Unimolecular dynamics of Cl−...CH3Cl intermolecular complexes formed by Cl−+CH3Cl association

Role of non-statistical effects in deciding the fate of HO3˙ in the atmosphere

HO3˙ has been postulated as a reservoir for OH˙ in various atmospheric reactions. Under collision-free conditions, experiments indicate that the lifetime of this species should be more than one microsecond. Interestingly, the binding energy of HO3˙ is estimated to be ∼3 kcal mol-1 by recent experimental as well as theoretical works. The value of the binding energy suggests that the lifetime of HO3˙ should be in the picosecond range, and with this lifetime, HO3˙ cannot act as a reservoir for OH˙. In the present work, using on-the-fly semiclassical dynamics, we argue that if non-RRKM effects are included, the lifetime of HO3˙ may be higher than that estimated from the binding energy.

On the intramolecular vibrational energy redistribution dynamics of aromatic complexes: A comparative study on C6H6-C6H5Cl, C6H6-C6H3Cl3, C6H6-C6Cl6 and C6H6-C6H5F, C6H6-C6H3F3, C6H6-C6F6

Chemical dynamics Simulation studies on benzene dimer (Bz2) and benzene-hexachlorobenzene (Bz-HCB) as performed in the past suggest that the coupling between the monomeric (intramolecular) vibrational modes and modes generated due to the association of two monomers (intermolecular) has to be neither strong nor weak for a fast dissociation of the complex. To find the optimum coupling, four complexes are taken into consideration in this work, namely, benzene-monofluorobenzene, benzene-monochlorobenzene, benzene-trifluorobenzene (Bz-TFB), and benzene-trichlorobenzene. Bz-TFB has the highest rate of dissociation among all seven complexes, including Bz2, Bz-HCB, and Bz-HFB (HFB stands for hexafluorobenzene). The set of vibrational frequencies of Bz-TFB is mainly the reason for this fast dissociation. The mass of chlorine in Bz-HCB is optimized to match its vibrational frequencies similar to those of Bz-TFB, and the dissociation of Bz-HCB becomes faster. The power spectrum of Bz-TFB, Bz-HCB, and Bz-HCB with the modified mass of chlorine is also computed to understand the extent of the said coupling in these complexes.

Regular reaction dynamics in analytical form in the vicinity of symmetrical transition states. Central barrier crossings in SN2 reactions

When an activated complex, as defined in transition state theory (TST), has a polyhedral shape, its kinetic energy is found to be diagonal in a system of spherical polar coordinates. If, in addition, the polyhedron is characterized by a high symmetry, then its dynamics considerably simplifies. An application of this approach to the most symmetrical TS known to date, i.e., that which controls the Cl- + CH3Cl → ClCH3 + Cl- SN2 nucleophilic substitution, is presented and an analytical expression of its potential energy surface is provided. In a substantial range around the saddle point, approximate equations of motion for the two components of the reaction coordinate, i.e., the antisymmetrical stretching motion of the ClCCl core and the wagging motion of the hydrogen triad, can be derived in an analytical form. During an extensive period of time, the main component of the reaction coordinate is governed by an unexpectedly simple equation of motion that depends on a single initial condition, irrespective of the other ones and of the internal energy. Reactive trajectories are observed to form a perfectly collimated bundle characterized by undetectable dispersion, thereby giving a spectacular example of regular dynamics in an anharmonic potential. Regularity and collimation are brought about by local symmetry, which is a widespread feature of potential energy surfaces. Anharmonicity is observed to influence the dynamics only at a late stage. As energy increases, trajectories tend to fan out and to deviate from the analytical equation. For the wagging motion, chaos sets in at much lower energies.

