Using quantum rotational polarization moments to describe the stereodynamics of the H+D2(v=0,j=0)→HD(v′,j′)+D reaction

Strong Angular Oscillation of Rotationally Resolved Differential Cross Section in the H + HD → H2 + D Reaction at the Collision Energy of 2.07 eV: Evidence of Geometric Phase Effects

Geometric phase (GP) effects in chemical reactions are subtle quantum phenomena that are challenging to identify. In this work, we report a joint experimental and theoretical study of the H + HD → H2 + D reaction at a collision energy of 2.07 eV, which is far below the energy of the conical intersection of 2.53 eV. The rotationally state-resolved differential cross sections were measured by a crossed-beam experiment with the scheme of D-atom Rydberg tagging time-of-flight detection. Experimental angular distributions of three rotational states of H2 products exhibit notable variation near the backward scattering direction. Time-dependent quantum mechanics calculations (TDQMs) were carried out at the same collision energy, with and without the inclusion of GP. The experimental angular distributions are in good agreement with TDQM results with the inclusion of GP but do not agree with TDQM results without the inclusion of GP. This work demonstrates the existence of GP effects at energy far below the conical intersection.

Spiers Memorial Lecture: New directions in molecular scattering

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

Geometric Phase Effects in the H + H2+ Reaction on the Lowest Triplet Ground State

To our knowledge, this is the first time geometric phase (GP) effects in the H + H2+ reaction on its lowest triplet ground state with collision energies lower than 1.85 eV have been studied using the quantum wave packet method and vector potential approach. We obtained the total reaction probabilities including and not including GP (NGP) effects for J ≤ 4. Visible GP effects could be seen at the lower energy regime but are tiny at the higher one. Moreover, they are more obvious in the product rovibrational state-resolved reaction probabilities, and the relative resonance magnitudes between GP and NGP results change with product rotational state values alternatively. The main reasons are the interferences between the one- and two-transition-state (1-TS and 2-TS) reaction paths, in that at the lower energy regime, the reaction probabilities from the 2-TS pathway show peaks of comparable probabilities compared with that of the 1-TS pathway. In addition, the "out-of-phase" trend observed in the H + H2 reaction does not exist rigorously in this system. Importantly, the visible GP effects exist in this H3+ system, which makes it a very useful candidate reaction for nonadiabatic investigations in both theory and experiment.

Charge Transfer Processes for H + H2+ Reaction Employing Coupled 3D Wavepacket Approach on Beyond Born-Oppenheimer Based Ab Initio Constructed Diabatic Potential Energy Surfaces

The dynamics of the H + H₂⁺ reaction has been analyzed from the electronically first excited state of diabatic potential energy surfaces constructed by employing the Beyond Born-Oppenheimer theory [J. Chem. Phys. 2014, 141, 204306]. We have employed the coupled 3D time-dependent wavepacket formalism in hyperspherical coordinates for multisurface reactive scattering problems. To be specific, the charge transfer processes have been investigated extensively by calculating state-to-state as well as total reaction probabilities and integral cross sections, when the reaction process is initiated from the first excited electronic state (2¹A'). We have depicted the convergence profiles of reaction probabilities for the competing charge transfer processes, namely, reactive charge transfer (RCT) and nonreactive charge transfer (NRCT) processes for different total energies with respect to total angular momentum, J. Total and state-to-state integral cross sections are calculated as a function of total energy for the initial rovibrational state, namely, v = 0, j = 0 level of H₂⁺ (²Σ_g⁺) molecule and are compared with previous theoretical calculations. Finally, we have calculated temperature-dependent rate constants using our presently evaluated cross sections and compared their average with the experimentally measured one.

Quantum interference in H + HD → H2 + D between direct abstraction and roaming insertion pathways

Understanding quantum interferences is essential to the study of chemical reaction dynamics. Here, we provide an interesting case of quantum interference between two topologically distinct pathways in the H + HD → H2 + D reaction in the collision energy range between 1.94 and 2.21 eV, manifested as oscillations in the energy dependence of the differential cross section for the H2 (v′ = 2, j′ = 3) product (where v′ is the vibrational quantum number and j′ is the rotational quantum number) in the backward scattering direction. The notable oscillation patterns observed are attributed to the strong quantum interference between the direct abstraction pathway and an unusual roaming insertion pathway. More interestingly, the observed interference pattern also provides a sensitive probe of the geometric phase effect at an energy far below the conical intersection in this reaction, which resembles the Aharonov–Bohm effect in physics, clearly demonstrating the quantum nature of chemical reactivity.

Observation of the geometric phase effect in the H + HD → H2+ D reaction

Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD → H2+ D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state–resolved differential cross sections in the forward scattering direction for H2products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.

