Theory Of Unimolecular Reactions Research Articles

The collision theory of unimolecular reactions: A second possibility to Lindemann’s proposal

Lindemann’s collision theory of unimolecular reactions was studied theoretically with comparative real-life assumptions. The result holds that there is a second possibility to the Lindemann’s proposal by applying quantitative/mathematical models, and assuming that in a bimolecular collision, both molecules are equally energized. This represents the second possibility of Lindemann’s proposal and is hereby presented to enhance the study of chemical kinetics.

Spiers Memorial Lecture: Theory of unimolecular reactions.

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our ability to model and predict the kinetics of such reactions has grown in leaps and bounds through the synergy of ever more sophisticated experimental studies with increasingly high level theoretical analyses. This review begins with a brief historical overview of the progress from the Lindemann mechanism to the master equation, which now provides the cornerstone for most theoretical analyses. The current status of ab initio transition state theory based implementations of the master equation is then reviewed, beginning with a discussion of the energy resolved chemical conversion rates, followed by a review of the pressure dependence of the thermal kinetics. The latter discussion focusses on the collisional energy and angular momentum transfer rates as well as the complexities of non-thermal effects and of multiple-well multiple-channel reactions. The synergy with recent state-of-the-art experiments is used to motivate these discussions. Attempts to automate the calculations are also briefly reviewed. Throughout the discussion, we provide our perspective on current understanding and continuing challenges and opportunities. One key challenge relates to the coupling of sequences of reactions, which frequently leads to deviations from the classic presumption of thermal reactants.

The Practice of Inspirational Teaching of Unimolecular Reaction Theory

The Practice of Inspirational Teaching of Unimolecular Reaction Theory

Power-law decay in the nonadiabatic photodissociation dynamics of alkali halides due to quantum wavepacket interference.

The nonadiabatic photodissociation dynamics of alkali halide molecules excited by a femtosecond laser pulse in the gas phase are investigated theoretically, and it is shown that the population of the photoexcited molecules exhibits power-law decay with exponent -1/2, in contrast to exponential decay, which is often assumed in femtosecond spectroscopy and unimolecular reaction theory. To elucidate the mechanism of the power-law decay, a diagrammatic method that visualizes the structure of the nonadiabatic reaction dynamics as a pattern of occurrence of dynamical events, such as wavepacket bifurcation, turning, and dissociation, is developed. Using this diagrammatic method, an analytical formula for the power-law decay is derived, and the theoretical decay curve is compared with the corresponding numerical decay curve computed by a wavepacket dynamics simulation in the case of lithium fluoride. This study reveals that the cause of the power-law decay is the quantum interference arising from the wavepacket bifurcation and merging due to nonadiabatic transitions.

Excitation Energies of V n O m + and Nb n O m + Clusters Sputtered under Ion Bombardment

The decay of V n O + and Nb n O + clusters sputtered under bombardment of the surfaces of vanadium and niobium with Xe+ ions and oxygen inflow is investigated by secondary-ion mass spectrometry. Based on experimental data, the excitation energy is calculated within the framework of the theory of unimolecular reactions. It is demonstrated that the numerical values of the specific excitation energy of V n O + and Nb n O + within the accuracy of the procedure do not depend significantly on the number of atoms that make up the clusters, nor on their type.

