Ramsberger – Kassel – Marcus Research Articles

Statistical modeling of capture, association, and exit-channel dynamics in the CH3+/CH3CN system

The ion–molecule reaction CH3++CH3CN is known to have an association channel leading to CH3CNCH3+ in competition with the exothermic binary channels H2CN++C2H4 and C2H5++HCN. This reaction has been modeled using a master equation treatment incorporating weak collisions. The parameters required for the Rice–Ramsberger–Kassel–Marcus (RRKM) treatment have been found from an ab initio investigation of the CH3+/CH3CN energy surface. A means of including capture rate coefficients in the RRKM approach is developed, in which only the hindered dipole rotation is coupled with the reaction coordinate at large separations. Existing experimental data from ion cyclotron resonance (ICR) spectroscopy and a selected ion flow tube are fitted by the model in the pressure range 10−7–0.3 Torr. The low pressure experimental results are accounted for by weak collisions of the complex with the bath gas (when M=He, <ΔEdown≳ and <ΔRdown≳∼100 cm−1) corresponding to a collision efficiency β=0.05 for M=He and 0.14 for M=CH3CN. Unimolecular rate coefficients for the (CH3CNCH3+)* complex are calculated for all product channels at a range of temperatures from 300 to 600 K. The rate coefficient for radiative stabilization was found to be 225 s−1 at the conditions of the ICR experiment. The average lifetime of the complex was calculated to vary between 29 μs at 600 K to 0.47 ms at 300 K and the termolecular association rates from 3.4×10−24–9.8×10−23 cm6 s−1 (M=He) and from 6.7×10−23–2.2×10−21 cm6 s−1 (M=CH3CN) over the temperature range 600–300 K.

Comparison of bending, C–C stretching, and collision energy effects on the reaction of C2H+2 with D2

We report the effects of vibrational excitation and collision energy on the cross sections and branching ratios for reaction of acetylene cations with D2, using two different guided-ion-beam instruments. Two major reaction channels are observed, both of which are nearly thermoneutral. Hydrogen atom exchange is slightly exoergic due to zero point energy, and is inhibited by both collision and vibrational energy. Formation of the two isotopic ‘‘C2H+3 ’’ products is enhanced by collision energy and C–C stretching vibration, but not by bending vibration. The branching ratios at low collision energies are consistent with reaction via an intermediate complex, and Rice–Ramsberger–Kassel–Marcus (RRKM) analysis is used to extract further information. At collision energies above 1 eV, D-atom transfer by a direct mechanism is also observed as a route to C2H2D+ production. Comparison of our results using both the Stony Brook and Freiburg instruments is made with the state-selected experiments of Honma, Kato, Tanaka, and Koyano [J. Chem. Phys. 81, 5666 (1984)], who previously studied both the C2H+2+D2 and C2D+2+H2 isotopic reactants. Our results for C2H+2+D2 are consistent with their C2D+2+H2 data for all collision energies and with their C2H+2+D2 data at 0.2 eV collision energy. We do not reproduce the anomalous vibrational effects they reported for 1 and 2 eV collision energies.

Towards elucidating the interplay of structure and dynamics in clusters: Small KCl clusters as models

An investigation of melting, freezing, and coexistence phenomena in binary clusters is presented with the salt clusters (KCl)4 and (KCl)5 as specific examples. The results of molecular dynamics simulations are combined with analyses of the potential surfaces, notably the energies and geometries at the minima and saddle points. On the basis of this knowledge, the molecular dynamics results are interpreted in terms of melting, freezing, and phase coexistence, and the ways a nonrigid system may explore its potential surface. A comparison is made of isomerization rates derived from molecular dynamics and Rice–Ramsberger–Kassel–Marcus (RRKM) theory.

Cylindrical manifolds and reactive island kinetic theory in the time domain

In a series of recent publications we discussed the concept of cylindrical manifolds and their role in mediating the reaction dynamics of chemical reactions. The cylindrical manifolds were used to develop a chemical reaction rate theory we called reactive island (RI) theory. RI theory was cast in terms of the map dynamics between n Poincaré mapping planes—which were referred to as the ‘‘n-map.’’ Therefore ‘‘time’’ did not explicitly appear within n-map RI theory. In this paper we extend n-map RI theory to the time domain. The formal theory, cast as a master equation, is used to obtain the temporal RI model. Temporal RI theory is applied to a two degree-of-freedom system exhibiting dynamical chaos. The results of temporal RI theory are compared with classical Rice–Ramsberger–Kassel–Marcus (RRKM) theory and it is found that even under, presumably, ‘‘ideal’’ dynamical conditions, RRKM theory can be in serious error with numerical simulation. It is also seen that temporal RI theory accurately accounts for the rates at energies far above the barrier, where RRKM theory is not expected to be applicable. We also discuss some rigorous comparisons between the decay rates obtained from n-map and temporal RI theories.