Dynamical Behavior of Aromatic Trimer Complexes in Unimolecular Dissociation Reaction at High Temperatures. Case Studies on C6H6-C6F6-C6H6 and C6H6 Trimer Complexes

The intramolecular vibrational energy redistribution (IVR) dynamics during unimolecular dissociation of aromatic trimers at high temperatures is the primary interest of this study. Chemical dynamics simulations are performed for the unimolecular dissociation of benzene-hexafluorobenzene-benzene (Bz-HFB-Bz) and benzene trimer (Bz-trimer) complexes at a temperature range of 1000-2000 K. Partial dissociation of both the complexes is observed, which leads to a dimer and a monomer in the dynamics. However, the probability of such dissociation was found much lower in the case of the Bz-trimer, which further decreases with the increase of temperature. The rate of partial dissociation of Bz-HFB-Bz is faster at 1500, 1800, and 2000 K, whereas the rate of complete dissociation of the Bz-trimer is significantly faster than Bz-HFB-Bz at all temperatures. This is just the opposite of the corresponding dimer's dissociation, where benzene-hexafluorobenzene (Bz-HFB) dissociates at a faster rate than the benzene dimer (Bz-dimer). Thus, the dissociation dynamics of the trimer is different than that of the dimer. Simulations with excited intramolecular and intermolecular modes of the trimer complexes reveal that energy flows from intermolecular to intramolecular modes of Bz-HFB-Bz more freely than the Bz-trimer, and the dissociation process becomes slower for the former. Calculated activation energies for both types of dynamics are much lower than the corresponding binding energies, which may be due to the anharmonicity. The Arrhenius equation with an anharmonic correction factor is considered to recalculate the activation energy and pre-exponential factor.

Unimolecular Dissociation of C6H6-C6Cl6 Complex and Effect of Mode-Mode Coupling

The unimolecular dissociation dynamics of the C₆H₆-C₆Cl₆ (Bz-HCB) complex is studied with initial excitation of all vibrational modes for a temperature range of 1000-2000 K and with mode-specific excitations at 1500 K. The results are compared with those of the C₆H₆-C₆F₆ [Bz- HFB] complex. When all modes of Bz-HCB are initially excited, the rate of dissociation is slower with respect to Bz-HFB. However, the rate of dissociation is faster when simulations with nonrandom excitation of the specific vibrational modes are performed. The rate of dissociation of Bz-HCB is found to become slower when a few intramolecular modes are excited along with all inter-fragment modes compared to the simulation when only inter-fragment modes of the same complex are excited. Such an energy-transfer dynamics is absent if both intramolecular and inter-fragment modes are not initially excited. Thus, a "stimulated" resonance energy-transfer dynamics is observed in Bz-HCB dissociation dynamics.

Nonstatistical Reaction Dynamics

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post–transition state dynamics is often highly complex and nonstatistical.

Time-resolved radiation chemistry: femtosecond photoelectron spectroscopy of electron attachment and photodissociation dynamics in iodide-nucleobase clusters

Iodide-nucleobase (I-·N) clusters studied by time-resolved photoelectron spectroscopy (TRPES) are an opportune model system for examining radiative damage of DNA induced by low-energy electrons. By initiating charge transfer from iodide to the nucleobase and following the dynamics of the resulting transient negative ions (TNIs) with femtosecond time resolution, TRPES provides a novel window into the chemistry triggered by the attachment of low-energy electrons to nucleobases. In this Perspective, we examine and compare the dynamics of electron attachment, autodetachment, and photodissociation in a variety of I-·N clusters, including iodide-uracil (I-·U), iodide-thymine (I-·T), iodide-uracil-water (I-·U·H2O), and iodide-adenine (I-·A), to develop a more unified representation of our understanding of nucleobase TNIs. The experiments probe whether dipole-bound or valence-bound TNIs are formed initially and the subsequent time evolution of these species. We also provide an outlook for forthcoming applications of TRPES to larger iodide-containing complexes to enable the further investigation of microhydration dynamics in nucleobases, as well as electron attachment and photodissociation in more complex nucleic acid constituents.

