Heavy‐Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial,and Bell's Formula Closely Approximates Multidimensional Tunneling at ≥250 K

Multidimensional tunneling calculations are carried out for 13 reactions, to test the scope of heavy‐atom tunneling in organic chemistry, and to check the accuracy of one‐dimensional tunneling models. The reactions include pericyclic, cycloaromatization, radical cyclization and ring opening, and S_N2. When compared at the temperatures that give the same effective rate constant of 3×10⁻⁵ s⁻¹, tunneling accounts for 25–95 % of the rate in 8 of the 13 reactions. Values of transmission coefficients predicted by Bell's formula, κ_Bell , agree well with multidimensional tunneling (canonical variational transition state theory with small curvature tunneling), κ_SCT. Mean unsigned deviations of κ_Bell vs. κ_SCT are 0.08, 0.04, 0.02 at 250, 300 and 400 K. This suggests that κ_Bell is a useful first choice for predicting transmission coefficients in heavy‐atom tunnelling.     

Heavy‐Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial,and Bell's Formula Closely Approximates Multidimensional Tunneling at ≥250 K

Multidimensional tunneling calculations are carried out for 13 reactions, to test the scope of heavy‐atom tunneling in organic chemistry, and to check the accuracy of one‐dimensional tunneling models. The reactions include pericyclic, cycloaromatization, radical cyclization and ring opening, and S_N2. When compared at the temperatures that give the same effective rate constant of 3×10⁻⁵ s⁻¹, tunneling accounts for 25–95 % of the rate in 8 of the 13 reactions. Values of transmission coefficients predicted by Bell's formula, κ_Bell , agree well with multidimensional tunneling (canonical variational transition state theory with small curvature tunneling), κ_SCT. Mean unsigned deviations of κ_Bell vs. κ_SCT are 0.08, 0.04, 0.02 at 250, 300 and 400 K. This suggests that κ_Bell is a useful first choice for predicting transmission coefficients in heavy‐atom tunnelling.     

Atom Tunneling in Chemistry

Quantum mechanical tunneling of atoms is increasingly found to play an important role in many chemical transformations. Experimentally, atom tunneling can be indirectly detected by temperature‐independent rate constants at low temperature or by enhanced kinetic isotope effects. In contrast, the influence of tunneling on the reaction rates can be monitored directly through computational investigations. The tunnel effect, for example, changes reaction paths and branching ratios, enables chemical reactions in an astrochemical environment that would be impossible by thermal transition, and influences biochemical processes.     

Fast Heavy‐Atom Tunneling in Trifluoroacetyl Nitrene

Chemical reactions involving quantum mechanical tunneling (QMT) increasingly attract the attention of scientists. In contrast to the hydrogen‐tunneling as frequently observed in chemistry and biology, tunneling solely by heavy atoms is rare. Herein, we report heavy‐atom tunneling in trifluoroacetyl nitrene, CF₃C(O)N. The carbonyl nitrene CF₃C(O)N in the triplet ground state was generated in cryogenic matrices by laser (193 or 266 nm) photolysis of CF₃C(O)N₃ and characterized by IR and EPR spectroscopy. In contrast to the theoretically predicted activation barriers (>10 kcal mol⁻¹), CF₃C(O)N undergoes rapid rearrangement into CF₃NCO with half‐life times of less than 10 min and unprecedentedly large ¹⁴N/¹⁵N kinetic isotope effects (1.18–1.33) in solid Ar, Ne, and N₂ matrices even at 2.8 K. The tunneling disappearance of CF₃C(O)N becomes much slower in the chemically active toluene and in 2‐methyltetrahydrofuran at 5 K.     

Insights Gained by Modeling the Kinetics of Archetypal Hydrogen Atom Transfer Reactions: NH3 + ·H ⇆ H2N· + H2 and CH4 + ·H ⇆ H3C· + H2

