Termolecular Rate Coefficients Research Articles

Three-Body Collisions Driving the Ion-Molecule Reaction C2- + H2 at Low Temperatures.

We report on the three-body reaction rate of C2- with H2 producing C2H- studied in a cryogenic 16-pole radio frequency ion trap. The reaction was measured in the temperature range from 10 to 28 K, where it was found to only take place via three-body collisions. The experimentally determined termolecular rate coefficient follows the form of with T0 = 20 K, where a = 8.2(3) × 10-30 cm6/s and b = -0.82(12) denotes the temperature dependence. We additionally performed accurate ab initio calculations of the forces between the interacting partners and carried out variational transition state theory calculations, including tunneling through the barrier along the minimum energy path. We show that, while a simple classical model can generally predict the temperature dependence, the variational transition state theoretical calculations, including accurate quantum interactions, can explain the dominance of three-body effects in the molecular reaction mechanism and can reproduce the experimentally determined reaction coefficients, linking them to a temperature-dependent coupling parameter for energy dissipation within the transition complex.

Complex Formation in Three-Body Reactions of Cl- with H2.

Three-body reaction rates of Cl– with H2 to form the weakly bound complex Cl–(H2) are measured between 10 and 26 K in a linear radio-frequency wire trap. Formation of larger clusters of the form Cl–(H2)2 are also observed. The three-body (or termolecular) rate coefficients follow the form aT–1, with a = 1.12(2) × 10–29 cm6 K s–1. Reverse reactions to repopulate the Cl– parent ion were measured, even though the binding energy of the complex makes bimolecular dissociative collisions energetically inaccessible at low temperatures. The back-reaction was found to be proportional to the cube of the hydrogen density, suggesting that the dissociation mechanism depends on multiple collisions. Comparisons of the rate coefficients measured in a 16-pole wire trap and a 22-pole trap demonstrate significantly lower ion temperatures in the wire trap.

Adsorption Kinetics of Nitrogen Molecules on Size-Selected Silver Cluster Cations

Abstract We present adsorption processes of dinitrogen on size-selected silver cluster cations, Ag n + (n = 1–10), studied by kinetics measurement using an ion trap. The cluster ions showed sequential adsorption of N2 molecules when the ion trap was cooled down to 105 K, excluding n = 8 and 9 that were exceptionally inactive at this temperature. Termolecular rate coefficients of each adsorption step are determined by analyzing time-dependent changes in the reactant and product ion signals. The first-step rate coefficients were found to increase exponentially from n = 1 to 7 due to increased internal degrees of freedom at larger sizes, which are favorable for accommodating the adsorption energy in a free cluster. In contrast, the adsorption rate turned to decrease for n > 7 due to weaker binding of dinitrogen as revealed by density-functional-theory (DFT) calculation. Adsorption sites on Ag n + are further discussed on the basis of the maximum number of adsorbing N2 molecules observed in the experiment.

Size dependent reaction kinetics of small gold clusters with carbon monoxide: Influence of internal degrees of freedom and carbonyl complex stability

The reactions of free gold clusters Au–, \( {\rm{Au}}_2^ - \), and \( {\rm{Au}}_3^ - \) with carbon monoxide are studied in an rf-octopole ion trap experiment at cryogenic temperatures. While Au– is unreactive toward CO over the whole temperature range investigated, the two and three atom cluster anions show a maximum adsorption of two CO molecules at temperatures below 250 K. From time resolved trapping experiments the strongly cluster size dependent reaction kinetics are obtained and a distinct reaction mechanism is deduced. The size dependence of the measured rate coefficients reveals the preferred formation and particular stability of the carbonyl complex \( {\rm{Au}}_3 ({\rm{CO}})_2^ - \). Through RRK analysis of the absolute termolecular rate coefficients we are able to estimate the binding energy of CO to \( {\rm{Au}}_2^ - \) and \( {\rm{Au}}_3^ - \).

