Hydrogen-atom tunneling in small thioamides: N-methylthiourea, thiobenzamide and 2-cyanothioacetamide

The most stable thione tautomeric forms of N-methylthiourea, thiobenzamide and 2-cyanothioacetamide were isolated in low-temperature argon matrices. The higher-energy thiol tautomers of these compounds were generated upon irradiation of matrix-isolated monomers with UV (λ > 270 nm) light. For N-methylthiourea and thiobenzamide, kept in the dark at 3.5 K for a long period of time, a spontaneous thiol → thione hydrogen atom tunneling transformation occurred. Only the thiol isomers with the favorably oriented hydrogen atom of the imino group underwent these hydrogen-atom tunneling processes. The other thiol isomers, with the hydrogen atom of the imino group oriented towards the sulfur atom, did not undergo the thiol → thione conversion. For the photogenerated thiol forms of 2-cyanothioacetamide, no spontaneous thiol → thione tautomeric transformation was detected. Instead, only the spontaneous conformational change of one S-H rotamer of the thiol 2-cyanothioacetamide tautomer into the other S-H rotamer was observed.

Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF)n, (HCl)n and (H2O)n where n = 3, 4, 5

The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)n, (HCl)n and (H2O)n where n = 3-5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)n are consistent with prior studies identifying Cnh and Dnh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through Cs TS structures for the C1 minima of (H2O)3 and (H2O)5, whereas the process goes through a TS with D2d symmetry for the S4 global minimum of (H2O)4. This work corroborates earlier findings that the minima for (HCl)3, (HCl)4 and (HCl)5 have C3h, S4 and C1 point group symmetry, respectively, and that the Cnh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)3, (HCl)4 and (HCl)5 have D3h, D2d, and C2 point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)4 and (HF)5 have the smallest electronic barrier heights for CPT (≈15 kcal mol-1 for both), followed by the HF trimer (≈21 kcal mol-1). The barriers are appreciably higher for the other clusters (around 27 kcal mol-1 for (H2O)4 and (HCl)3; roughly 30 kcal mol-1 for (H2O)3, (H2O)5 and (HCl)4; up to 38 kcal mol-1 for (HCl)5). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol-1 for the pentamers of HF, H2O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.

A personal perspective of the present status and future challenges facing thermal reaction rate theory

Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.

Unraveling Water Solvation Effects with Quantum Mechanics/Molecular Mechanics Semiclassical Vibrational Spectroscopy: The Case of Thymidine

We introduce a quantum mechanics/molecular mechanics semiclassical method for studying the solvation process of molecules in water at the nuclear quantum mechanical level with atomistic detail. We employ it in vibrational spectroscopy calculations because this is a tool that is very sensitive to the molecular environment. Specifically, we look at the vibrational spectroscopy of thymidine in liquid water. We find that the C═O frequency red shift and the C═C frequency blue shift, experienced by thymidyne upon solvation, are mainly due to reciprocal polarization effects, that the molecule and the water solvent exert on each other, and nuclear zero-point energy effects. In general, this work provides an accurate and practical tool to study quantum vibrational spectroscopy in solution and condensed phase, incorporating high-level and computationally affordable descriptions of both electronic and nuclear problems.

Proton tunneling in the dissociation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses

Light-induced deprotonation of molecules is an important process in photochemical reactions. Here, we theoretically investigate the tunneling deprotonation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses. The quasi-static picture shows that the field-dressed potential barrier is significantly lowered for the deprotonation channel when the mass asymmetry of the diatomic molecule increases. Our numerical simulations demonstrate that when the mass symmetry breaks, the tunneling deprotonation is significantly enhanced and the proton tunneling becomes the dominant dissociation channel in the THz driving fields. In addition, the simulated nuclear momentum distributions show that the emission of the proton is directed by the effective vector potential for the deprotonation channel and, meanwhile, the angular distribution of the emitting proton is affected by the alignment and rotation of the molecule induced by the rotating field.