A Better Understanding of the Unimolecular Dissociation Dynamics of Weakly Bound Aromatic Compounds at High Temperature: A Study on C6H6-C6F6 and Comparison with C6H6 Dimer

Chemical dynamics simulations are performed to study the unimolecular dissociation of the benzene (Bz)-hexafluorobenzene (HFB) complex at five different temperatures ranging from 1000 to 2000 K, and the results are compared with that of the Bz dimer at common simulation temperatures. Bz-HFB, in comparison with Bz dimer, possesses a much attractive intermolecular interaction, a very different equilibrium geometry, and a lower average quantum vibrational excitation energy at a given temperature. Six low-frequency modes of Bz-HFB are formed by Bz + HFB association which are weakly coupled with the vibrational modes of Bz and HFB. However, this coupling is found much stronger in Bz-HFB compared to the same in the Bz dimer. The simulations are done with very good potential energy parameters taken from the literature. Considering the canonical (TST) model, the unimolecular dissociation rate constant at each temperature is calculated and fitted to the Arrhenius equation. An activation energy of 5.0 kcal/mol and a pre-exponential factor of 2.39 × 10¹² s^-1 are obtained, which are of expected magnitudes. The responsible vibrational mode for dissociation is identified by performing normal-mode analysis. Simulations with random excitations of high-frequency Bz and HFB modes and low-frequency inter-Bz-HFB vibrational modes of the Bz-HFB complex are also performed. The intramolecular vibrational energy redistribution (IVR) time and the unimolecular dissociation rate constants are calculated from these simulations. The latter shows good agreement with the same obtained from simulation with random excitation of all vibrational modes.

Unimolecular Rate Constants versus Energy and Pressure as a Convolution of Unimolecular Lifetime and Collisional Deactivation Probabilities. Analyses of Intrinsic Non-RRKM Dynamics

Following work by Slater and Bunker, the unimolecular rate constant versus collision frequency, k_uni(ω, E), is expressed as a convolution of unimolecular lifetime and collisional deactivation probabilities. This allows incorporation of nonexponential, intrinsically non-RRKM, populations of dissociating molecules versus time, N( t)/ N(0), in the expression for k_uni(ω, E). Previous work using this approach is reviewed. In the work presented here, the biexponential f₁ exp(- k₁ t) + f₂ exp(- k₂ t) is used to represent N( t)/ N(0), where f₁ k₁ + f₂ k₂ equals the RRKM rate constant k( E) and f₁ + f₂ = 1. With these two constraints, there are two adjustable parameters in the biexponential N( t)/ N(0) to represent intrinsic non-RRKM dynamics. The rate constant k₁ is larger than k( E) and k₂ is smaller. This biexponential gives k_uni(ω, E) rate constants that are lower than the RRKM prediction, except at the high and low pressure limits. The deviation from the RRKM prediction increases as f₁ is made smaller and k₁ made larger. Of considerable interest is the finding that, if the collision frequency ω for the RRKM plot of k_uni(ω, E) versus ω is multiplied by an energy transfer efficiency factor β_c, the RRKM k_uni(ω, E) versus ω plot may be scaled to match those for the intrinsic non-RRKM, biexponential N( t)/ N(0), plots. This analysis identifies the importance of determining accurate collisional intermolecular energy transfer (IET) efficiencies.

Perspective: chemical dynamics simulations of non-statistical reaction dynamics

Non-statistical chemical dynamics are exemplified by disagreements with the transition state (TS), RRKM and phase space theories of chemical kinetics and dynamics. The intrinsic reaction coordinate (IRC) is often used for the former two theories, and non-statistical dynamics arising from non-IRC dynamics are often important. In this perspective, non-statistical dynamics are discussed for chemical reactions, with results primarily obtained from chemical dynamics simulations and to a lesser extent from experiment. The non-statistical dynamical properties discussed are: post-TS dynamics, including potential energy surface bifurcations, product energy partitioning in unimolecular dissociation and avoiding exit-channel potential energy minima; non-RRKM unimolecular decomposition; non-IRC dynamics; direct mechanisms for bimolecular reactions with pre- and/or post-reaction potential energy minima; non-TS theory barrier recrossings; and roaming dynamics.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Time-resolved photoelectron imaging of iodide–nitromethane (I−·CH3NO2) photodissociation dynamics

Dissociation to reform iodide was found to be non-statistical and is predicted to be limited by intramolecular vibrational energy redistribution.

