Exact state-to-state quantum dynamics of the F + HD --> HF(v' = 2) + D reaction on model potential energy surfaces

In this paper, we present the results of a theoretical investigation on the dynamics of the title reaction at collision energies below 1.2 kcal/mol using rigorous quantum reactive scattering calculations. Vibrationally resolved integral and differential cross sections, as well as product rotational distributions, have been calculated using two electronically adiabatic potential energy surfaces, developed by us on the basis of semiempirical modifications of the entrance channel. In particular, we focus our attention on the role of the exothermicity and of the exit channel region of the interaction on the experimental observables. From the comparison between the theoretical results, insight about the main mechanisms governing the reaction is extracted, especially regarding the bimodal structure of the HF(v = 2) nascent rotational state distributions. A good overall agreement with molecular beam scattering experiments has been obtained.     

Anatomy of the S(1D) + H2 reaction: the dynamics on two new potential energy surfaces from quantum dynamics calculations

We present exact quantum integral and differential cross sections for the title reaction from a time-dependent wavepacket method which takes account of all Coriolis couplings. We employ two new potential energy surfaces fitted using the double many-body expansion (DMBE) method. The difference between the two surfaces is that for the first the data was extrapolated to the complete basis set limit (CBS) and for the second the data was corrected semi-empirically (SEC). While the DMBE/CBS surface is, on first impressions, regarded as the most accurate, our results show that this surface gives consistent smaller cross section when compared to previous results employing an earlier surface, named Ho after its first author. We also find that the DMBE/CBS surface features an unphysical barrier for contracted H(2) distances which explains the smaller results. The DMBE/SEC surface, which is based on the same data, does not show the same barrier and the results compare much better to previous theoretical results as well as those from experiment. While we find that overall the differential cross sections from the DMBE/SEC surface are forward scattered, which is in line with experiment, the cross sections do not rise steeply enough with decreasing energy showing that this surface is not sufficiently attractive at low energies. We find this is due to a shallow van der Waals well present for the Ho surface but not on the DMBE surfaces.     

Exact quantum calculations of the kinetic isotope effect: cross sections and rate constants for the F+HD reaction and role of tunneling

In this paper we present integral cross sections (in the 5-220 meV collision energy range) and rate constants (in the 100-300 K range of temperature) for the F+HD reaction leading to HF+D and DF+H. The exact quantum reactive scattering calculations were carried out using the hyperquantization algorithm on an improved potential energy surface which incorporates the effects of open shell and fine structure of the fluorine atom in the entrance channel. The results reproduce satisfactorily molecular beam scattering experiments as well as chemical kinetics data for both the HF and DF channels. In particular, the agreement of the rate coefficients and the vibrational branching ratios with experimental measurements is improved with respect to previous studies. At thermal and subthermal energies, the rates are greatly influenced by tunneling through the reaction barrier. Therefore exchange of deuterium is shown to be penalized with respect to exchange of hydrogen, and the isotopic branching exhibits a strong dependence on translational energy. Also, it is found that rotational excitation of the reactant HD molecule enhances the production of HF and decreases the reactivity at the D end, obtaining insight on the reaction stereodynamics.     

Cross sections and rate constants for OH + H2 reaction on three different potential energy surfaces for ro-vibrationally excited reagents

A systematic study of the reagent ro-vibrational excitations in H(2) + OH reaction is presented on three different potential energy surfaces using the multiconfiguration time-dependent Hartree method. An exact form of the kinetic energy operator including Coriolis coupling has been used. Coupled channel results on WDSE surface for vibrational excitation of H(2) produce very large cross sections in accordance with the previous approximate results. The rate constant obtained for H(2)(v = 1) at 300 K on the YZCL2 surface shows an excellent agreement with the most recent experimental result. Quantum dynamical results for ro-vibrational excitation of reagents obtained on the WSLFH surface show similar behavior to previous quasiclassical trajectory studies. The integral cross sections obtained for excited reagent rotations exhibit contrasting trends on the three surfaces. The effects are explained considering the different orientations of the transition state structure and the individual surface characteristics.     