Barrier Height Breakpoint in Employing the Arrhenius Equation to Proton Isotope Permeation through Stone-Wales Graphene

Although the Arrhenius equation has been used in proton isotope transfer across graphene membranes, concerns have arisen about its validity in this scenario. As the strong quantum tunneling during the permeation would cause curvature from the conventional linear Arrhenius plot, it potentially results in misleading activation energies. Here, we investigate the validity of the Arrhenius equation in proton isotope permeation through the topological Stone-Wales 55-77 graphene and report the actual effective activation energy of the permeation. We show that the Arrhenius equation breaks down in proton permeation through a conventional six-membered ring (6MR), in contrast to the normal Arrhenius behavior in a seven-membered ring (7MR). Notably, we demonstrate a barrier height breakpoint beyond which the Arrhenius equation becomes invalid. This study offers an important reference point of the Arrhenius equation, which could provide new insight into the future to accurately determine effective activation energies.

Photochemistry of 1-(2- and 3-Thienyl)diazoethanes: Spectroscopy and Tunneling Reaction of Triplet 1-(3-Thienyl)ethylidene

Photolysis (λ > 613 nm) of 1-(3-thienyl)diazoethane (21) yields the s-E rotamer of triplet 1-(3-thienyl)ethylidene (3), as characterized by UV/vis and EPR spectroscopy. The s-Z rotamer of 3 was not observed. EPR and UV/vis signals attributed to carbene 3 decrease by approximately 50% upon standing in the dark for 68 h at 10 K. Although formally spin-forbidden, an intramolecular [1,2]-hydrogen shift in triplet carbene 3 to afford singlet s-E 3-vinylthiophene (8) is presumed to occur via quantum mechanical tunneling. The behavior of the CD3 analogue supports this interpretation. Photolysis (λ > 613 nm) of 1-(3-thienyl)diazoethane-d3 (21-d3) yields triplet 1-(3-thienyl)ethylidene-d3 (3-d3), as characterized by IR, UV/vis, and EPR spectroscopy. No change in the signal intensity of EPR and UV/vis signals of triplet 3-d3 is observed upon standing in the dark for 68 h at 10 K. In a series of 2-substituted thienyl derivatives, irradiation of 1-(2-thienyl)diazoethane (22), 1-(2-thienyl)diazoethane-d3 (22-d3), or (3-methyl-2-thienyl)diazomethane (23) does not yield triplet carbene intermediates. Positioning and labeling of the methyl group proved to have a large effect on products observed for these species. 1-(2-Thienyl)diazoethane (22) yields the products of [1,2]-hydrogen migration, s-Z and s-E 2-vinylthiophene (7), while 22-d3 and 23 give products derived from opening of the thiophene ring.

Coupled Cluster Semiclassical Estimates of Experimental Reaction Rates: The Interconversion of Glycine Conformer VIp to Ip

We apply the full-dimensional Semiclassical Transition State Theory (SCTST) to estimate the rate constant of glycine molecule interconversion between the VIp and Ip conformers. We have reached an electronic structure accuracy up to the explicitly correlated Coupled Cluster method (CCSD(T)-F12b/cc-pVDZ-F12) thanks to our parallel implementation. The reaction has been experimentally investigated in the literature and is known to proceed by quantum mechanical tunneling. The SCTST rates improve over other theoretical methods, and our results align with the experimental measurements, thus confirming the accuracy of the fully coupled anharmonic semiclassical tunneling treatment, providing that the level of electronic structure theory gives a reliable estimate of the reaction barrier height and shape. The comparison with experimental half-life times supports the validity of SCTST for glycine VIp-Ip conformer conversion in the cryogenic temperature range, where this theory is usually not considered applicable due to the onset of the deep tunneling regime.

Uniform Semiclassical Instanton Rate Theory

The instanton expression for the thermal transmission probability through a one-dimensional barrier is derived by using the uniform semiclassical energy-dependent transmission coefficient of Kemble. The resulting theory does not diverge at the "crossover temperature" but changes smoothly. The temperature-dependent energy of the instanton is the same as the barrier height when ℏβω‡ = π and not 2π as in the "standard" instanton theory. The concept of a crossover temperature between tunneling and thermal activation, based on the divergence of the instanton rate, is obsolete. The theory is improved by assuring that at high energy when the energy-dependent transmission coefficient approaches unity the integrand decays exponentially as dictated by the Boltzmann factor and not as a Gaussian. This ensures that at sufficiently high temperatures the uniform theory reduces to the classical. Application to Eckart barriers demonstrates that the uniform theory provides a good estimate of the numerically exact result over the whole temperature range.