Experimental measurements of the kinetics of the title reactions extend to temperature ranges of 1360 K for the ammonia‐hydrogen reaction and of 1602 K for the methane‐hydrogen reaction. Curved plots of ln(k) versus 1/T are obtained. Many theoretical calculations modeling these reactions routinely use tunneling corrections to match experiment. The steepness and curvatures of the plots are modeled successfully in this work and are shown to be caused solely by changes in the bond dissociation energies of the bonds involved in the reactions without invoking tunneling or any other adjustable parameters. The conclusion that tunneling does not contribute significantly to the rates in the temperature range of the measurements is in stark contrast with those theoretical calculations invoking large tunneling factors in the experimental temperature range. Support for the conclusion is provided by theoretical calculations of harmonic quantum transition state theory implementing instanton theory. There is direct experimental evidence that significant tunneling occurs in some H atom transfers, as with isotopomers of H₂ + ·H and other H transfers at very low temperatures. However, there is no direct experimental evidence of significant tunneling contributions to the rates of the title reactions in the temperature range of the measurements. Insights are gained into what specific forces must be overcome by the enthalpy of activation for reaction to occur.     

Heavy‐Atom Tunneling Through Crossing Potential Energy Surfaces: Cyclization of a Triplet 2‐Formylarylnitrene to a Singlet 2,1‐Benzisoxazole

Not long ago, the occurrence of quantum mechanical tunneling (QMT) chemistry involving atoms heavier than hydrogen was considered unreasonable. Contributing to the shift of this paradigm, we present here the discovery of a new and distinct heavy‐atom QMT reaction. Triplet syn‐2‐formyl‐3‐fluorophenylnitrene, generated in argon matrices by UV‐irradiation of an azide precursor, was found to spontaneously cyclize to singlet 4‐fluoro‐2,1‐benzisoxazole. Monitoring the transformation by IR spectroscopy, temperature‐independent rate constants (k≈1.4×10^?3 s^?1; half‐life of ≈8 min) were measured from 10 to 20 K. Computational estimated rate constants are in fair agreement with experimental values, providing evidence for a mechanism involving heavy‐atom QMT through crossing triplet to singlet potential energy surfaces. Moreover, the heavy‐atom QMT takes place with considerable displacement of the oxygen atom, which establishes a new limit for the heavier atom involved in a QMT reaction in cryogenic matrices.     

Full-dimensional quantum dynamics study of exchange processes for the D + H2O and D + HOD reactions

The exchange processes of D + H(2)O and D + HOD reactions are studied using initial state-selected time-dependent wave packet approach in full dimension. The total reaction probabilities for different partial waves, together with the integral cross sections, are obtained both by the centrifugal sudden (CS) approximation and exact coupled-channel (CC) calculations, for the H(2)O(HOD) reactant initially in the ground rovibrational state. In the CC calculations, small resonance peaks in the reaction probabilities and quick diminishing of the resonance peaks with the increase of total angular momenta J do not lead to clear step-like features just above the threshold in the cross sections for the title reactions, which are different in other isotopically substituted reactions where the hydrogen atom was included as the reactant instead of the deuterium atom [B. Fu, Y. Zhou, and D. H. Zhang, Chem. Sci. 3, 270 (2012); B. Fu and D. H. Zhang, J. Phys. Chem. A 116, 820 (2012)]. It is interesting that the shape resonance-induced features resulting from the reaction tunneling are significantly diminished accordingly in the reactions of the deuterium atom and H(2)O or HOD, owing to the weaker tunneling capability of the reagent deuterium atom in the title reactions than the reagent hydrogen atom in other reactions. In the CS calculations, the resonance peaks persist in many partial waves but cannot survive the partial-wave summations. The cross sections for the D(') + H(2)O → D(')OH + H and D(') + HOD → D(')OD + H reactions are substantially larger than those for the D(') + HOD → HOD(') + D reaction, indicating that the D(')/H exchange reactions are much more favored than the D(')/D exchange.     

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

As an experimental test of the theoretical prediction that heavy‐atom tunneling is involved in the degenerate Cope rearrangement of semibullvalenes at cryogenic temperatures, monodeuterated 1,5‐dimethylsemibullvalene isotopomers were prepared and investigated by IR spectroscopy using the matrix isolation technique. As predicted, the less thermodynamically stable isotopomer rearranges at cryogenic temperatures in the dark to the more stable one, while broadband IR irradiation above 2000 cm⁻¹ results in an equilibration of the isotopomeric ratio. Since this reaction proceeds with a rate constant in the order of 10⁻⁴ s⁻¹ despite an experimental barrier of E_a=4.8 kcal mol⁻¹ and with only a shallow temperature dependence, the results are interpreted in terms of heavy‐atom tunneling.     

