (4) possesses a low energy barrier, and is thermodynamically favourable, the high exothermic S 1 →S 0 relaxation energy leads to the separation of the weakly associated H2O…CH2NH…CO complex into single molecules. The NVE-MDSH results also confirmed that the molecular processes after the S 1 →S 0 relaxations are thermally selective, and because the non-radiative S 1 →S 0 relaxation temperatures are exceedingly higher than T s, the formation of Gly on consecutive reaction pathways is non-synergistic with low yields and several side products. Based on the theoretical results, photo-to-thermal control strategies to promote desirable photochemical products are proposed. They could be used as guidelines for future theoretical and experimental research on photochemical reactions.

Activation volume and quantum tunneling in the hydrogen transfer reaction between methyl radical and methane: A first computational study

We present a theory of the effect of quantum tunneling on the basic parameter that characterizes the effect of pressure on the rate constant of chemical reactions in a dense phase, the activation volume. This theory results in combining, on the one hand, the extreme pressure polarizable continuum model, a quantum chemical method to describe the effect of pressure on the reaction energy profile in a dense medium, and, on the other hand, the semiclassical version of the transition state theory, which includes the effect of quantum tunneling through a transmission coefficient. The theory has been applied to the study of the activation volume of the model reaction of hydrogen transfer between methyl radical and methane, including the primary isotope substitution of hydrogen with deuterium (H/D). The analysis of the numerical results offers, for the first time, a clear insight into the effect of quantum tunneling on the activation volume for this hydrogen transfer reaction: this effect results from the different influences that pressure has on the competing thermal and tunneling reaction mechanisms. Furthermore, the computed kinetic isotope effect (H/D) on the activation volume for this model hydrogen transfer correlates well with the experimental data for more complex hydrogen transfer reactions.

Gas-Phase vs. Grain-Surface Formation of Interstellar Complex Organic Molecules: A Comprehensive Quantum-Chemical Study

Several organic chemical compounds (the so-called interstellar complex organic molecules, iCOMs) have been identified in the interstellar medium (ISM). Examples of iCOMs are formamide (HCONH2), acetaldehyde (CH3CHO), methyl formate (CH3OCHO), or formic acid (HCOOH). iCOMs can serve as precursors of other organic molecules of enhanced complexity, and hence they are key species in chemical evolution in the ISM. The formation of iCOMs is still a subject of a vivid debate, in which gas-phase or grain-surface syntheses have been postulated. In this study, we investigate the grain-surface-formation pathways for the four above-mentioned iCOMs by transferring their primary gas-phase synthetic routes onto water ice surfaces. Our objective is twofold: (i) to identify potential grain-surface-reaction mechanisms leading to the formation of these iCOMs, and (ii) to decipher either parallelisms or disparities between the gas-phase and the grain-surface reactions. Results obtained indicate that the presence of the icy surface modifies the energetic features of the reactions compared to the gas-phase scenario, by increasing some of the energy barriers. Therefore, the investigated gas-phase mechanisms seem unlikely to occur on the icy grains, highlighting the distinctiveness between the gas-phase and the grain-surface chemistry.

Reducing the Cost of Neural Network Potential Generation for Reactive Molecular Systems

Although machine learning potentials have recently had a substantial impact on molecular simulations, the construction of a robust training set can still become a limiting factor, especially due to the requirement of a reference ab initio simulation that covers all the relevant geometries of the system. Recognizing that this can be prohibitive for certain systems, we develop the method of transition tube sampling that mitigates the computational cost of training set and model generation. In this approach, we generate classical or quantum thermal geometries around a transition path describing a conformational change or a chemical reaction using only a sparse set of local normal mode expansions along this path and select from these geometries by an active learning protocol. This yields a training set with geometries that characterize the whole transition without the need for a costly reference trajectory. The performance of the method is evaluated on different molecular systems with the complexity of the potential energy landscape increasing from a single minimum to a double proton-transfer reaction with high barriers. Our results show that the method leads to training sets that give rise to models applicable in classical and path integral simulations alike that are on par with those based directly on ab initio calculations while providing the computational speedup we have come to expect from machine learning potentials.