Competing quantum effects in heavy-atom tunnelling through conical intersections

Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.

Hydrogen-Atom Tunneling in a Homochiral Environment

The role-exchanging concerted torsional motion of two hydrogen atoms in the homochiral dimer of trans-1,2-cyclohexanediol was characterized through a combination of broadband rotational spectroscopy and theoretical modeling. The results reveal that the concerted tunneling motion of the hydrogen atoms leads to the inversion of the sign of the dipole moment components along the a and b principal axes, due to the interchange motion that cooperatively breaks and reforms one intermolecular hydrogen bond. This motion is also coupled with two acceptor switching motions. The energy difference between the two ground vibrational states arising from this tunneling motion was determined to be 29.003(2) MHz. The corresponding wavefunctions suggest that the two hydrogen atoms are evenly delocalized on two equivalent potential wells, which differs from the heterochiral case where the hydrogen atoms are confined in separate wells, as the permutation-inversion symmetry breaks down. This intriguing contrast in hydrogen-atom behavior between homochiral and heterochiral environments could further illuminate our understanding of the role of chirality in intermolecular interactions and dynamics.

The Marcus dimension: identifying the nuclear coordinate for electron transfer from ab initio calculations

The Marcus model forms the foundation for all modern discussion of electron transfer (ET). In this model, ET results in a change in diabatic potential energy surfaces, separated along an ET nuclear coordinate. This coordinate accounts for all nuclear motion that promotes electron transfer. It is usually assumed to be dominated by a collective asymmetric vibrational motion of the redox sites involved in the ET. However, this coordinate is rarely quantitatively specified. Instead, it remains a nebulous concept, rather than a tool for gaining true insight into the ET pathway. Herein, we describe an ab initio approach for quantifying the ET coordinate and demonstrate it for a series of dinitroradical anions. Using sampling methods at finite temperature combined with density functional theory calculations, we find that the electron transfer can be followed using the energy separation between potential energy surfaces and the extent of electron localization. The precise nuclear motion that leads to electron transfer is then obtained as a linear combination of normal modes. Once the coordinate is identified, we find that evolution along it results in a change in diabatic state and optical excitation energy, as predicted by the Marcus model. Thus, we conclude that a single dimension of the electron transfer described in Marcus-Hush theory can be described as a well-defined nuclear motion. Importantly, our approach allows the separation of the intrinsic electron transfer coordinate from other structural relaxations and environmental influences. Furthermore, the barrier separating the adiabatic minima was found to be sufficiently thin to enable heavy-atom tunneling in the ET process.

Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates

A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.

A combined spectroscopic and computational investigation on the solvent-to-chromophore excited-state proton transfer in the 2,2'-pyridylbenzimidazole-methanol complex

This article demonstrates experimental proof of excited state 'solvent-to-chromophore' proton transfer (ESPT) in the isolated gas phase PBI (2,2'-pyridylbenzimidazole)-CH₃OH complex, aided by computational calculations. The binary complexes of PBI with CH₃OH/CH₃OD were produced in a supersonic jet-cooled molecular beam and the energy barrier of the photo-excited process was determined using resonant two-colour two-photon ionization spectroscopy (R2PI). The ESPT process in the PBI-CH₃OH complex was confirmed by the disappearance of the Franck-Condon active vibrational transitions above 000 + 390 cm^-1. In the PBI-CH₃OD complex, the reappearance of the Franck-Condon transitions till 000 + 800 cm^-1 confirmed the elevation of the ESPT barrier upon isotopic substitution due to the lowering of the zero-point vibrational energy. The ESPT energy barrier in PBI-CH₃OH was bracketed as 410 ± 20 cm^-1 (4.91 ± 0.23 kJ mol^-1) by comparing the spectra of PBI-CH₃OH and PBI-CH₃OD. The solvent-to-chromophore proton transfer was confirmed based on the significantly decreased quantum tunnelling of the solvent proton in the PBI-CH₃OD complex. The computational investigation resulted in an energy barrier of 6.0 kJ mol^-1 for the ESPT reaction in the PBI-CH₃OH complex, showing excellent agreement with the experimental value. Overall, the excited state reaction progressed through an intersection of ππ* and nπ* states before being deactivated to the ground state via internal conversion. The present investigation reveals a novel reaction pathway for the deactivation mechanism of the photo-excited N-containing biomolecules in the presence of protic-solvents.