Quantum chemical and kinetic study of the CCl2 self-recombination reaction

The temperature and pressure dependencies of the rate constant of the recombination reaction CCl2 + CCl2 + M → C2Cl4 + M have been theoretically studied between 300 and 2000 K. Quantum-chemical calculations were employed to characterize relevant parts of the potential energy surface of this process. The limiting rate constants were analyzed using the unimolecular reaction theory. The resulting low pressure rate constant can be represented as k0 = [Ar] 3.5 × 10−23 (T/300 K)−8.7 exp(−1560 K/T) cm3 molecule−1 s−1.The high pressure rate constants derived from a simplified statistical adiabatic channel model (SSACM) and from a SACM combined with classical trajectory calculations (SACM/CT) are k∞ = (1.7 ± 1.0) × 10−12 (T/300)0.8±0.1 cm3 molecule−1 s−1 and k∞ = (5.4 ± 3.0) × 10−13 (T/300)0.7±0.1 cm3 molecule−1 s−1. The falloff curves were represented in terms of these limiting rate constants. Reported experimental results are satisfactorily described with the present model. The calculations indicate that the CCl2 + CCl2 reaction proceeds via the stabilization of C2Cl4, with a contribution of the C2Cl3 + Cl → C2Cl4 reaction, and at sufficiently high temperatures the channel CCl2 + CCl2 → C2Cl2 + 2Cl becomes relevant.

The Generalized Reaction Rate Theories in the Systems with Power-Law Distributions

The calculations of reaction rate are important in studying the different processes in physics, chemistry, biology, engineering etc. There exist many theories of reaction rate, such as transition state theory, collision theory, and unimolecular reaction theory. One key assumption in these theories is that thermodynamic equilibrium prevails throughout the entire system studied for all degrees of freedom. According to the Boltzmann-Gibbs statistical mechanics, a Maxwell-Boltzmann distribution whose form is exponential law holds in the whole time. This exponential law form of reaction rate is usually called Arrhenius behavior in chemistry. However, plenty of experimental results show non-Arrhenius behavior, such as power-law behavior. Besides, in reacting systems, the processes of evolution from one meta-stable state to another neighboring metastable state happen all the time, therefore the equilibrium assumption would be quite far-fetched. In these cases, current theories are no longer valid, and they can not even serve as a conceptual guide for understanding the critical factors that determine rates. Therefore, providing corresponding theoretical description for non-Arrhenius behavior or power-law behavior becomes urgent. In this general paper, generalized reaction rate theories with power-law distributions in the framework of nonextensive statistical mechanics were discussed based on experimental and observing facts.

On some characteristics of Marcus’ work in the light of the history of science

Professor Rudolph A. Marcus, recipient of the 1992 Nobel Prize in Chemistry, is a distinguished theoretical chemist. Two important theories happen to bear his name: the Rice Ramsperger Kassel Marcus (RRKM) theory of unimolecular reactions and the Marcus theory of electron transfer reactions. When considering Marcus’ work, one finds characteristics of it that bear striking similarity to those that can be found in the work of some famous scientists. Such characteristics appear then as common recurring patterns in the work of theoreticians. Among them we find the following: (1) the creation of new theories, driven by experiments that preceding theories were unable to explain; (2) the use of thought experiments; (3) the generalization and extensions from one realm of science to another; (4) the making of predictions and the finding of new properties from correlations among series of data; (5) the use of variational principles; (6) the providing of different demonstrations of an equation; (7) the introduction of new types of coordinates; (8) the innovative capacity to use, by somehow recreating it under the pressure of the physical problem, a mathematical method previously unknown to the author; and finally, (9) the presentation of formulations of the same theory in different mathematical and physical languages. Before discussing in some detail the above points, a brief description of Marcus’ work is first presented for the convenience of the reader.

The atmospheric oxidation mechanism of 2-methylnaphthalene.

The atmospheric oxidation mechanism of 2-methylnaphthalene (2-MN) initiated by OH radicals is investigated by using quantum chemistry at BH&HLYP/6-311++G(2df,2p) and ROCBS-QB3 levels and kinetic calculations by transient state theory and unimolecular reaction theory coupled with master equation (RRKM-ME). This reaction is mainly initiated by OH additions, forming adducts Rn (2-MN-n-OH, n = 1-8). The fates of R1 and R3, representing the α- and β-adducts, are examined. The fates of R1 and R3 are found to be drastically different. In the atmosphere, R1 reacts with O2via O2 addition to the C2 position to form R1-2OO-a/s, which will undergo a bimolecular reaction with the atmospheric NO or unimolecular isomerization via intramolecular H-shifts, of which the latter is found to be dominant and accounts for the formation of dicarbonyl compounds observed in experimental studies. The role of the tricyclic radical intermediates formed from the ring-closure of R1-2OO is rather limited because their formation is endothermic and reversible, being contrary to the important role of the analogous bicyclic radical intermediates in the oxidation of benzenes. On the other hand, the fate of R3 is similar to that of the benzene-OH adduct, and the tricyclic intermediates will play an important role. An oxidation mechanism is proposed based on the theoretical predictions, and the routes for the experimentally observed products are suggested and compared.