Modification of the Duchovic–Hase–Schlegel potential energy function for H+CH3↔CH4. Comparison of canonical variational transition state theory, trajectory, and experimental association rate constants

The Duchovic–Hase–Schlegel analytic potential energy function for H+CH3→CH4 association is modified to have the correct asymptotic behavior at large separations. Canonical variational transition state theory calculations performed on this modified potential yield the same association transition state structures and rate constants as reported previously for the unmodified potential. This modified potential is also used in a classical trajectory calculation of the association rate constant. The canonical variational transition state theory and trajectory association rate constants agree for both H+CH3 and D+CH3. Trajectories are used to study the unimolecular decomposition of the excited methane molecules formed by association. Most of the molecules decay exponentially. However, an initial nonrandom transient constitutes ∼5%–7% of the decomposition. Trajectory rate constants, derived from the exponential decay, are compared with harmonic Rice–Ramsberger–Kassel–Marcus (RRKM) rate constants to derive anharmonic correction factors.

A quasiclassical trajectory study of the OH+CO reaction

We present a quasiclassical trajectory study of the OH+CO reaction using a potential surface that has been derived from ab initio calculations. Among quantities that have been studied are cross sections for reaction and for HOCO complex formation, cross sections associated with reaction from excited vibrational and rotational states, product energy partitioning and CO2 vibrational-state distributions, HOCO lifetime distributions, and thermal and state-resolved rate constants. We also present the results of Rice–Ramsberger–Kassel–Marcus (RRKM) calculations, using the same potential-energy surface, of HOCO lifetimes and of reactive and complex formation rate constants. The trajectory results indicate that the dominant mechanism for reaction involves complex formation at low energies. However, a direct reaction mechanism is responsible for half the reactive cross section at higher energies. This leads to a rate constant that is weakly temperature dependent at low temperatures, and becomes strongly temperature dependent at high temperature. Our trajectory results agree with measured rates over a wide range of temperatures, but the trajectory results at low temperatures are dominated by classical ‘‘leak’’ through zero-point barriers, so this agreement may be somewhat fortuitous. Rate constants for nonreactive processes such as OH(v=1) deactivation by CO that are controlled by the HOCO formation step are well above experiment (factor of 6), while rate constants for processes such as CO(v=1) reaction with OH that are controlled by decay of HOCO into H+CO2 are much closer (factor of 2). This suggests that the entrance channel barrier on our surface is too loose while the exit barrier is accurate. The error in the entrance channel barrier is studied using RRKM, and it is found to be due to an incorrect out-of-plane bend potential in the analytical surface used. Modifying the potential so that it is more consistent with ab initio calculations leads to greatly improved HOCO formation rates. The RRKM rate constant for HOCO formation is in good agreement with trajectories, but the RRKM reactive rate constant is well below either the trajectory value or experiment. This reactive rate is found to be very sensitive to tunneling through the exit channel barrier, so that by changing the barrier frequency from the fitted surface value to one which is more consistent with ab initio calculations, overall rates in agreement with experiment are obtained. Our trajectory cross section for highly translationally and rotationally excited OH is over an order of magnitude smaller than a value reported by Wolfrum. HOCO lifetimes are in the 0.4–2.0 ps range, about equal to RRKM theory near threshold but dropping more slowly with energy. Both trajectory and RRKM lifetimes are below the values measured by picosecond methods. Product energy partitioning is dominated by conversion of the exit channel barrier energy into product translation. Product rotational excitation is strongly controlled by angular momentum constraints. Product vibrational distributions are colder than statistical, with a propensity towards simultaneous bend–stretch excitation and not pure stretch excitation.