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.

A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde

We developed an approximate method for quantum reaction dynamics simulations, namely, a structure-based Gaussian (SBG) expansion approach, where SBG bases for the expansion of the wave function Ψ, expressed by a product of single-atom Cartesian Gaussians centered at the positions of respective nuclei, are mainly placed around critical structures on reaction pathways such as on the intrinsic reaction coordinate (IRC) through a transition state. In the present approach, the "pseudo-lattice points" at which SBGs are deployed are selected in a perturbative manner so as to make moderate the expansion length. We first applied the SBG idea to a two-dimensional quadruple-well model and obtained accurate tunneling splitting values between the lowest four states. We then applied it to hydrogen tunneling in malonaldehyde and achieved a tunneling splitting of 27.1 cm^-1 with only 875 SBGs at the MP2/6-31G(d,p) level of theory, in good agreement with 25 cm^-1 by the more elaborate multiconfiguration time-dependent Hartree method. Reasonable results were also obtained for singly and doubly deuterated malonaldehyde. We analyzed the tunneling states by utilizing expansion coefficients of individual SBGs and found that 40-45% of the SBGs in Ψ are nonplanar structures and SBGs away from the IRC contribute a little to hydrogen transfer.

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.

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.

Radical-like reactivity for dihydrogen activation by coinage metal-aluminyl complexes: computational evidence inspired by experimental main group chemistry

The computational study of an unprecedented reactivity of coinage metal-aluminyl complexes with dihydrogen is reported. In close resemblance to group 14 dimetallenes and dimetallynes, the complexes are predicted to activate H₂ under mild conditions. Two different reaction pathways are found disclosing a common driving force, i.e., the nucleophilic behavior of the electron-sharing M-Al (M = Cu, Ag, Au) bond, which enables a cooperative and diradical-like mechanism. This mode of chemical reactivity emerges as a new paradigm for dihydrogen activation and calls for experimental feedback.

Wavepacket dynamical study of H-atom tunneling in catecholate monoanion: the role of intermode couplings and energy flow

We present a study of H-atom tunneling in catecholate monoanion through wavepacket dynamical simulations. In our earlier study of this symmetrical double-well system [Phys. Chem. Chem. Phys., 2022, 24, 10887], a limited number of transition state modes were identified as being important for the tunneling process. These include the imaginary frequency mode Q₁, the CO scissor mode Q₁₀, and the OHO bending mode Q₂₉. In this work, starting from non-stationary initial states prepared with excitations in these modes, we have carried out wavepacket dynamics in two and three dimensional spaces. We analyse the dynamical effects of the intermode couplings, in particular the role of energy flow between the studied modes on H-atom tunneling. We find that while Q₁₀ strongly modulates the donor-acceptor distance, it does not exchange energy with Q₁. However, excitation in Q₂₉ or Q₁ does lead to rapid energy exchange between these modes, which modifies the tunneling rate at early times.

Assessing Thermal Response of Redox Conduction for Anti-Arrhenius Kinetics in a Microbial Cytochrome Nanowire

A micrometers-long helical homopolymer of the outer-membrane cytochrome type S (OmcS) from Geobacter sulfurreducens is proposed to transport electrons to extracellular acceptors in an ancient respiratory strategy of biogeochemical and technological significance. OmcS surprisingly exhibits higher conductivity upon cooling (anti-Arrhenius kinetics), an effect previously attributed to H-bond restructuring and heme redox potential shifts. Herein, the temperature sensitivity of redox conductivity is more thoroughly examined with conventional and constant-redox and -pH molecular dynamics and quantum mechanics/molecular mechanics. A 30 K drop in temperature constituted a weak perturbation to electron transfer energetics, changing electronic couplings (⟨H_mn⟩), reaction free energies (ΔG_mn), reorganization energies (λ_mn), and activation energies (E_a) by at most |0.002|, |0.050|, |0.120|, and |0.045| eV, respectively. Changes in ΔG_mn reflected -0.07 ± 0.03 V shifts in redox potentials that were caused in roughly equal measure by altered electrostatic interactions with the solvent and protein. Changes in intraprotein H-bonding reproduced the earlier observations. Single-particle diffusion and multiparticle steady-state flux models, parametrized with Marcus theory rates, showed that biologically relevant incoherent hopping cannot qualitatively or quantitatively describe electrical conductivity measured by atomic force microscopy in filamentous OmcS. The discrepancy is attributed to differences between solution-phase simulations and solid-state measurements and the need to model intra- and intermolecular vibrations explicitly.