A Short Account of RRKM Theory of Unimolecular Reactions and of Marcus Theory of Electron Transfer in a Historical Perspective

The RRKM Theory of Unimolecular Reactions and Marcus Theory of Electron Transfer are here briefly discussed in a historical perspective. In the final section, after a general discussion on the educational usefulness of teaching chemistry in a historical framework, hints are given on how some characteristics of Marcus’ work could be introduced in courses of physical chemistry or chemical kinetics to show how experiments drive the formulation of theories and, on the other hand, how the predictions of theories may suggest experiments and even predate their results.

Atmospheric oxidation mechanism of toluene.

The atmospheric oxidation mechanism of toluene initiated by OH radical addition is investigated by quantum chemistry calculations at M06-2X, G3MP2-RAD, and ROCBS-QB3 levels and by kinetics calculation by using transition state theory and unimolecular reaction theory coupled with master equation (RRKM-ME). The predicted branching ratios are 0.15, 0.59, 0.05, and 0.14 for OH additions to ipso, ortho, meta, and para positions (forming R1-R4 adducts), respectively. The fate of R2, R4, and R1 is investigated in detail. In the atmosphere, R2 reacts with O2 either by irreversible H-abstraction to form o-cresol (36%), or by reversible recombination to R2-1OO-syn and R2-3OO-syn, which subsequently cyclize to bicyclic radical R2-13OO-syn (64%). Similarly, R4 reacts with O2 with branching ratios of 61% for p-cresol and 39% for R4-35OO-syn, while reaction of R1 and O2 leads to R1-26OO-syn. RRKM-ME calculations show that the reactions of R2/R4 with O2 have reached their high-pressure limits at 760 Torr and the formation of R2-16O-3O-s is only important at low pressure, i.e., 5.4% at 100 Torr. The bicyclic radicals (R2-13OO-syn, R4-35OO-syn, and R1-26OO-syn) will recombine with O2 to produce bicyclic alkoxy radicals after reacting with NO. The bicyclic alkoxy radicals would break the ring to form products methylglyoxal/glyoxal (MGLY/GLY) and their corresponding coproducts butenedial/methyl-substituted butenedial as proposed in earlier studies. However, a new reaction pathway is found for the bicyclic alkoxy radicals, leading to products MGLY/GLY and 2,3-epoxybutandial/2-methyl-2,3-epoxybutandial. A new mechanism is proposed for the atmospheric oxidation mechanism of toluene based on current theoretical and previous theoretical and experimental results. The new mechanism predicts much lower yield of GLY and much higher yield of butenedial than other atmospheric models and recent experimental measurements. The new mechanism calls for detection of proposed products 2,3-epoxybutandial and 2-methyl-2,3-epoxybutandial.

Kinetic-energy release distributions and stability of niobium-carbon clusters sputtered from the surface of niobium carbide by xenon ions

The results of studying the emission and fragmentation of niobium-carbon clusters NbmCn+ synthesized upon sputtering a niobium carbide surface with Xe+ ions are presented. The fragmentation channels of NbmCn+ clusters are studied. We present the values of the dissociation energy of some NbmCn+ clusters (m = 1–7, n = 2–8) calculated within the context of the “evaporation ensemble” model and theory of unimolecular reactions based on performed measurements of the kinetic-energy spectra of fragment ions. The obtained results are compared with published data.