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.

Tunneling Effect in Proton Transfer: Transfer Matrix Approach

The transfer matrix (TM) method was applied to calculate the transmission probability (TP) for proton transfer reactions. The tunneling factors in the reaction rate constants were also evaluated using the TPs. To test this method, TPs for the Eckart potentials modeled as a guanine-cytosine base pair were calculated by the TM method and compared to TPs by the analytical solution. As a result, the errors in the TPs by the TM method were quite small. The tunneling factors for the guanine-thymine (G-T) and adenine-cytosine (A-C) mispair reactions were then evaluated by the TM method. A shoulder appears on each potential for these reactions [Odai, K.; Umesaki,K. J. Phys. Chem. A. 2021, 125, 8196-8204]. As a result, the shoulder for the G-T mispair reaction contributes significantly to the tunneling, while the shoulder for the A-C mispair reaction contributes little to the tunneling. These results are difficult to obtain with methods such as Wigner's tunneling factor.

Mactanamide and lariciresinol as radical scavengers and Fe2+ ion chelators - A DFT study

A DFT based kinetic study of OOH radical scavenging potency of mactanamide (MA) and lariciresinol (LA), two natural polyphenols, indicates their nearly equal potential via the proton coupled electron transfer (PCET) mechanism in lipid media. Contribution of C-H bond breaking to this potency is negligible compared to O-H bond breaking, contrary to recent claims. The predicted potency of both compounds is not sufficient to protect biological molecules from oxidative damage in lipid media. In aqueous media, the scavenging potency of MA and LA phenoxide anions via the single electron transfer (SET) mechanism is much higher and may contribute to the protection of lipids, proteins, and DNA from OOH radical damage. Also, MA and LA have the potential to chelate catalytic Fe2+ ions, thus suppressing the formation of dangerous OH radicals via Fenton-type reactions. The monoanionic species of MA and LA show stronger monodentate chelating ability with Fe2+ ion compared to its neutral form. The dianionic specie LA2- exhibited the highest chelation ability with Fe2+ ion via bidentate 1:2 coordination. However, direct radical scavenging and metal chelation could be rarely operative in vivo because MA and LA presumably achieve very low concentrations in systemic circulation.

Infrared Spectra and Phototransformations of meta-Fluorophenol Isolated in Argon and Nitrogen Matrices

Monomers of meta-fluorophenol (mFP) were trapped from the gas phase into cryogenic argon and nitrogen matrices. The estimated relative energies of the two conformers are very close, and in the gas phase they have nearly equal populations. Due to the similarity of their structures (they only differ in the orientation of the OH group), the two conformers have also similar predicted vibrational signatures, which makes the vibrational characterization of the individual rotamers challenging. In the present work, it has been established that in an argon matrix only the most stable trans conformer of mFP exists (the OH group pointing away from the fluorine atom). On the other hand, the IR spectrum of mFP in a nitrogen matrix testifies to the simultaneous presence in this matrix of both the trans conformer and of the higher-energy cis conformer (the OH group pointing toward the fluorine atom), which is stabilized by interaction with the matrix gas host. We found that the exposition of the cryogenic N₂ matrix to the Globar source of the infrared spectrometer affects the conformational populations. By collecting experimental spectra, either in the full mid-infrared range or only in the range below 2200 cm^-1, we were able to reliably distinguish two sets of experimental bands originating from individual conformers. A comparison of the two sets of experimental bands with computed infrared spectra of the conformers allowed, for the first time, the unequivocal vibrational identification of each of them. The joint implementation of computational vibrational spectroscopy and matrix-isolation infrared spectroscopy proved to be a very accurate method of structural analysis. Some mechanistic insights into conformational isomerism (the quantum tunneling of hydrogen atom and vibrationally-induced conformational transformations) have been addressed. Finally, we also subjected matrix-isolated mFP to irradiations with UV light, and the phototransformations observed in these experiments are also described.