Thermally-Activated Tunneling in the Two-Water Bridge Catalyzed Tautomerization of Phosphinylidene Compounds

Phosphinylidenes are an important class of organophosphorus compounds that can exhibit tautomerization between tricoordinated P(III) hydroxide (R¹ R² POH) and a pentacoordinated P(V) oxide (R¹ R² P(O)H) form. Herein we show, using the canonical variational transition state theory combined with multidimensional small-curvature tunneling approximation, the dominance of proton tunneling in the two-water-bridged tautomerizations of phosphinous acid and model phosphinylidenes comprising phosphosphinates, H-phosphonates, H-phosphinates and secondary phosphine oxides. Based on the studied system, the contribution of thermally-activated tunneling is predicted to speed up the semiclassical reaction rate by ca. threefold to as large as two orders of magnitude at 298.15 K in the gas phase. The large KIE and the concavity in the Arrhenius plots are further fingerprints of tunneling. The simulations also predicted that the rapid tunneling rate and short half-life span for the forward reaction, as opposed to the reverse reaction in fluorinated secondary phosphine oxides, would result in P(V) being elusive and only P(III) being isolable, which agrees with previous experiments where only P(III) was detected by IR and NMR spectroscopy. We also explored the role of solvent and predicted tunneling to be substantial.

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.

Importance of Nuclear Quantum Effects on Aqueous Electrolyte Transport under Confinement in Ti3C2 MXenes

Protons display a high chemical activity and strongly affect the charge storage capability in confined interlayer spaces of two-dimensional (2D) materials. As such, an accurate representation of proton dynamics under confinement is important for understanding and predicting charge storage dynamics in these materials. While often ignored in atomistic-scale simulations, nuclear quantum effects (NQEs), e.g., tunneling, can be significant under confinement even at room temperature. Using the thermostatted ring polymer molecular dynamics implementation of path integral molecular dynamics (PIMD) in conjunction with the ReaxFF force field, density functional tight binding (DFTB), and NequIP neural network potential simulations, we investigate the role of NQEs on proton and water transport in bulk water and aqueous electrolytes under confinement in Ti₃C₂ MXenes. Although overall NQEs are relatively small, especially in bulk, we find that they can alter both quantitative values and qualitative trends on both proton transport and water self-diffusion under confinement relative to classical MD predictions. Therefore, our results suggest the need for NQEs to be considered to simulate aqueous systems under confinement for both qualitative and quantitative accuracy.

Halogen-atom and group transfer reactivity enabled by hydrogen tunneling

The generation of carbon radicals by halogen-atom and group transfer reactions is generally achieved using tin and silicon reagents that maximize the interplay of enthalpic (thermodynamic) and polar (kinetic) effects. In this work, we demonstrate a distinct reactivity mode enabled by quantum mechanical tunneling that uses the cyclohexadiene derivative γ-terpinene as the abstractor under mild photochemical conditions. This protocol activates alkyl and aryl halides as well as several alcohol and thiol derivatives. Experimental and computational studies unveiled a noncanonical pathway whereby a cyclohexadienyl radical undergoes concerted aromatization and halogen-atom or group abstraction through the reactivity of an effective H atom. This activation mechanism is seemingly thermodynamically and kinetically unfavorable but is rendered feasible through quantum tunneling.