Unimolecular Dissociation of H<sup>+</sup><sub style="margin-left:-6px;">2n+1</sub> Hydrogen Clusters: Measured Cross Sections and Theoretically Calculated Rate Constants

In this paper, we studied the process of dissociation unimolecular of the evaporation of H+2n+1 hydrogen clusters according to size, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The rate constants k(E) were determined with the use of statistical theory of unimolecular reactions using various approximations. In our work, we used the products frequencies instead of transitions frequencies in the calculation of unimolecular dissociation rates obtained by three models RRKM. The agreement between the experimental cross section ratio and calculated rate ratio with direct count approximation seems to be reasonable.

Fragmentation of sputtered vanadium and niobium cluster ions, kinetic release and dissociation energy

The generation and unimolecular fragmentation of Vn+ and Nbn+ clusters formed in sputtering vanadium and niobium surfaces by Xe+ ions has been studied. The method of measuring the kinetic energy of fragment ions (kinetic energy release distribution) has been used to determine the dissociation energy. Kinetic energy spectra have been measured in the field-free zone (corresponding to a time window of 10−5–10−4 sec after emission) of an ion microanalyzer with double focusing in reverse geometry. The results of spectra measurement were treated using the Rice-Ramsperge-Kassel theory of unimolecular reactions and the “evaporative ensemble”, which allowed us to calculate the dissociation energies of homonuclear Vn1 (n= 5–11) and Nbn1 (n = 3–8) clusters.

A quantitative kinetic analysis of CO elimination from phenoxy radicals

AbstractPhenoxy radicals are expected to play an important role in the thermal decomposition of lignin. At high enough temperatures, the dissociation to cyclopentadienyl radicals plus carbon monoxide dominates over bimolecular channels. While earlier experimental and theoretical studies agree on the mechanism, the experimental data suggest a substantially lower overall barrier than that found in theoretical studies. To address this discrepancy, we performed electronic structure calculations at the CBS‐QB3 level of theory and at a modified version of it to construct the relevant portion of the C6H5O potential energy surface (PES). The new results are in good agreement with previous studies. We then used the molecular information to calculate thermodynamic properties of the reactants and activated complexes, the high‐pressure rate constants, and the pressure dependence. Three different methods were employed for the last step: the quantum version of the Rice–Ramsperger–Kassel/modified strong collision theory approach by Dean (J Phys Chem 1985, 89, 4600–4608), the stochastic treatment by Barker (Int J Chem Kinet 2001, 33, 232–245) using the MultiWell package, and the master equation program Unimol by Gilbert and coworkers. Theory of Unimolecular and Recombination Reactions. Oxford, Blackwell Scientific Publications. All methods predict the experimentally determined phenoxy decomposition rate constant to be in the falloff region. This explains the almost 10 kcal mol−1 difference between reported activation energies and calculated barriers. Both the Lin and Lin (J Phys Chem 1986, 90, 425–431) and Frank et al. (Proc Combust Inst 1994, 25, 833–840) data can be reproduced within the assumed uncertainty limits without any adjustments of the PES. We also report on falloff behavior in the CO elimination from methyl‐, hydroxy‐, and methoxy‐substituted phenoxy radicals in the para position and compare it to that of the unsubstituted phenoxy radical. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 44: 75–89, 2012

Unimolecular Reactions of CF2ClCFClCH2F and CF2ClCF2CH2Cl: Observation of ClF Interchange

