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.     

C2H3与CH3F氢抽提反应机理与动力学性质

采用双水平直接动力学方法对C₂H₃与CH₃F氢抽提反应进行了研究. 在QCISD(T)/6-311++G(d, p)//B3LYP/6-311G(d, p)水平上, 计算的三个反应通道R1、R2和R3的能垒(ΔE^≠)分别为43.2、43.9和44.1 kJ·mol^-1, 反应热为-38.2 kJ·mol^-1. 此外, 利用传统过渡态理论(TST)、正则变分过渡态理论(CVT)和包含小曲率隧道效应(SCT)的CVT, 分别计算了200-3000 K温度范围内反应的速率常数k^TST、k^CVT和k^CVT/SCT. 结果表明: (1) 三个氢抽提反应通道的速率常数随温度的增加而增大, 其中变分效应的影响可以忽略, 隧道效应则在低温段影响显著; (2) R1反应是主反应通道, 但随着温度的升高, R2反应的竞争力增大, 而R3反应对总速率常数的影响很小.     

On the parallel mechanism of the dissociation of energy-selected P(CH3)3+ ions

Energy selected trimethyl phosphine ions were prepared by threshold photoelectron photoion coincidence (TPEPICO) spectroscopy. This ion dissociates via H, CH(3), and CH(4) loss, the latter two involving hydrogen transfer steps. The ion time-of-flight distribution and the breakdown diagram are analyzed in terms of the statistical RRKM theory, which includes tunneling. Ab initio and DFT calculations provide the vibrational frequencies required for the RRKM modeling. CH(3) loss could produce both the P(CH(3))(2)(+) by a simple bond dissociation step, and the more stable HP(CH(2))CH(3)(+) ion by a hydrogen transfer step. Quantum chemical calculations are extensively used to uncover the reaction scheme, and they strongly suggest that the latter product is exclusively formed via an isomerization step in the energy range of the experiment. The data analysis, which includes modeling with the trimethyl phosphine thermal energy distribution, provides accurate onset energies for both H (E(0K) = 1024.1 +/- 3.5 kJ/mol) and CH(3) (E(0K) = 1024.8 +/- 3.5 kJ/mol) loss reactions. From this analysis, we conclude that the Delta(f)H(298K) degrees [HP(CH(2))(CH(3))(+)] = 783 +/- 8 kJ/mol and Delta(f)H(298K) degrees [P(CH(2))(CH(3))(2)(+)] = 711 +/- 8 kJ/mol.     

Double hydrogen tunneling revisited: the breakdown of experimental tunneling criteria

Formic acid dimer was chosen as a model system to investigate synchronous double proton transfer by means of variational transition state theory (VTST) for various isotopically modified hydrogen species. The electronic barrier for the double proton transfer was evaluated to be 7.9 kcal/mol, thus being significantly lower than it was determined in previous studies. The tunneling probabilities were evaluated at temperatures from 100 up to 400 K and typical Arrhenius behavior with enhancement by tunneling is observed. When comparing the transmission factors kappa in dependence of the mass of the tunneling hydrogen, it was found that there are two maxima, one at very low masses (e.g., 0.114 amu, corresponding to the muonium entity) and one maximum at around 2 amu (corresponding to deuterium). With the knowledge of the VTST-hydrogen transfer rates and the corresponding tunneling corrections, various tunneling criteria were tested (e.g., Swain-Schaad exponents) and were shown to fail in this reaction in predicting the extent of tunneling. This finding adds another aspect in the ongoing "Tunneling-Enhancement by Enzymes" discussion, as the used tunneling criteria based on experimental reaction rates may fail to predict tunneling behavior correctly.     

