Long-lived Collision Complex Research Articles

Reactive scattering of a supersonic chlorine atom beam: Cl + C2H5I

Reactive scattering of Cl atoms with C2H5I molecules has been studied over the range of initial translational energy E = 63 - 24 kJ mol-1, using a supersonic beam of Cl atoms seeded in He and Ne buffer gas. Laboratory angular and velocity distributions of ICl product were measured which show that reaction proceeds via a long-lived collision complex at low initial translational energy. However at intermediate and higher initial translational energy, a forward scattered component emerges with a higher product translational energy than that of the long-lived complex component. This breakdown of long-lived complex dynamics occurs more readily in collisions at large impact parameters in contrast to the osculating complex model which assumes a statistical distribution of lifetimes independent of impact parameter.

Reactive scattering of a supersonic chlorine atom beam: Cl + CH3I

Reactive scattering of Cl atoms with CH3I molecules has been studied over the range of initial translational energy E = 62-23 kJ mol-1, using a supersonic beam of Cl atoms seeded in He and Ne buffer gas. Laboratory angular and velocity distributions of ICl product were measured which indicate that reaction occurs via a long-lived collision complex with forward scattering appearing only at the highest collision energy. The dependence of the total reaction cross section on initial translational energy was also determined. The observed reactive scattering arises from an endoergic dissociation of the collision complex. The results are interpreted by a model which accounts for the effect of angular momentum conservation on this endoergic dissociation compared with the favoured dissociation of the complex back to reactants.

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. III. Application to angular distributions and branching fractions for the system K + CsF

The experiments on the reactive systems K + CsF and K + RbF by Stolte et al. are unique in that product angular distributions and branching fractions with variation of both translational and rotational energies have been obtained. The results for the reaction K + CsF with translational energy variation have now been re-evaluated using an algorithm recently published by us. A satisfactory fit to the experimental data is found by a long-lived collision complex model including strict angular momentum conservation in both the reactive and the non-reactive channels. No “osculating” behaviour has to be added to the model. Angular momentum limits have to be included in the model to reach agreement with the measured branching fractions and cross sections. This indicates that the internal dynamics of the complexes is important. The calculation shows that the reactants giving reactive complexes have large rotational and vibrational energies, while their translational energy is nearly average. The internal energy of reactive pairs of molecules decreases with increasing translational energy. The question how rapidly the branching fraction varies with translational energy is thus more complicated to answer than believed previously.

Effect of reaction exothermicity on the fate of long-lived collision complexes: The reaction C3H+4(C3H4,H)C6H+7 in propyne and allene

The reaction C3H+4(C3H4,H)C6H+7 has been studied in propyne and allene by photoionization mass spectrometry (PIMS). In contrast to allene where the reaction cross section decreases with increasing internal energy, the reaction cross section in propyne is independent of internal energy. The results are explained by model RRKM calculations.

Reactive scattering of a supersonic oxygen atom beam O + I2

Reactive scattering of O atoms with I2 molecules has been studied at an initial translational energy E = 43 kJ mol-1 using a supersonic beam of O atoms seeded in He and E = 18 kJ mol-1 using O atoms seeded in Ne. Velocity distributions of OI product were measured by cross-correlation time-of-flight analysis. Full contour maps of the differential reaction cross section were obtained which show predominantly rebound scattering at both initial translational energies. Scattering in the forward direction has a product translational energy distribution similar to that predicted for a long-lived collision complex but scattering in the backward direction has a much higher product translational energy. The greater predominance of rebound scattering observed for O + I2 compared with O + Br2 may be attributed to the greater exoergicity of the O + I2 reaction. However, comparison with the O + IBr reaction which exhibits a long-lived collision complex mechanism indicates that the predominance of backward scattering fo...

