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

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

Tunneling in the 1,5-hydrogen shift reactions of 1,3-cyclopentadiene and 5-methyl-1,3-cyclopentadiene

MPW1K/6-31+G(d,p) calculations which include the effects of small curvature tunneling find that, around room temperature, thermally activated tunneling dominates the 1,5-hydrogen shift reactions of 1,3-cyclopentadiene (2a) and 5-methyl-1,3-cyclopentadiene (2c). The calculated temperature dependence of the H/D kinetic isotope effect (KIE) for the latter rearrangement agrees well with experimental measurements that were published nearly 40 years ago. It is argued that the experimental KIEs provide prima facie evidence for tunneling in this reaction. The calculations also predict that it should be possible, at least in principle, to confirm this conclusion by observing curvature in the Arrhenius plot for the rearrangement of 2c.     

Calculations of the effect of tunneling on the Swain-Schaad exponents (SSEs) for the 1,5-hydrogen shift in 5-methyl-1,3-cyclopentadiene. Can SSEs be used to diagnose the occurrence of tunneling?

MPW1K density functional calculations, carried out with the 6-31+G(d,p) basis set, have been combined with canonical variational transition state theory (CVT) and small-curvature tunneling (SCT) corrections in order to compute the primary kinetic isotope effects for rearrangement of 5-methyl-1,3-cyclopentadiene (1) to 1-methyl-1,3-cyclopentadiene (2). The Swain-Schaad exponents, SSE = ln(kH/kT)/ln(kD/kT), for this reaction have been computed over the temperature range 100-600 K. Tunneling results in both large positive and large negative deviations from the value of SSE = 3.26, expected from consideration of only the effect of the isotopic mass on passage over the reaction barrier. In the rearrangement of 1 to 2, SSE approximately 3.26, not only at temperatures >400 K, where tunneling is relatively unimportant, but also around 170 K, where tunneling by both H and D is the dominant mode of reaction. Thus, from an experimental finding that SSE approximately 3.26 at a single temperature, it cannot be rigorously concluded that tunneling is unimportant. Measurement of SSEs over a broad temperature range is advisable; but measurement of the temperature dependence of just kH/kD can be used to establish more unequivocally whether tunneling is important, without the necessity of measuring kT.     

Heavy-Atom Tunneling in Bicyclo[4.1.0]hepta-2,4,6-trienes

Heavy-atom tunneling limits the lifetime and observability of bicyclo[4.1.0]hepta-2,4,6-triene, a key intermediate in the rearrangement of phenylcarbene. Bicyclo[4.1.0]hepta-2,4,6-triene had been proposed as the primary intermediate of the rearrangement of phenylcarbene, but despite many efforts evaded its characterization even in cryogenic matrices. By introducing fluorine substituents into the ortho-positions of the phenyl ring of phenylcarbene, the highly strained cyclopropene 1,5-difluorobicyclo[4.1.0]hepta-2,4,6-triene becomes stable enough to be characterized in argon matrices. However, even at 3 K this cyclopropene is only metastable and rearranges via heavy-atom tunneling to the corresponding cycloheptatetraene. Calculations suggest that fluorination is necessary to slow down the tunneling rearrangement of the bicycloheptatriene. The parent bicycloheptatriene rapidly rearranges via heavy-atom tunneling and therefore cannot be detected under matrix isolation conditions.     

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

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

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

Heavy‐Atom Tunneling in the Ring Opening of a Strained Cyclopropene at Very Low Temperatures

The highly strained 1H‐bicyclo[3.1.0]‐hexa‐3,5‐dien‐2‐one 1 is metastable, and rearranges to 4‐oxacyclohexa‐2,5‐dienylidene 2 in inert gas matrices (neon, argon, krypton, xenon, and nitrogen) at temperatures as low as 3 K. The kinetics for this rearrangement show pronounced matrix effects, but in a given matrix, the reaction rate is independent of temperature between 3 and 20 K. This temperature independence means that the activation energy is zero in this temperature range, indicating that the reaction proceeds through quantum mechanical tunneling from the lowest vibrational level of the reactant. At temperatures above 20 K, the rate increases, resulting in curved Arrhenius plots that are also indicative of thermally activated tunneling. These experimental findings are supported by calculations performed at the CASSCF and CASPT2 levels by using the small‐curvature tunneling (SCT) approximation.     

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.     

The contribution of quantum mechanical tunneling to the 1,2-hydrogen rearrangement of methylbromocarbene

The rate constants for the 1,2-hydrogen rearrangement of methyl- and methyl-d₃-bromocarbene have been determined as a function of temperature. The Arrhenius plots are curved, and the intermolecular isotope effect is small and may increase with increasing temperature. We believe that although the rearrangement proceeds classically at high temperatures, as suggested by theory, quantum mechanical tunneling contributes significantly to the reaction at low temperatures. Alternative explanations are presented and discussed.     