Ab Initio Kinetics for Thermal Decomposition of CH(3)N(•)NH(2), cis-CH(3)NHN(•)H, trans-CH(3)NHN(•)H, and C(•)H(2)NNH(2) Radicals

The thermal decomposition of the CH(3)N(?)NH(2), cis-CH(3)NHN(?)H, trans-CH(3)NHN(?)H, and C(?)H(2)NNH(2) radicals, which are the four radical products from the H-abstraction reactions of monomethylhydrazine, were theoretically studied by using ab initio Rice-Ramsperger-Kassel-Marcus (RRKM) transition-state theory and master equation analysis. Various decomposition pathways were identified by using either the QCISD(T)/cc-pV∞Z//CASPT2/aug-cc-pVTZ or the QCISD(T)/cc-pV∞Z//B3LYP/6-311++G(d,p) quantum chemistry methods. The results reveal that the β-scission of NH(2) to form methyleneimine is the predominant channel for the decomposition of the C(?)H(2)NNH(2) radical due to its small energy barrier of 13.8 kcal mol(-1). The high pressure limit rate coefficient for the reaction is fitted by 3.88 × 10(19)T(-1.672) exp(-9665.13/T) s(-1). In addition, the pressure dependent rate coefficients exhibit slight temperature dependence at temperatures of 1000-2500 K. The cis-CH(3)NHN(?)H and trans-CH(3)NHN(?)H radicals are the two distinct spatial isomers with an energy barrier of 26 kcal mol(-1) for their isomerization. The β-scission of CH(3) from the cis-CH(3)NHN(?)H radical to form trans-diazene has an energy barrier of 35.2 kcal mol(-1), and the β-scission of CH(3) from the trans-CH(3)NHN(?)H radical to form cis-diazene has an energy barrier of 39.8 kcal mol(-1). The CH(3)N(?)NH(2) radical undergoes the β-scission of methyl hydrogen and amine hydrogen to form CH(2)═NNH(2), trans-CH(3)N═NH, and cis-CH(3)N═NH products, with the energy barriers of 42.8, 46.0, and 50.2 kcal mol(-1), respectively. The dissociation and isomerization rate coefficients for the reactions were calculated via the E/J resolved RRKM theory and multiple-well master equation analysis at temperatures of 300-2500 K and pressures of 0.01-100 atm. The calculated rate coefficients associated with updated thermochemical property data are essential components in the development of kinetic mechanisms for the pyrolysis and oxidation of MMH and its derivatives.     

A direct ab initio dynamics study of the water-assisted tautomerization of formamide

Direct ab initio dynamics calculations based on a canonical variational transition-state theory with several multidimensional semiclassical tunneling approximations were carried out to obtain rate constants for the water-assisted tautomerization of formamide. The accuracy of the density functionals, namely, B-LYP, B3-LYP, and BH&H-LYP, were examined. We found that the BH&H-LYP method yields the most accurate transition-state properties when comparing it to ab initio MP2 and QCISD results, whereas B-LYP and B3-LYP methods predict barrier heights too low. Reaction path information was calculated at both the MP2 and nonlocal hybrid BH&H-LYP levels using the 6–31G(d,p) basis set. At the BH&H-LYP level, we found that the zero-point energy motion lowers the barrier to tautomerization in the formamide-water complex by 3.6 kcal/mol. When tunneling is considered, the activation energy at the BH&H-LYP level at 300 K is 17.1 kcal/mol. This is 3.4 kcal/mol below the zero-point-corrected barrier and 7.0 kcal/mol below the classical barrier. Excellent agreement between BH&H-LYP and MP2 rate constants further supports the use of BH&H-LYP for rate calculations of large systems. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 861–874, 1997     

Quantum chemical and master equation simulations of the oxidation and isomerization of vinoxy radicals

The vinoxy radical, a common intermediate in gas-phase alkene ozonolysis, reacts with O2 to form a chemically activated alpha-oxoperoxy species. We report CBS-QB3 energetics for O2 addition to the parent (*CH2CHO, 1a), 1-methylvinoxy (*CH2COCH3, 1b), and 2-methylvinoxy (CH3*CHCHO, 1c) radicals. CBS-QB3 predictions for peroxy radical formation agree with experimental data, while the G2 method systematically overestimates peroxy radical stability. RRKM/master equation simulations based on CBS-QB3 data are used to estimate the competition between prompt isomerization and thermalization for the peroxy radicals derived from 1a, 1b, and 1c. The lowest energy isomerization pathway for radicals 4a and 4c (derived from 1a and 1c, respectively) is a 1,4-shift of the acyl hydrogen requiring 19-20 kcal/mol. The resulting hydroperoxyacyl radical decomposes quantitatively to form *OH. The lowest energy isomerization pathway for radical 4b (derived from 1b) is a 1,5-shift of a methyl hydrogen requiring 26 kcal/mol. About 25% of 4a, but only approximately 5% of 4c, isomerizes promptly at 1 atm pressure. Isomerization of 4b is negligible at all pressures studied.     

