Statistical Theory Calculations Research Articles

Computational study of the kinetics and mechanisms for the reaction of H atoms with c-C 5H 6

The H+c-C5H6 reaction has been studied at the modified Gaussian-2 level of theory. Statistical theory calculations have been performed using a theoretical potential energy surface and molecular parameters. It has been shown that the reaction can occur by both the abstraction and the addition mechanisms. Theoretical rate constants have been calculated for the low-lying product channels and relative contributions of the addition and abstraction channels have been assessed. The previously neglected role of openchain intermediates in the evaluation of the reaction kinetics has been suggested and the corresponding rate constants have been recommended for inclusion in the modeling of the H+c-C5H6 reaction.

Temperature and pressure effects on the elimination reactions of diethyl ether with hydroxide and amide ions

Hydroxide and amide ion-induced elimination reactions of diethyl ether and diethyl ether- d 10 were investigated with a variable temperature flowing afterglow apparatus. Temperature effects on reaction rates, kinetic isotope effects, and product distributions are reported. The pressure dependence of these transformations also were explored and mechanistic arguments are presented. This data confirms predictions based on statistical rate theory and ab initio calculations and provides valuable information on the potential energy surfaces for base-induced eliminations.

A computational study of the mechanism for the C6H5+CH2O reaction

The mechanism for the C6H5 + CH2O reaction has been investigated with hybrid density functional quantum-chemical and statistical theory calculations. The results reveal three possible reaction channels: (1) The abstraction reaction producing C6H6 + HCO; (2) addition to the C atom yielding C6H5CH2O and (3) addition to the O atom giving C6H5OCH2. The barriers for these 3 reactions, calculated at the B3LYP/aug-cc-pvtz level of theory using the geometry optimized with B3LYP/cc-pvdz are 0.8, 1.4 and 9.1 kcal mol−1, respectively. The C6H5CH2O radical can fragment to form C6H5CHO + H with a barrier of 19.4 kcal mol−1. It can also undergo isomerization reactions ia two cyclic epoxy intermediates to give C6H5OCH2 with a maximum barrier of 20.4 kcal mol−1. Transition-state theory calculations using the predicted energy barriers and structures for the rate constants of the abstraction reaction (1) lead to very good agreement with our recently measured values, while the result of RRKM calculations for the isomerization/decomposition of C6H5OCH2 to C6H5CHO + H also agrees quantitatively with available experimental data.

Production of HCl in the OH + ClO Reaction: Laboratory Measurements and Statistical Rate Theory Calculations

The branching ratio for the OH + ClO reaction has been measured using the turbulent flow technique with high-pressure chemical ionization mass spectrometry for the detection of reactants and products. In our earlier study, OD was used instead of OH due to the large HCl background produced by the ClO source (J. Chem. Soc., Faraday Trans. 1997, 93, 2665). Improvements to our experimental technique have significantly reduced this HCl background, thus making it possible to observe directly the production of very small concentrations of HCl (∼109 molecule cm-3) from the minor channel of the OH + ClO reaction. At room temperature and ∼100 Torr pressure, the rate constant for this minor channel was determined to be (9.5 ± 1.6) × 10-13 cm3 molecule-1 s-1 with a two standard deviation error limit, which remained unchanged when the pressure was increased to 200 Torr. The temperature dependence of the rate constant for this minor channel was also investigated between 207 and 298 K, and the data were fit to the following Arrhenius expression: (3.2 ± 0.8) × 10-13 exp[(325 ± 60)/T] cm3 molecule-1 s-1. The branching ratio for the HCl channel was determined to be 0.07 ± 0.03 at all pressures and temperatures investigated in this study. Statistical rate theory calculations were also performed on the OH + ClO reaction system and are in good agreement with the experimental results.

Scalar and angular correlations in CF3NO photodissociation: statistical and nonstatistical channels

Polarized 1+1′ REMPI combined with TOFMS detection was used to obtain recoil speed distributions, NO product rotational distributions, and μ–v–jNO angular correlations in the photofragmentation of CF3NO between 585 and 650 nm. At wavelengths longer than 610 nm dissociation occurs only on the S0 potential energy surface of CF3NO. At 585 nm the product recoil speed distribution is bimodal, with the higher speed component attributed to dissociation across a potential barrier on the T1 surface. Measurements of the T1 channel NO product trajectory show it has no laboratory frame rotational alignment or recoil anisotropy, but has a significant preference for v⊥jNO angular correlation, reaching a maximal value of β00(22)=−0.308±0.052. The results are interpreted using the results of statistical phase space theory and classical trajectory calculations. It is concluded that S0 channel dissociation occurs by a statistical dissociation mechanism whereas the T1 channel dynamics is dominated by exit channel recoil forces due to a potential barrier.