Understanding the Mechanisms of Unusually Fast HH,CH,and CC Bond Reductive Eliminations from Gold(III) Complexes

Carbon–carbon bond reductive elimination from gold(III) complexes are known to be very slow and require high temperatures. Recently, Toste and co‐workers have demonstrated extremely rapid C?C reductive elimination from cis‐[AuPPh₃(4‐F‐C₆H₄)₂Cl] even at low temperatures. We have performed DFT calculations to understand the mechanistic pathway for these novel reductive elimination reactions. Direct dynamics calculations inclusive of quantum mechanical tunneling showed significant contribution of heavy‐atom tunneling (>25 %) at the experimental reaction temperatures. In the absence of any competing side reactions, such as phosphine exchange/dissociation, the complex cis‐[Au(PPh₃)₂(4‐F‐C₆H₄)₂]⁺ was shown to undergo ultrafast reductive elimination. Calculations also revealed very facile, concerted mechanisms for H?H, C?H, and C?C bond reductive elimination from a range of neutral and cationic gold(III) centers, except for the coupling of sp³ carbon atoms. Metal–carbon bond strengths in the transition states that originate from attractive orbital interactions control the feasibility of a concerted reductive elimination mechanism. Calculations for the formation of methane from complex cis‐[AuPPh₃(H)CH₃]⁺ predict that at ?52 °C, about 82 % of the reaction occurs by hydrogen‐atom tunneling. Tunneling leads to subtle effects on the reaction rates, such as large primary kinetic isotope effects (KIE) and a strong violation of the rule of the geometric mean of the primary and secondary KIEs.     

On‐Surface Formation of Cumulene by Dehalogenative Homocoupling of Alkenyl gem‐Dibromides

The on‐surface activation of carbon–halogen groups is an efficient route to produce radicals for constructing various hydrocarbons and carbon nanostructures. To date, the employed halide precursors have only one halogen attached to a carbon atom. It is thus of interest to study the effect of attaching more than one halogen atom to a carbon atom with the aim of producing multiple unpaired electrons. By introducing an alkenyl gem‐dibromide, cumulene products were fabricated on a Au(111) surface by dehalogenative homocoupling reactions. The reaction products and pathways were unambiguously characterized by a combination of high‐resolution scanning tunneling microscopy and non‐contact atomic force microscopy measurements together with density functional calculations. This study further supplements the database of on‐surface synthesis strategies and provides a facile manner for incorporation of more complicated carbon scaffolds into surface nanostructures.     

Heavy-Atom Tunneling in Organic Reactions

In the past few years, numerous investigations have been reported on the role of heavy-atom tunneling in the area of pericyclic reactions, π-bond-shifting, and other processes. These studies illustrate unique strategies for the experimental detection of heavy-atom tunneling and the increased use of calculations to predict it. This Minireview focuses primarily on carbon tunneling in ground-state processes but also highlights nitrogen tunneling and the first example of excited-state heavy-atom tunneling. Salient features of these reactions along with potential limitations are discussed, as well as challenges and directions for future investigation.     

The tunneling dynamics of the low temperature H exchange reactions

A simple method for calculating of the tunneling linear hydrogen atom exchange reaction is proposed for heavy reactants Its main feature is the competing of two sniall probabilities of a sufficientiv close reactant approaching and of H transfer. The good accuracy and the validity of the whole tunnel dynamics picture are confirmed by the numerical results obtained bv the classical S-matrix method modified for strongly exothermic reactions. The study of temperature dependences and isotopic effects of the linear H exchange reactions with a number of typical potential energy surfaces yields for the reaction barrier a value significantly higher than that given by simple one-dimensional barrier penetrability calculations.     

σ‐Alkylpalladium Intermediates in Intramolecular Heck Reactions:Isolation and Catalytic Activity

The isolation of σ‐alkylpalladium Heck intermediates, possible when β‐hydride elimination is inhibited, is a rather rare event. Performing intramolecular Heck reactions on N‐allyl‐2‐halobenzylamines in the presence of [Pd(PPh₃)₄], we isolated and characterized a series of stable bridged palladacycles containing an iodine or bromine atom on the palladium atom. Indolyl substrates were also tested for isolation of the corresponding complexes. X‐ray crystallographic analysis of one of the indolyl derivatives revealed the presence of a five‐membered palladacycle with the metal center bearing a PPh₃ ligand and an iodine atom in a cis position with respect to the nitrogen atom. The stability of the σ‐alkylpalladium complexes is probably a consequence of the strong constraint resulting from the bridged junction that hampers the cisoid conformation essential for β‐hydride elimination. Subsequently, the thus obtained bridged five‐membered palladacycles were proven to be effective precatalysts in Heck reactions as well as in cross‐coupling processes such as Suzuki and Stille reactions.     