A product branching ratio controlled by vibrational adiabaticity and variational effects: kinetics of the H + trans-N2H2 reactions

The abstraction and addition reactions of H with trans-N(2)H(2) are studied by high-level ab initio methods and density functional theory. Rate constants were calculated for these two reactions by multistructural variational transition state theory with multidimensional tunneling and including torsional anharmonicity by the multistructural torsion method. Rate constants of the abstraction reaction show large variational effects, that is, the variational transition state yields a smaller rate constant than the conventional transition state; this results from the fact that the variational transition state has a higher zero-point vibrational energy than the conventional transition state. The addition reaction has a classical barrier height that is about 1 kcal∕mol lower than that of the abstraction reaction, but the addition rates are lower than the abstraction rates due to vibrational adiabaticity. The calculated branching ratio of abstraction to addition is 3.5 at 200 K and decreases to 1.2 at 1000 K and 1.06 at 1500 K.     

Theoretical prediction of the heats of formation of C2H5O* radicals derived from ethanol and of the kinetics of beta-C-C scission in the ethoxy radical

Thermochemical parameters of three C(2)H(5)O* radicals derived from ethanol were reevaluated using coupled-cluster theory CCSD(T) calculations, with the aug-cc-pVnZ (n = D, T, Q) basis sets, that allow the CC energies to be extrapolated at the CBS limit. Theoretical results obtained for methanol and two CH(3)O* radicals were found to agree within +/-0.5 kcal/mol with the experiment values. A set of consistent values was determined for ethanol and its radicals: (a) heats of formation (298 K) DeltaHf(C(2)H(5)OH) = -56.4 +/- 0.8 kcal/mol (exptl: -56.21 +/- 0.12 kcal/mol), DeltaHf(CH(3)C*HOH) = -13.1 +/- 0.8 kcal/mol, DeltaHf(C*H(2)CH(2)OH) = -6.2 +/- 0.8 kcal/mol, and DeltaHf(CH(3)CH(2)O*) = -2.7 +/- 0.8 kcal/mol; (b) bond dissociation energies (BDEs) of ethanol (0 K) BDE(CH(3)CHOH-H) = 93.9 +/- 0.8 kcal/mol, BDE(CH(2)CH(2)OH-H) = 100.6 +/- 0.8 kcal/mol, and BDE(CH(3)CH(2)O-H) = 104.5 +/- 0.8 kcal/mol. The present results support the experimental ionization energies and electron affinities of the radicals, and appearance energy of (CH(3)CHOH+) cation. Beta-C-C bond scission in the ethoxy radical, CH(3)CH2O*, leading to the formation of C*H3 and CH(2)=O, is characterized by a C-C bond energy of 9.6 kcal/mol at 0 K, a zero-point-corrected energy barrier of E0++ = 17.2 kcal/mol, an activation energy of Ea = 18.0 kcal/mol and a high-pressure thermal rate coefficient of k(infinity)(298 K) = 3.9 s(-1), including a tunneling correction. The latter value is in excellent agreement with the value of 5.2 s(-1) from the most recent experimental kinetic data. Using RRKM theory, we obtain a general rate expression of k(T,p) = 1.26 x 10(9)p(0.793) exp(-15.5/RT) s(-1) in the temperature range (T) from 198 to 1998 K and pressure range (p) from 0.1 to 8360.1 Torr with N2 as the collision partners, where k(298 K, 760 Torr) = 2.7 s(-1), without tunneling and k = 3.2 s(-1) with the tunneling correction. Evidence is provided that heavy atom tunneling can play a role in the rate constant for beta-C-C bond scission in alkoxy radicals.     