Unimolecular isomerization/decomposition of ortho-benzyne: ab initio MO/statistical theory study

High level molecular-orbital calculations have been carried out to investigate the potential energy surface for the o-benzyne decomposition to 1,3-butadiyne and acetylene as well as that for the isomerization sequence, ortho- to meta- to para-benzyne. The latter species can easily undergo Bergman decyclization. It is shown by statistical theory calculations that the isomerization channel may affect significantly the rate of o-benzyne disappearance in the thermal decomposition process, particularly, at T<2000 K. At 1000 K, the isomerization of o-C6H4 to its m- and p-isomers accounts for as much as 99% of the total disappearance rate. The first order rate coefficients for the production of 1,3-butadiyne, meta- and para-benzynes at 100 Torr, 1 atm and 10 atm pressures over the temperature range 1000–3000 K have been calculated for combustion applications.

Theoretical studies of nitroamino radical reactions: Rate constants for the unimolecular decomposition of HNNO2 and related bimolecular processes

The unimolecular decomposition of HNNO2 and the related bimolecular reaction of NH with NO2 have been studied by high-level ab initio molecular orbital and statistical theory calculations. The potential energy surface for the bimolecular association leading to the formation of HNNO2 and HNONO, the formation of exothermic products N2O and OH via the HNNO2 intermediate, and of HNO and NO via the HNONO intermediate have been computed with a modified GAUSSIAN 2 (G2M) method. The rate constants for these two bimolecular reaction channels have been calculated by means of the canonical variational Rice–Ramsperger–Kassel–Marcus (RRKM) approach over a broad temperature range. The predicted values at room temperature correlate reasonably well with the experimental overall rate and also with the experimental product branching probability for the formation of N2O vs HNO via the nitro and nitrite intermediates. The effect of multiple reflections within the potential well of the HN-ONO complex was found to be quite significant. It reduces the rate constant for the formation of the HNO+NO products by as much as 350%.

Theoretical study of the OH+NO 2 reaction: formation of nitric acid and the hydroperoxyl radical

The reaction of OH with NO 2 has been studied by high level ab initio molecular orbital and statistical theory calculations. The potential energy surface for the association leading to the formation of HNO 3 by collisional deactivation and the formation of endothermic products, HO 2 and NO via the HOONO intermediate have been computed with a modified Gaussian 2 (G2M) method. The rate constants for these two channels have been calculated by means of the canonical variational RRKM approach. The predicted values correlate reasonably well with experimental data for both the forward and reverse processes.

Ab Initio MO Study of the Unimolecular Decomposition of the Phenyl Radical

The unimolecular decomposition of the C6H5 radical has been studied by ab initio molecular orbital and statistical-theory calculations. Three low-energy decomposition channels, including the commonly assumed decyclization/fragmentation process yielding n-C4H3 + C2H2, have been identified. With a modified Gaussian-2 method of Mebel et al. (ref 17), the energy barrier for the decyclization of C6H5 was calculated to be 66.5 kcal/mol with the corresponding recyclization energy of 5.6 kcal/mol. The two open-chain 1-dehydrohexa-1,3-dien-5-yne radicals (with HCĊH cis and trans structures) may undergo further fragmentation reactions producing n-C4H3 + C2H2 and l-C6H4 (1,5-hexadiyn-3-ene) + H with the predicted barriers of 44.0 and 36.1 kcal/mol, respectively. The dominant decomposition channel of C6H5 was found to take place barrierlessly by C−H breaking, producing o-C6H4 (o-benzyne) + H with the predicted endothermicity of 76.0 kcal/mol. RRKM calculations have been carried out for the production of n-C4H3 + C2H2, l-C6H4 + H, and o-C6H4 + H with the coupled multichannel mechanism, which includes the reversible decyclization/recyclization reactions. The results of the calculations indicate that at T < 1500 K o-C6H4 is the major product of the decomposition reaction. Above 1500 K, the formation of l-C6H4 becomes competitive with its cyclic isomer. However, the formation of the commonly assumed n-C4H3 + C2H2 products was found to be least competitive. Rate constants for all three product channels from C6H5 as well as those from the bimolecular reaction of n-C4H3 with C2H2 producing C6H5, o-C6H4 + H, and l-C6H4 + H have been calculated as functions of temperature and pressure for practical applications.