Reactive scattering of a supersonic oxygen atom beam: O + Br2

Reactive scattering of O atoms with Br2 molecules has been studied at an initial translational energy E = 40 kJ mol-1 using a supersonic beam of O atoms seeded in He, and at E = 15 kJ mol-1 using O atoms seeded in Ne. Velocity distributions of OBr product were measured by cross-correlation time-of-flight analysis. Full contour maps of the differential reaction cross-section have been obtained. For O atoms seeded in Ne, there is peaking in the forward direction with a lower intensity 0·6 ± 0·1 in the backward direction. The product translational energy distribution agrees with that predicted by a long-lived collision complex model with a tight linear transition state for dissociation. For O atoms seeded in He, the scattering in the backward direction is increased to 1·2 ± 0·1 and has a higher product translational energy than the scattering in the forward direction. The reactive scattering observed at the lower initial translational energy indicates a short-lived O-Br-Br collision complex with a lifetime a...

Reactive scattering of a supersonic oxygen atom beam : O + IBr

Reactive scattering of O atoms with IBr molecules has been studied at an initial translational energy E = 40 kJ mol-1 using a supersonic beam of O atoms seeded in He, and at E = 15 kJ mol-1 using O atoms seeded in Ne. Velocity distributions of OI product were measured by cross-correlation time-of-flight analysis. Full contour maps of the differential reaction cross section were obtained which show mild peaking equally in the forward and backward directions at both initial translational energies. The product translational energy distributions are consistent with a long-lived collision complex dissociating via a loose transition state. The triplet O-I-Br complex is more stable with respect to reaction products than the corresponding O-Br-Br complex of the O + Br2 reaction, due to the lower electronegativity of the central halogen atom. The emergence of rebound dynamics in the O + Br2 reaction is attributed to a shallower well in the exit valley of the potential energy surface compared with that for O + IBr.

A photoionization mass spectrometry (PIMS) study of the reaction C 3H 4+ + C 3H 4 → C 6H 7+ + H in allene

The reaction cross-section for C 3H 4 +(C 3H 4H 4, H) C 6H 4 + in allene has been studied as a function of the internal energy of the reactant ion. The reaction is known from previous studies to be exothermic and to proceed via a long-lived collision complex. The experimental data, which demonstrate a reduced cross-section at higher internal energies, are reproduced by an RRKM calculation.

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. I. Basic considerations and calculational procedure

A simulation method is described for the comparison of a molecular decomposition theory, based on the fundamental RRKM theory, with crossed molecular beam experiments. In the present formulation, the method is applied to the case with long-lived collision complexes surrounded by a centrifugal barrier. The procedure uses Monte Carlo techniques to simulate the formation and decomposition of the complexes, thus effectively solving the high-dimensional integrals resulting but seldom solved in the analytical treatments. Several computational problems, like singularities in the c.m. angular distributions, have been circumvented in this procedure. Angular momentum conservation, the simultaneous interaction of several decomposition channels and strict flux conservation are included in the procedure. Dynamical features can be introduced, as will be shown in forthcoming papers.

Reactive scattering of a supersonic oxygen atom beam : O+C3F7I

Reactive scattering of O atoms with C3F7I molecules has been studied at an initial translational energy E = 28 kJ mol-1 using a supersonic beam of O atoms seeded in He buffer gas. Velocity distributions of OI product were measured by cross-correlation time-of-flight analysis. A full contour map was obtained for the differential reaction cross-section which shows essentially isotropic scattering. Only a single velocity scan in the direction of the laboratory centroid vector could be measured using O atoms seeded in Ne buffer gas at an initial translational energy E = 14·6 kJ mol-1 due to the low signal of OI reactive scattering. The product translational energy distributions for both sets of measurements were found to be skewed with respect to the initial translational energy distributions indicating significant energy transfer to internal modes of the reaction products. However the product translational energy distributions extend to much higher energies than those predicted for a long-lived collision complex. Comparison of these results with previous measurements on the O + CF3I, C2F5I reactions indicates increasing energy transfer from initial translational energy to vibrational and torsional modes of the perfluoroalkyl radical along the series CF3, C2F5, C3F7. However this appears to involve primarily bonds close to the ruptured C-I bond in the C3F7 radical. These results are in accord with a previously proposed mechanism involving hard sphere scattering at small impact parameters and energy transfer to low frequency modes of the perfluoroalkyl radical.