Hydrogen Tunneling in Catalytic Hydrolysis and Alcoholysis of Silanes

An unprecedented quantum tunneling effect has been observed in catalytic Si−H bond activations at room temperature. The cationic hydrido‐silyl‐iridium(III) complex, {Ir[SiMe(o‐C₆H₄SMe)₂](H)(PPh₃)(THF)}[BAr^F₄], has proven to be a highly efficient catalyst for the hydrolysis and the alcoholysis of organosilanes. When triethylsilane was used as a substrate, the system revealed the largest kinetic isotopic effect (KIE_{Si−H/Si−D}=346±4) ever reported for this type of reaction. This unexpectedly high KIE, measured at room temperature, together with the calculated Arrhenius preexponential factor ratio (A_H/A_D=0.0004) and difference in the observed activation energy [(EaD −EaH )=34.07 kJ mol⁻¹] are consistent with the participation of quantum tunneling in the catalytic process. DFT calculations have been used to unravel the reaction pathway and identify the rate‐determining step. Aditionally, isotopic effects were considered by different methods, and tunneling effects have been calculated to be crucial in the process.

Upgrading the peroxi-coagulation treatment of complex water matrices using a magnetically assembled mZVI/DSA anode: Insights into the importance of ClO radical

The electrochemical technologies for water treatment have flourished over the last decades. However, it is still challenging to treat the actual complex water effluents by a single electrochemical process, often requiring coupling of technologies. In this study, an upgraded peroxi-coagulation (PC) process with a magnetically assembled mZVI/DSA anode has been devised for the first time. COD, NH₃-N and total phosphorous were simultaneously and effectively removed from livestock wastewater. The advantages, influence of key parameters and evolution of electrogenerated species were systematically investigated to fully understand this novel PC process. The fluorescent substances in livestock wastewater could also be almost removed under optimal conditions (300 mA, 0.2 g ZVI particles and pH 6.8). The interaction between OH and active chlorine yielded ClO with a high steady-state concentration of 6.85 × 10^-13 M, which did not cause COD removal but accelerated the oxidation of NH₃-N. The Mulliken population suggested that OH and NH₃-N had similar electron-donor behavior, whereas ClO acted as an electron-withdrawing species. Besides, although the energy barrier for the reaction between OH and NH₃-N (17.0 kcal/mol) was lower than that with ClO (18.8 kcal/mol), considering the tunneling in the H abstraction reaction, the Skodje-Truhlar method adopted for calculations evidenced a 17-fold faster NH₃-N oxidation rate with ClO. In summary, this work describes an advantageous single electrochemical process for the effective treatment of a complex water matrix.

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.

How Does Electronic Activity Drive Chemical Reactions? Insights from the Reaction Electronic Flux for the Conversion of Dopamine into Norepinephrine

Hydrogen atom transfer (HAT) is a crucial step in the physiological conversion of dopamine into norepinephrine catalyzed by dopamine β-monooxygenase. The way the reaction takes place is unclear, and a rational explanation on how the electronic activity drives the HAT seems to be necessary. In this work, we answer this question using the reaction electronic flux (REF), a DFT-based descriptor of electronic activity. Two reaction mechanisms will be analyzed using the REF's decomposition in polarization and electron transfer effects. Results show that both mechanisms proceed as follows: (1) polarization effects initiate the reactions producing structural distortions; (2) electron transfer processes take over near the transition states, triggering specific chemical events such as bond forming and breaking which are responsible to push the reactions toward the products; (3) after passing the transition state, polarization shows up again and drives the relaxation process toward the product. Similar polarization effects were observed in both reactions, but they present an opposite behavior of the electronic transfer flux disclosing the fact that electron transfer phenomena govern the reaction mechanisms.

Dissipative tunneling rates through the incorporation of first-principles electronic friction in instanton rate theory. II. Benchmarks and applications

In Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], we presented the ring-polymer instanton with explicit friction (RPI-EF) method and showed how it can be connected to the ab initio electronic friction formalism. This framework allows for the calculation of tunneling reaction rates that incorporate the quantum nature of the nuclei and certain types of non-adiabatic effects (NAEs) present in metals. In this paper, we analyze the performance of RPI-EF on model potentials and apply it to realistic systems. For a 1D double-well model, we benchmark the method against numerically exact results obtained from multi-layer multi-configuration time-dependent Hartree calculations. We demonstrate that RPI-EF is accurate for medium and high friction strengths and less accurate for extremely low friction values. We also show quantitatively how the inclusion of NAEs lowers the crossover temperature into the deep tunneling regime, reduces the tunneling rates, and, in certain regimes, steers the quantum dynamics by modifying the tunneling pathways. As a showcase of the efficiency of this method, we present a study of hydrogen and deuterium hopping between neighboring interstitial sites in selected bulk metals. The results show that multidimensional vibrational coupling and nuclear quantum effects have a larger impact than NAEs on the tunneling rates of diffusion in metals. Together with Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], these results advance the calculations of dissipative tunneling rates from first principles.

Iterative Synthesis of 2-Deoxyoligosaccharides Enabled by Stereoselective Visible-Light-Promoted Glycosylation

The photoinitiated intramolecular hydroetherification of alkenols has been used to form C-O bonds, but the intermolecular hydroetherification of alkenes with alcohols remains an unsolved challenge. We herein report the visible-light-promoted 2-deoxyglycosylation of alcohols with glycals. The glycosylation reaction was completed within 2 min in a high quantum yield (ϕ=28.6). This method was suitable for a wide array of substrates and displayed good reaction yields and excellent stereoselectivity. The value of this protocol was further demonstrated by the iterative synthesis of 2-deoxyglycans with α-2-deoxyglycosidic linkages up to a 20-mer in length and digoxin with β-2-deoxyglycosidic linkages. Mechanistic studies indicated that this reaction involved a glycosyl radical cation intermediate and a photoinitiated chain process.

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.

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.

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.

Quantum tunneling of hydrogen atom transfer affects mandrel degradation in inertial confinement fusion target fabrication

Poly-α-methylstyrene (PAMS) is considered as the preferred mandrel material, whose degradation is crucial for the fabrication of high-quality inertial confinement fusion (ICF) targets. Herein, we reveal that hydrogen atom transfer (HAT) during PAMS degradation, which is usually attributed to the thermal effect, unexpectedly exhibits a strong high-temperature tunneling effect. Specifically, although the energy barrier of the HAT reaction is only 10⁻² magnitude different from depolymerization, the tunneling probability of the former can be 14–32 orders of magnitude greater than that of the latter. Furthermore, chain scission following HAT will lead to a variety of products other than monomers. Our work highlights that quantum tunneling may be an important source of uncertainty in PAMS degradation, which will provide a direction for the further development of key technology of target fabricating in ICF research and even the solution of plastic pollution.

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Tunneling of hydrogen atom transfer (HAT) brings uncertainty to mandrel degradation

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Lower energy barrier and stronger tunneling make active-end HAT occur more easily

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Chain scission following HAT leads to a variety of products other than monomers

Simultaneous H/D and 13C/12C Anomalous Kinetic Isotope Effects during the Sonolysis of Water in the Presence of Carbon Monoxide

Splitting of water molecules driven by ultrasound plays a central role in sonochemistry. While studies of sonoluminescence revealed the formation of a plasma inside the cavitation bubble, much less is known about the contribution of plasma chemical processes to the sonochemical mechanisms. Herein, we report for the first time sonochemical processes in water saturated with pure CO. The presence of CO causes a large increase in the H/D kinetic isotope effect (KIE) to α_H = 14.6 ± 1.8 in a 10% H₂O/D₂O mixture under 20 kHz ultrasound. The anomalous H/D KIE is attributed to electron quantum tunneling in the plasma produced by cavitation. In addition, CO₂ formed simultaneously with hydrogen during the sonochemical process is enriched with the ¹³C isotope, which indicates a V-V pumping mechanism typical for non-equilibrium plasma. Both observed KIEs unambiguously point to the contribution of quantum effects in sonochemical mechanisms.

Palladium-Catalyzed Direct γ-C(sp3)-H Arylation of β-Alkoxy Cyclohexenones: Reaction Scope and Mechanistic Insights

Direct γ-C(sp3)-arylation of unactivated electron-rich enones is a long-standing challenge. Herein, we report a mild Pd-catalyzed method for direct γ-C(sp3)-arylation of various unactivated β-alkoxy cyclohexenones. The method is not only...