Theoretical study of the reaction of hydrogen with nitric acid: ab initio MO and TST/RRKM calculations

The kinetics and mechanism of the H + HNO 3 reaction have been elucidated with ab initio molecular orbital and statistical theory calculations. Our room temperature reaction rate results accord well with available experimental data. The reaction is dominated by an indirect metathetical process taking place via vibrationally excited dihydroxyl nitroxide, ON(OH) 2, producing OH + cis-HONO. The excited ON(OH) 2 also undergoes molecular elimination, yielding H 2O + NO 2 as a minor competing reaction. The direct H abstraction reaction forming H 2 + NO 3 was found to be the least important one. At atmospheric pressure, we recommend the following expressions for the three rate constants, in units of cm 3/molecule s, from the 300–3000 K temperature range for H + HNO 3 collision yielding the products H 2 + NO 3 by direct mechanism k a = (9.24 × 10 −16) T 1.53e −8253/ T based on CTST calculations, OH + cis-HONO by indirect mechanism k b = (6.35 × 10 −19) T 2.30e −1.53/ T ), and H 2O + NO 2 by indirect mechanism k c = (1.01 × 10 −22) T 3.29e −3126/ T , the latter two are based on Arrhenius fits to the solution of the master equation which includes RRKM microscopic rate constants and tunneling corrections.

Ab initio molecular orbital study of the HCO+O2 reaction: Direct versus indirect abstraction channels

The reaction of HCO with O2 has been studied by ab initio molecular orbital and statistical theory calculations. Both the direct abstraction and the association–elimination processes have been considered. The direct abstraction of H by O2 producing the HO2+CO products was found to be unimportant below 2000 K. The association reaction occurs by the attack of O2 at the C atom to form a vibrationally excited complex, HC(O)OO°, which can undergo two reactions. The first possibility is H migration via TS2 forming HOOCO, which rapidly dissociates into either OH+CO2 via TS4 or HO2+CO via TS3; the latter is energetically less favorable. The second possibility is the direct production of HO2+CO from HC(O)OO° via TS5 in a concerted manner. The barrier of TS5 at the G2M level of theory is 23.5 kcal/mol relative to HC(O)OO; this is the major channel for the reaction. Variational transition state theory and Rice–Ramsperger–Kassel–Marcus calculations have been carried out for the direct abstraction and the indirect metathetical mechanisms, respectively. The calculated total rate constant at 1.5 Torr exhibits a small positive activation energy and its absolute values agree closely with experimental data.

Molecular Mechanics and Statistical Thermodynamics Studies of Complexes of a Flexible Hemicarcerand with Neutral Guests

Computational studies of the structures and conformational properties of hemicarcerand 2, a model for 1, studied experimentally by Cram et al., and the complexation and decomplexation of guest molecules by this host have been carried out with MACROMODEL/MM3*. Energy minimizations, molecular dynamics, and statistical perturbation theory calculations were performed. Conformational processes in the intrahemispheric bridges (OCH2O) of the host molecule have been shown to be important for the passage of guest molecules in and out of the cavity. This transient gate-opening phenomenon has a significant influence on the complexation of bicyclic guests, while smaller aromatic guests can pass in and out without gate-opening. Constrictive binding is crucial for the isolation of hemicarceplexes, since it provides a kinetic barrier which permits isolation of complexes. The 1:1 complexes of hemicarcerand 2 with bicyclic guests and benzene derivatives were found to be energetically favorable by 12−23 kcal/mol in the gas phase. Nevertheless, only the bicyclic guests and some substituted monocyclics form stable complexes. If guests are too large, kinetic barriers prevent complexation. Aromatic guests with disk-like shapes are predicted to form complexes in solution, but to be unstable because of their low decomplexation energy barriers.

Kinetic Isotope Effects as Tools To Reveal Solvation Changes Accompanying a Proton Transfer. A Canonical Unified Statistical Theory Calculation

Primary and solvent kinetic isotope effects (KIEs) for the proton transfer between a butanone molecule and the microsolvated ion OH-(H2O)n=0,1,2 to give the (H2O)n+1···butenolate complex have been theoretically calculated in order to study solvation changes that take place along the proton transfer process. To take into account in the transition state calculations the two dynamical bottlenecks involved in those cluster reactions (one corresponding to the ion−dipole approach and the other one to the actual proton transfer), the canonical unified statistical theory has been used. Only for the n = 2 case, the local bottleneck in the proton transfer region controls the global process at the whole range of temperatures studied. The different values of the KIEs as a function of temperature and depending on the relative weight of the two dynamical bottlenecks are analyzed. The degree of coupling between the motion of solvent molecules and the motion of the proton that is being transferred is studied by testing the rule of the geometrical mean. This empirical rule holds very well when only one bottleneck governs the global process, but an important breakdown of this rule is found when the two bottlenecks are comparable. Assuming a monotonical variation of solvent isotope effect from reactants to product, the solvent KIE, by comparison with the equilibrium solvent isotope effect, indicates that the hydroxide ion is 44% desolvated at the transition state of the reaction with n = 2 at 298 K. All these results have been obtained without including tunneling effects. A first estimation of the tunneling contribution to kinetic isotope effects has been evaluated by interpolated variational transition state theory.