Chemical Kinetics of the NaO (A 2Σ+) + O(3P) Reaction

Recent evidence has shown that the mesospheric sodium nightglow, a chemiluminescent process which produces atomic sodium D-line radiation in the Earth's upper atmosphere, proceeds through the first excited (A 2Σ+) electronic state of NaO. The rate of D-line radiation production is proportional to the rate constant for the reaction of NaO(A 2Σ+) + O(3P) and its branching ratio to produce excited Na(2P) rather than ground-state Na(2S). The only previously published measurement of the NaO + O(3P) reaction rate and branching ratio was performed under slow flow conditions and almost certainly primarily represents the reaction of ground-state NaO (X 2Π). We present low-pressure measurements of the NaO + O reaction kinetics using an NaO source reaction known to produce NaO in the (A 2Σ+) state and determine the 290 K reaction rate constant to be (5.1 ± 1.8) × 10-10 cm3 s-1 and the branching ratio to produce Na(2P) to be 0.14 ± 0.04. New data on the termolecular rate coefficient for the reaction Na + O2 + He → NaO2 + He at 290 K are also presented.

Gas-phase association reactions of hydroxide, methoxide, ethoxide, and their deuterated analogs

The selected ion flow tube technique is used to study 14 termolecular association reactions of hydroxide–water (OH − + H 2O and OD − + D 2O), methoxide–water (CH 3O − + H 2O, CH 3O − + D 2O, CD 3O − + H 2O, and CD 3O − + D 2O), methoxide–methanol (CH 3O − + CH 3OH, CH 3O − + CH 3OD, CD 3O − + CD 3OH, and CD 3O − + CD 3OD), and ethoxide–ethanol (CH 3CH 2O − + CH 3CH 2OH, CH 3CD 2O − + CH 3CD 2OH, CD 3CH 2O − + CD 3CH 2OH, and CD 3CD 2O − + CD 3CD 2OD) where the cluster bond dissociation energies are similar (∼24–30 kcal/mol). The apparent second-order rate coefficients for association (k IIapp) are measured as a function of helium pressure over the range of 0.25–1.2 Torr at 300 K. The derived termolecular rate coefficients and complex lifetimes are generally larger for systems with more degrees of freedom in the intermediate ion–molecule complex. In all reactions with alkoxides, association rates are significantly enhanced by deuteration of the alkyl groups (by factors of 1.4–3.0) whereas deuteration of the bridging hydrogen does not affect the association rates. Potential energy surfaces for association (single versus double well) are discussed based on the pressure dependence of the association rates.

Rate Coefficients for the Propargyl Radical Self-Reaction and Oxygen Addition Reaction Measured Using Ultraviolet Cavity Ring-down Spectroscopy

By using 193 nm laser photolysis and cavity ring-down spectroscopy to produce and monitor the propargyl radical (CH2CCH), the self-reaction and oxygen termolecular association rate coefficients for the propargyl radical were measured at 295 K between total pressures of 300 Pa and 13300 Pa (2.25 and 100 Torr) in Ar, He, and N2 buffer gases. The rate coefficients obtained by simple second-order fits to the decay data were observed to vary with the photolytic precursors: allene, propargyl chloride, and propargyl bromide. By using a numerical fitting routine and more comprehensive mechanisms, a distinct rate coefficient for the self-reaction was determined, k∞(C3H3+C3H3) = (4.3 ± 0.6) × 10-11 cm3 molecule-1 s-1 at 295 K. This rate coefficient, which is a factor of 2.8 times slower than reported previously, was independent of total pressure and buffer choice over the entire pressure range. Other rate coefficients derived during the modeling included k(C3H3+H 665 Pa He) = (2.5 ± 1.1) × 10-10 cm3 molecule-1 s-1...

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.

Reactions of CH3+ with C2N2, CH2CHCN, and HC3N: A Low-Pressure/High-Pressure Study

The association of CH3(+) with the three molecules C2N2, CH2CHCN, and HCCCN has been examined using ion cyclotron resonance (ICR) and selected ion flow tube (SIFT) techniques at room temperature. In each reaction, the mean lifetime of the complex (CH3 x N-=C-R(+))(sup *) formed in the association has a major influence on the outcome of the reaction and the product channels that are observed using ICR and SIFT. Termolecular rate coefficients are reported for the association of CH3(+) + C2N2 for the bath gases M = He, Ar, N2, and C2N2. k(sub 3) = 8.2 x 10(exp-24) cm(sup 6)/s (M = C2N2). In each system the association product channel occurs in competition with exothermic bimolecular channels. The complex lifetimes in all three systems are in the range 30-70 microsec. Very rapid ion-molecule association reactions have been observed in several systems of hydrocarbons and nitriles, and the implications for Titan ion chemistry are discussed briefly.

