Four-dimensional quantum study on exothermic complex-forming reactions: Cl- + CH3Br-->ClCH3+Br-

The exothermic gas-phase bimolecular nucleophilic substitution (S(N)2) reaction Cl(-)+CH(3)Br (upsilon1',upsilon2',upsilon3')-->ClCH(3) (upsilon1,upsilon2,upsilon3)+Br- and the corresponding endothermic reverse reaction have been studied by time-independent quantum scattering calculations in hyperspherical coordinates on a coupled-cluster potential-energy surface. The dimensionality-reduced model takes four degrees of freedom into account [Cl-C and C-Br stretching modes (quantum numbers upsilon3' and upsilon3); totally symmetric modes of the methyl group, i.e., C-H stretching (upsilon1' and upsilon1) and umbrella bending vibrations (upsilon2' and upsilon2)]. Diagonalization of the Hamiltonian was performed employing the Lanczos algorithm with a variation of partial reorthogonalization. A narrow grid in the total energy was employed so that long-living resonance states could be resolved and extracted. While excitation of the reactant umbrella bending mode already leads to a considerable enhancement of the reaction probability, its combination with vibrational excitation of the broken C-Br bond, (0, 1, 1), results in a strong synergic effect that can be rationalized by the similarity with the classical transitional normal mode. Exciting the C-H stretch has a non-negligible effect on the reaction probability, while for larger translational energies this mode follows the expected spectatorlike behavior. Combination of C-Br stretch and symmetric C-H, (1,0,1), stretch does not show a cooperative effect. Contrary to the spectator mode concept, energy originally stored in the C-H stretching mode is by no means conserved, but almost completely released in other modes of the reaction products. Products are most likely formed in states with a high degree of excitation in the new C-Cl bond, while the internal modes of the methyl group are less important. Reactants with combined umbrella/C-Br stretch excitation, (0, 1, 1), may yield products with two quanta in the umbrella mode.     

Four-mode quantum calculations of resonance states in complex-forming bimolecular reactions: C- + CH3Br

The vibrational resonance states of the complexes formed in the nucleophilic bimolecular substitution (S(N)2) reaction Cl(-)+CH(3)Br-->ClCH(3)+Br(-) were calculated by means of the filter diagonalization method employing a coupled-cluster potential-energy surface and a Hamiltonian that incorporates an optical potential and is formulated in Radau coordinates for the carbon-halogen stretching modes. The four-dimensional model also includes the totally symmetric vibrations of the methyl group (C-H stretch and umbrella bend). The vast majority of bound states and many resonance states up to the first overtone of the symmetric stretching vibration in the exit channel complex have been calculated, analyzed, and assigned four quantum numbers. The resonances are classified into entrance channel, exit channel, and delocalized states. The resonance widths fluctuate over six orders of magnitude. In addition to a majority of Feshbach-type resonances there are also exceedingly long-lived shape resonances, which are associated with the entrance channel and can only decay by tunneling. The state-selective decay of the resonances was studied in detail. The linewidths of the resonances, and thus the coupling to the energetic continuum, increase with excitation in any mode. Due to the strong mixing of the many progressions in the intermolecular stretching modes of the intermediate complexes, this increase as a function of the corresponding quantum numbers is not monotonic, but exhibits pronounced fluctuations.     

Theoretical study of the complex-forming CH + H2 --> CH2 + H reaction

The complex-forming CH + H2 --> CH2 + H reaction is studied employing a recently developed global potential energy function. The reaction probability in the total angular momentum J = 0 limit is estimated with a four-atom quantum wave packet method and compared with classical trajectory and statistical theory results. The formation of complexes from different reactant internal states is also determined with wave packet calculations. While there is no barrier to reaction along the minimum energy path, we find that there are angular constraints to complex formation. Trajectory-based estimates of the low-pressure rate constants are made and compared with experimental results. We find that zero-point energy violation in the trajectories is a particularly severe problem for this reaction.     

Reduced dimensionality quantum scattering calculations on the F + CH(4) --> FH + CH(3) reaction

The existence of recently observed scattering resonances in the hydrogen abstraction reaction F + CH4 --> FH + CH3 was investigated using the reduced dimensionality rotating line umbrella (RLU) quantum scattering model and employing an analytical potential energy surface, PES-2006, recently developed by our group. The calculations were performed in hyperspherical coordinates. The wells found in the hyperspherical adiabats, the oscillatory pattern in the cumulative and state-to-state reaction probabilities, the forward/backward predominance in the differential cross section at a collision energy of 1.8 kcal mol(-1), and the dramatic change of the scattering angle with energy are related to scattering resonances, and they are assigned to a quasi-bound complex on the vibrationally adiabatic ground-state potential.     

