Time-dependent quantum wave packet studies of the F+HCl and F+DCl reactions

Nuclear wave-packet-propagation-based study of the electron-coupled, proton-transfer process in the charge-transfer state of FHCl exhibiting three electronic states in full-dimensional space

The charge-transfer (CT) excited state of FHCl (F⁺H-Cl^-), generated by the photodetachment of an electron from its precursor anion (FHCl^-) by a photon energy of ∼9.5 eV, is a realistic prototype of two bidirectional-coupled reaction pathways, namely the proton-transfer (PT) and electron-transfer (ET) channels, that produce F + HCl and FH + Cl combinations, respectively. The early-time dynamics of the CT was studied via the time-dependent propagations of nuclear wave packets comprising three nonadiabatically coupled electronic states defined within a three-dimensional space. The detailed analyses of the early-time dynamics revealed an interesting phenomenon in which the onset of PT was ∼80 fs earlier than that of ET, indicating that PT dominated ET in this case. A more significant finding was that the proper adjustment of the electronic-charge distribution for the onset of ET was obtained ∼80 fs after the onset of PT; this adjustment was mediated by the initial movement of the H atom, i.e., the F-H vibration mode. To avail experimental observables, the branching ratio, χ = PT/(PT + ET), and absorption spectrum generating the neutral FHCl molecule from its precursor anion were also simulated. The results further demonstrated the dependences of the χs and spectrum on the change in the initial vibration level of the precursor anion, as well as the isotopic substitution of the connecting H atom with deuterium, tritium, and muonium.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Ring-polymer molecular dynamical calculations for the F + HCl → HF + Cl reaction on the ground 12A' potential energy surface

The reaction kinetics of the heavy-light-heavy abstraction reaction F + HCl → HF + Cl on the ground electronic state potential energy surface (PES) is investigated theoretically by a recently developed ring polymer molecular dynamics (RPMD) approach. First, a new PES is developed by the permutation invariant polynomial neural network (PIP-NN) approach based on 30 620 points sampled over a large configuration space from the latest and most accurate Deskevich-Hayes-Takahashi-Skodje-Nesbitt (DHTSN) PES (J. Chem. Phys., 2006, 124, 224303). Excellent fitting performance was achieved with only 521 parameters. The PIP-NN PES is 11 times faster than the DHTSN PES. Besides, the first analytical derivatives with respect to the coordinates of the atoms have been obtained for the PIP-NN PES. The RPMD rate coefficients on the PIP-NN PES are calculated and compared with available theoretical and experimental results. It is found that the experimental rate coefficients are significantly larger than the theoretical results on the DHTSN PES, due to its overestimated reaction barrier. We conclude that a reliable PES for this important heavy-light-heavy reaction is highly desirable.

Revisiting the F + HCl → HF + Cl reaction using a multireference coupled-cluster method

A potential energy surface for the title reaction is constructed using a multireference coupled-cluster method, giving rate constant in excellent agreement with experiments.

Product rotational angular momentum polarization of H+FCl (v=0-5; j=0, 3, 6, 9) → HF+Cl and HCl+F at Erel=0.5-20 kcal mol(-1)