Nightglow emissions from oxygen in the lower thermosphere

Several independent trains of reasoning lead to the conclusion that O 2( c 1 Σ − u ) is the precursor for the emission of the 557.7 nm line of atomic oxygen. It is shown that the measured altitude profile of the volume emission rate of the Herzberg I system is reproduced by using the expected rate coefficient for the production of O 2( A 3 Σ u +) by termolecular association and rate coefficients for quenching by atomic and molecular oxygen that accord with laboratory evidence. Termolecular association does not contribute directly to the Atmospheric system because the O 2( b 1 Σ + g ) it generates is mainly in high vibrational levels and vibrational deactivation of these by interchange of electronic energy with normal oxygen molecules is not rapid enough to prevent deactivation to O 2( a 1 Δ g or X 3 Σ − g ) from occurring. The prime source of the O 2( b 1 Σ + g , υ =0) is excitation of the O 2 X 3 Σ − g ν = 0) collision partner involved in O 2( A 3 Σ + u , A′ 3 Δ u and c 1 Σ − u ) deactivation. This source can account for the measured altitude profile of the volume emission rate of the Atmospheric system.

Association reactions at low pressure. IV. The HC3N+/HC3N system

The reactions between HC3N+ and HC3N, and between HC5N+ and HC3N have been examined at pressures from 1×10−7 to 1×10−3 Torr by ion cyclotron resonance mass spectrometry. The reaction between HC3N+ and HC3N has both a bimolecular reaction path and a termolecular reaction path. The overall bimolecular reaction rate coefficient was found to be 1.3×10−9 cm3 s−1. The primary product, HC5N+, represents 90% of the product ions, while the minor products HC6N+2 and H2C6N+2 each represent 5%. The termolecular association rate coefficient was 3.7×10−24 cm6 s−1 with He as the third body. From double resonance experiments the mean lifetime of the collision complex was determined to be 180 μs. HC5N+ was found to react with HC3N and form the adduct ion H2C8N+2 through both bimolecular and termolecular channels. The bimolecular rate coefficient was 5.0×10−10 cm3 s−1 and the termolecular rate coefficient was observed to be 1.2×10−22 cm6 s−1 with HC3N as the third body. With He as the stabilizing molecule, the termolecular rate coefficient was 6.0×10−24 cm6 s−1. The mean unimolecular lifetime of the collision complex was estimated to be ≥15 μs and the mean radiative lifetime for the radiative association channel was found to be ≥89 μs. HC5N+ was found to be formed with excess internal energy and did not react by bimolecular association until relaxed by several nonreactive collisions with HC3N.

Termolecular rate coefficients and the standard enthalpy of the reaction hydroxyl + carbon disulfide + M .fwdarw. HOCS2 + M

The reaction between OH and CS{sub 2} has been studied in He in the pressure range 9-270 Torr and the temperature range 249-298 K by means of the laser-photolysis/laser-induced-fluorescence technique. Analysis of the temporal profile of (OH) yielded the rate coefficients for the forward and reverse reactions for the equilibrium OH + CS{sub 2} + M {r equilibrium} HOCS{sub 2} + M and hence the equilibrium constant. Study of the temperature dependence of the equilibrium constant leads to the standard enthalpy of reaction {Delta}H{degree} = {minus}43.9 {plus minus} 5.3 kJ mol{sup {minus}1} and the standard entropy of reaction {Delta}S{degree} = {minus}102.9 {plus minus} 15.4 J K{sup {minus}1} mol{sup {minus}1}. The termolecular rate coefficients for the forward reaction at 298 K have also been determined to be k{sub He}{sup III} = (5.04 {plus minus} 1.01) {times} 10{sup {minus}32} cm{sup 6} molecule{sup {minus}2} s{sup {minus}1} and k{sub CS{sub 2}}{sup III} = (4.28 {plus minus} 1.07) {times} 10{sup {minus}31} cm{sup 6} molecule{sup {minus}2} s{sup {minus}1}.

