Theory Of Unimolecular Reactions Research Articles

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.

A Kinetic Model for Boron and Phosphorus Doping in Silicon Epitaxy by CVD

A kinetic model based on (i) the collision theory of heterogeneous unimolecular elementary reactions, (ii) statistical physics, and (iii) the concept of competitive adsorption is proposed for both p-type and n-type doping in silicon epitaxy by chemical vapor deposition (CVD). It takes into account both homogeneous and heterogeneous reactions, which involve the precursors (silane and dopant precursor) and their homogeneous decomposition products, and four types of surface sites, hydrogen-terminated silicon and dopant sites and hydrogen-free silicon and dopant sites. The model provides analytical equations to describe dopant concentration and silicon growth rate as a function of deposition conditions, including temperature and partial pressure of dopant precursor. At low temperatures, the enhancement in growth rate with diborane is attributed to enhanced hydrogen desorption from boron sites, which act as catalytic sites for silicon growth. The relationship between boron concentration and diborane partial pressure is more complicated than a simple linear one. The suppression in growth rate with phosphine is modeled by a blocking factor that represents the extent of the “poisoning” effect of phosphorous on the surface. Homogeneous decomposition of phosphine accounts for phosphorous doping behavior at high phosphine partial pressures. The model agrees well with the experimental data.

Experimental and theoretical study of the recombination reaction F + FC(O)O + M → FC(O)OF + M

The kinetics of the F+FC(O)O+M→FC(O)OF+M recombination reaction (1) has been experimental and theoretically investigated. Both F atoms and FC(O)O radicals were generated by 193-nm laser flash photolysis of FC(O)OO(O)CF in mixtures with He or CF4 at 295 K. From the extrapolation of the fall-off curves measured from 55 to 790 Torr total pressure, the high pressure rate coefficient (2.1±0.3)×10−11 cm3 molecule−1 s−1 and the low pressure rate coefficients (1.6±0.3)×10−29[He], (3.3±0.7)×10−29[CF4] and (7.1±1.5)×10−29[FC(O)OO(O)CF] cm3 molecule−1 s−1 were determined. The rate coefficient for the reaction between F atoms and FC(O)OO(O)CF has been found to be (1.5±0.5)×10−15 cm3 molecule−1 s−1. The limiting rate coefficients were analyzed using the unimolecular reaction theory on an ab initio potential energy surface derived at the G3S level of theory. Structural properties, harmonic vibrational frequencies and heats of formation for the FC(O)O radical and for the cis and trans conformers of FC(O)OF calculated with the B3LYP/6-311+G(3df) functional are presented. The values −87.9, −103.4 and −104.6 kcal mol−1, respectively, for the heats of formation of the three molecules were obtained at 298 K from isodesmic energies computed at the G3//B3LYP/6-311++G(3df,3pd) level.

Treatment of the K-quantum number in unimolecular reaction theory: insights from product correlations.

The connection between the K-quantum number and product correlations in the barrierless unimolecular dissociation of symmetric-top molecules is explored to establish a qualitative diagnostic for the treatment of the K-rotor dynamics in unimolecular reaction theory. We find that fragment scalar and vector correlations can provide guidance in this matter, and the photodissociation dynamics of thermal NCNO to form CN and NO at several dissociation wavelengths are presented to demonstrate the utility of this approach. The "goodness" of the K-quantum number can be related to the amount of energy in the conserved vibrational modes at the inner transition state. On the basis of measured correlated vibrational distributions, the K-quantum number is found to be approximately conserved at the inner transition state for the photodissociation of NCNO at 514, 520, and 526 nm. The methodology, involving a comparison of product distributions from the photodissociation of jet and thermal ensembles at identical wavelengths, is general and may be applied to previously studied systems that dissociate along barrierless potential energy surfaces, CF(3)NO and CH(2)CO. In addition, vector correlations serve as a means to probe the K-mixing at the outer transition state, and measured v-j correlations in the photodissociation of thermal NCNO are presented.