Formation of a Tunneling Product in the Photorearrangement of o‐Nitrobenzaldehyde

The photochemical rearrangement of o ‐nitrobenzaldehyde to o ‐nitrosobenzoic acid, first reported in 1901, has been shown to proceed via a distinct ketene intermediate. In the course of matrix isolation experiments in various host materials at temperatures as low as 3 K, the ketene was re‐investigated in its electronic and vibrational ground states. It was shown that hitherto unreported H‐tunneling dominates its reactivity, with half‐lives of a few minutes. Unexpectedly, the tunneling product is different from o ‐nitrosobenzoic acid formed in the photoprocess: Once prepared by irradiation, the ketene spontaneously rearranges to an isoxazolone via an intriguing mechanism initiated by H‐tunneling. CCSD(T)/cc‐pVTZ computations reveal that this isoxazolone is neither thermodynamically nor kinetically favored under the experimental conditions, and that formation of this unique tunneling product constitutes a remarkable and new example of tunneling control.     

Novel rearrangement of an isocaryolane sesquiterpenoid under mitsunobu conditions

Under modified Mitsunobu reaction conditions, a novel skeleton rearrangement of terpenes has been obtained. The reactivity of 8, 9-dioxygenated isocaryolane derivatives has been investigated. When either (8R,9R)-8-methoxyisocaryolane-9-ol (7) or (8R, 9R)-isocaryolane-8,9-diol (10) are treated under acidic conditions, isocaryolan-9-one (9) and the rearrangement compound (1S,2S,5R,8S)-1, 4,4-trimethyltricyclo[6.2.1.0(2,5)]undecane-8-carbaldehyde (11) are obtained. Otherwise treatment of compounds 7 and 10 under modified Mitsunobu conditions leads to the novel sesquiterpene derivative (1S, 2S,5R,9R)-1,4,4-trimethyltricyclo[7.2.1.0(2,5)]dodecan-8-one (8). This is the first example, to our knowledge, of a Mitsunobu-induced pinacol rearrangement. The influences of the substrate and reaction conditions on the evolution of the reaction are both explored. This modification of the Mitsunobu reaction conditions introduces a new, one-pot, procedure for preparing this class of rearrangement product.     

Tunneling effects of dyadic prototropic rearrangement of hypophosphorous acid

The structures and energies of the tautomeric forms of hypophosphorous acid and phosphine oxide were calculated by DFT. The tautomeric forms are in equilibrium, and intramolecular hydrogen bonding is shown to be possible in both tautomeric forms of phthalimidophosphorous acid. The equilibrium constants are estimated within a wide temperature range. The necessity to take into account the tunneling contribution to the rate constant of the rearrangement is demonstrated.     

Electronic Bond‐to‐Bond Fluxes in Pericyclic Reactions: Synchronous or Asynchronous?

One at a time or all at once? Electronic fluxes during a pericyclic reaction in the electronic ground state--exemplified for the degenerate Cope rearrangement of semibullvalene--may proceed either synchronously or asynchronously. Quantum simulations show that the mechanism is determined by the preparation of the reactants, for example, synchronous at cryogenic temperatures (tunneling) but asynchronous when induced by selective laser pulses (with energy over the barrier).     

Direct-dynamics VTST study of the [1,7] hydrogen shift in 7-methylocta-1,3(Z),5(Z)-triene. A model system for the hydrogen transfer reaction in previtamin D3

Direct-dynamics canonical variational transition-state theory calculations with microcanonically optimized multidimensional transmission coefficient (CVT/muOMT) for tunneling were carried out at the MPWB1K/6-31+G(d,p) level to study the [1,7] sigmatropic hydrogen rearrangement in 7-methylocta-1,3(Z),5(Z)-triene. This compound has seven conformers, of which only one leads to products, although all of them have to be included in the theoretical treatment. The calculated CVT/muOMT rate constants are in good agreement with the available experimental data. To try to understand the role of tunneling in the hydrogen shift reaction, we have also calculated the thermal rate constants for the monodeuterated compound in the interval T = 333.2-388.2 K. This allowed us to evaluate primary kinetic isotope effects (KIEs) and make a direct comparison with the experiment. Our calculations show that both the large measured KIE and the large measured difference in the activation energies between the deuterated and root compounds are due to the quantum tunneling. The tunneling contribution to the KIE becomes noticeable only when the coupling between the reaction coordinate and the transverse modes is taken into account. Our results confirm previous experimental and theoretical works, which guessed that the obtained kinetic parameters pointed to a reaction with an important contribution due to tunneling. The above conclusion would be essentially valid for the case of the [1,7] hydrogen shift in previtamin D3 because of the similarity to the studied model system.     