A 3-fold "butterfly valve" in command of the encapsulation's kinetic stability. Molecular baskets at work

Molecular basket 1, composed of a semirigid tris-norbornadiene framework and three revolving pyridine-based gates at the rim, has been built to "dynamically" enclose space and as such regulate molecular encapsulation. The gates were shown to fold via intramolecular hydrogen bonding and thereby form a C3nu symmetrical receptor: the 1H NMR resonance for the amide N-H protons of the pyridine gates appeared downfield (delta= 10.98 ppm), and the N-H vibrational stretch (IR) was observed at 3176 cm(-1). Accordingly, density functional theory (DFT, B3LYP) investigations revealed for the closed conformers of 1 to be energetically the most stable and dominant. The gearing of the pyridine "gates", about their axis, led to the interconversion of two dynamic enantiomers 1A and 1B comprising the clockwise and counterclockwise seam of intramolecular hydrogen bonds. Dynamic 1H NMR spectroscopic measurements and line-shape simulations suggested that the energy barrier of 10.0 kcal/mol (DeltaG++(A/B), 298 K) is required for the 1A/B interconversion, when CCl4 occupies the cavity of 1. Likewise, the activation free energy for CCl4 departing the basket was found to be 13.1 kcal/mol (DeltaG++, 298 K), whereas the thermodynamic stability of 1:CCl4 complex was -2.7 kcal/mol (DeltaGdegrees, 298 K). In view of that, CCl4 (but also (CH3)3CBr) was proposed to escape from, and a molecule of solvent to enter, the basket when the gates rotate about their axis: the exit of CCl4 requires the activation energy of 12.7 kcal/mol (DeltaG++(A/B) + DeltaGdegrees), similar to the experimentally found 13.1 kcal/mol (DeltaG++).     

Hydroxy peroxy nitrites and nitrates from OH initiated reactions of isoprene

The reaction of hydroxy peroxy radicals (RO(2)) with NO represents one of the most crucial tropospheric processes, leading to terrestrial ozone formation or NO(x)() removal and chain termination. We investigate the formation of hydroxy peroxy nitrites (ROONO) and nitrates (RONO(2)) from the OH-isoprene reactions using DFT and ab initio theories and variational RRKM/master equation (vRRKM/ME) formalism. The binding energies of ROONO from NO addition to RO(2) are determined to be in the range of 20-22 kcal mol(-)(1), and the bond dissociation energies of ROONO to form an alkoxy radical (RO) and NO(2) range from 6 to 9 kcal mol(-)(1). Isomerization of ROONO to RONO(2) is exothermic by 22-28 kcal mol(-)(1). The entrance and exit channels of the RO(2)-NO reaction are found to be barrierless, and the rate constants to form ROONO are calculated to be 3 x 10(-)(12) to 2 x 10(-)(11) cm(3) molecule(-)(1) s(-)(1) using the canonical variational transition state theory. The vRRKM/ME analysis reveals negligible stabilization of excited ROONO and provides an assessment of ROONO isomerization to RONO(2).     

Nonclassical Aryl Radicals: Intermediates or Transition States for the Hydrogen Shift Reactions?

Electronic properties of aryl radicals obtained by removing single hydrogen atoms from the sterically congested regions of benzo[c]phenanthrene, biphenyl, triphenylene, phenanthrene, and perylene are studied at the UBLYP/6-311G level of theory. Two structures are considered by each radical, the classical one involving a C-H.C arrangement of atoms and the nonclassical one possessing a three-center C-H-C linkage. The five nonclassical radicals under study are found to be transition states for degenerate 1,4- and 1,5-hydrogen shift reactions that interconvert the classical species. However, the results of the present calculations indicate that the nonclassical structures with the C-H distances in the C-H-C linkages shorter than 1.34 ? should be energy minima representing potentially observable chemical systems. The predicted energy barrier to the 1,5-hydrogen shift in the 1-benzo[c]phenanthrenyl radical is only 9.3 kcal/mol (6.1 kcal/mol with the zero-point energies included), making the hydrogen migration in this system facile at relatively low temperatures. Rigorous analysis of the computed electronic wave functions provides a clear-cut picture of bonding in both the classical and nonclassical aryl radicals.     