Density dynamics in some quantum systems

The quantum domain behavior of classical nonintegrable systems is well‐understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov–Arnold–Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field‐induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories. Quantum fluid density functional theory may be used to understand different time‐dependent processes like ion‐atom/molecule collisions, atom‐field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained. © 2013 Wiley Periodicals, Inc.     

Theoretical Study of the Reaction Mechanism and Kinetics of HO2 with XCHO (X = F,Cl)

The reactions of HO₂ with FCHO and ClCHO have been theoretically investigated by combining beyond‐CCSD(T) electronic structure benchmarks, validated density functional theory, and canonical variational transition state theory with small‐curvature tunneling, coupled‐torsions anharmonicity, and high‐frequency anharmonicity. This investigation explores three different reaction mechanisms: radical addition plus a hydrogen transfer, radical addition, and hydrogen abstraction. The calculated results show that the dominant reaction pathway is the terminal oxygen atom of HO₂ added to the carbon atom of XCHO (X = F, Cl) and simultaneously the hydrogen atom of HO₂ transferred to the oxygen atom of the C=O group in XCHO. The reaction barriers of the other reaction pathways are so high that these processes are negligible in the atmosphere. Although the barrier height of the dominant reaction pathway in the HO₂ + FCHO reaction is 0.61 kcal/mol higher than that of the corresponding HO₂ + ClCHO reaction, the HO₂ + FCHO reaction is faster than the HO₂ + ClCHO reaction because the variational effects of HO₂ + ClCHO is more obvious than that of the HO₂ + FCHO. The present results show that the HO₂ + FCHO reaction may be important in the atmosphere. The present results should be useful in evaluating the atmospheric fate of XCHO (X = F, Cl).     

Theoretical study of thermal rearrangements of α‐silylalcohols: Effects of substituents attached to the silicon atom on the reactions

To investigate the effects of substituents attached to the silicon atom on the thermal rearrangement reactions of α‐silyl alcohols, the thermal rearrangement reactions of dimethylsilyl methanol (CH₃)₂SiHCH₂OH and vinylsilyl methanol CH₂?CHSiH₂CH₂OH were studied by ab initio calculations at the G3 level. Geometries of various stationary points were fully optimized at the MP2(full)/6‐31G(d) and MP2(full)/6‐311G(d,p) levels, and harmonic vibrational frequencies were calculated at the same levels. The reaction paths were investigated and confirmed by intrinsic reaction coordinate (IRC) calculations at the MP2(full)/6‐31G(d) level. The results show that two dyotropic reactions could occur when (CH₃)₂SiHCH₂OH or CH₂?CHSiH₂CH₂OH is heated. One is Brook rearrangement reaction (reaction A), and the dimethylsilyl or vinylsilyl groups migrates from carbon atom to oxygen atom coupled with a simultaneous migration of a hydrogen atom from oxygen atom to carbon atom passing through a double three‐membered ring transition state, forming dimethylmethoxylsilane (CH₃)₂SiHOCH₃ or methoxylvinylsilane CH₂?CHSiH₂OCH₃; the other is a hydroxyl group migration (reaction B) from carbon atom to silicon atom, coupled with a simultaneous migration of a hydrogen atom from silicon atom to carbon atom, via a double three‐membered ring transition state, forming trimethylsilanol (CH₃)₃SiOH or methylvinylsilanol CH₃SiH(OH)CH?CH₂. The G3 barriers of the reactions A and B were computed to be 312.8 and 241.4 kJ/mol for (CH₃)₂SiHCH₂OH, and 317.6 and 233.7 kJ/mol for CH₂?CHSiH₂CH₂OH, respectively. On the basis of the MP2(full)/6‐31G(d) optimized parameters, vibrational frequencies, and G3 energies, the reaction rate constants k(T) and equilibrium constants K(T) were calculated using canonical variational transition state theory (CVT) with centrifugal‐dominant small‐curvature tunneling (SCT) approximation over a temperature range of 400–1800 K. The influences of methyl and vinyl groups attached to the silicon atom on reactions are discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Hydrogen Radical Additions to Unsaturated Hydrocarbons and the Reverse β‐Scission Reactions: Modeling of Activation Energies and Pre‐Exponential Factors