Chemical Dynamics Simulations of Benzene Dimer Dissociation

Classical chemical dynamics simulations were performed to study the intramolecular and unimolecular dissociation dynamics of the benzene dimer, Bz2 → 2 Bz. The dissociation of microcanonical ensembles of Bz2 vibrational states, at energies E corresponding to temperatures T of 700-1500 K, were simulated. For the large Bz2 energies and large number of Bz2 vibrational degrees of freedom, s, the classical microcanonical (RRKM) and canonical (TST) rate constant expressions become identical. The dissociation rate constant for each T is determined from the initial rate dN(t)/dt of Bz2 dissociation, and the k(T) are well-represented by the Arrhenius eq k(T) = A exp(-E(a)/RT). The E(a) of 2.02 kcal/mol agrees well with the Bz2 dissociation energy of 2.32 kcal/mol, and the A-factor of 2.43 × 10(12) s(-1) is of the expected order-of-magnitude. The form of N(t) is nonexponential, resulting from weak coupling between the Bz2 intramolecular and intermolecular modes. With this weak coupling, large Bz2 vibrational excitation, and low Bz2 dissociation energy, most of the trajectories dissociate directly. Simulations, with only the Bz2 intramolecular modes excited at 1000 K, were also performed to study intramolecular vibrational energy redistribution (IVR) between the intramolecular and intermolecular modes. Because of restricted IVR, the initial dissociation is quite slow, but N(t) ultimately becomes exponential, suggesting an IVR time of 20.7 ps.

Roaming dynamics in ion-molecule reactions: phase space reaction pathways and geometrical interpretation

A model Hamiltonian for the reaction CH4(+) -> CH3(+) + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of time-invariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom NHIMS are unstable periodic orbits which, in conjunction with their stable and unstable manifolds, unambiguously define the (locally) non-recrossing dividing surfaces assumed in statistical theories of reaction rates. By constructing periodic orbit continuation/bifurcation diagrams for two values of the potential function parameter corresponding to late and early transition states, respectively, and using the total energy as another parameter, we dynamically assign different regions of phase space to reactants and products as well as to conventional and roaming reaction pathways. The classical dynamics of the system are investigated by uniformly sampling trajectory initial conditions on the dividing surfaces. Trajectories are classified into four different categories: direct reactive and non-reactive trajectories, which lead to the formation of molecular and radical products respectively, and roaming reactive and non-reactive orbiting trajectories, which represent alternative pathways to form molecular and radical products. By analysing gap time distributions at several energies, we demonstrate that the phase space structure of the roaming region, which is strongly influenced by nonlinear resonances between the two degrees of freedom, results in nonexponential (nonstatistical) decay.

Chemical dynamics simulations of X- + CH3Y → XCH3 + Y- gas-phase S(N)2 nucleophilic substitution reactions. Nonstatistical dynamics and nontraditional reaction mechanisms

Extensive classical chemical dynamics simulations of gas-phase X(-) + CH(3)Y → XCH(3) + Y(-) S(N)2 nucleophilic substitution reactions are reviewed and discussed and compared with experimental measurements and predictions of theoretical models. The primary emphasis is on reactions for which X and Y are halogen atoms. Both reactions with the traditional potential energy surface (PES), which include pre- and postreaction potential energy minima and a central barrier, and reactions with nontraditional PESs are considered. These S(N)2 reactions exhibit important nonstatistical atomic-level dynamics. The X(-) + CH(3)Y → X(-)---CH(3)Y association rate constant is less than the capture model as a result of inefficient energy transfer from X(-)+ CH(3)Y relative translation to CH(3)Y rotation and vibration. There is weak coupling between the low-frequency intermolecular modes of the X(-)---CH(3)Y complex and higher frequency CH(3)Y intramolecular modes, resulting in non-RRKM kinetics for X(-)---CH(3)Y unimolecular decomposition. Recrossings of the [X--CH(3)--Y](-) central barrier is important. As a result of the above dynamics, the relative translational energy and temperature dependencies of the S(N)2 rate constants are not accurately given by statistical theory. The nonstatistical dynamics results in nonstatistical partitioning of the available energy to XCH(3) +Y(-) reaction products. Besides the indirect, complex forming atomic-level mechanism for the S(N)2 reaction, direct mechanisms promoted by X(-) + CH(3)Y relative translational or CH(3)Y vibrational excitation are possible, e.g., the roundabout mechanism.