Ligand‐Enabled Disproportionation of 1,2‐Diphenylhydrazine at a P V ‐Center**

We present herein the synthesis of a nearly square‐pyramidal chlorophosphorane supported by the tetradentate bis(amidophenolate) ligand, N,N′‐bis(3,5‐di‐tert‐butyl‐2‐phenoxy)‐1,2‐phenylenediamide. After chloride abstraction the resulting phosphonium cation efficiently promotes the disproportionation of 1,2‐diphenylhydrazine to aniline and azobenzene. Mechanistic studies, spectroscopic analyses and theoretical calculations suggest that this unprecedented reactivity mode for P^V‐centres is induced by the high electrophilicity at the cationic P^V‐center, which originates from the geometry constraints imposed by the rigid pincer ligand, combined with the ability of the o‐amidophenolate moieties to act as electron reservoir. This study illustrates the promising role of cooperativity between redox‐active ligands and phosphorus for the design of organocatalysts able to promote redox processes.

Instanton theory for Fermi's golden rule and beyond

Instanton theory provides a semiclassical approximation for computing quantum tunnelling effects in complex molecular systems. It is typically applied to proton-transfer reactions for which the Born-Oppenheimer approximation is valid. However, many processes in physics, chemistry and biology, such as electron transfers, are non-adiabatic and are correctly described instead using Fermi's golden rule. In this work, we discuss how instanton theory can be generalized to treat these reactions in the golden-rule limit. We then extend the theory to treat fourth-order processes such as bridge-mediated electron transfer and apply the method to simulate an electron moving through a model system of three coupled quantum dots. By comparison with benchmark quantum calculations, we demonstrate that the instanton results are much more reliable than alternative approximations based on superexchange-mediated effective coupling or a classical sequential mechanism. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Quantum Tunnelling Driven H2 Formation on Graphene

It is commonly believed that it is unfavorable for adsorbed H atoms on carbonaceous surfaces to form H₂ without the help of incident H atoms. Using ring-polymer instanton theory to describe multidimensional tunnelling effects, combined with ab initio electronic structure calculations, we find that these quantum-mechanical simulations reveal a qualitatively different picture. Recombination of adsorbed H atoms, which was believed to be irrelevant at low temperature due to high barriers, is enabled by deep tunnelling, with reaction rates enhanced by tens of orders of magnitude. Furthermore, we identify a new path for H recombination that proceeds via multidimensional tunnelling but would have been predicted to be unfeasible by a simple one-dimensional description of the reaction. The results suggest that hydrogen molecule formation at low temperatures are rather fast processes that should not be ignored in experimental settings and natural environments with graphene, graphite, and other planar carbon segments.

Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory

Isotope substitution is an important experimental technique that offers deep insight into reaction mechanisms, as the measured kinetic isotope effects (KIEs) can be directly compared with theory. For multiple proton transfer processes, there are two types of mechanisms: stepwise transfer and concerted transfer. The Bell-Limbach model provides a simple theory to determine whether the proton transfer mechanism is stepwise or concerted from KIEs. Recent STM experiments have studied the proton switching process in water tetramers on NaCl(001). Theoretical studies predict that this process occurs via a concerted mechanism, however, the experimental KIEs resemble the Bell-Limbach model for stepwise tunneling, raising question on the underlying mechanism or the validity of the model. We study this system using ab initio instanton theory, and in addition to thermal rates, we also considered microcanonical rates, as well as tunneling splittings. Instanton theory predicts a concerted mechanism, and the KIEs for tunneling rates (both thermal and microcanonical) upon deuteration are consistent with the Bell-Limbach model for concerted tunneling, but could not explain the experiments. For tunneling splittings, partial and full deuteration changes the size of it in a similar fashion to how it changes the rates. We further examined the Bell-Limbach model in another system, porphycene, which has both stepwise and concerted tunneling pathways. The KIEs predicted by instanton theory are again consistent with the Bell-Limbach model. This study highlights differences between KIEs in stepwise and concerted tunneling, and the discrepancy between theory and recent STM experiments. New theory/experiments are desired to settle this problem.