Hybrid QM/MM molecular dynamics simulations for an ionic SN2 reaction in the supercritical water: OH- + CH3Cl --> CH3OH + Cl-

A hybrid real space quantum mechanical/molecular mechanical (RS-QM/MM) method has been applied to an ionic S(N)2 reaction (OH- + CH3Cl --> CH3OH + Cl-) in water solution to investigate dynamic solvation effects of the supercritical water (SCW) on the reaction. It has been demonstrated that the approaching process of OH- to methyl group is prevented by water molecules in the ambient water (AW), while the reaction takes place easily in the gas phase. Almost the same solvation effect on the dynamics of OH- is observed in the SCW, though the bulk density of water is substantially reduced compared with that of the AW. It has been shown that the solvation of the SCW around the OH anion is locally identical to that of the AW due to the strong ion-dipole interactions between OH- and water molecules. At the transition state, the QM/MM simulations have revealed that the excess electron is quite flexible, and the charge volume, as well as the fractional charges on atoms, vary seriously depending on the instantaneous solvent configurations. However, it has been found that the solvation energy in the SCW can be qualitatively related to the HOMO volume of the system by Born's equation.     

Searching for resonances in the reaction Cl+CH4-->HCl+CH3: quantum versus quasiclassical dynamics and comparison with experiments

A quantum-mechanical (QM) and quasiclassical trajectory (QCT) study was performed on the title reaction, using a pseudotriatomic ab initio based surface. Probabilities and integral cross sections present some clear peaks versus the collision energy E(col), which we assign to Feshbach resonances of the transition state, where the light H atom oscillates between the heavy Cl and CH(3) groups. For ground-state reactants, reactivity is essentially of quantum origin (QCT observables and oscillations are smaller, or much smaller, than QM ones), and the calculated integral cross section and product distributions are in reasonable agreement with the experiment. The reaction occurs through an abstraction mechanism, following both a direct and an indirect mechanism. The quasiclassical trajectory calculations show the participation of a short-lived collision complex in the microscopic reaction mechanism. Finally, QCT differential cross sections of Cl+CH(4)-->HCl (nu(')=0 and 1)+CH(3) oscillate versus E(col), whereas experimentally this only occurs for HCl (nu(')=1). This theoretical result and other oscillating properties found here could, however, be related to the existence of a Feshbach resonance for the production of HCl (nu(')=1), as suggested by experimentalists.     

State-to-state dynamics of the Cl + CH3OH --> HCl + CH2OH reaction

Molecular chlorine, methanol, and helium are co-expanded into a vacuum chamber using a custom designed "late-mixing" nozzle. The title reaction is initiated by photolysis of Cl2 at 355 nm, which generates monoenergetic Cl atoms that react with CH3OH at a collision energy of 1960 +/- 170 cm(-1) (0.24 +/- 0.02 eV). Rovibrational state distributions of the nascent HCl products are obtained via 2 + 1 resonance enhanced multiphoton ionization, center-of-mass scattering distributions are measured by the core-extraction technique, and the average internal energy of the CH3OH co-products is deduced by measuring the spatial anisotropy of the HCl products. The majority (84 +/- 7%) of the HCl reaction products are formed in HCl(v = 0) with an average rotational energy of [Erot] = 390 +/- 70 cm(-1). The remaining 16 +/- 7% are formed in HCl(v = 1) and have an average rotational energy of [Erot] = 190 +/- 30 cm(-1). The HCl(v = 1) products are primarily forward scattered, and they are formed in coincidence with CH2OH products that have little internal energy. In contrast, the HCl(v = 0) products are formed in coincidence with CH2OH products that have significant internal energy. These results indicate that two or more different mechanisms are responsible for the dynamics in the Cl + CH3OH reaction. We suggest that (1) the HCl(v = 1) products are formed primarily from collisions at high impact parameter via a stripping mechanism in which the CH2OH co-products act as spectators, and (2) the HCl(v = 0) products are formed from collisions over a wide range of impact parameters, resulting in both a stripping mechanism and a rebound mechanism in which the CH2OH co-products are active participants. In all cases, the reaction of fast Cl atoms with CH3OH is with the hydrogen atoms on the methyl group, not the hydrogen on the hydroxyl group.     