Quantum dynamical study of the He + NeH+ reaction on a new analytical potential energy surface

An analytical potential energy surface (PES) for the ground state of the [HeHNe](+) system has been constructed from a set of 19,605 ab initio data points, obtained from coupled cluster singles and doubles with perturbative triples correction calculations and the aug-cc-pVQZ basis set. The PES is based on the many-body expansion form proposed by Aguado and Paniagua (J. Chem. Phys. 1992, 96, 1265), and it has a root-mean-square error of 0.03 kcal/mol. The minimum energy pathways (MEPs) for different Ne-H-He angles are calculated, and it is found that the MEP for 180° (linear) goes through the deepest potential energy well. Preliminary quantum dynamical studies are performed for the He + NeH(+) (v = 0-2, j = 0-3) → HeH(+) + Ne reaction in the 0.0-0.5 eV collision energy range. Quantum calculations are carried out using a time-dependent wave packet method within the centrifugal sudden approximation. Reaction probabilities exhibit strong oscillatory behavior arising because of the metastable [HeHNe](+). Vibrational excitation has been found to enhance the reaction cross sections.

VECTOR CORRELATIONS AND PRODUCT POLARIZATIONS IN THE N(2D) + D2 → ND + D REACTIVE SYSTEM

The vector correlations between products and reagents of the N (2D) + D 2 reaction are investigated by employing quasi-classical trajectory (QCT) calculation on the accurate DMBE potential energy surface (PES) of the 2A″ state. Stereo-dynamic quantities, including the four generalized polarization-dependent differential cross-sections (PDDCSs), the angular distribution P(θr), the dihedral-angle distribution P(φr), as well as the product rotational angular distribution in the polar form of P(θr, φr), are calculated in the center-of-mass (CM) frame. The results indicate that the product rotational angular momentum j′ not only aligns along the y-axis, but also orients to the negative direction of the y-axis. The isotope effect in the context of chemical stereo-dynamics and influences of different versions of ground-state PESs on vector correlations are shown and discussed.

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 .

ROTATIONAL ALIGNMENT OF PRODUCT MOLECULES FROM THE REACTION Ca + HCl→CaCl + H

The product rotational polarization in the Ca + HCl→CaCl + H reaction at collision energy of 20 kcal/mol has been studied via the quasiclassical trajectory method on a new ab initio potential surface. The P(θ r ) distribution of angle between k and j′, and the dihedral angular distribution P(Φ r ) characterizing k - k′ - j′ correlation are discussed, the angle distribution P(θ r , Φ r ) of product rotational vectors in the form of polar plot in θ r and Φ r are shown. Furthermore, four PDDCSs (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt) and (2π/σ)(dσ21-/dωt) are also presented. The present calculations reveal that the product rotational alignment is very strong. Finally, the state distributions of the product CaCl are investigated. The results showed that the CaCl product was formed with high vibrational and rotational excitation.

QUASICLASSICAL TRAJECTORY STUDY OF THE STEREODYNAMICS FOR THE REACTION D+ + H2 (ν=0, j = 0) → HD + H+

The vector correlations between products and reactants for the reactive noncharge transfer ion–molecule collisions D + + H 2 (ν=0, j = 0)→ HD + H + have been determined by means of the quasiclassical trajectory method on the ground state in the KBNN potential energy surface (J Chem Phys116:654, 2002) at collision energies of 0.224, 0.524, 0.824, and 1.024 eV. The calculated differential cross section (DCS) results indicate that the lifetime of the complex [Formula: see text] in the deep well on the ground PES becomes shorter as collision energy increases. The existence of long-lived complex leads to a weak product rotational polarization at a low collision energy of 0.224 eV. However, the product rotational angular momentum j′ aligns and orients preferentially along the positive direction of the y-axis at a high collision energy of 1.024 eV. The distribution of P(θr, ϕr) indicates that the product molecules are preferentially polarized perpendicular to the scattering plane and that the reaction is dominated by an in-plane mechanism.

THEORETICAL STUDIES OF STEREODYNAMICS FOR THE H+ + H2 (ν = 0–3, j = 0) → H2 + H+ REACTION

The stereodynamics calculation was carried out for the title reaction by quasiclassical trajectory method on the ground surface of KBNN potential energy surface. The vector correlations are determined at initial ground state and vibrational excitation of the reagent H 2. The results show that the rotational polarization is affected lightly by collision energy and strongly by reagent excitation for title reaction. The rotational alignments are almost isotropic at several collision energies on initial ground state of the reagent H 2, which means that the product rotational angular momentum is weakly polarized (or no polarized). Nevertheless, the polarization of product rotational angular momentum is enhanced remarkably at the vibrational excitations of the reagent H 2 in collision energy of 0.524 eV.

Constraints at the transition state of the D + H2 reaction: quantum bottlenecks vs. stereodynamics

This article presents a quasiclassical trajectory method for the calculation of cumulative reaction probabilities by sampling of the helicity quantum number of the reagents (k). The method is applied to the D + H(2) reaction at various total angular momentum (J) values, and the helicity-resolved quasiclassical cumulative reaction probabilities are compared to their quantum mechanical counterparts. The agreement between the two sets of results is fairly good. In particular, k-dependent, J-independent reaction thresholds found with quantum methods are reproduced by the quasiclassical calculations. The shift of these thresholds with increasing k, which has been previously attributed to the quantum bottleneck states taking part in the reaction, is revisited and discussed also in terms of the reaction stereodynamics.