The rotational angular momentum polarizations of product molecules of the title reactions on the ground potential energy surface 1 (2)A' of DHTSN [Deskevic et al. J Chem Phys 2006, 124, 224303] have been studied using the quasi-classical trajectory method. Reaction dynamic results of the HF product channel comparing with another channel of HCl with 100,000 trajectories can be accurately resolved. We show the value of the polar p(ϑr) in the range of 0° ≤ ϑr ≤ 180(°), azimuthal p(φr) in the range of 0° ≤ φr ≤ 360(°), and dihedral p(ϑr, φr) in the ranges of 0(°) ≤ ϑr ≤ 180(°) and 0(°) ≤ φr ≤ 360(°); the angular distributions of the product molecules HF and HCl at relative Erel = 0.5, 1, 2, 5, 10, 15, and 20 kcal mol(-1); and four polarization-dependent differential cross sections (PDDCSs) of HF and HCl at Erel = 0.5, 1, 2, 5, 10, and 15 kcal mol(-1). p(φr) distributions at v = 0-5, and j = 0, 3, 6, 9 at every Erel are plotted cylindrically together. The stereo dynamic transformation reaction dependent upon the rovibrational states of the reactant molecule FCl and its relative translational energies around 0.5-5 kcal mol(-1) can be significantly differentiated. Translational and rovibrational enhancements of the title reactions on both early barrier potential energy surfaces have been shown in great detail and clarified. Reaction mechanisms of forward and backward scattering of the product molecules HF and HCl, respectively, have been obtained. Graphical Abstract H + FCl → either HF + Cl (left) or HCl + F (right) is moving along a trajectory on the respective PES.

Quantum mechanical calculations of state-to-state cross sections and rate constants for the F + DCl → Cl + DF reaction

We present accurate state-to-state quantum wave packet calculations of integral cross sections and rate constants for the title reaction. Calculations are carried out on the best available ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged state-to-state reaction cross sections have been calculated for collision energies up to 0.5 eV and different initial rotational and vibrational excitations, DCl(v = 0, j = 0 - 1; v = 1, j = 0). Also, initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-400 K. It is found that the initial rotational excitation of the DCl molecule does not enhance reactivity, in contract to the reaction with the isotopologue HCl in which initial rotational excitation produces an important enhancement. These differences between the isotopologue reactions are analyzed in detail and attributed to the presence of resonances for HCl(v = 0, j), absent in the case of DCl(v = 0, j). For vibrational excited DCl(v = 1, j), however, the reaction cross section increases noticeably, what is also explained by another resonance.

Vibrational excitation influence on the H + BrO → HBr + O reaction: a quasi-classical trajectory investigation

Quasi-classical trajectory calculations are employed to investigate the vibrational excitation effect on the scalar and vector properties of the H + BrO → HBr + O reaction using a X1A′ state ab initio potential energy surface (J. Chem. Phys. 2000, 113, 4598). The reaction probability, cross section, and rate constant are carried out with the effect of the collision energy (Ecol = 0.1–6 kcal/mol) and vibrational levels (v = 0–3). A significant vibrational dependency has been observed in the reaction probability and cross section at a relatively low collision energy area and has also been found in a low-temperature (T < 150 K) region of the rate constant. In addition, two product angular distributions, P(θr) and P(ϕr), and two generalized polarization-dependent differential cross sections, PDDCS00 and PDDCS20, are calculated as well. All of these scalar and vector properties have shown sensitive behaviors to the vibrational levels.

Time-dependent wave packet quantum scattering and quasi-classical trajectory calculations of the H + FCl(v=0,j=0) → HF + Cl/HCl + F reaction

The dynamics of the title reaction are investigated using both time-dependent wave packet quantum scattering and quasi-classical trajectory (QCT) methods on adiabatic ground 1(2)A' potential energy surface (PES). Compared with the quantum results of reaction probabilities of H + FCl(J=0) → HF + Cl/HCl + F, the QCT method is proven feasible and further employed to produce integral cross sections and rate constants. Significant resonance structures are observed in the reaction probabilities using the quantum method; however, there are some undulations in the calculated QCT integral cross sections for both product channels. A comparison between the quantum mechanical coupled-channel (CC) calculation and centrifugal sudden approximation calculation reveals the very important role of Coriolis coupling effects in the quantum calculation. Comparisons between the calculated thermal rate constants for both reactions and the previous theoretical and experimental results have been done. HCl product formation is favored over the HF product in the reactive system. Finally, the HF products are found to be mainly forward scattering, and the HCl products are mainly backward scattering.