The addition of hydrogen atoms to diacetylene and the heats of formation of i-C4H3 and n-C4H3

In this article, we discuss in detail the addition of hydrogen atoms to diacetylene and the reverse dissociation reactions, H + C(4)H(2)<==>i-C(4)H(3) (R1) and H + C(4)H(2)<==>n-C(4)H(3) (R2). The theory utilizes high-level electronic structure methodology to characterize the potential energy surface, Rice-Ramsperger-Kassel-Marcus (RRKM) theory to calculate microcanonical/J-resolved rate coefficients, and a two-dimensional master-equation approach to extract phenomenological (thermal) rate coefficients. Comparison is made with experimental results where they are available. The rate coefficients k1(T, p) and k2(T, p) are cast in forms that can be used in chemical kinetic modeling. In addition, we predict values of the heats of formation of i-C(4)H(3) and n-C(4)H(3) and discuss their importance in flame chemistry. Our basis-set extrapolated, quadratic-configuration-interaction with single and double excitations (and triple excitations added perturbatively), QCISD(T), predictions of these heats of formation at 298 K are 130.8 kcal/mol for n-C(4)H(3) and 119.3 kcal/mol for the i-isomer; multireference CI calculations with a nine-electron, nine-orbital, complete-active-space (CAS) reference wavefunction give just slightly larger values for these parameters. Our results are in good agreement with the recent focal-point analysis of Wheeler et al. (J. Chem. Phys. 2004, 121, 8800-8813), but they differ substantially for DeltaH0(f 298)(n-C(4)H(3)) with the earlier diffusion Monte Carlo predictions of Krokidis et al. (Int. J. Chem. Kinet.2001, 33, 808-820).     

Implementation of a microcanonical variational transition state theory for direct dynamics calculations of rate constants

Calculation of microcanonical rate constants has been an important field in chemical dy-namic studies for many years because it can be used not only to give good prediction of rate con-stants in microcanonical assembly, but also to calculate rate constants with certain conserved quantum numbers such as the total angular momentum, and in turn, can be easily converted into thermal rate constants[1—3]. The widely used method for calculating microcanonical rate constants of unimolecular reac-tions…     

Thermochemical kinetics of hydrogen-atom transfers between methyl, methane, ethynyl, ethyne, and hydrogen

Saddle point properties of three symmetric and one asymmetric hydrogen transfer and the energy of reaction of the asymmetric reactions are investigated in the present work. These reactions were calculated by various density functionals, many of which were developed in recent years, by coupled cluster theory, and by multicoefficient correlation methods based on wave function theory. Instead of comparing calculated results to "semi-experimental" values, we compared them to very accurate theoretical values (e.g., to values obtained by the Weizmann-1 method). Coupled cluster theory and the multicoefficient correlation methods MC-QCISD/3 and MCQCISD-MPW are very accurate for these reactions with mean unsigned errors below 0.94 kcal/mol. Diagnostics for multireference character add additional reliability to these results. The newly developed hybrid density functional M06-2X shows very good performance for these reactions with a mean unsigned error of only 0.77 kcal/mol; the BHandHLYP, MPW1K, and BB1K density functionals, can also predict these reactions well with mean unsigned errors less than 1.42 kcal/mol.     

DFT and ab initio calculations on two reactions between hydrogen atoms and the fire suppressants 2-H heptafluoropropane and CF3Br