Deuterium Kinetic Isotope Effects and Their Temperature Dependence in the Gas-Phase SN2 Reactions X- + CH3Y .fwdarw. CH3X + Y- (X, Y = Cl, Br, I)

Extended-basis-set calculations with electron correlation have been carried out for the reactant and transition state properties of the gas-phase S{sub N}2 reactions Cl{sup -1} + CH{sub 3}Br {yields} CH{sub 3} Cl + Br{sup -1}, Cl{sup -1} + CH{sub 3}I {yields} CH{sub 3}Cl + I{sup -1}, and Br{sup -1} + CH{sub 3}I {yields} CH{sub 3}Br + I{sup -1}. The resulting force fields are used for canonical unified statistical theory calculations of the rate constants of these reactions and their perdeuterated analogs. Kinetic isotope effects (KTEs) and their temperature dependences have been calculated and analyzed, and they are compared to available experimental data. We find only small deviations of the generalized transition state theory results from conventional transition state theory, and we obtain reasonable agreement (nearly 10%) with experimental results for the KIEs of the first two reactions, but the KIEs that we predict for the third reaction are up to 26% higher than experiment. 38 refs., 8 figs., 9 tabs.

Level density dependence of the transient states on the nuclear shape symmetry in fissionable nuclei

We investigate the dependence of the level density in the second potential well on the nuclear shape symmetry for actinide nuclei. We compare statistical theory calculations with the experimental results deduced by observing the fission times of Pa and Np isotopes. In the weak-coupling approximation of the two classes of excited states we find that the level density in the second well, higher than the one in the first well, is related to a symmetry breakdown of the nuclear shape of the second saddle point.

CH3 state distributions form the reactions of O(1D) with saturated and chlorinated hydrocarbons

CH3 product state distributions arising from the reaction of O(1D) with CH4, C2H6, C3H8, and i-C4H10 were characterized using resonantly enhanced multiphoton ionization (REMPI). The vibrational distributions in the ν1 symmetric stretch and in the ν2 ‘‘umbrella’’ mode are noninverted in all cases. The results are compared to statistical adiabatic channel-phase space theory (SACM-PST) calculations. The ν2 excitation is much less excited than statistically expected for the reactions with CH4 and C2H6 but nearly statistical in the case of the heavier hydrocarbons. For all reactions but the one with C2H6, the ν1 excitation is similar to the distribution statistically expected. The CH3 rotational distribution from the reaction of O(1D) with CH4 is much hotter than room temperature as comparison with simulated rotational band contours showed. From the integrated CH3 band intensities, we obtained approximate reaction cross sections for the CH3 channel with a decrease in the order CH3≳C2H6≳C3H8≳i-C4H10. In the reactions of O(1D) with CH3Cl, CH3CH2Cl, and CH3CH2CH2Cl, we observed CH3 as a primary product. CH3–ν1 excitation is small in all cases but ν2 excitation is considerable with even an inverted v=1/v=0 distribution in the case of the reaction with C2H5Cl. The relative reaction cross sections for the CH3 channel decrease in the order CH4≫CH3Cl≳CH3CH2Cl≳CH3CH2CH2Cl.

Theoretical aspects of H/N/O-chemistry relevant to the thermal reduction of NO by H 2

Kinetic modeling of existing data on the reduction of NO by H 2, initiated photolytically or thermally, with a comprehensive reaction mechanism established by means of ab initio quantum-chemical and statistical rate-constant calculations, allows us to identify several key elementary processes which are important in different temperature and NO-concentration regimes. At T < 900 K, the reduction of NO by H 2 and other hydrides induced photolytically occurs primarily by the bimolecular reaction HNO + HNO → cis/trans-(HNO) 2 under NO-lean conditions, and by the termolecular process HNO + 2NO → HN 2O + NO 2, followed by the fast redox reaction, HN 2O + NO → HN 2 + NO 2 and N 2 + HONO under NO-rich conditions. In the temperature range of 900 K < T < 1500 K, the reduction of NO by H 2, initiated by the H 2 + NO → H + HNO reaction, occurs readily and the global reduction rate is dominated by the HNO + NO → N 2O + OH reaction. At temperatures higher than 1500 K, commonly heated by shock waves, the rate of NO reduction is controlled almost exclusively by the H + NO → N + OH reaction. The N atom thus formed generates efficiently the O atom by the fast N + NO → N 2 + O process. These two NO reduction reactions are greatly enhanced in this temperature regime by the abundance of H atoms, produced by the fast chain processes: O + H 2 → H + OH and OH + H 2 → H + H 2O. The rate constants as well as the mechanisms of these key elementary processes involving H/N/O-species have been interpreted in terms of the theoretical results derived from ab initio quantum-chemical and statistical-theory calculations.