Using a family of dividing surfaces normal to the minimum energy path for quantum instanton rate constants

One of the outstanding issues in the quantum instanton (QI) theory (or any transition-state-type theory) for thermal rate constants of chemical reactions is the choice of an appropriate "dividing surface" (DS) that separates reactants and products. (In the general version of the QI theory, there are actually two dividing surfaces involved.) This paper shows one simple and general way for choosing DSs for use in QI theory, namely, using the family of (hyper) planes normal to the minimum energy path on the potential energy surface at various distances s along it. Here the reaction coordinate is not one of the dynamical coordinates of the system (which will in general be the Cartesian coordinates of the atoms), but rather simply a parameter which specifies the DS. It is also shown how this idea can be implemented for an N atom system in three-dimensional space in a way that preserves overall translational and rotational invariance. Numerical application to a simple system (the collinear H+H(2) reaction) is presented to illustrate the procedure.     

Exploring potential energy surfaces for chemical reactions: an overview of some practical methods

Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.     

On the role of scattering resonances in the F+HD reaction dynamics

We study scattering resonances in the F+HD-->HF+D reaction using a new method for direct evaluation of the lifetime Q-matrix [Aquilanti et al., J. Chem. Phys. 2005, 123, 054314]. We show that most of the resonances are due to van der Waals states in the entrance and exit reaction channels. The metastable states observed in the product reaction channel are assigned by calculating the energy levels and wave functions of the HF...D van der Waals complex. The behavior of resonance energies, widths, and decay branching ratios as functions of total angular momentum is analyzed. The effect of isotopic substitution on resonance energies and lifetimes is elucidated by comparison with previous results for the F+H2 reaction. It is demonstrated that HF(v'=3) products near threshold are formed by decay of the narrow resonances supported by van der Waals wells in the exit channel. State-to-state differential cross sections in the HF(v'=3) channel exhibit characteristic forward-backward peaks due to the formation of a long-lived metastable complex. The role of the exit-channel resonances in the interpretation of molecular beam experiments is discussed.     

An ab initio spin-orbit-corrected potential energy surface and dynamics for the F + CH4 and F + CHD3 reactions

We report an analytical ab initio three degrees of freedom (3D) spin-orbit-correction surface for the entrance channel of the F + methane reaction obtained by fitting the differences between the spin-orbit (SO) and non-relativistic electronic ground state energies computed at the MRCI+Q/aug-cc-pVTZ level of theory. The 3D model surface is given in terms of the distance, R(C-F), and relative orientation, Euler angles ? and θ, of the reactants treating CH(4) as a rigid rotor. The full-dimensional (12D) "hybrid" SO-corrected potential energy surface (PES) is obtained from the 3D SO-correction surface and a 12D non-SO PES. The SO interaction has a significant effect in the entrance-channel van der Waals region, whereas the effect on the energy at the early saddle point is only ～5% of that at the reactant asymptote; thus, the SO correction increases the barrier height by ～122 cm(-1). The 12D quasiclassical trajectory calculations for the F + CH(4) and F + CHD(3) reactions show that the SO effects decrease the cross sections by a factor of 2-4 at low collision energies and the effects are less significant as the collision energy increases. The inclusion of the SO correction in the PES does not change the product state distributions.     

Study of the H+O2 reaction by means of quantum mechanical and statistical approaches: the dynamics on two different potential energy surfaces

The possible existence of a complex-forming pathway for the H+O(2) reaction has been investigated by means of both quantum mechanical and statistical techniques. Reaction probabilities, integral cross sections, and differential cross sections have been obtained with a statistical quantum method and the mean potential phase space theory. The statistical predictions are compared to exact results calculated by means of time dependent wave packet methods and a previously reported time independent exact quantum mechanical approach using the double many-body expansion (DMBE IV) potential energy surface (PES) [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)] and the recently developed surface (denoted XXZLG) by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. The statistical approaches are found to reproduce only some of the exact total reaction probabilities for low total angular momenta obtained with the DMBE IV PES and some of the cross sections calculated at energy values close to the reaction threshold for the XXZLG surface. Serious discrepancies with the exact integral cross sections at higher energy put into question the possible statistical nature of the title reaction. However, at a collision energy of 1.6 eV, statistical rotationally resolved cross sections managed to reproduce the experimental cross sections for the H+O(2)(v=0,j=1)-->OH(v(')=1,j('))+O process reasonably well.     