Collision-Induced Dissociation in Quadrupole Ion Traps: Application of a Thermal Model to Diatomic Ions

Dissociation of the tantalum oxide cation, a strongly bound diatomic, is simulated for the multiple-collision environment of a quadrupole ion trap mass spectrometer using a model based on thermal unimolecular reaction theory. The intact diatomic ion is assigned a specific internal temperature at which it undergoes collisional activation and deactivation during a random walk in energy space. Collisional energy transfer is assumed to proceed via independent vibrational and rotational processes, as described by the refined impulse approximation and exponential transition probability, with dissociation occurring when the vibrational energy exceeds the rotational-energy-dependent barrier for dissociation. Processing the data from many such random walks yields the simulated dissociation kinetics and time-dependent internal energy distribution of an ion population at the specified internal temperature. Comparison of experimental dissociation rates with those obtained via simulations performed over a series of temperatures enables prediction of internal temperatures and corresponding internal energy distributions for tantalum oxide ion populations undergoing resonance excitation. Although the simulations indicate that rotational-energy transfer can lead to significantly higher dissociation rates than those associated with purely vibrational-energy transfer, the results obtained in this study suggest that ion internal temperatures in the tens of thousands of degrees are required nonetheless to dissociate a strongly bound diatomic ion such as tantalum oxide, and the experimental data demonstrate that resonance excitation in a quadrupole ion trap can achieve the necessary temperatures.

Kinetics of the O(3P) + N2O Reaction. 2. Interpretation and Recommended Rate Coefficients

The reaction O(3P) + N2O is important to models of NOx pollutant and propellant chemistry and to the understanding of the thermal decomposition of N2O, which has historically played a key role in the development of unimolecular reaction theory. The reaction has two important product channels: O + N2O → NO + NO (ΔH0 = −36 kcal/mol) (R1); O + N2O → O2 + N2 (ΔH0 = −79 kcal/mol) (R2). Rate coefficients of these reactions have been the subject of several reviews. However, clear reasons why many of the evaluated, nonretained data differ from recommendations have not previously been known. There has been a great deal of controversy over the rate coefficients, particularly for reaction R2. Here, the relevant data are critically evaluated using detailed chemical modeling as an important tool. The results explain many of the discrepancies. Some of the data of central importance in earlier evaluations are shown to be incorrect. Additionally, some important features of the global behavior of the mixtures studied, which had previously not been understood, are explained, and the possible effects of hypothetical H2O contamination on N2O shock tube studies was quantitatively investigated. It is shown that the bulk of the rate coefficient results remaining after the evaluations can be combined with the intermediate temperature results for ktot = k1 + k2 from FGFAM (Fontijn, A.; Goumri, A.; Fernandez, A.; Anderson, W. R.; Meagher, N. E. J. Phys. Chem., preceding paper in this issue) to obtain fitted recommendations: k1 = 1.52 × 10-10 exp(−13 930/T) cm3 molecule-1 s-1 (1370−4080 K); k2 = 6.13 × 10-12 exp(−8,020/T) cm3 molecule-1 s-1 (1075−3340 K). Until recently, it was believed rate coefficients of the two product channels were approximately equal over a very wide temperature range. In contrast, the present study has led to the conclusion that reaction R2 dominates below, and reaction R1 above, 1840 K.

Role of tunneling of hydrogen in the Norrish type II processes in a thione and a ketone

Intra-molecular hydrogen abstraction reactions were examined in pentane-2-thione in its lowest triplet state using the AM-1 semiempirical molecular orbital method with the geometry optimisation in the unrestricted Hartree-Fock frame. Results were compared with those of pentane-2-one. The role of tunneling of hydrogen was examined in both the conventional transition-state approach and in the RRKM theory of unimolecular reactions. Results reveal that tunneling of hydrogen is less significant to sulfur than to oxygen.

Modern studies of intramolecular vibrational energy redistribution

Intramolecular vibrational energy redistribution has been much studied because of the important role it plays in theories of unimolecular reactions and in dictating the feasibility of bond-selective chemistry. In this review we survey some of the more recent experimental studies and hope to provide a general introduction along with some present day conclusions.