A comparison of classical trajectory and statistical unimolecular rate theory calculations of Al3 decomposition

Classical trajectories are used to simulate the dissociation of microcanonical ensembles of Al3 clusters with 0.25–2.00 kcal/mol energy in excess of the dissociation threshold. Unimolecular lifetime distributions for the ensembles are in accord with the random lifetime prescription of Rice–Ramsperger–Kassel–Marcus (RRKM) theory and Al3 is identified as an intrinsic RRKM molecule. Unimolecular rate constants determined from the trajectories are compared with the predictions of variational RRKM theory with harmonic vibrator and flexible transition state models, phase space theory (PST), and the orbiting transition state model of phase space theory (OTS/PST). The flexible RRKM model, PST, and OTS/PST give Al2- - -Al transition state sums of state which agree to within 1%. The harmonic vibrator RRKM model gives a sum of states which varies from only 40% to 10% larger as the excess energy is increased from 0.25 to 2.0 kcal/mol. Adiabatic switching and direct integration of the phase integral are used to determine the reactant Al3 anharmonic density of states. For the energies considered in this work, anharmonicity determined by adiabatic switching increases the Al3 density of states from the harmonic value by a factor of 2.5–2.9. The anharmonic density of states determined by solving the phase integral depends on where the reactant/product phase space boundary is positioned. Placing it at the vibrator transition state gives an anharmonic density of states nearly the same as that determined by adiabatic switching, while placing it at the looser flexible transition state gives a density of states 35% larger at the highest energy. Using this latter anharmonic density of states gives OTS/PST and flexible RRKM unimolecular rate constants which agree with the trajectory results to within 25% at the lowest energy and 10% at the highest energy. Product energy partitioning distributions determined from the trajectories are compared with the predictions of PST, OTS/PST, and the Engelking model. Both OTS/PST and PST give product energy partitioning distributions which are in near quantitative agreement with the trajectory results.

Free energy of solvation of a small Lennard–Jones particle

AbstractIn molecular dynamics (MD) and Monte Carlo (MC) free energy calculations, the choices of the thermodynamic paths from state a to state b affect the accuracy of the result and the efficiency of the programs. Most of the problems occur at the initial stages of growing in a new particle into a solvent. Based on statistical mechanical perturbation theory, an accurate and efficient direct calculation of inserting a small Lennard–Jones particle into solvent is derived. This eliminates the need for calculation of the initial stages of growing in a new particle by MD or MC simulation. Examples are given to show the utility of direct calculation. The recommended procedure is to use direct calculation for a small Lennard–Jones particle and then use MD or MC simulations to calculate the ΔG of changing the small Lennard–Jones particle into the target molecule. © 1994 by John Wiley &amp; Sons, Inc.

Reaction of O2+(X 2Πg) with H2 , D2 , and HD: Guided ion beam studies, MO correlations, and statistical theory calculations

Absolute cross sections are measured for the reactions of O2+(X 2Πg) with H2 , D2 , and HD from thermal energies to over 4 eV. The OH++OH, HO2++H, O++H2O, and H2O++O product channels (and the corresponding isotopic analogs) are observed, although H2++O2 is not. While the first three products appear at their thermodynamic thresholds, formation of H2O++O, the least endothermic channel, exhibits a barrier to reaction. In the HD system, the DO2+ product ion is strongly favored over the HO2+ product. Results for internally excited O2+ reactants, probably the a 4Πu state, are also presented. Analysis of the excitation functions, molecular orbital arguments, and statistical kinetic theories are used to understand the mechanisms and dynamics of this reaction. It is shown that the inefficiency of the O+ product channel is due to spin and symmetry constraints. The other three product channels proceed through a long-lived intermediate, but formation of this intermediate from reactants requires surmounting a barrier measured to be 1.1±0.1 eV. The intramolecular isotope effects are shown to be due to statistical and dynamic effects.