Quantum chemical calculations of the Cl- + CH3I --> CH3Cl + I- potential energy surface

Electronic structure theory calculations, using MP2 theory and the DFT functionals OPBE, OLYP, HCTH407, BhandH, and B97-1, were performed to characterize the structures, vibrational frequencies, and energies for stationary points on the Cl(-) + CH(3)I --> ClCH(3) + I(-) potential energy surface. The aug-cc-pVDZ and aug-cc-pVTZ basis sets, with an effective core potential (ECP) for iodine, were employed. Single-point CCSD(T) calculations were performed to obtain the complete basis set (CBS) limit for the reaction energies. DFT was found to give significantly longer halide ion/carbon atom bond lengths for the ion-dipole complexes and central barrier transition state than MP2. BhandH, with either the aug-cc-pVDZ or aug-cc-pVTZ basis sets, gives good agreement with the experimental structures for both CH(3)I and CH(3)Cl. The frequencies of CH(3)I and CH(3)Cl, obtained with the different levels of theory and basis sets, are in excellent agreement with experiment. The major difference between the MP2 and DFT frequencies is for the imaginary frequency of the central barrier. Using the aug-cc-pVTZ basis the MP2 value for this frequency ranges from 1.26 to 1.59 times larger than those for the DFT functionals. Thus, the MP2 and DFT theories have different PES shapes in the vicinity of the [Cl--CH(3)--I](-) central barrier. The CCSD(T)/CBS energies are in good agreement with experiments for the complexation energies and reaction exothermicity, with a small 1 kcal/mol difference for the latter. The CCSD(T)/CBS central barrier height is lower than values deduced by using statistical theoretical models to fit the Cl(-) + CH(3)I --> ClCH(3) + I(-) experimental rate constant, which is consistent with the expected nonstatistical dynamics for the reaction. The BhandH energies are in overall best agreement with the CCSD(T) values, with a largest difference of only 0.7 kcal/mol.

Inverse temperature dependent lifetimes of transient S(N)2 ion-dipole complexes

The association and collisional stabilization of the S(N)2 entrance channel complex [Cl(-)...CH3Cl]* is studied in a low-temperature radiofrequency ion trap. The temperature dependence of the ternary rate coefficient is measured and a much stronger inverse temperature dependence than expected from a simple statistical calculation is found. From these data the lifetime of the transient S(N)2 complex has been derived as a function of temperature. It is suggested that the inverse temperature dependent rates of nonsymmetric S(N)2 reactions are related to the observed inverse temperature dependence of the transient ion-dipole complexes.

A direct dynamics trajectory study of F- + CH(3)OOH reactive collisions reveals a major non-IRC reaction path

A direct dynamics simulation at the B3LYP/6-311+G(d,p) level of theory was used to study the F- + CH3OOH reaction dynamics. The simulations are in excellent agreement with a previous experimental study (J. Am. Chem. Soc. 2002, 124, 3196). Two product channels, HF + CH2O + OH- and HF + CH3OO-, are observed. The former dominates and occurs via an ECO2 mechanism in which F- attacks the CH3- group, abstracting a proton. Concertedly, a carbon-oxygen double bond is formed and OH- is eliminated. Somewhat surprisingly this is not the reaction path, predicted by the intrinsic reaction coordinate (IRC), which leads to a deep potential energy minimum for the CH2(OH)2...F- complex followed by dissociation to HF + CH2(OH)O-. None of the direct dynamics trajectories followed this path, which has an energy release of -63 kcal/mol and is considerably more exothermic than the ECO2 path whose energy release is -27 kcal/mol. Other product channels not observed, and which have a lower energy than that for the ECO2 path, are F- + CO + H2 + H2O (-43 kcal/mol), F- + CH2O + H2O (-51 kcal/mol), and F- + CH2(OH)2 (-60 kcal/mol). Formation of the CH3OOH...F- complex, with randomization of its internal energy, is important, and this complex dissociates via the ECO2 mechanism. Trajectories which form HF + CH3OO- are nonstatistical events and, for the 4 ps direct dynamics simulation, are not mediated by the CH3OOH...F- complex. Dissociation of this complex to form HF + CH3OO- may occur on longer time scales.