Seven-dimensional quantum dynamics study of the O(3P)+CH4 reaction

The initial state selected time-dependent wave packet calculations have been carried out to study the title reaction with seven degrees of freedom included by restricting the nonreacting CH(3) group under C(3V) symmetry and the CH bond length in the group. Total reaction probabilities as well as integral cross sections were calculated for the ground and four vibrationally excited reagent states. Our calculation shows that the reactivity is very small for the reaction for collision energy up to 1.0 eV for all the initial states. Initial vibration excitation of CH(4), in particular, the CH stretch excitation, enhances the reactivity, but only part of the excitation energy deposited can be used to reduce the reaction threshold. The rate constant for the ground initial state agrees rather well with that from a recent quasiclassical trajectory study and is larger than that from the semirigid vibrating rotor target calculations, in particular, in the low temperature region. On the other hand, the thermal rate constant calculated from the integral cross sections for these five vibrational states is about a factor of 20 smaller than that from the multiconfiguration time-dependent Hartree study.     

Potential energy surface, kinetics, and dynamics study of the Cl+CH4-->HCl+CH3 reaction

A modified and recalibrated potential energy surface for the gas-phase Cl+CH4-->HCl+CH3 reaction is reported and tested. It is completely symmetric with respect to the permutation of the four methane hydrogen atoms and is calibrated with respect to updated experimental and theoretical stationary point properties and experimental forward thermal rate constants. From the kinetics point of view, the forward and reverse thermal rate constants and the activation energies were calculated using the variational transition-state theory with semiclassical transmission coefficients over a wide temperature range of 150-2500 K. The theoretical results reproduce the available experimental data, with a small curvature of the Arrhenius plot which indicates the role of tunneling in this hydrogen abstraction reaction. A dynamics study was also performed on this PES using quasiclassical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories. First, we found a noticeable internal energy in the coproduct methyl radical, both in the ground-state [CH4 (v=0)] and vibrationally excited [CH4 (v=1)] reactions. This CH3 internal energy was directly precluded in some experiments or oversimplified in previous theoretical studies using pseudotriatomic models. Second, our QCT calculations give HCl rotational distributions slightly hotter than those in experiment, but correctly describing the experimental trend of decreasing the HCl product rotation excitation in going from HCl (v'=0) to HCl (v'=1) for the CH4 (v=1) reaction. Third, the state specific scattering distributions present a reasonable agreement with experiment, although they tend to make the reaction more forward and backward scattered than found experimentally probably because of the hotter rotational distribution and the deficiencies of the QCT methods.     

Nonadiabatic dynamics in the CH3+HCl-->CH4+Cl(2PJ) reaction

Nonadiabatic dynamics in the title reaction have been investigated by 2+1 REMPI detection of the Cl(2P(3/2)) and Cl*(2P(1/2)) products. Reaction was initiated by photodissociation of CH(3)I at 266 nm within a single expansion of a dilute mixture of CH(3)I and HCl in argon, giving a mean collision energy of 7800 cm(-1) in the center-of-mass frame. Significant production of Cl* was observed, with careful checks made to ensure that no additional photochemical or inelastic scattering sources of Cl* perturbed the measurements. The fraction of the total yield of Cl(2P(J)) atoms formed in the J=1/2 level at this collision energy was 0.150+/-0.024, and must arise from nonadiabatic dynamics because the ground potential energy surface correlates to CH(4)+Cl(2P(3/2)) products.     

Imaging the nonadiabatic dynamics of the CH3 + HCl reaction

LAB-frame velocity distributions of Cl-atoms produced in the photoinitiated reaction of CH(3) radicals with HCl have been measured for both the ground Cl ((2)P(3/2)) and excited Cl* ((2)P(1/2)) spin-orbit states using a DC slice velocity-map ion imaging technique. The similarity of these distributions, as well as the average internal excitation of methane co-products for both Cl and Cl* pathways, suggest that all the reactive flux proceeds through the same transition state on the ground potential energy surface (PES) and that the couplings which promote nonadiabatic transitions to the excited PES correlating to Cl* occur later in the exit channel, beyond the TS region. The nature of these couplings is discussed in light of initial vibrational excitation of CH(3) radicals as well as previously reported nonadiabatic reactivity in other polyatomic molecule reactions. Furthermore, the scattering of the reaction products, derived using the photoloc method, suggests that at the high collision energy of our experiment (E(coll) = 22.3 kcal mol(-1)), large impact parameter collisions are favoured with a reduced kinematic constraint on the internal excitation of the methane co-product.     