Hydrogen-atom tunneling in isomerization around the C-O bond of 2-chloro-6-fluorophenol in low-temperature argon matrixes

Infrared spectra of 2-chloro-6-fluorophenol in argon matrixes at 20 K revealed the presence of a "Cl-type" isomer, which has the OH···Cl hydrogen bond, but no "F-type" isomer with OH···F bonding, in striking contrast to the existence of both isomers in the gas and liquid phases at room temperature. This finding suggests that the F-type isomer changes to the more stable Cl-type one by hydrogen-atom tunneling in the matrixes. Similar experiments on the OD···X analog species were performed to confirm the tunneling isomerization, resulting in an O-D stretching band of the F-type isomer appearing as well as that of the Cl type, like the spectra reported in the gas and liquid phases. This implies that tunneling migration of the D atom is inhibited in the argon matrix. In addition, UV-induced photoreactions of 2-chloro-6-fluorophenol were studied by a joint use of matrix-isolation IR spectroscopy assisted by density functional theory calculations. It was found that 2-fluorocyclopentadienylidenemethanone and 4-chloro-2-fluorocyclohexadienone were produced from the Cl type; the former was by the Wolff rearrangement after dissociation of the H atom in the OH group and the Cl atom, and the latter was by intramolecular migration of the H and Cl atoms. As for the deuterated F-type isomer, however, 2-chlorocyclopentadienylidenemethanone was produced by the Wolff rearrangement after dissociation of the D atom in the OD group and the F atom, besides other photoproducts of the deuterated Cl-type isomer. It is thus concluded that the tunneling isomerization around the C-O bond occurs in the OH···X species but not in the OD···X species.     

The effect of hydrogen adsorption on the electronic structure of gold nanoparticles

It has been demonstrated that hydrogen adsorption has an effect on the electronic structure of gold nanoparticles. The physicochemical properties of separate gold nanoparticles have been studied under an ultrahigh vacuum scanning tunneling microscope. The structure and electronic structure of gold–hydrogen clusters were modeled by the quantum-chemical density functional theory method. Hydrogen adsorption onto gold nanoparticles 4–5 nm is size at room temperature was experimentally revealed, and the lower limit of 1.7 eV for the Au–H bond energy was determined. The interaction of hydrogen with gold leads to a considerable rearrangement of the electronic subsystem of nanoparticles. The experimentally observed effects were supported by quantum-chemical calculations. The rearrangement mechanism is related to strong correlations in the electronic subsystem.     

Tunneling chemical reactions in solid parahydrogen: direct measurement of the rate constants of R + H2 --> RH + H (R = CD3,CD2H,CDH2,CH3) at 5 K

Tunneling chemical reactions between deuterated methyl radicals and the hydrogen molecule in a parahydrogen crystal have been studied by Fourier transform infrared spectroscopy. The tunneling rates of the reactions R + H2 --> RH + H (R = CD3,CD2H,CDH2) in the vibrational ground state were determined directly from the temporal change in the intensity of the rovibrational absorption bands of the reactants and products in each reaction in solid parahydrogen observed at 5 K. The tunneling rate of each reaction was found to differ definitely depending upon the degree of deuteration in the methyl radicals. The tunneling rates were determined to be 3.3 x 10(-6) s(-1), 2.0 x 10(-6) s(-1), and 1.0 x 10(-6) s(-1) for the systems of CD3, CD2H, and CDH2, respectively. Conversely, the tunneling reaction between a CH3 radical and the hydrogen molecule did not proceed within a week's time. The upper limit of the tunneling rate of the reaction of the CH3 radical was estimated to be 8 x 10(-8) s(-1).     

With a little help from my friends: forty years of fruitful chemical collaborations

Over the past 40 years, much of the author's research, both computational and experimental, has involved collaborations. This Perspective describes some of the author's collaborative research in eight different areas of organic and theoretical chemistry: (1) hydrocarbons containing unsaturatively, 1,3-bridged cyclobutane rings, (2) the use of orbital topology for predicting the ground states of diradicals, (3) violations of Hund's rule, (4) the chemistry of phenylnitrenes, (5) tunneling by carbon in organic reactions, (6) the Cope rearrangement and the effect of substituents on it, (7) pyramidalized alkenes, dehydrocubanes, cubyl cation, and octanitrocubane, and (8) the effects of geminal fluorine substitution at C-2 of 1,3-diradicals. Highlighted in this Perspective are the synergism between calculations and experiments in the author's research and the many different roles that serendipity has played in the collaborations that are described herein.     