Gas Phase SN2 Reactions of Halide Ions with Trifluoromethyl Halides: Front- and Back-Side Attack vs. Complex Formation

Density functional theory computations and pulsed-ionization high-pressure mass spectrometry experiments have been used to explore the potential energy surfaces for gas-phase S(N)2 reactions between halide ions and trifluoromethyl halides, X(-) + CF(3)Y --> Y(-) + CF(3)X. Structures of neutrals, ion-molecule complexes, and transition states show the possibility of two mechanisms: back- and front-side attack. From pulsed-ionization high-pressure mass spectrometry, enthalpy and entropy changes for the equilibrium clustering reactions for the formation of Cl(-)(BrCF(3)) (-16.5 +/- 0.2 kcal mol(-1) and -24.5 +/- 1 cal mol(-1) K(-1)), Cl(-)(ICF(3)) (-23.6 +/- 0.2 kcal mol(-1)), and Br(-)(BrCF(3)) (-13.9 +/- 0.2 kcal mol(-1) and -22.2 +/- 1 cal mol(-1) K(-1)) have been determined. These are in good to excellent agreement with computations at the B3LYP/6-311+G(3df)//B3LYP/6-311+G(d) level of theory. It is shown that complex formation takes place by a front-side attack complex, while the lowest energy S(N)2 reaction proceeds through a back-side attack transition state. This latter mechanism involves a potential energy profile which closely resembles a condensed phase S(N)2 reaction energy profile. It is also shown that the Cl(-) + CF(3)Br --> Br(-) + CF(3)Cl S(N)2 reaction can be interpreted using Marcus theory, in which case the reaction is described as being initiated by electron transfer. A potential energy surface at the B3LYP/6-311+G(d) level of theory confirms that the F(-) + CF(3)Br --> Br(-) + CF(4) S(N)2 reaction proceeds through a Walden inversion transition state.

Secondary Kinetic Isotope Effect in Nucleophilic Substitution: A Quantum-Mechanical Approach

Four-dimensional time-independent quantum scattering calculations have been carried out on the perdeuterated exothermic and complex-forming gas-phase S(N)2 reaction Cl- + CD3Br --> ClCD3 + Br- and the reverse process Br- + CD3Cl --> BrCD3 + Cl-, employing a fine energetic resolution to resolve all scattering resonances. The two totally symmetric modes of the methyl group, C-D symmetric stretch and umbrella bend, are explicitly taken into account. Converged state-selected reaction probabilities and product distributions have been calculated up to 2960 cm(-1) above the vibrational ground state of CD3Br, i.e., up to initial vibrational excitation of the second overtone of the umbrella bending vibration. The inverse secondary kinetic isotope effect found experimentally is nicely confirmed by the calculated state-selected reaction probabilities. One contribution to this originates from excitation of the high-frequency symmetric C-D stretching vibration, which increases the reaction probability as a function of translational energy more than the corresponding vibration in the undeuterated system. Although transition state theory (TST) suffices to explain this effect qualitatively, the dynamics of S(N)2 reactions is well-known to show strong nonstatistical features. A striking example is given by the umbrella mode: Contrary to estimates obtained from TST, we find a significant enhancement of the reactivity in the perdeuterated system that is attributed to the increased density of states and the higher number of avoided crossings of the hyperspherical adiabats compared to the undeuterated system. Furthermore, compared to the system Cl- + CH3Cl'/CD3Cl', the influence of tunneling is negligible in this net-barrierless reaction. In the reverse endothermic reaction, the kinetic isotope effect of the umbrella mode is normal.