Tunneling in the Hydrogen-Transfer Reaction from a Vitamin E Analog to an Inclusion Complex of 2,2-Diphenyl-1-picrylhydrazyl Radical with β-Cyclodextrin in an Aqueous Buffer Solution at Ambient Temperature

Recently, increasing attention has been paid to quantum mechanical behavior in biology. In this study, we investigated the involvement of quantum mechanical tunneling in the hydrogen-transfer reaction from Trolox, a water-soluble analog of vitamin E (α-tocopherol), to 2,2-diphenyl-1-picrylhydrazyl radical (DPPH•) in a phosphate buffer solution (0.05 M, pH 7.0). DPPH• was used as a reactivity model of reactive oxygen species and solubilized in water using β-cyclodextrin (β-CD). The second-order rate constants, kH and kD, in 0.05 M phosphate buffer solutions prepared with H2O (pH 7.0) and D2O (pD 7.0), respectively, were determined for the reaction between Trolox and DPPH•, using a stopped-flow technique at various temperatures (283-303 K). Large kinetic isotope effects (KIE, kH/kD) were observed for the hydrogen-transfer reaction from Trolox to the β-CD-solubilized DPPH• in the whole temperature range. The isotopic ratio of the Arrhenius prefactor (AH/AD = 0.003), as well as the isotopic difference in the activation energies (19 kJ mol-1), indicated that quantum mechanical tunneling plays a role in the reaction.

Exploring Dihydroflavonol-4-Reductase Reactivity and Selectivity by QM/MM-MD Simulations

Flavonoids are secondary metabolites ubiquitously found in plants. Their antioxidant properties make them highly interesting natural compounds for use in pharmacology. Therefore, unravelling the mechanisms of flavonoid biosynthesis is an important challenge. Among all the enzymes involved in this biosynthetic pathway, dihydroflavonol-4-reductase (DFR) plays a key role in the production of anthocyanins and proanthocyanidins. Here, we provide new information on the mechanism of action of this enzyme by using QM/MM-MD simulations applied to both dihydroquercetin (DHQ) and dihydrokaempferol (DHK) substrates. The consideration of these very similar compounds shed light on the major role played by the enzyme on the stabilization of the transition state but also on the activation of the substrate before the reaction through near-attack conformer effects.

Large Isotope Effects in Organometallic Chemistry

The kinetic isotope effect (KIE) is key to understanding reaction mechanisms in many areas of chemistry and chemical biology, including organometallic chemistry. This ratio of rate constants, k_H /k_D , typically falls between 1-7. However, KIEs up to 105 have been reported, and can even be so large that reactivity with deuterium is unobserved. We collect here examples of large KIEs across organometallic chemistry, in catalytic and stoichiometric reactions, along with their mechanistic interpretations. Large KIEs occur in proton transfer reactions such as protonation of organometallic complexes and clusters, protonolysis of metal-carbon bonds, and dihydrogen reactivity. C-H activation reactions with large KIEs occur with late and early transition metals, photogenerated intermediates, and abstraction by metal-oxo complexes. We categorize the mechanistic interpretations of large KIEs into the following three types: (a) proton tunneling, (b) compound effects from multiple steps, and (c) semi-classical effects on a single step. This comprehensive collection of large KIEs in organometallics provides context for future mechanistic interpretation.

Boron Tunneling in the "Weak" Bond-Stretch Isomerization of N-B Lewis Adducts

Some nitrile-boron halide adducts exhibit a double-well potential energy surface with two distinct minima: a "long bond" geometry (LB, a van der Waals interaction mostly based on electrostatics, but including a residual charge transfer component) and a "short bond" structure (SB, a covalent dative bond). This behavior can be considered as a "weak" form of bond stretch isomerism. Our computations reveal that complexes RCN-BX₃ (R=CH₃ , FCH₂ , BrCH₂ , and X=Cl, Br) exhibit a fast interconversion from LB to SB geometries even close to the absolute zero thanks to a boron atom tunneling mechanism. The computed half-lives of the meta-stable LB compounds vary between minutes to nanoseconds at cryogenic conditions. Accordingly, we predict that the long bond structures are practically impossible to isolate or characterize, which agrees with previous matrix-isolation experiments.

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.