The unimolecular reactions of CF(2)ClCFClCH(2)F and CF(2)ClCF(2)CH(2)Cl molecules formed with 87 and 91 kcal mol(-1), respectively, of vibrational energy from the recombination of CF(2)ClCFCl with CH(2)F and CF(2)ClCF(2) with CH(2)Cl at room temperature have been studied by the chemical activation technique. The 2,3- and 1,2-ClF interchange reactions compete with 2,3-ClH and 2,3-FH elimination reactions. The total unimolecular rate constant for CF(2)ClCF(2)CH(2)Cl is 0.54 +/- 0.15 x 10(4) s(-1) with branching fractions for 1,2-ClF interchange of 0.03 and 0.97 for 2,3-FH elimination. The total rate constant for CF(2)ClCFClCH(2)F is 1.35 +/- 0.39 x 10(4) s(-1) with branching fractions of 0.20 for 2,3-ClF interchange, 0.71 for 2,3-ClH elimination and 0.09 for 2,3-FH elimination; the products from 1,2-ClF interchange could be observed, but the rate constant was too small to be measured. The D(CH(2)F-CFClCF(2)Cl) and D(CH(2)Cl-CF(2)CF(2)Cl) were evaluated by calculations for some isodesmic reactions and isomerization energies of CF(3)CFClCH(2)Cl as 84 and 88 kcal mol(-1), respectively; these values give the average energies of formed molecules at 298 K as noted above. Density functional theory was used to assign vibrational frequencies and moments of inertia for the molecules and their transition states. These results were combined with statistical unimolecular reaction theory to assign threshold energies from the experimental rate constants for ClF interchange, ClH elimination and FH elimination. These assignments are compared with results from previous chemical activation experiments with CF(3)CFClCH(2)Cl, CF(3)CF(2)CH(3,) CF(3)CFClCH(3) and CF(2)ClCF(2)CH(3).

High-temperature decomposition of azomethane in shock waves: 4. On the unimolecularity of azomethane decomposition: An analysis of high-temperature data

Our own measurements and published experimental data on azomethane (AM) decomposition at 850–1430 K, in conjunction with a theoretical analysis of this reaction, provide convincing evidence for its occurrence via the concerted mechanism in this temperature range. Most of the available experimental data cannot be described within the framework of the classical theory of unimolecular reactions. The need for direct time-resolved low-temperature data on AM decomposition is emphasized.

Fragmentation of sputtered Si n O m + clusters: Release kinetic and dissociation energies

The spectra of kinetic energies of positive SinOm+ cluster ions (n = 2–5, m = 2–7) have been measured using a double focusing ion microanalyzer with reverse geometry at instants 10−5 to 10−4 s after emission. The dissociation energies have been determined within the evaporative ensemble model and the theory of unimolecular decay reactions. The results obtained are compared with the binding energies of neutral SinOm clusters.

A Kinetic Model for Si1 − xGex Growth from SiH4 and GeH4 by CVD

A kinetic model is proposed for silicon-germanium alloy growth from silane and germane by chemical vapor deposition. It takes into account both homogeneous and heterogeneous reactions, which involve the precursors ( and ) and the homogeneous decomposition product of germane, germylene , and three types of surface sites: silicon sites, hydrogen-terminated silicon sites, and germanium sites. The growth of can be divided into two regimes: a heterogeneous decomposition dominated regime and a homogeneous decomposition dominated regime. For the heterogeneous regime, analytical equations based on the collision theory of heterogeneous unimolecular reactions, statistical physics, and the concept of competitive adsorption are derived to quantitatively describe growth rate and film composition as a function of deposition conditions, including deposition temperature, silane flow rate, and germane flow rate. Homogeneous decomposition of germane into germylene complicates the gas phase chemistry for both germane and silane, and an empirical linear relation is employed to describe the growth behavior in the homogeneous regime. The model agrees well with the experimental data by Jang et al. [ J. Electrochem. Soc. 142 , 3513 (1995) ].

Demonstrating Energy Migration in Coupled Oscillators. A Central Concept in the Theory of Unimolecular Reactions

This physical chemistry lecture demonstration is designed to aid the understanding of intramolecular energy transfer processes as part of the presentation of the theory of unimolecular reaction rates. Coupled pendulums are used to show the rate of migration of energy between oscillators under resonant and nonresonant conditions with varying degrees of coupling and how that relates to chemical reaction.