State-selected dynamics of the complex-forming bimolecular reaction Cl[sup −]+CH[sub 3]Cl[sup ʹ]→ClCH[sub 3]+Cl[sup ʹ−]: A four-dimensional quantum scattering study

Time-independent quantum scattering calculations have been carried out on the Walden inversion S(N)2 reaction Cl(-)+CH(3)Cl(')(v(1),v(2),v(3))-->ClCH(3)(v(1) ('),v(2) ('),v(3) ('))+Cl('-). The two C-Cl stretching modes (quantum numbers v(3) and v(3) (')) and the totally symmetric internal modes of the methyl group (C-H stretching vibration, v(1) and v(1) ('), and inversion bending vibration, v(2) and v(2) (')) are treated explicitly. A four-dimensional coupled cluster potential energy surface is employed. The scattering problem is formulated in hyperspherical coordinates using the exact Hamiltonian and exploiting the full symmetry of the problem. Converged state-selected reaction probabilities and product distributions have been calculated up to 6100 cm(-1) above the vibrational ground state of CH(3)Cl, i.e., up to initial vibrational excitation (2,0,0). In order to extract all scattering resonances, the energetic grid was chosen to be very fine, partly down to a resolution of 10(-12) cm(-1). Up to 2500 cm(-1) translational energy, initial excitation of the umbrella bending vibration, (0,1,0), is more efficient for reaction than exciting the C-Cl stretching mode, (0,0,1). The combined excitation of both vibrations results in a synergic effect, i.e., a considerably higher reaction probability than expected from the sum of both independent excitations, even higher than (0,0,2) up to 1500 cm(-1) translational energy. Product distributions show that the umbrella mode is strongly coupled to the C-Cl stretching mode and cannot be treated as a spectator mode. The reaction probability rises almost linearly with increasing initial excitation of the umbrella bending mode. The effect with respect to the C-Cl stretch is five times larger for more than two quanta in this mode, and in agreement with previous work saturation is found. Exciting the high-frequency C-H stretching mode, (1,0,0), yields a large increase for small energies [more than two orders of magnitude larger than (0,0,0)], while for translational energies higher than 2000 cm(-1), it becomes a pure spectator mode. For combined initial excitations including the symmetric C-H stretch, the spectator character of the latter is even more pronounced. However, up to more than 1500 cm(-1) translational energy, the C-H vibration does not behave adiabatically during the course of reaction, because only 20% of the initial energy is found in the same mode of the product molecule. The distribution of resonance widths and peak heights is discussed, and it is found that individual resonances pertinent to intermediate complexes Cl(-)...CH(3)Cl show product distributions independent of the initial vibrational state of the reactant molecule. The relatively high reactivity, of resonance states with respect to excitation of any mode, found in previous work is confirmed in the present calculations. However, reactivity of intermediate states and reactivity with respect to initial vibrational excitation have to be distinguished. There is a strong mixing between the vibrational states reflected in numerous avoided crossings of the hyperspherical adiabatic curves.

Trajectory studies of S(N)2 nucleophilic substitution. 8. Central barrier dynamics for gas phase Cl(-) + CH(3)Cl

Quasiclassical direct dynamics trajectories, calculated at the MP2/6-31G level of theory, are used to study the central barrier dynamics for the C1(-) + CH(3)Cl S(N)2 reaction. Extensive recrossings of the central barrier are observed in the trajectories. The dynamics of the Cl(-)-CH(3)Cl complex is non-RRKM and transition state theory (TST) is predicted to be an inaccurate model for calculating the Cl(-) + CH(3)Cl S(N)2 rate constant. Direct dynamics trajectories also show that Cl(-) + CH(3)Cl trajectories, which collide backside along the S(N)2 reaction path, do not form the Cl(-)-CH(3)Cl complex. This arises from weak coupling between the Cl(-)-CH(3)Cl intermolecular and CH(3)Cl intramolecular modes. The trajectory results are very similar to those of a previous trajectory study, based on a HF/6-31G* analytic potential energy function, which gives a less accurate representation of the central barrier region of the Cl(-) + CH(3)Cl reaction than does the MP2/6-31G* level of theory used here. Experiments are suggested for investigating the non-RRKM and non-TST dynamics predicted by the trajectories.