Conventional transition state theory/Rice–Ramsperger–Kassel–Marcus theory calculations of thermal termolecular rate coefficients for H(D)+O2+M

Several ab initio studies have focused on the minimum energy path region of the hydroperoxyl potential energy surface (PES) [J. Chem. Phys. 88, 6273 (1988)] and the saddle point region for H-atom exchange via a T-shaped HO2 complex [J. Chem. Phys. 91, 2373 (1989)]. Further, the results of additional calculations [J. Chem. Phys. 94, 7068 (1991)] have been reported, which, when combined with the earlier studies, provide a global description (but not an analytic representation) of the PES for this reaction. In this work, information at the stationary points of the ab initio PES is used within the framework of conventional Transition State Theory (TST)/RRKM. Theory to compute estimates of the thermal termolecular rate coefficients for the reaction between the H(D) atom and O2 in the presence of two different bath gases, argon and nitrogen, as a function of pressure and temperature. These calculations span a pressure range from 1.0 Torr to the high-pressure limit and a temperature range from 298.15 to 6000.0 K. Conventional TST/RRKM Theory was utilized within the framework of two models: an equilibrium model employing the strong collision assumption (model I), [R. G. Gilbert and S. C. Smith, Theory of Unimolecular and Recombination Reactions (Blackwell, Oxford, 1990), as implemented in the UNIMOL program suite]; and a steady-state model that includes chemical activation (model II), using the collisional energy transfer approximation proposed by J. Troe [J. Chem. Phys. 66, 4745, 4758 (1977); 97, 288 (1992)]. In this work we first summarize the pressure-dependent fall-off curves (calculated with model I) and the high-pressure limit rate coefficients (calculated with models I and II) over the entire temperature range, and then focus on the fall-off behavior for temperatures between 298.15 and 2000.0 K. Direct comparisons are made between the experimentally determined termolecular rate coefficients (either from direct measurements or based on recommended pressure/temperature-dependent expressions) and the estimates of these rate coefficients calculated in this work as a function of pressure at 298.15 and 500.0 K. In the fall-off region, we find better agreement between the theoretical and experimental values at low pressures than at pressures approaching the high-pressure limit. Significant deviations are observed between theory and experiment as the high-pressure limit is approached. The disagreement at 298.15 K is greater for N2 than for Ar.

On the quantum mechanical theory of unimolecular reactions through a narrow bottleneck: the prompt and delayed dissociation

On the quantum mechanical theory of unimolecular reactions through a narrow bottleneck: the prompt and delayed dissociation

On the quantum mechanical theory of unimolecular reactions through a narrow bottleneck: the prompt and delayed dissociation

The quantum dynamics of unimolecular dissociation are discussed for a typical situation where the number of energy rich but bound (zero order) states far exceeds the number of states with enough energy along the reaction coordinate in order to dissociate. It is shown that one can introduce a new basis of states, the ‘trapping’ states, which diagonalize the effective Hamiltonian that governs the dynamics in the bound subspace. The properties of these states are discussed with special reference to the two distinct time regimes (prompt and delayed) for the dissociation that are expected for such a congested level structure.

Fully Quantum-State Resolved Study of NO2 Photodissociation: Correlated NO(2.PI..OMEGA., .nu. = 0,J,.LAMBDA.) + O(3Pj) Distributions

Relative O(3Pj=~,~,~) spin-orbit populations correlated with specific N0[2nQ=l/2,3/2; Y = 0; J; A = II(A’), n(A”)] product states were obtained following photolysis of NO2 at excess energies Zi? = 390, 425, and 1054 cm-I. These fully quantum state-resolved measurements were carried out by recording spatial profiles of recoiling N0(213~,J,A) products using polarized radiation for photolysis and state-selective laser ionization detection. The relative O(3P,) populations correlated with each N0(213~,J,A) state show marked fluctuations at each excess energy as a function of rotational state and A-doublet component. The relative populations also fluctuate as a function of excess energy. The O(3Pj) spin-orbit population ratios, when averaged over all measurements, exhibit distributions that are colder than statistical, in agreement with previous results. In particular, we find that, on average, O(3P~):O(3P2) population ratios correlated with the ground N0(2171/2) state are colder than the corresponding ratios correlated with the excited NO(TI3/2) spin-orbit state. These results are in agreement with the state-specific calculations of Katigiri and Kat0 [J. Chem. Phys. 1993, 99, 88051 and are discussed in terms of long-range nonadiabatic transitions among electronic states correlating asymptotically with different spin-orbit states of the ground NO(TI) + O(3P) dissociation channel. I. Introduction The photodissociation of NO:! has attracted considerable experimental and theoretical attention. Due to its unique properties, NO:! has become a model system for testing statistical theories of unimolecular reactions. Usually, in a bond fission reaction proceeding without a barrier, high density of states and intramolecular vibrational redistribution in the excited molecule lead to product state distributions that can be well described by statistical theories, i.e., the product levels are populated as per their degeneracies and quantum state-specific effects are averaged out. In contrast, the unimolecular decomposition of NO:! represents a case in which both statistical and state-specific dynamical effects are manifest.’-19 Due to vibronic chaos at excitation energies > 16 000 cm-I, which results from strong couplings between the bright 12B2 state and the ground 12A1 state via a conical inter~ection,~.~~ the eigenstates in the vicinity of the dissociation threshold (DO = 25 130.6 cm-1)lc-14 are strongly mixed and have predominantly 12A1 chara~ter.~~~~~. ~~ Dissociation following 12B2