Theoretical Identification of the Factors Governing the Reactivity of C-H Bond Activation by Non-Heme Iron(IV)-Oxo Complexes

Selective functionalization of C-H bonds provides a straightforward approach to a large variety of well-defined derivatives. High-valent mononuclear iron(IV)-oxo complexes are proposed to carry out these C-H activation reactions in enzymes or in biomimetic syntheses. In this Minireview, we aim to highlight the features that delineate the distinct reactivity of non-heme oxo-iron(IV) motifs to cleave strong C-H bonds in hydrocarbons, primarily focusing on the hydrogen atom transfer (HAT) process. We describe how the structural and electronic properties of supporting ligands modulate the oxidative property of the iron(IV)-oxo complexes. Furthermore, we highlight the decisive role played by spin-state in these biomimetic reactions. We also discuss how tunneling and external perturbations like electric field influence the transfer of hydrogen atoms. Lastly, we emphasize how computations could work as a practical guide to sketch and develop synthetic models with greater efficacy.

Instanton rate constant calculations using interpolated potential energy surfaces in nonredundant, rotationally and translationally invariant coordinates

A trivial flaw in the utilization of artificial neural networks in interpolating chemical potential energy surfaces (PES) whose descriptors are Cartesian coordinates is their dependence on simple translations and rotations of the molecule under consideration. A different set of descriptors can be chosen to circumvent this problem, internuclear distances, inverse internuclear distances or z-matrix coordinates are three such descriptors. The objective is to use an interpolated PES in instanton rate constant calculations, hence information on the energy, gradient, and Hessian is required at coordinates in the vicinity of the tunneling path. Instanton theory relies on smoothly fitted Hessians, therefore we use energy, gradients, and Hessians in the training procedure. A major challenge is presented in the proper back-transformation of the output gradients and Hessians from internal coordinates to Cartesian coordinates. We perform comparisons between our method, a previous approach and on-the-fly rate constant calcuations on the hydrogen abstraction from methanol and on the hydrogen addition to isocyanic acid. © 2018Wiley Periodicals, Inc.

Effects of tunnelling and asymmetry for system-bath models of electron transfer

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.

Kinetic Isotope Effect Determination Probes the Spin of the Transition State, Its Stereochemistry, and Its Ligand Sphere in Hydrogen Abstraction Reactions of Oxoiron(IV) Complexes

This Account outlines interplay of theory and experiment in the quest to identify the reactive-spin-state in chemical reactions that possess a few spin-dependent routes. Metalloenzymes and synthetic models have forged in recent decades an area of increasing appeal, in which oxometal species bring about functionalization of hydrocarbons under mild conditions and via intriguing mechanisms that provide a glimpse of Nature's designs to harness these reactions. Prominent among these are oxoiron(IV) complexes, which are potent H-abstractors. One of the key properties of oxoirons is the presence of close-lying spin-states, which can mediate H-abstractions. As such, these complexes form a fascinating chapter of spin-state chemistry, in which chemical reactivity involves spin-state interchange, so-called two-state reactivity (TSR) and multistate reactivity (MSR). TSR and MSR pose mechanistic challenges. How can one determine the structure of the reactive transition state (TS) and its spin state for these mechanisms? Calculations can do it for us, but the challenge is to find experimental probes. There are, however, no clear kinetic signatures for the reactive-spin-state in such reactions. This is the paucity that our group has been trying to fill for sometime. Hence, it is timely to demonstrate how theory joins experiment in realizing this quest. This Account uses a set of the H-abstraction reactions of 24 synthetic oxoiron(IV) complexes and 11 hydrocarbons, together undergoing H-abstraction reactions with TSR/MSR options, which provide experimentally determined kinetic isotope effect (KIE_exp) data. For this set, we demonstrate that comparing KIE_exp results with calculated tunneling-augmented KIE (KIE_TC) data leads to a clear identification of the reactive spin-state during H-abstraction reactions. In addition, generating KIE_exp data for a reaction of interest, and comparing these to KIE_TC values, provides the mechanistic chemist with a powerful capability to identify the reactive-TS in terms of not only its spin state but also its geometry and ligand-sphere constitution. Since tunneling "cuts through" barriers, it serves as a chemical selectivity factor. Thus, we show that in a family of oxoirons reacting with one hydrocarbon, the tunneling efficiency increases as the ligands become better electron donors. This generates counterintuitive-reactivity patterns, like antielectrophilic reactivity, and induces spin-state reactivity reversals because of differing steric demands of the corresponding ^2S+1TS species, etc. Finally, for the same series, the Account reaches intuitive understanding of tunneling trends. It is shown that the increase of ligand's donicity results in electrostatic narrowing of the barrier, while the decrease of donicity and increase of bond-order asymmetry in the TS (inter alia due to Bell-Evans-Polanyi effects) broadens the barrier. Predictions are made that usage of powerful electron-donating ligands may train H-abstractors to activate the strongest C-H bond in a molecule. The concepts developed here are likely to be applicable to other oxometals in the d- and f-blocks.

Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals

Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic tops and those with broad tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping, to shallow tunneling, to deep tunneling as the temperature (T) decreases, and noticeable quantum effects persist at moderate T. In contrast, with broad-top barriers quantum effects become important only at low T and the classical-to-quantum transition is sharp, at which classical hopping and deep tunneling both occur. This coexistence indicates that more than one mechanism contributes to the quantum reaction rate. The conventional definition of the classical-to-quantum crossover T is invalid for the broad tops, and we give a new definition. Extending this, we propose a model to predict the transition T for broad-top diffusion, providing a general guide for theory and experiment.

Isotope-Controlled Selectivity by Quantum Tunneling: Hydrogen Migration versus Ring Expansion in Cyclopropylmethylcarbenes

Using the tunneling-controlled reactivity of cyclopropylmethylcarbene, we demonstrate the viability of isotope-controlled selectivity (ICS), a novel control element of chemical reactivity where a molecular system with two conceivable products of tunneling exclusively produces one or the other, depending only on isotopic composition. Our multidimensional small-curvature tunneling (SCT) computations indicate that, under cryogenic conditions, 1-methoxycyclopropylmethylcarbene shows rapid H-migration to 1-methoxy-1-vinylcyclopropane, whereas deuterium-substituted 1-methoxycyclopropyl-d₃-methylcarbene undergoes ring expansion to 1-d₃-methylcyclobutene. This predicted change in reactivity constitutes the first example of a kinetic isotope effect that discriminates between the formation of two products.

Hydrogen Tunneling above Room Temperature Evidenced by Infrared Ion Spectroscopy

While hydrogen tunneling at elevated temperatures has, for instance, often been postulated in biochemical processes, spectroscopic proof is thus far limited to cryogenic conditions, under which thermal reactivity is negligible. We report spectroscopic evidence for H-tunneling in the gas phase at temperatures around 320-350 K observed in the isomerization reaction of a hydroxycarbene into an aldehyde. The charge-tagged carbene was generated in situ in a tandem mass spectrometer by decarboxylation of oxo[4-(trimethylammonio)phenyl]acetic acid upon collision induced dissociation. All ion structures involved are characterized by infrared ion spectroscopy and quantum chemical calculations. The charge-tagged phenylhydroxycarbene undergoes a 1,2-H-shift to the corresponding aldehyde with an half-life of about 10 s, evidenced by isomer-selective two-color (IR-IR) spectroscopy. In contrast, the deuterated (OD) carbene analogue showed much reduced 1,2-D-shift reactivity with an estimated half-life of at least 200 s under the experimental conditions, and provides clear evidence for hydrogen atom tunneling in the H-isotopologue. This is the first spectroscopic confirmation of hydrogen atom tunneling governing 1,2-H-shift reactions at noncryogenic temperatures, which is of broad significance for a range of (bio)chemical processes, including enzymatic transformations and organocatalysis.