MNDO Study of reaction pathways for SN2 reactions. Menschutkin reaction potential energy surfaces

MNDO molecular orbital calculations have been employed to investigate limited reaction pathways and potential energy surfaces for a series of S_N2 reactions. Model calculations for X^? + CH₃X (X = H, F, OH, OCH₃, and CN) indicate that the MNDO method gives qualitative agreement with ab initio studies except for the hydride–CH₄ exchange. Studies involving alkylation of pyridine (Menschutkin reaction) were also carried out. For the reaction of pyridine with CH₃Cl, which involves charge separation, our MNDO studies (which do not include solvation effects) do not produce a characteristic S_N2 pathway. For the reaction of pyridine with trimethyloxonium cation [(CH₃)₃O⁺] as the alkylating agent, a well defined S_N2 reaction pathway was obtained; this reaction involves charge transfer. A potential energy surface for the pyridine–trimethyloxonium cation reaction shows the presence of a saddle point transition state that resembles starting materials, in agreement with the Hammond postulate for this exothermic reaction.     

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.     

State-to-state quantum dynamics calculations of the C + OH reaction on the second excited potential energy surface

Accurate three-dimensional quantum-mechanical scattering calculations using a time-indepedent hyperspherical method have been performed for the C((3)P) + OH(X(2)Π) → CO(a(3)Π) + H((2)S) reaction on the second excited potential energy surface of 1(4)A″ symmetry. State-to-state reaction probabilities at a total angular momentum J = 0 have been computed in a wide range of collision energies. Many pronounced resonances have been found, espcially at low energy. The product vibrational distributions are noninverted. The present results therefore suggest that the title reaction proceeds via a long-lived intermediate complex. An approximate quantum-mechanical rate constant has also been calculated, and large differences are observed with the quasi-classical trajectory prediction.     

An improved potential energy surface for the F+H2 reaction

A new ground state potential energy surface has been developed for the F+H₂ reaction. Using the UCCSD(T) method, ab initio calculations were performed for 786 geometries located mainly in the exit channel of the reaction. The new data was used to correct exit channel errors that have become apparent in the potential energy surface of Stark and Werner [J. Chem. Phys. 104 (1996) 6515]. While the entrance channel and saddlepoint properties of the Stark–Werner surface are unchanged on the new potential, the exit channel behavior is more satisfactory. The exothermicity on the new surface is much closer to the experimental value. The new surface also greatly diminishes the exit channel van der Waals well that was too pronounced on the Stark–Werner surface. Several preliminary dynamical scattering calculations were carried out using the new surface for total angular momentum equal to zero for F+H₂ and F+HD. It is found that gross features of the reaction dynamics are quite similar to those predicted by the Stark–Werner surface, in particular the reactive resonance for F+HD and F+H₂ survive. However, the most of the exit channel van der Waals resonances disappear on the new surface. It is predicted that the differential cross-sections at low collision energy for the F+H₂ reaction may be drastically modified from the predictions based on the Stark–Werner surface.     

An eight-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction on a new modified potential energy surface

An eight-dimensional time-dependent quantum dynamics wave packet approach is performed for the study of the H2+C2H-->H+C2H2 reaction system on a new modified potential energy surface (PES) [L.-P. Ju et al., Chem. Phys. Lett. 409, 249 (2005)]. This new potential energy surface is obtained by modifying Wang and Bowman's old PES [J. Chem. Phys. 101, 8646 (1994)] based on the new ab initio calculation. This new modified PES has a much lower transition state barrier height at 2.29 kcal/mol than Wang and Bowman's old PES at 4.3 kcal/mol. This study shows that the reactivity for this diatom-triatom reaction system is enhanced by vibrational excitations of H2, whereas the vibrational excitations of C2H only have a small effect on the reactivity. Furthermore, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. The comparison of the rate constant between this calculation and experimental results agrees with each other very well. This comparison indicates that the new modified PES corrects the large barrier height problem in Wang and Bowman's old PES.     

Global dynamics and transition state theories: Comparative study of reaction rate constants for gas-phase chemical reactions

In this review article, we present a systematic comparison of the theoretical rate constants for a range of bimolecular reactions that are calculated by using three different classes of theoretical methods: quantum dynamics (QD), quasi-classical trajectory (QCT), and transition state theory (TST) approaches. The study shows that the difference of rate constants between TST results and those of the global dynamics methods (QD and QCT) are seen to be related to a number of factors including the number of degrees-of-freedom (DOF), the density of states at transition state (TS), etc. For reactions with more DOF and higher density of states at the TS, it is found that the rate constants from TST calculations are systematically higher than those obtained from global dynamics calculations, indicating large recrossing effect for these systems. The physical insight of this phenomenon is elucidated in the present review.     