High-resolution continuous-wave-diode laser cavity ring-down spectroscopy of the hydrogen fluoride dimer in a pulsed slit jet expansion: two components of the N=2 triad near 1.3 microm

The near-infrared overtone spectra of the prototypical hydrogen-bond hydrogen fluoride dimer (HF)2 contain rich information on hydrogen bond dynamics. We report a study of the N=2 triad involving excitations with two quanta of HF stretching in (HF)2 around 1.3 microm (7500-7800 cm(-1)) by means of continuous-wave-diode laser cavity ring-down spectroscopy in a pulsed supersonic slit jet expansion. The analysis of the rotationally resolved overtone spectra allows the study of vibrational mode-selective kinetics, such as hydrogen bond predissociation with lifetimes tauPD and tunneling rearrangement (switching) processes with periods tausw obtained from the tunneling splitting DeltaT in highly excited vibrational states. The Ka=1<--0 transition of the Nj=22 band of (HF)2 has been reinvestigated by us in a supersonic jet expansion; the much improved data obtained here are in excellent agreement with several previous experimental results. Our analysis provides subband-level positions and properties 0(Ka=1(A+))=7711.37956(66) cm(-1), DeltaT=0.0936(10) cm(-1), and tauPD=1.3-1.9x10(-9) s, depending on the level symmetry A+ and B+. We have also analyzed spectra of the Nj=21 band, which we have observed for the first time in a supersonic jet with rotational resolution. For the Ka=0<--0 transition of this band, we find the band center at 0(A+)=7550.3555(26) cm(-1) and a tunneling splitting of DeltaT=0.0150(37) cm(-1). This level involves mostly excitation of the H-bonded HF stretching with two quanta. The mode-selective tunneling switching is in agreement with a simple picture of inhibited tunneling. These experimental values are close to those calculated on the "SO(-3)" potential energy hypersurface of Klopper, Quack, and Suhm. The N=2 triad also exhibits a strongly mode-selective predissociation dynamics, with a predissociation lifetime tauPD=4.99(84)x10(-11) s in the Nj=21 level, which is more than 20 times shorter than that for the Nj=22 level.     

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.     

Thermal and photochemical rearrangement of bicyclo[3.1.0]hex-3-en-2-one to the ketonic tautomer of phenol. Computational evidence for the formation of a diradical rather than a zwitterionic intermediate

The ground state (S(0)) and lowest-energy triplet state (T(1)) potential energy surfaces (PESs) concerning the thermal and photochemical rearrangement of bicyclo[3.1.0]hex-3-en-2-one (8) to the ketonic tautomer of phenol (11) have been extensively explored using ab initio CASSCF and CASPT2 calculations with several basis sets. State T(1) is predicted to be a triplet pipi lying 66.5 kcal/mol above the energy of the S(0) state. On the S(0) PES, the rearrangement of 8 to 11 is predicted to occur via a two-step mechanism where the internal cyclopropane C-C bond is broken first through a high energy transition structure (TS1-S(0)()), leading to a singlet intermediate (10-S(0)()) lying 25.0 kcal/mol above the ground state of 8. Subsequently, this intermediate undergoes a 1,2-hydrogen shift to yield 11 by surmounting an energy barrier of only 2.7 kcal/mol at 0 K. The rate-determining step of the global rearrangement is the opening of the three-membered ring in 8, which involves an energy barrier of 41.2 kcal/mol at 0 K. This high energy barrier is consistent with the fact that the thermal rearrangement of umbellulone to thymol is carried out by heating at 280 degrees C. Regarding the photochemical rearangement, our results suggest that the most efficient route from the T(1) state of 8 to ground state 11 is the essentially barrierless cleavage of the internal cyclopropane C-C bond followed by radiationless decay to the S(0) state PES via intersystem crossing (ISC) at a crossing point (S(0)()/T(1)()-1) located at almost the same geometry as TS1-S(0)(), leading to the formation of 10-S(0)() and the subsequent low-barrier 1,2-hydrogen shift. The computed small spin-orbit coupling between the T(1) and S(0) PESs at S(0)()/T(1)()-1 (1.2 cm(-)(1)) suggests that the ISC between these PESs is the rate-determining step of the photochemical rearrangement 8 --> 11. Finally, computational evidence indicates that singlet intermediate 10-S(0)() should not be drawn as a zwitterion, but rather as a diradical having a polarized C=O bond.