Reaction dynamics on barrierless reaction surfaces: A model for isoergic gas-phase proton-transfer reactions

The kinetics of some gas-phase alcohol/alkoxide proton-transfer reactions is slower than predicted by simple Rice–Ramsberger–Kassel–Marcus (RRKM) rate theory modeling on the near-barrierless reaction surfaces. Reaction dynamics can be investigated in isolation from nonequilibrium and/or thermodynamic considerations through the study of a generic isoergic ion–molecule system X−+X−H. Monte Carlo quasiclassical trajectory simulations on barrierless reaction surfaces show that the slow experimental kinetics is consistent with both (i) locking of the external rotations of the reactants and (ii) passage over the (orbital angular momentum) centrifugal barrier being the rate-determining steps in bimolecular association, rather than only the latter process. In addition, there may be non-RRKM product selectivity.

Slow time-resolved photodissociation ofp-iodotoluene ion

Using time-resolved photodissociation in the ion cyclotron resonance mass spectrometer, the dissociation of p-iodotoluene ion was time resolved at five wavelengths between 532 and 630 nm. This is the slowest dissociation which has been time resolved for ions of well defined internal energies, giving inverse time constants for fragment ion appearance ranging from 2×102 to 1.1×103 s−1. At the longer wavelengths, dissociation is in clear competition with infrared-radiative relaxation of the photoexcited ion, which is calculated by kinetic modeling of the observed curves to give an energy loss rate of 6.2 eV s−1 (50 000 cm−1 s−1). The dissociation kinetics of this ion are in complete accord with a Rice–Ramsberger–Kassel–Marcus (RRKM) model with E0 of 1.9 eV and ΔS1000 K of −4 eu. It is concluded from the high activation energy that the rate limiting step in the dissociation kinetics is a molecular rearrangement preceding dissociation.

Bond-breaking without barriers. II. Vibrationally excited products

Ketene is photolyzed in a supersonic jet, and the vibrationally excited singlet methylene CH2 (ã 1A1), produced is detected by laser-induced fluorescence. The appearance thresholds and yield curves of individual methylene rovibrational states are obtained by scanning the photolysis laser wavelength. As observed previously by probing the (0,0,0) state at lower photolysis energies, there are no barriers to dissociation and nuclear spin is conserved. Sharp steps are observed just above the energetic threshold in each of these photofragment excitation (PHOFEX) curves. This suggests that the rotational state distributions are given by phase space theory (PST). The quantum yield of the (0,1,0)101 rovibrational state is measured and the quantum yield for (0,1,0) inferred. These values are larger than predicted by PST, and are close to values predicted by variational Rice–Ramsberger–Kassel–Marcus (RRKM) theory and by the separate statistical ensembles (SSE) method. This indicates that near the (0,1,0) energy threshold the (0,0,0) yield is constrained, as by a tight transition state. The appearance of steps spaced by the energies of a free CO rotor in the PHOFEX curves close to the thresholds of each vibrational state probed indicates that the near threshold flux of vibrationally excited products is controlled by a loose ‘‘transition state’’ on a vibrationally adiabatic surface. These observations are consistent with the variational RRKM theory for dissociations without barriers in which each product vibrational state evolves on its own vibrationally adiabatic potential surface and has its own transition state. As the energy increases above the threshold for a vibrational state, its transition state moves in along the reaction coordinate and tightens. Thus total rates increase less rapidly with energy than in PST and vibrational distributions are skewed towards higher levels than in PST.

Determination of the singlet/triplet branching ratio in the photodissociation of ketene

The rotational distributions of CO products from the dissociation of ketene at photolysis energies 10 cm−1 below, 56, 110, 200, 325, 425, 1107, 1435, 1720, and 2500 cm−1 above the singlet threshold (30 116.2 cm−1 ), are measured in a supersonic free jet of ketene. The CO(v″=0) rotational distributions at 56, 110, 200, 325, and 425 cm−1 are bimodal. The peaks at low J′s, which are due to CO from the singlet channel, show that the product rotational distribution of CO product from ketene dissociation on the singlet surface is well described by phase space theory (PST). For CO(v″=0) rotational distributions at higher excess energies (1107, 1435, 1720, and 2500 cm−1 ), the singlet and triplet contributions are not clearly resolved, and the singlet/triplet branching ratios are estimated by assuming that PST accurately predicts the CO rotational distribution from the singlet channel and that the distribution from the triplet channel changes little from that at 10 cm−1 below the singlet threshold. The singlet yield shows a rapid increase in the low excess energy region (0–300 cm−1 ), and a slower increase above. The singlet and triplet rate constants are derived from the directly measured total rate constants using the singlet yields. The triplet rate constant increases monotonically with increasing photolysis energy through the singlet threshold region. The singlet rate constant is accurately established in the threshold region and found to increase much less rapidly than predicted by phase space theory. At 2500 cm−1 excess energy, the CO(v″=1) rotational distribution is obtained, and the ratio of CO(v″=1) to CO(v″=0) products for the singlet channel is measured to be 0.045±0.017. This ratio is close to the variational Rice–Ramsberger–Kassel–Marcus (RRKM) calculation 0.038, and the separate statistical ensembles (SSE) prediction 0.041, but much greater than the PST prediction, 0.016.

Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of CH2CO into CH2 and CO. II. Photofragment excitation spectra for vibrationally-excited fragments

Results on vibrationally-excited ketene photofragment excitation (PHOFEX) spectra of Moore and co-workers are interpreted in terms of a previously described variational implementation of Rice–Ramsberger–Kassel–Marcus (RRKM) theory. At subvibrational excitations, the predictions of this theory reduce to those of phase space theory (PST). However, for excess energies just above the threshold of excitation of a particular vibrational mode of the products, the present theory predicts a significantly greater probability for vibrational excitation, compared with PST, in closer agreement with the experimental results, and predicts an energy dependence of the PHOFEX spectrum that is closer to the observed one. A key feature, to which the present calculations lead, is a two-transition state (TS) description for each vibrational excitation of the products, the PST TS region dominating at the threshold for that excitation and an inner TS region dominating at somewhat higher (∼200 cm−1) energies. The behavior contrasts partly with that of the unimolecular dissociation rate constant kEJ (except at the threshold for kEJ), because of the different focus of the two types of measurements. The theory provides a consistent interpretation of both properties.

Optical and near-infrared spectroscopy of neutral indium phosphide clusters

Spectra are obtained for a wide distribution of sizes and stoichiometries of indium phosphide clusters using photodissociation techniques. These spectra are presented at two different cluster temperatures throughout the spectral range of 0.65 eV (1900 nm) to 2.0 eV (640 nm) for indium phosphide clusters containing from 5 to 14 atoms. Though the spectral behaviors of the clusters are found to be qualitatively similar, significant quantitative differences exist. A Rice–Ramsberger–Kassel–Marcus (RRKM) dissociation model employing significant fitting constraints is found to accurately describe the observed dissociation behaviors at both temperatures. Dissociation energies ranging from 2.0 to 2.4 eV are determined for the In5Py–In9Py clusters using the RRKM model. Experimental evidence suggests that the dissociation process involves loss of a small phosphorus containing moiety such as P1–2 or InP1–2. Results of the RRKM fitting process also clearly indicate that most of these InxPy clusters have nearly uniform absorption cross sections from 0.65 to 2.0 eV. This range extends well below the band gap of bulk InP. This is the first clear evidence of the presence of electronic states in closed shell semiconductor clusters at energies well below the band gap of the bulk material. Select clusters show significant deviations from pure RRKM behavior. Their behavior is consistent with the presence of spectral structure in their absorption cross sections in the energy range of 0.65–2.0 eV.

Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of CH2CO into CH2 and CO

A previously described implementation of Rice–Ramsberger–Kassel–Marcus (RRKM) theory for unimolecular dissociation processes involving a highly flexible transition state is applied to the dissociation of CH2CO into CH2 and CO. Results of theoretical calculations for the energy and angular momentum resolved rate constants are presented. Using an added dynamical approximation, the product vibrational–rotational distributions are also calculated. The calculated rate constants are compared with the corresponding experimentally determined quantities where possible. Comparison is also made with phase space theory (PST). The RRKM-based calculations are in good agreement with both the experimentally determined rate constants of Zewail and co-workers and the experimentally determined photofragment excitation spectra of Moore and co-workers. The results on rates are in contrast to the corresponding results from PST calculations. The RRKM-based theory for the product vibrational–rotational distributions predicts a moderately greater probability for vibrational excitations than does PST (particularly for excess energies just above the threshold for excitation of a particular vibrational mode of the products). In other respects the RRKM-based predictions of the ro-vibrational product state distributions are quite similar to those of PST.