Microcanonical rate constant in nonequilibrium distribution of vibrational energy on the basis of Slater's theory of unimolecular reactions

Abstract A model based on Slater's treatment about uncoupled harmonic oscillators has been developed toward strong couplings, allowing intramolecular vibrational energy redistribution (IVR) fast enough to justify the averaging over the states involved in IVR. There are possibilities of taking into account the nonequilibrium distributions of energy among normal modes with different effective temperatures on each oscillator on this model. Computational results imply that there exist such distributions which increase the rate constant by several orders of magnitude. The effect of the restricted IVR was considered and also found to increase the rate constant; as well as the dependence of the IVR from the vibrational anharmonicity is taken under discussion.

Ion‐recombination nucleation and growth of ice particles in noctilucent clouds

Formation of ice particles in the polar summer mesosphere is simulated with the proton hydrate, H+(H2O)n, as the origin. In an ion‐recombination nucleation scheme, electrons in the mesosphere play a role in removing heavy proton hydrates from the ionic system to the background neutral system, making an ionic system a steady source of neutral embryonic nuclei for condensation. Referring to the laboratory data of n ≤ 6, a model of reaction coefficients up to the hydration order of n = 1000 is constructed with the help of both the nucleation theory and the unimolecular reaction theory. For a model nucleation layer 600 m in thickness with a minimum temperature of 125 K, produced fluxes of embryonic nuclei are calculated as a strong function of [H2O], 10³ cm−2 s−1 at [H2O] = 2.16 parts per million by volume, for example. In the time dependent simulations, stable limit cycle oscillations of the cloud formation are found with periods of 3 to 4 days depending of the magnitude of diffusion. A cloud becomes bright after an active nucleation with a delay of ∼ 1.3 days which is a sedimentation time of embryonic nuclei. Deposition of water vapors in ice particles switches off the nucleation, and evaporation of particles at the bottom of a cloud recovers the nucleation activity with a lag of diffusion‐advection time. Out of phase oscillations are predicted between the cloud brightness and the polar mesospheric summertime echo from the region of heavy proton hydrates, which will be a crucial evidence for the in situ origin of the clouds.

Experimental and theoretical study of monoligand complexes of nickel atoms with simple alkynes

Monoligand complexes of nickel atoms with simple alkynes have been investigated by kinetic studies of association reactions of nickel atoms with ethyne, propyne, and 2-butyne in the gas phase near room temperature, and by quantum chemical calculations on the Ni[C2H2] complex using a Linear Combination of Gaussian-Type Orbitals – Density Functional (LCGTO–DF) method. Experimental estimates of binding energies of the monoligand complexes have been made by using RRKM unimolecular reaction theory to model the pressure dependence of second-order rate coefficients for the association reactions: [Formula: see text] and 29 ± 5 kcal mol−1, for Ni[C2H2], Ni[propyne], and Ni[2-butyne], respectively. The trend in binding energy with methyl substitution on ethyne is discussed and compared with similar data for monoligand complexes of alkynes with copper atoms. The harmonic vibrational frequencies and binding energy for the 1A1 ground state of Ni[C2H2] have been calculated using the LCGTO–DF method, and the results are compared with experimental data on the infrared spectrum of matrix-isolated Ni[C2H2] and with the estimate of the binding energy of Ni[C2H2] from the present experimental study. There is excellent agreement between the experimental and theoretical results. The calculations indicate that at least one triplet state of Ni[C2H2] is bound relative to ground state Ni + C2H2 reactants. This is consistent with indications from the kinetic results that the association reaction occurs on more than one potential energy surface.