Temperature dependence of the atomic three-body association reaction Ar+ + 2Ar .fwdarw. Ar2+ + Ar below 3 K

Absolute termolecular association rate coefficients for the reaction Ar{sup +} + 2Ar {yields} Ar{sub 2}{sup +} + Ar were measured at translational temperatures between 0.5 and 3 K by using the free jet flow rector technique. The values of k{sub 3} are found to be strongly temperature dependent and fit an inverse temperature rate law, k{sub 3} = 9.52 {times} 10{sup {minus}29}T{sup {minus}1.1} cm{sup 6} s{sup {minus}1}, incorporating data between 0.5 and 300 K. There is some evidence that this fit is dominated by the low-temperature limiting behavior and that the strict T{sup {minus}n} dependence with a constant value of n is currently unjustified for atomic ion-atom association processes.

Temperature dependence of termolecular association reactions N2+ + 2N2 .fwdarw. N4+ + N2 and O2+ + 2O2 .fwdarw. O4+ + O2 occurring in free jet expansions below 20 K

A new experimental technique that combines supersonic expansions and laser ionization mass spectrometry has been used to measure the termolecular association rate coefficients, k{sub 3}, for the gas-phase reactions N{sub 2}{sup +} + 2N{sub 2} {yields} N{sub 4}{sup +} + N{sub 2} and O{sub 2}{sup +} + 2O{sub 2} {yields} O{sub 4}{sup +} + O{sub 2} below 20 K. The continuity of the proposed inverse temperature law of k{sub 3} = CT{sup -n} was observed down to 4 K for both reactions. Statistical analysis of our results along with the higher temperature data obtained by other authors gives the values of 1.92 {plus minus} 0.15 and 1.86 {plus minus} 0.15 for n for the reactions of N{sub 2}{sup +} and O{sub 2}{sup +}, respectively. The results of phase space calculations are presented for these reactions and excellent agreement between theory and experiment is obtained.

The methylidyne radical + carbon monoxide reaction: rate coefficient for carbon atom exchange at 294 K

A fast-flow reactor equipped with isotope-specific laser-excited fluorescence detection of CH radicals has been used to study carbon atom exchange in the reaction between CH and CO at 294 K and 2 Torr of total pressure. The rate coefficient for exchange, k{sub 3} = (2.1 {times} 0.3) {times} 10{sup {minus}12} cm{sup 3} s{sup {minus}1}, is about an order of magnitude larger than the bimolecular rate for the addition reaction, k{sub 2} = (2.7 {plus minus} 0.4) {times} 10{sup {minus}13}. High-pressure limiting bimolecular and low-pressure termolecular recombination rate coefficients of 1.1 {times} 10{sup {minus}10} cm{sup 3} s{sup {minus}1} and 4.9 {times} 10{sup {minus}30} cm{sup 6} s{sup {minus}1} are derived. The results are discussed in the context of previous work on the title reaction and on the chemistry of singlet CH{sub 2}.

Theoretical studies of termolecular thermal recombination of silicon atoms

Termolecular recombination of silicon atoms in the presence of an atomic third body M is studied for thermal reactions on the ground-state 3Σ−g potential curve for Si2 dimers. The total potential surface is assumed to have pairwise form with the Si2 term being a Morse potential fitted to multireferenced double-excitation, configuration interaction (MRDCI) results. Lennard-Jones (LJ) (12,6) potentials are used for the two M–Si interactions. The termolecular rate coefficients for the temperature range 200≤T≤300 K are found to be in the range 1.69×1015≤kr(T) ≤2.56×1015 cm6/mol s if a statistical factor of unity is employed. It is argued that the most appropriate statistical factor is 1/9 for which the rate coefficients fall in the range 1.88×1014≤kr(T) ≤2.85×1014 cm6/mol s. The statistical error in the calculation precludes an accurate calculation of the small activation energy for the recombination. The limiting values are −1.24≤Ea ≤2.32 kcal/mol with a least-squares result of Ea =−0.028 kcal/mol.