Accurate quantum wave packet calculations for the F + HCl → Cl + HF reaction on the ground 1(2)A' potential energy surface

We present converged exact quantum wave packet calculations of reaction probabilities, integral cross sections, and thermal rate coefficients for the title reaction. Calculations have been carried out on the ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged wave packet reaction probabilities at selected values of the total angular momentum up to a partial wave of J = 140 with the HCl reagent initially selected in the v = 0, j = 0-16 rovibrational states have been obtained for the collision energy range from threshold up to 0.8 eV. The present calculations confirm an important enhancement of reactivity with rotational excitation of the HCl molecule. First, accurate integral cross sections and rate constants have been calculated and compared with the available experimental data.

PRODUCT ROTATIONAL ANGULAR MOMENTUM POLARIZATION IN REACTIONS D + FCl(v = 0,j = 0) → DCl + F, DF + Cl

A comparative quasi-classical trajectory study on the product alignment and orientation of reactions D + FCl (v,j) → DCl + F , DF + Cl are carried out on a recently computed 12A′ ground-state surface reported by Deskevich et al. The reaction probabilities, integral and differential cross-sections as a function of collision energy are presented. The differential cross-sections and 〈P2(j′ ⋅ k)〉 are governed by different reaction mechanisms for these two reactions. P(θr) and P(ϕr) distributions of products DCl and DF at four selected collision energies of 5, 10, 16 and 30 kcal/mol indicate that DCl and DF product molecules are not only aligned, but also oriented along y-axis. By comparing the P(θr) and P(ϕr) distributions of reactions H + FCl (v = 0,j = 0) → HCl + F and H + FCl (v = 0,j = 0) → HF + Cl , mass factor has some influence on stereodynamics of the title reactions, but the features of PES should have major influence on the difference between dynamics of reactions D + FCl (v = 0,j = 0) → DCl + F and D + FCl (v = 0,j = 0) → DF + Cl .

A QUASI-CLASSICAL TRAJECTORY STUDY ON STEREODYNAMICS OF THE F + HCl (v = 0, j = 0) → HF + Cl REACTION

Quasiclassical trajectory (QCT) calculations for the title reaction are carried out by employing the recent developed accurate potential energy surface of the 12A′ ground state. Two angular distributions, P(θr) and P(ϕr), with θr, ϕr being the polar angles of the product angular momentum, and two commonly used polarization dependent differential cross sections, (2π/σ)(dσ00/dωt) and (2π/σ)(dσ20/dωt), with ωt being the polar coordinates of the product velocity, are generated in the center-of-mass frame. It was found that the product rotational angular momentum j′ is not only aligned, but also oriented along the negative direction of y-axis. We also investigated the product state distributions in the present work, and found that the vibrational and rotational state distributions are inverted. Influences of collision energies on the product polarization and state distributions are also shown and discussed.

STRONG VIBRATIONAL ENHANCEMENT OF SUBSTANTIALLY ENDOTHERMIC REACTION K + HF: A TIME-DEPENDENT QUANTUM WAVE PACKET STUDY

Detailed dynamics of the substantially endothermic reaction K + HF on a new ab initio ground potential energy surface has been studied by means of time-dependent quantum wave packet calculation. The calculations showed that the reaction could be significantly enhanced by vibrational excitation of HF , but not very sensitive to initial rotational excitation. The relative and absolute integral cross sections and the logarithm of the σ(v = 1)/σ(v = 0) ratio have been calculated and compared with available experimental and theoretical results. Relatively good agreement with experiment and other calculations was obtained. Reaction rate constants of this reaction was also calculated and discussed.