Reaction enthalpies and barrier heights of the reactions CF3Br+H-->CF3+HBr {reaction (1)} and CF3CHFCF3+H-->CF3CFCF3+H2 {reaction (2)} have been calculated at the near state-of-the-art ab initio level, and also by employing the B3LYP, BH&HLYP, BB1K, MPW1K, MPWB1K and TPSS1KCIS functionals. In addition, the integrated molecular orbital+molecular orbital (IMOMO) method has been used to study reaction (2). The ab initio benchmark values of the reaction enthalpy (298 K) and barrier height (0 K) of reaction (2) are reported for the first time {-(0.7+/-0.7) and 13.3+/-0.5 kcal/mole respectively}. When density functional theory (DFT) results are compared with ab initio benchmarks for both reactions (1) and (2), the MPWB1K functional is found to have the best performance of the six functionals used. The IMOMO method with the RCCSD/aug-cc-pVTZ and/or RCCSD(T)/aug-cc-pVTZ levels, as the high levels of calculation on the model system, gives reaction enthalpies and barrier heights of reaction (2), which agree with ab initio benchmark values to within 1 kcal/mole. Computed key geometrical parameters and imaginary vibrational frequencies of the transition state structures of reactions (1) and (2) obtained at different levels of calculation are compared. The magnitudes of the computed imaginary vibrational frequencies of the transition states of both reactions considered are found to be very sensitive to the levels of calculation used to obtain them. The heat of formation (298 K) of CF3CFCF3 calculated at the near state-of-the-art level has a value of -(318+/-3) kcal/mole.     

Direct ab initio dynamics studies on the hydrogen-abstraction reactions of OH radicals with HOX (X = F, Cl, and Br)

The hydrogen abstract reactions of OH radicals with HOF (R1), HOCl (R2), and HOBr (R3) have been studied systematically by a dual-level direct-dynamics method. The geometries and frequencies of all the stationary points are optimized at the MP2/6-311+G(2d, 2p) level of theory. A hydrogen-bonded complex is located at the product channel for the OH + HOBr reaction. To improve the energetics information along the minimum energy path (MEP), single-point energy calculations are carried out at the CCSD(T)/6-311++G(3df, 3pd) level of theory. Interpolated single-point energy (ISPE) method is employed to correct the energy profiles for the three reactions. It is found that neither the barrier heights (DeltaE) nor the H-O bond dissociation energies [D(H-O)] exhibit any clear-cut linear correlations with the halogen electronegative. The decrease of DeltaE and D(H-O) for the three reactions are in order of HOF > HOBr > HOCl. Rate constants for each reaction are calculated by canonical variational transition-state theory (CVT) with a small-curvature tunneling correction (SCT) within 200-2000 K. The agreement of the rate constants with available experimental values for reactions R2 and R3 at 298 K is good. Our results show that the variational effect is small while the tunneling correction has an important contribution in the calculation of rate constants in the low-temperature range. Due to the lack of the kinetic data of these reactions, the present theoretical results are expected to be useful and reasonable to estimate the dynamical properties of these reactions over a wide temperature range where no experimental value is available.     

Singlet hydrocarbon carbenes with high barriers toward isomerization: a computational investigation

A prerequisite for a stable singlet hydrocarbon carbene is the existence of high barriers toward isomerization. Four derivatives of cyclopentylidene (1-4) with rigid and varying carbon cages are examined computationally at the B3LYP/6-311+G(d,p) level of theory. Singlet ground states are predicted for carbenes 1-4, with DeltaE(ST)'s = 7-22 kcal/mol. The rearrangement paths considered are 1,3-hydrogen shift, 1,2-carbon shift and beta-CC bond-cleavage. Carbenes 3 and 4 lie in relatively shallow potential-energy wells (around 4 and 6 kcal/mol, respectively) and are expected to rearrange via 1,3-hydrogen shifts to cyclopropane derivatives. For 1 and 2, the lowest energy rearrangement path is beta-CC bond-cleavage requiring about 12 and 20 kcal/mol, respectively, placing 2 in the deepest potential-energy well among the four carbenes.     

Ab initio calculations on 1,2-hydrogen shifts in the benzene radical cation and on carbon scrambling via an isomerization to the fulvene structure

Multireference configuration interaction (MRCI//6-31G**) ab initio calculations show that the barrier for hydrogen scrambling in the benzene radical cation is about 50 kcal mol^?1. Once the internal energy is sufficient for a 1,2-hydrogen shift, the moving hydrogen can go to any position in the ring. The barrier for carbon scrambling via an isomerization to the fulvene structure is about 17 kcal mol^?1 higher than that for hydrogen scrambling. Both of these values are far below the dissociation limit.