A quantum mechanical study of the collinear Li+FH reaction

A quantum mechanical collinear model of the LiFH reaction is studied using the semiempirical potential energy surface of Zeiri and Shapiro. Accurate reaction probabilities are presented over the total scattering energy range from 0.5 to 1.6 eV. At 1.6 eV, three HF reactant vibrational states are energetically accessible, and 15 LiF product vibrational states are accessible. The reaction probabilities show extensive resonance features over the energy range considered, and there is considerable evidence for the formation of a long-lived collision complex from the initial v=1 state of HF.

Reactive scattering of a supersonic oxygen atom beam : O+C2F4

Reactive scattering of O atoms with C2F4 molecules has been studied at an initial translational energy E = 36 kJ mol-1 using a supersonic beam of O atoms seeded in He. Velocity distributions of F2CO product were measured at the FCO+ mass peak by cross-correlation time-of-flight analysis. A full contour map of the differential reaction cross-section has been obtained which favours the forward hemisphere. The average product translational energy represents only a small fraction f′av = 0·10 of the total energy available to products in their ground electronic states but is slightly greater than that predicted for a long-lived collision complex. These results are consistent with the Cvetanovic mechanism whereby reaction proceeds via a diradical intermediate in which the O atom remains bonded to one C atom of the C2F4 molecule. However, the lifetime of the diradical intermediate is comparable to its rotational period due to the reaction exoergicity which is large even for the formation of the electronically excited CF2 (3 B 1) radical. These results are consistent with the ready formation of triplet CF2 (3 B 1) product but do not preclude the formation of singlet CF2 (1 A 1) following a triplet-singlet transition.

Reactive scattering of hydroxyl radicals : OH + Br2

Angular and velocity distribution measurements of HOBr reactive scattering from crossed beams of OH radicals and Br2 molecules are reported. The OH radical beam was generated by the reaction of H atoms, formed in a microwave discharge through a low pressure flow of H2, with NO2 gas in a pyrex mixing source. The Br2 beam was generated from a supersonic nozzle source at ∼400 K with a stagnation pressure ∼100 Torr. Product velocity distributions were measured at each laboratory scattering angle by the cross-correlation time-of-flight method. The scattering data are found to be in good agreement with the RRKM-AM model of reactive scattering via a long-lived collision complex, with similar parameters to the O + Br2, I2 reactions. This indicates the existence of an HOBrBr collision complex, whose stability and possible structure are rationalized in terms of Walsh molecular orbital theory.

Theory of V–V and V–T/R energy transfer for HF (n=1 to 7)+HF (0)

Rate constants for vibrational relaxation of HF in vibrational states n=1 to 7 are calculated semiclassically for HF(n)+HF. The variation with n agrees well with experiment. The absolute values are about 55% of the experimental results. Orbiting collisions are important. The relaxation mechanism found disagrees with three well-known more approximate theories. V–T/R transfer is found to be important especially for the higher levels. A renormalization procedure is suggested as a remedy for the well-known numerical inaccuracy of trajectories with very long-lived collision complexes. This renormalization was not important for the present work.

Erratum: A comparison of exact classical and quantum mechanical calculations of vibrational energy transfer. II. The effect of long-lived collision complexes

First Page

Transition state theory for ion-molecule reactions

The standard formula for the rate coefficient given by transition state theory is not valid for exothermic ion-molecule reactions having no activation energy. A formula covering these is derived. For monatomic reactants Langevin’s formula is recovered. In the general case, account must be taken of the long-lived collision complex which arises because of the transfer of orbital energy into the rotational and vibrational modes of the reactants. The theory is applied to bimolecular reactions (most of which it gives to be rapid whether or not an electronic transition is involved), to termolecular association and to radiative association. The major conflict with experiment concerns N 2 + N 2 + + He---- >N 4 + + He which Bohme, Dunkin, Fehsenfeld & Ferguson (1968) have studied at a temperature of 80 K. According to their measurements, the apparent binary rate coefficient is a linear function of the helium pressure, if this is low, but above about a torr it reaches a saturation limit of only around one hundredth of the Langevin rate coefficient, the transition from the linear to the saturation region being quite sharp. Only the initial slope is in agreement with expectation.