Gas phase kinetic and quantum chemical studies of the reactions of silylene with the methylsilanes. Absolute rate constants, temperature dependences, RRKM modelling and potential energy surfaces

Time resolved studies of silylene, SiH2, generated by the 193 nm laser flash photolysis of phenylsilane, have been carried out to obtain rate coefficients for its bimolecular reactions with methyl-, dimethyl- and trimethyl-silanes in the gas phase. The reactions were studied over the pressure range 3-100 Torr with SF6 as bath gas and at five temperatures in the range 300-625 K. Only slight pressure dependences were found for SiH2+MeSiH3(485 and 602 K) and for SiH2+Me2SiH2(600 K). The high pressure rate constants gave the following Arrhenius parameters: [TABLE: SEE TEXT]. These are consistent with fast, near to collision-controlled, association processes. RRKM modelling calculations are consistent with the observed pressure dependences (and also the lack of them for SiH2+Me3SiH). Ab initio calculations at both second order perturbation theory (MP2) and coupled cluster (CCSD(T)) levels, showed the presence of weakly-bound complexes along the reaction pathways. In the case of SiH2+MeSiH3 two complexes, with different geometries, were obtained consistent with earlier studies of SiH2+SiH4. These complexes were stabilised by methyl substitution in the substrate silane, but all had exceedingly low barriers to rearrangement to product disilanes. Although methyl groups in the substrate silane enhance the intrinsic SiH2 insertion rates, it is doubtful whether the intermediate complexes have a significant effect on the kinetics. A further calculation on the reaction MeSiH+SiH4 shows that the methyl substitution in the silylene should have a much more significant kinetic effect (as observed in other studies).     

Collision theory thermal rate constants for H + H2 reactions on the SLTH potential surface

Rate constants for the reactions H + D₂ → HD + D and D + H₂ → HD + D were computed from collision theory using an excitation function derived assuming that reaction proceeds vibrationally adiabatically on the SLTH potential surface at fixed approach angles with reaction probability described by the line-of-centers model and an angle-dependent barrier. Most of the experimentally observed steric factor is accounted for by the excitation function of this model. The computed increase of activation energy with temperature can be understood as the consequence of opening up the cone of acceptance for the incoming atom with increasing relative translational energy.     

Ab initio potential energy surfaces of the ion-molecule reaction: C2H2 + O+

High level ab initio calculations using complete active space self-consistent field and multi reference single and double excitation configuration interaction methods with cc-pVDZ (correlation consistent polarized valence double zeta) and cc-pVTZ (triple zeta) basis sets have been performed to elucidate the reaction mechanism of the ion-molecule reaction, C2H2(1Sigmag+) + O+(4S), for which collision experiment has been performed by Chiu et al. [J. Chem. Phys. 109, 5300 (1998)]. The minor low-energy process leading to the weak spin-forbidden product C2H2+ (2Piu) + O(1D) has been studied previously and will not be discussed here. The major pathways to form charge-transfer (CT) products, C2H2+ (2Piu) + O(3P) (CT1) and C2H2+ (4A2) + O(3P) (CT2), and the covalently bound intermediates are investigated. The approach of the oxygen atom cation to acetylene goes over an energy barrier TS1 of 29 kcal/mol (relative to the reactant) and adiabatically leads the CT2 product or a weakly bound intermediate Int1 between CT2 products. This transition state TS1 is caused by the avoided crossing between the reactant and CT2 electronic states. As the C-O distance becomes shorter beyond the above intermediate, the C1 reaction pathway is energetically more favorable than the Cs pathway and goes over the second transition state TS2 of a relative energy of 39 kcal/mol. Although this TS connects diabatically to the covalent intermediate Int2, there are many states that interact adiabatically with this diabatic state and these lead to the other charge-transfer product CT1 via either of several nonadiabatic transitions. These findings are consistent with the experiment, in which charge transfer and chemical reaction products are detected above 35 and 39 kcal/mol collision energies, respectively.