Experimental and theoretical study of oxidative addition reaction of nickel atom to O–H bond of water

The reaction of atomic nickel with water in the gas phase has been investigated by kinetic studies under static pressure conditions near room temperature, and by accurate quantum chemical calculations. Experimental and theoretical results are consistent with a reaction mechanism involving formation of a weakly bound nickel–water adduct, which may react further by oxidative addition of nickel to the O–H bond of water to form the insertion product HNiOH. Experimental estimates of reaction energetics have been made by using unimolecular reaction theory calculations to model rate coefficients obtained by fitting kinetic data to a simple rate equations model. These experimental estimates are in agreement with the theoretical results, and indicate that the insertion product is bound by at least 20–25 kcal/mol, relative to nickel plus water. There is also agreement that the barrier to oxidative addition is no greater than 1–2 kcal/mol, and may be smaller. This theoretical result was obtained only at the highest level treatments in the geometry optimization. The reaction mechanism involves a spin–orbit induced surface crossing from the ground state triplet surface of the reactants to a singlet surface, followed by a second crossing back to the triplet surface in the product region. The oxidative addition reaction thus proceeds on a singlet potential surface which correlates with excited (d9s1)1D nickel atoms. The electronic configuration of the 1D state is favorable for oxidative addition because repulsion between nickel and water may be reduced by sd hybridization. The presence of the low lying 1D state is responsible for the unique reactivity of nickel, among the late first row transition metal atoms, with respect to the oxidative addition reaction with water.

Isotope effect in Ni + C2H4 (C2D4) association reaction

AbstractThe association reactions of atomic nickel with ethene and fully deuterated ethene in carbon dioxide buffer gas at 295 K have been investigated in the pressure range 5–100 torr, using a laser photolysis‐laser fluorescence technique. By comparison with results of ab initio quantum chemistry calculations for the complex Ni[C2H4], the data are shown to be consistent with reaction on both ground and excited state potential energy surfaces. A simple rate equations treatment is described which shows the form of the pressure dependence of the second‐order recombination rate coefficient in this case. Under conditions which are expected to hold for the Ni + C2H4 (C2D4) reaction, the pressure dependence has the standard Lindemann‐Hinshelwood form, with the limiting high pressure rate constant given by an apparent value which reflects the degree to which the participating electronic states are coupled by nonadiabatic transitions. The limiting high pressure behavior of the recombination rate coefficient for Ni + C2H4 is not strongly affected by deuterium isotope substitution. However, the effect on the low pressure rate constant is large and consistent with RRKM unimolecular reaction theory. This validates the use of RRKM calculations for estimating the binding energy of the complex from kinetic data. The binding energy of Ni[C2H4] is estimated to be 35.2 ± 4.2 kcal mol−1. © 1994 John Wiley & Sons, Inc.

Unimolecular dissociation in the regular regime

The unimolecular dissociation of a model triatomic molecule is analyzed. The model, which is loosely based on the radical HO2, shows mostly regular dynamical behavior although it has enough energy to dissociate. By analyzing the progress towards dissociation, we find that dissociation takes place due to concerted and correlated motions as in the Slater theory of unimolecular reactions rather than the steady accumulation of energy in the dissociative mode.

Rapid Approximate Calculation of Numbers of Quantum States W(E,J) in the Phase Space Theory of Unimolecular Bond Fission Reactions

AbstractA facile and rapid approximation for counting numbers of quantum states W(E,J) is described for application in the phase space theory of unimolecular bond fission reactions. The method accounts for J‐conservation. It is based on an empirical interpolation between analytical expressions of W(E,J) in the low J‐ and high J‐limits, and it is checked by extensive accurate state counting for sets of representative model molecules.

Theory of thermal unimolecular reactions at low pressures. III. Superposition of weak and strong collisions

Biexponential models for collisional energy transfer are formulated representing superimposed weak and strong collisions. Analytical solutions of the master equation for low pressure thermal unimolecular reactions at steady state are derived for such models. Nonequilibrium populations of excited states as well as collision efficiencies βc in the low pressure rate constant differ considerably from the corresponding quantities for simple exponential collision models. The results are analyzed in terms of general expressions of the collision efficiency βc as a function of the average energy transfer quantities 〈ΔE〉 and 〈ΔE2〉.