Product rotational angular momentum polarization in the H+FCl(v=0-5, j=0, 3, 6, 9)→HF+Cl reaction

The product alignment and orientation of the title reaction on the ground potential energy surface of 1 (2)A' have been studied using the quasi-classical trajectory method. The calculations were carried out for case (a) at collision energies of 0.5-20 kcal mol(-1) with the initially rovibrational state of the reagent FCl molecule being at the v = 0 and j = 0 level to especially reveal in detail the dependence of the product integral cross section on collision energy. Further calculations at the collision energy of 15 kcal mol(-1) for case (b) at v = 0-5, and j = 0, and (c) at v = 0, and j = 3, 6, 9 initial states were carried out to reveal the effect of initially vibrational and rotational excitations on stereodynamics, respectively. Possessing final relative velocity k' (defined as a vector in the xz-plane), product alignment perpendicular to the reagent relative velocity vector k (defined as z- or parallel to the z-axis), for case (a) is found to be weaker at all collision energies, for case (b) is found to be vibrationally enhanced by the reactant molecule FCl, but for case (c), rather insensitive to initially rotational excitation. The rotational vector of product molecular orientation pointing to either negative or positive direction of the y-axis in the center of mass frame, e.g. origin of the coordinate system, is enhanced by collision energies regarding to 0.5-20 kcal mol(-1), while it becomes weaker at higher vibrational (v = 0-5) or rotational (j = 0, 3, 6, 9) excitation levels. Effects of collision energies and of rotational excitation at these collision energies, with 15 kcal mol(-1) as an example on the calculated PDDCSs are also shown and discussed. Detailed plots P(φ(r)) in the range of 0 ≤φ(r)≤ 360(o), and P(θ(r), φ(r)) in the ranges of 0 ≤θ(r)≤ 180° and 0 ≤φ(r)≤ 360° at collision energies 0.5-20 kcal mol(-1) have been presented. Overall, results of PDDCSs of the product alignment and product orientation at these collision energies in the title reaction are not very strongly distinguishable.

Coriolis coupling and nonadiabaticity in chemical reaction dynamics

The nonadiabatic quantum dynamics and Coriolis coupling effect in chemical reaction have been reviewed, with emphasis on recent progress in using the time-dependent wave packet approach to study the Coriolis coupling and nonadiabatic effects, which was done by K. L. Han and his group. Several typical chemical reactions, for example, H+D(2), F+H(2)/D(2)/HD, D(+)+H(2), O+H(2), and He+H(2)(+), have been discussed. One can find that there is a significant role of Coriolis coupling in reaction dynamics for the ion-molecule collisions of D(+)+H(2), Ne+H(2)(+), and He+H(2)(+) in both adiabatic and nonadiabatic context.

Quantum state resolved scattering dynamics of F+HCl→HF(v,J)+Cl

State-to-state reaction dynamics of the reaction F+HCl-->HF(v,J)+Cl have been studied under single-collision conditions using an intense discharge F atom source in crossed supersonic molecular beams at Ecom=4.3(1.3) kcal/mol. Nascent HF product is monitored by shot-noise limited direct infrared laser absorption, providing quantum state distributions as well as additional information on kinetic energy release from high resolution Dopplerimetry. The vibrational distributions are highly inverted, with 34(4)%, 44(2)%, and 8(1)% of the total population in vHF=1, 2, and 3, respectively, consistent with predominant energy release into the newly formed bond. However, there is a small [14(1)%] but significant formation channel into the vHF=0 ground state, which is directly detectable for the first time via direct absorption methods. Of particular dynamical interest, both the HF(v=2,J) and HF(v=1,J) populations exhibit strongly bimodal J distributions. These results differ significantly from previous flow and arrested-relaxation studies and may signal the presence of microscopic branching in the reaction dynamics.