A comparison of exact classical and quantum mechanical calculations of vibrational energy transfer. II. The effect of long-lived collision complexes

Exact classical and quantum mechanical calculations of V–T relaxation were carried out for the model system He+O2(v=1). The diatomic molecule was treated as a harmonic oscillator, and a spherically symmetric Lennard-Jones intermolecular potential was assumed. The bin and two-moment methods were used to quantize the classical energy transfer. For a deep well both classical and quantal calculations showed evidence of complex formation. In this case inelastic transitions were classically allowed even at low collision energies. The classical transition probabilities generally agreed within a factor of 2 with the quantal results. The final energy distribution of the complex trajectories was not completely random, as compared with the information-theoretic prior expectation.

On the theory of translational energy distributions of product molecules of molecular beam reactions involving transient complexes. II

A statistically adiabatic model for chemical reactions involving a tight or loose transition state in the exit channel was used in Part I to obtain an integral equation for the individual reaction probabilities, i.e., for the magnitude of the S matrix elements. In the present paper this integral equation is explicitly solved for the general case of product orbital (l) and rotational (j) angular momenta constrained only by energy and angular momentum conservation. The reaction probabilities are shown to be related to a contour integral of a product of canonical partition functions. The theory includes an effect of the evolution of the bending vibrations of the transition state into free rotations of the product molecules. The distribution of final translational energy for the general (l,j) case is then obtained by averaging the reaction probabilities over various quantum states of the product molecules. The results are compared with the special cases in the literature for which (i) the transition state in the exit channel is loose (’’phase space theory’’), (ii) this case but with l≫j, and (iii) tight transition state theory with l≫j (Part I). The results are also compared with experimental data obtained from the molecular beam reaction F+(CH3)2C=CH2 →F(CH3)2ĊCH2*→CH3+FCH3C=CH2. The data and the theoretical results are now in better agreement. In the treatment described here and in Part I a loose transition state in the entrance channel was assumed. Expressions for the energy distribution are also given for the case when the entrance channel transition state is tight. Finally, a statistically adiabatic S matrix, which is useful for reactions proceeding through long-lived collision complexes having tight transition states, is described, and its possible application to angular distributions and angular momentum polarization experiments is discussed.

Realistic translational energy distributions for decomposition of RRKM complexes with a centrifugal barrier

The RRKM unimolecular decomposition theory and its application to long-lived collision complexes with centrifugal barriers have been studied. A comparison with a Monte Carlo simulation method has shown that the previously used formulas for the translational energy distribution from decomposition of such complexes are not consistent with flux conservation requirements, i.e., each complex formed does not have unit probability of decomposing. Correct expressions for both one- and two-channel decomposition have been developed, and comparisons have been made with existing experimental data. Unfortunately, most data have been fitted to the earlier expressions using arbitrary assumptions or incorrect procedures, which makes comparisons difficult without complete recalculations. However, it is for example demonstrated that the peak of the correct distribution does not shift strongly with the number of oscillators used in the RRKM theory, and that it is always at higher energy than the previously used distribution. This means, that the interpretation of experiments in terms of a low number of “effective” oscillators probably is invalid. Some inconsistencies in previous work are also pointed out.

Alkali atom-dimer exchange reactions: Na + Rb2

Velocity analysis measurements of reactive scattering from the reaction Na + Rb2→ NaRb + Rb are reported. The product translational energy distribution is close to that predicted by a long-lived collision complex model with an average product translational energy E′av∼ 30% of the total available energy. A limited range of angular forms for the differential reaction cross section is compatible with the experimental data. The total reaction cross section is large Q= 120 ± 20 A2, indicating that a major fraction of collisions captured by the long-range van der Waals attraction, leads to reaction. These features of the reactive scattering are discussed in terms of the form of the reaction potential energy surface, with particular regard to the orientation dependence of reaction.