Seven-dimensional quantum dynamics study of the H+NH3-->H2+NH2 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H+NH3-->H2+NH2 reaction using a seven-dimensional model and an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values. The total reaction probabilities are calculated for the initial ground and seven excited states of NH3 with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants are calculated for the temperature range 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the total reaction probabilities are overall very small, (b) the symmetric and asymmetric NH stretch excitations enhance the reaction significantly and almost all of the excited energy deposited was used to reduce the reaction threshold, (c) the excitation of the umbrella and bending motion have a smaller contribution to the enhancement of reactivity, (d) the main contribution to the thermal rate constants is thought to come from the ground state at low temperatures and from the stretch excited states at high temperatures, and (e) the calculated thermal rate constants are three to ten times smaller than the experimental data and transition state theory results.     

Quantum Monte Carlo study of the reaction: Cl+CH3OH-->CH2OH+HCl

A theoretical study is reported of the Cl+CH3OH-->CH2OH+HCl reaction based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using a DMC trial function constructed as a product of Hartree-Fock and correlation functions, we have computed the barrier height, heat of reaction, atomization energies, and heats of formation of reagents and products. The DMC heat of reaction, atomization energies, and heats of formation are found to agree with experiment to within the error bounds of computation and experiment. M?ller-Plesset second order perturbation theory (MP2) and density functional theory, the latter in the B3LYP generalized gradient approximation, are found to overestimate the experimental heat of reaction. Intrinsic reaction coordinate calculations at the MP2 level of theory demonstrate that the reaction is predominantly direct, i.e., proceeds without formation of intermediates, which is consistent with a recent molecular beam experiment. The reaction barrier as determined from MP2 calculations is found to be 2.24 kcal/mol and by DMC it is computed to be 2.39(49) kcal/mol.     

Ab initio rate constants from hyperspherical quantum scattering: application to H + CH4 --> H2 + CH3

A general and practical procedure is described for calculating rate constants for chemical reactions using a minimal number of ab initio calculations and quantum-dynamical computations. The method exploits a smooth interpolating functional developed in the hyperspherical representation. This functional is built from two Morse functions and depends on a relatively small number of parameters with respect to conventional functionals developed to date. Thus only a small number of ab initio points needs to be computed. The method is applied to the H + CH4 --> H2 + CH3 reaction. The quantum scattering calculations are performed treating explicitly the bonds being broken and formed. All the degrees of freedom except the breaking and forming bonds are optimized ab initio and harmonic vibrational frequencies and zero-point energies for them are calculated at the MP2(full) level with a cc-pVTZ basis set. Single point energies are calculated at a higher level of theory with the same basis set, namely CCSD(T, full). We report state-to-state cross sections and thermal rate constants for the title reaction and make comparisons with previous results. The calculated rate constants are in good agreement with experiments.     

Computational studies on density function theory for the bimolecular metathesis reaction CH3+HCl⇔︁CH4+Cl

Density function theory has been applied to alkyl radical reaction to get helpful data for its geometric parameters, energy, and vibrational frequency compared with results obtained by ab initio methods and experimental values. The geometry optimization of the transition state, the precursor complex and the successor complex were performed at the 6‐311G* basis set level. The transition state of the CH₄Cl system of the reaction computed was in agreement with the prediction of Benson. From analysis of the vibration frequency and the net charge on the atom of the precursor complex, transition state, successor complex and the isolated state, the reaction mechanism was derived which we complicated with the bond‐rupture electron‐transfer theory. The atom H in molecule HCl attacks the atom C, forming a transition state via the precursor complex and the electron transfer happens in the precursor complex. The reaction rate of the electron transfer determines the rate of the whole reaction to a certain extent, and active energy, electronic coupling matrix element, and reorganization energy were obtained. © 2001 Wiley Periodicals, Inc. Int J Quantum Chem, 2001     

Accurate potential energy surface and quantum reaction rate calculations for the H+CH4-->H2+CH3 reaction

Calculations for the cumulative reaction probability N(E) (for J=0) and the thermal rate constant k(T) of the H+CH(4)-->H(2)+CH(3) reaction are presented. Accurate electronic structure calculations and a converged Shepard-interpolation approach are used to construct a potential energy surface which is specifically designed to allow the precise calculation of k(T) and N(E). Accurate quantum dynamics calculations employing flux correlation functions and multiconfigurational time-dependent Hartree wave packet propagation compute N(E) and k(T) based on this potential energy surface. The present work describes in detail the various convergence test performed to investigate the accuracy of the calculations at each step. These tests demonstrate the predictive power of the present calculations. In addition, approximate approaches for reaction rate calculations are discussed. A quite accurate approximation can be obtained from a potential energy surface which includes only interpolation points on the minimum energy path.     