The group additivity method for Arrhenius parameters is applied to hydrogen addition to alkenes and alkynes and the reverse β‐scission reactions, an important family of reactions in thermal processes based on radical chemistry. A consistent set of group additive values for 33 groups is derived to calculate the activation energy and pre‐exponential factor for a broad range of hydrogen addition reactions. The group additive values are determined from CBS‐QB3 ab‐initio‐calculated rate coefficients. A mean factor of deviation of only two between CBS‐QB3 and experimental rate coefficients for seven reactions in the range 300–1000 K is found. Tunneling coefficients for these reactions were found to be significant below 400 K and a correlation accounting for tunneling is presented. Application of the obtained group additive values to predict the kinetics for a set of 11 additions and β‐scissions yields rate coefficients within a factor of 3.5 of the CBS‐QB3 results except for two β‐scissions with severe steric effects. The mean factor of deviation with respect to experimental rate coefficients of 2.0 shows that the group additive method with tunneling corrections can accurately predict the kinetics and is at least as accurate as the most commonly used density functional methods. The constructed group additive model can hence be applied to predict the kinetics of hydrogen radical additions for a broad range of unsaturated compounds.     

Exceptional Isotopic‐Substitution Effect: Breakdown of Collective Proton Tunneling in Hexagonal Ice due to Partial Deuteration

Multiple proton transfer controls many chemical reactions in hydrogen‐bonded networks. However, in contrast to well‐understood single proton transfer, the mechanisms of correlated proton transfer and of correlated proton tunneling in particular have remained largely elusive. Herein, fully quantized ab initio simulations are used to investigate H/D isotopic‐substitution effects on the mechanism of the collective tunneling of six protons within proton‐ordered cyclic water hexamers that are contained in proton‐disordered ice, a prototypical hydrogen‐bonded network. At the transition state, isotopic substitution leads to a Zundel‐like complex, [HO???D???OH], which localizes ionic defects and thus inhibits perfectly correlated proton tunneling. These insights into fundamental aspects of collective proton tunneling not only rationalize recent neutron‐scattering experiments, but also stimulate investigations into multiple proton transfer in hydrogen‐bonded networks much beyond ice.     

The role of long range tunneling in electron transfer processes in condensed media

Experimental evidence is given for the importance of long range tunneling in electron transfer reactions in condensed media: the unusually weak effect of electrostatic repulsion on the rate of some electron transfer and spin exchange processes; electron transfer between distant (up to ≈ 30 A) species in solids at a rate considerably exceeding that of thermal diffusion; the unusual concentration dependence of radiation yields in the presence of scavengers, etc. The concept of long range tunneling is shown to permit quantitative explanation and correlation of experimental data on electron transfer in quite different fields.The factors determining the efficiency of tunneling, as well as some peculiar features of tunneling kinetics are considered.The role of long range tunneling in various chemical processes involving electron transfer in condensed media are discussed (ion reactions in solutions, photochemistry, radiation chemistry, reactions with polymers, some biochemical reactions).     

On the Role of the Electronic Structure of the Heteronuclear Oxide Cluster [Ga2Mg2O5].+ in the Thermal Activation of Methane and Ethane: An Unusual Doping Effect

The reactivity of the heteronuclear oxide cluster [Ga₂Mg₂O₅]^.+, bearing an unpaired electron at a bridging oxygen atom (O_b^.?), towards methane and ethane has been studied using Fourier transform ion cyclotron resonance mass spectrometry (FT‐ICR‐MS). Hydrogen‐atom transfer (HAT) from both methane and ethane to the cluster ion is identified experimentally. The reaction mechanisms of these reactions are elucidated by state‐of‐the‐art quantum chemical calculations. The roles of spin density and charge distributions in HAT processes, as revealed by theory, not only deepen our mechanistic understanding of C? H bond activation but also provide important guidance for the rational design of catalysts by pointing to the particular role of doping effects.