Coordinate transformation methods to calculate state-to-state reaction probabilities with wave packet treatments

A procedure for the transformation from reactant to product Jacobi coordinates is proposed, which is designed for the extraction of state-to-state reaction probabilities using a time-dependent method in a body-fixed frame. The method consists of several steps which involve a negligible extra computational time as compared with the propagation. Several intermediate coordinates are used, in which the efficiency depends on the masses of the atoms involved in the reaction. A detailed study of the relative efficiency of using reactant and product Jacobi coordinates is presented for several systems, and simple arguments are found depending on the masses of the atoms involved in the reaction. It is found that the proposed method is, in general, more efficient than the use of product Jacobi coordinates, specially for nonzero total angular momentum. State-to-state reaction probabilities are obtained for Li+FH-->LiF+H and F+HO-->FH+O collisions for several total angular momenta.

A full dimensional, nine-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction

A full dimensional, nine-degree-of-freedom (9DOF), time-dependent quantum dynamics wave packet approach is presented for the study of the H2+C2H-->H+C2H2 reaction system. This is the first full dimensional quantum dynamics study for a diatom-triatom reaction system. The effects of the initial vibrational and rotational excitations of the reactants on the reactivity of this reaction are investigated. This study shows that vibrational excitations of H2 enhance the reactivity; whereas, the vibrational excitations of C2H only have a small effect on the reaction probability. In addition, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. Comparison of the ground state reaction probabilities of the 9DOF and 8DOF shows the reaction probability from the full dimensional calculation is larger, with more prominent resonance features.

Analysis of the H + D2reaction mechanism through consideration of the intrinsic reactant polarisation

The effect of reactant polarisation on the dynamics of the title reaction at collision energies up to 1.6 eV is analysed in depth. The analysis takes advantage of two novel theoretical concepts: intrinsic reaction properties and stereodynamical portraits. Exact quantum methods are used to determine the polarisation moments that quantify the intrinsic reactant polarisation at various levels of detail, including or not product state and/or scattering angle resolution. The data is then examined with the aid of stereodynamical portraits, which facilitate the rationalisation of the stereochemical effects that are relevant for the reaction dynamics. This allows for detailed characterisations of the so-called direct and delayed reaction mechanisms.

An eight-degree-of-freedom quantum dynamics study for the H2+C2H system

An eight-degree-of-freedom (8DOF) time-dependent wave-packet approach has been developed to study the H(2)+C(2)H-->H+C(2)H(2) reaction system. The 8DOF model is obtained by fixing one of the Jacobi torsion angle in the nine-degree-of-freedom AB+CDE reaction system. This study is an extension of the previous seven-degree-of-freedom (7DOF) computation [J. Chem. Phys. 119, 12057 (2003)] of this reaction system. This study shows that vibrational excitations of H(2) enhance the reaction probability, whereas the stretching vibrational excitations of C(2)H have only a small effect on the reactivity. Furthermore, the bending excitation of C(2)H, compared to the ground-state reaction probability, hinders the reactivity. A comparison of the rate constant between the 7DOF calculation and the present 8DOF results has been made. The theoretical and experimental results agree with each other very well when the present 8DOF results are adjusted to account for the lower transition state barrier heights found in recent ab initio calculations.

F+OH reactive collisions on new excited A″3 and A′3 potential-energy surfaces

Global three-dimensional adiabatic potential-energy surfaces for the excited 2(3)A" and 1(3)A' triplet states of OHF are obtained to study the F(2P)+OH(2pi)-->O(3P)+HF(1sigma+) reaction. Highly accurate ab initio calculations are obtained for the two excited electronic states and fitted to analytical functions with small deviations. The reaction dynamics is studied using a wave-packet treatment within a centrifugal sudden approach, which is justified by the linear transition state of the two electronic states studied. The reaction efficiency presents a marked preference for perpendicular orientation of the initial relative velocity vector and the angular momentum of the OH reagent, consistent in the body-fixed frame used with an initial collinear geometry which facilitates the access to the transition state. It is also found that the reaction cross section presents a rather high threshold so that, in an adiabatic picture, the two excited triplet states do not contribute to the rate constant at room temperature. Thus, only the lowest triplet state leads to reaction under these conditions and the simulated rate constants are too low as compared with the experimental ones. Such disagreement is likely to be due to nonadiabatic transitions occurring at the conical intersections near the transition state for this reaction.

Quantum-instanton evaluation of the kinetic isotope effects

A general quantum-mechanical method for computing kinetic isotope effects is presented. The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements. It computes the kinetic isotope effect directly, using a thermodynamic integration with respect to the mass of the isotope, thus avoiding the more computationally expensive process of computing the individual rate constants. The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator. While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms, we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H2 --> H2 + H. In all seven test cases, for temperatures between 250 and 600 K, the error of the quantum instanton approximation for the kinetic isotope effects is less than approximately 10%.