Seven dimensional quantum dynamics study of the H2+NH2-->H+NH3 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H2+NH2-->H+NH3 reaction using a seven dimensional model on an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values and nonreactive NH2 group keeps C2v symmetry and the rotation-vibration coupling in NH2 is neglected. The total reaction probabilities are calculated when the two reactants are initially at their ground states, when the NH2 bending mode is excited, and when H2 is on its first vibrational excited state, with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants and equilibrium constants are calculated for the temperature range of 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the reaction is dominated by ground-state reactivity and the main contribution to the thermal rate constants is thought to come from this state, (b) the excitation energy of H2 was used to enhance reactivity while the excitation of the NH2 bending mode hampers the reaction, (c) the calculated thermal rate constants are very close to the experimental data and transition state theory results at high and middle temperature, while they are ten times higher than that of transition state theory at low temperature (T=200 K), and (d) the equilibrium constants results indicate that the approximations applied may have different roles in the forward and reverse reactions.     

Reduced dimensionality quantum dynamics of Cl + CH4 --> HCl + CH3 on an ab initio potential

We study the reaction Cl + CH(4)--> HCl + CH(3) using a 2-D potential energy surface obtained by fitting a double Morse analytical function to high level (CCSD(T)/cc-pVTZ//MP2/cc-pVTZ)ab initio data. Dynamics simulations are performed in hyperspherical coordinates with the close-coupled equations being solved using R-matrix propagation. Quantum contributions from spectator modes are included via a harmonic zero-point correction to the ab initio data prior to fitting the potential. This is the first time this method has been applied to a heavy-light-heavy reaction and the first time it has been used to study differential cross sections. We find thermal rate constants and state-to-state differential cross sections which are in good agreement with experimental data. We discuss the applicability of our method to the study of kinetic isotope effects (KIEs), which we derive for the CH(4)/CD(4) substitution. The calculated KIE compares favourably with experiment. Finally, we discuss the sensitivity of the results of dynamics simulations on the accuracy of the fitted potential.     

Reaction‐path dynamics and theoretical rate constants for the reaction CH4 + O3 → HOOO + CH3

We present a direct ab initio dynamics study of thermal rate constants of the hydrogen abstraction reaction of CH₄ + O₃ → HOOO +CH₃. The geometries of all the stationary points are optimized at MPW1K/6‐31+G(d,p), MPWB1K/6‐31+G(d,p), and BHandHLYP/6‐31+G(d,p) levels of theory. The energies are refined at a multi‐high‐level method. The extended Arrhenius expression fitted from the CVT/SCT and μVT/Eckart rate constants of ozonolysis of methane in the temperature range 200–2500 K are k^CVT/SCT(T) = 5.96 × 10^?29T^4.49e^(?17321.3/T) and k^μVT/Eckart(T) = 7.92 × 10^?29T^4.46e^(?17301.7/T), respectively. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

CH3NHNH2 + OH reaction: Mechanism and dynamics studies

A direct dynamics study was carried out for the multichannel reaction of CH₃NHNH₂ with OH radical. Two stable Conformers (I, II) of CH₃NHNH₂ are identified by the rotation of the ? CH₃ group. For each conformer, five hydrogen‐abstraction channels are found. The reaction mechanisms of product radicals (CH₃NNH₂ and CH₃NHNH) with OH radical are also investigated theoretically. The electronic structure information on the potential energy surface is obtained at the B3LYP/6‐311G(d,p) level and the energetics along the reaction path is refined by the BMC‐CCSD method. Hydrogen‐bonded complexes are presented at both the reactant and product sides of the five channels, indicating that the reaction may proceed via an indirect mechanism. The influence of the basis set superposition error (BSSE) on the energies of all the complexes is discussed by means of the CBS‐QB3 method. The rate constants of CH₃NHNH₂ + OH are calculated using canonical variational transition‐state theory with the small‐curvature tunneling correction (CVT/SCT) in the temperature range of 200–1000 K. Slightly negative temperature dependence of rate constant is found in the temperature range from 200 to 345 K. The agreement between the theoretical and experimental results is good. It is shown that for Conformer I, hydrogen‐abstraction from ? NH? position is the primary pathway at low temperature; the hydrogen‐abstraction from ? NH₂ is a competitive pathway as the temperature increases. A similar case can be concluded for Conformer II. The overall rate constant is evaluated by considering the weight factors of each conformer from the Boltzmann distribution function, and the three‐term Arrhenius expressions are fitted to be k_T = 1.6 × 10^?24T^4.03exp (1411.5/T) cm³ molecule^?1 s^?1 between 200–1000 K. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009