Multireference configuration interaction calculations for the F(P2)+HCl→HF+Cl(P2) reaction: A correlation scaled ground state (1A′2) potential energy surface

This paper presents a new ground state (1 (2)A(')) electronic potential energy surface for the F((2)P)+HCl-->HF+Cl((2)P) reaction. The ab initio calculations are done at the multireference configuration interaction+Davidson correction (MRCI+Q) level of theory by complete basis set extrapolation of the aug-cc-pVnZ (n=2,3,4) energies. Due to low-lying charge transfer states in the transition state region, the molecular orbitals are obtained by six-state dynamically weighted multichannel self-consistent field methods. Additional perturbative refinement of the energies is achieved by implementing simple one-parameter correlation energy scaling to reproduce the experimental exothermicity (DeltaE=-33.06 kcalmol) for the reaction. Ab initio points are fitted to an analytical function based on sum of two- and three-body contributions, yielding a rms deviation of <0.3 kcalmol for all geometries below 10 kcalmol above the barrier. Of particular relevance to nonadiabatic dynamics, the calculations show significant multireference character in the transition state region, which is located 3.8 kcalmol with respect to F+HCl reactants and features a strongly bent F-H-Cl transition state geometry (theta approximately 123.5 degrees ). Finally, the surface also exhibits two conical intersection seams that are energetically accessible at low collision energies. These seams arise naturally from allowed crossings in the C(infinityv) linear configuration that become avoided in C(s) bent configurations of both the reactant and product, and should be a hallmark of all X-H-Y atom transfer reaction dynamics between ((2)P) halogen atoms.

Quantum Mechanical Study of the Correlation of Attack and Recoil Angles for the Cl + H2 Reaction Using the Stereodirected and Discrete Variable Representations on Two Potential Energy Surfaces

The zero total angular momentum (J = 0) S matrix elements, calculated using a time-dependent wave packet method for the Cl (2P) + H2 reaction on two different potential energy surfaces, have been matrix transformed to the stereodirected and Gauss-Legendre discrete variable representations. Although the results in the two representations are (as expected) quantitatively different with respect to the angular selectivity and specificity of the reactive process, the qualitative similarity has allowed us to draw for the first time conclusions with respect to some characteristics of the potential energy surface.

A Simple Picture for the Rotational Enhancement of the Rate for the F + HCl → HF + Cl Reaction: A Dynamical Study Using a New ab initio Potential Energy Surface

Quantum scattering calculations for the reaction F + HCl --> HF + Cl are performed on a new ground-state ab initio potential energy surface. The reagent rotation is found to have a dramatic effect on the reaction probability. Furthermore, the exit channel rotational thresholds leave a strong imprint on the reaction probabilities and even on the cumulative reaction probability. A very simple vibrationally adiabatic model is shown to account for most aspects of the reaction dynamics. In this model, the fast vibrational motion is adiabatically eliminated leaving the key reaction dynamics represented by a reduced atom + rotor collision. The shape of the adiabatic potential surface immediately yields to a simple and intuitive interpretation for the rotational enhancement of the rate. The rotational enhancement is shown to be an effect of the entrance channel dynamics of the atom-rotor problem.

Valence Bond Calculations of Hydrogen Transfer Reactions: A General Predictive Pattern Derived from Theory

Hydrogen abstraction reactions of the type X(*) + H-H' --> X-H + H'(*) (X = F, Cl, Br, I) are studied by ab initio valence bond methods and the VB state correlation diagram (VBSCD) model. The reaction barriers and VB parameters of the VBSCD are computed by using the breathing orbital valence bond and valence bond configuration interaction methods. The combination of the VBSCD model and semiempirical VB theory leads to analytical expressions for the barriers and other VB quantities that match the ab initio VB calculations fairly well. The barriers are influenced by the endo- or exothermicity of the reaction, but the fundamental factor of the barrier is the average singlet-triplet gap of the bonds that are broken or formed in the reactions. Some further approximations lead to a simple formula that expresses the barrier for nonidentity and identity hydrogen abstraction reactions as a function of the bond strengths of reactants and products. The semiempirical expressions are shown to be useful not only for the model reactions that are studied in this work, but also for other nonidentity and identity hydrogen abstraction reactions that have been studied in previous articles.

Quantum scattering calculations on chemical reactions

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.