The influence of the effective potential on the strong collision limiting low–pressure rate coefficients

AbstractThe influence of the effective potential energy curves on the calculation of the strong collision limiting low‐pressure rate coefficients of thermal dissociation‐recombination reactions was analyzed in terms of the factorized formalism of Troe. An analysis of 26 reactions employing a Morse potential coupled with a quasitriatomic molecular model and an explicit account of the adiabatic zero‐point barriers, as originallyproposed by Troe, was performed. A comparison between calculations realizedwith an exactly fitted looseness parameter, α, and with a standard value of α = 1.0 Å−1, indicates that the use of this last value is satisfactorily justified in the evaluation of thestrong collision limiting low‐pressure rate coefficients. A study interms of restrictive relationships between the looseness and Morse parameters and ab initio, radial potentials (for CH4, CH3O2, and HO2) was also realized. The uncertainties in the evaluation of termolecular rate coefficients due to the lack of a complete knowledge of the long‐range potentials are also briefly discussed.

The importance of three-body processes to reaction kinetics at atmospheric pressures--I: Archetype reactions of He species with N<inf>2</inf>

This paper concerns a reexamination of the significance of three-body effects that enhance the reaction rates for energy transfer and for ion-molecule reactions that occur in atmospheric pressures of inert gas diluent, even in the absence of any formation of product clusters. The archetype case of the reactions of the energy-storing species of helium with molecular nitrogen has been studied in two different preionized discharge systems capable of operation to 6 atm pressure. Earlier results suggesting the critical importance to kinetic modeling of three-body channels were confirmed in this work. The termolecular rate coefficient for the particular reaction He+ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> + N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> + He was concluded to be <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">13.1 \times 10^{-30}</tex> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> /s with no evidence of saturation up to pressures of 6.0 atm. Effective rates of reaction were observed to be increased by this channel to a value three times in excess of the Langevin rate that has been traditionally considered to be an upper limit on the overall rate of reaction. The close conformity to the older <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</tex> -beam results in this test case implies that the general conclusion of those studies must be seriously considered. In 95 percent of the cases of the reactions of inert gas ions with other species diluted in inert gases at atmospheric pressures it must be expected that rates can greatly exceed the traditional bimolecular values and can even exceed the Langevin rates by substantial amounts.

XeI(^2π_1/2–^2Σ_1/2) excimer emission at 13 μm

The collisional enhancing of the magnetic dipole transition I(52P1/2–52P3/2) at 1.3152 μm by Xe is shown to proceed over an exciplex channel: I(52P1/2) + Xe → XeI(2π1/2) → I(52P3/2) + Xe + hν(1.3 μm). The pseudo-first-order rate coefficient for this process is (1.6 ± 0.2) × 10−18 molecule−1 cm3 sec−1. The termolecular rate coefficient for XeI(2π1/2) excimer production is (2 ± 1) × 10−35 molecule−2 cm6 sec−1. The radiative lifetime of the XeI excimer state is of the order of 100 nsec. Similar effects are briefly reported for C2F6, SF6 Kr, Ar, and i-C3F7I.

OH chemiluminescent radiation from lean hydrogen-oxygen flames

The OH radiation intensity in the 3064 Å band, the temperature, and the OH concentration were measured as a function of the height above the face of a premixed H2/O2 flat flame burner. The burner was operated fuel lean at subatmospheric ambient conditions. Examination of possible reaction mechanisms that could produce chemiluminescent OH radiation from these hydrogen-lean flames led to results consistent with those obtained in hydrogen-rich flames. The termolecular rate coefficient for the reaction H+OH+OH→H2O+OH* was found to be (2.3±0.9) × 10−32 cm6 molecules−2 · sec−1. The value represents an upper bound for the rate coefficients of the reactions which might contribute to the excitation of OH.