Quantum stereodynamics of the Li+HF(v,j) reactive collision for different initial states of the reagent

The role of intersystem crossing in the reactive collision of S+(4S) with H2

We report a study on the reactive collision of S+(4S) with H2, HD, and D2 combining guided ion beam experiments and quantum-mechanical calculations. It is found that the reactive cross sections reflect the existence of two different mechanisms, one being spin-forbidden. Using different models, we demonstrate that the spin-forbidden pathway follows a complex mechanism involving three electronic states instead of two as previously thought. The good agreement between theory and experiment validates the methodology employed and allows us to fully understand the reaction mechanism. This study also provides new fundamental insights into the intersystem crossing process.

Li + HF and Li + HCl Reactions Revisited I: QCT Calculations and Simulation of Experimental Results

The Li + HF and Li + HCl reactions share some common features. They have the same kinematics, relatively small barrier heights, bent transition states, and are both exothermic when the zero point energy is considered. Nevertheless, the pioneering crossed beam experiments by Lee and co-workers in the 80s (Becker et al., J. Chem. Phys. 1980, 73, 2833) revealed that the dynamics of the two reactions differ significantly, especially at low collision energies. In this work, we present theoretical simulations of their results in the laboratory frame (LAB), based on quasiclassical trajectories and obtained using accurate potential energy surfaces. The calculated LAB angular distributions and time-of-flight spectra agree well with the raw experimental data, although our simulations do not reproduce the experimentally derived center-of-mass (CM) differential cross section and velocity distributions. The latter were derived by forward convolution fitting under the questionable assumption that the CM recoil velocity and scattering angle distribution were uncoupled, while our results show that the coupling between them is relevant. Some important insights into the reaction mechanism discussed in the article by Becker et al. had not been contrasted with those that can be extracted from the theoretical results. Among them, the correlation between the angular momenta involved in the reactions has also been examined. Given the kinematics of both systems, the reagent orbital angular momentum, l , is almost completely transformed into the rotation of the product diatom, j'. However, contrary to the coplanar mechanism proposed in the original paper, we find that the initial and final relative orbital angular momenta are not necessarily parallel. Both reactions are found to be essentially direct, although about 15% of the LiFH complexes live longer than 200 fs.

The long-lived reactive nitrogen species in the troposphere: DFTB model for atmospheric applications

The longest lived reactive NO₂ molecule formation in a dry and clean air environment under a high-temperature shock wave was investigated under three basic reactions (R2 for the O + NO system, R6 for the NO + NO₃ system, and R7 for the NO + O₃ system) in the atmospheric environment. With certain approaches, a DFTB3 model was used, which gave results close to the density functional theory. In the calculations, the related reactions up to 250 ps were examined at individual specific temperatures, and the temperature ranges that contributed to the formation of the NO₂ molecule were determined. Moreover, a shock wave with both heating and cooling channels was applied only on R2 to see whether molecular concentrations were in good agreement with atmospheric information. The reaction products were examined under a shock wave of about 20 ps. At the end of the study, the applicability of the DFTB model to atmospheric systems was demonstrated by comparing it with experimental data and information. QCT approach was also used for the calculation of reaction rate constants of only O₂-formation on the O + NO system. Here, all systems are focused on nitrogen species containing oxygen. In particular, the highest-population NO molecule that emerged in the lightning flash event was used as the reactant, while systems existing with the longest lived NO₂ in the atmosphere after the lightning flash were focused in the product channel. As a result of the study, the hypothesis of geophysicists that almost all NO₂ formed in the lightning flash event originates from the NO + O system was disproved. It has been proven that the presence of NO₃ molecules that can withstand high temperatures in such systems should be evaluated.

Oxygen Molecule Formation and the Puzzle of Nitrogen Dioxide and Nitrogen Oxide during Lightning Flash

Unlike the compounds of the natural air atmosphere, the lightning systems are primarily focused on NO(X²Π), NO₂(1²A'), and O(³P) concentrations that occurred newly and highly in the ground electronic structure. While the NO/NO₂ concentrations ratio is about 2000 during the lightning flash, this ratio becomes about 0.8 right after the lightning flash. The reason for this decrease in the ratio is the disappearance of the high temperature that prevents the formation of NO₂ (with the combination of NO and O) and of the photon energy that causes its dissociation (NO₂ + hv → NO + O) right after the lightning flash. However, this study will focus on the reactions that contribute to the NO concentration, except for the combination of N and O atoms during lightning flash. To do this, it was focused on the reactive scattering states (especially the NO-exchange) of the NO + O collision and the photo-dissociation of NO₂, which provide the formation of the NO molecule in the ground electronic state. This case raises important questions. To what extent do the NO-exchange reaction and the photo-dissociation of NO₂ contribute to the atmospherically observed NO molecules? or how can the vibrational quantum states of the NO molecules formed by the photo-dissociation be effected on the NO + O¹ collision to produce a NO¹ molecule? These conditions may contribute to the concentrations of NO high during lightning flashes. Under low collision energy (between 0.1 and 0.3 eV), the NO (v = 0) population dissociated by a photon can act as reactants in the NO-exchange reactive scattering on the doublet electronic state. Since it is assumed that all of the NO₂ molecules are due to NO in the lightning flash system, this is one of the reasons that makes the NO population so high during lightning flash. Therefore, in the light of considering that the lightning system supports the formation of highly vibrating molecular groups, it might also support the formation of O₂ molecules. In particular, it was shown that the v = 4 quantum state of the NO molecule over the doublet state between collision energies of 0.9-1.5 eV and the v = 5 quantum state of the NO molecule over the quartet state between collision energies of 1.0-1.5 eV contribute to O₂ formation.

Quantum Wave Packet Treatment of Cold Nonadiabatic Reactive Scattering at the State-To-State Level

Cold and ultracold collisions are dominated by quantum effects, such as resonances, tunneling, and nonadiabatic transitions between different electronic states. Due to the extremely long de Broglie wavelength in such processes, quantum reactive scattering is most conveniently characterized using the time-independent close-coupling (TICC) methods. However, the TICC approach is difficult for systems with a large number of channels because of its steep numerical scaling laws. Here, a recently proposed quantum wave packet (WP) approach for solving adiabatic reactive scattering problems at low collision energies is extended to include nonadiabatic transitions. To impose the outgoing boundary conditions, the total scattering wavefunction is split into three parts, the interaction, the asymptotic, and the long-range regions. Each region is associated with a different set of basis functions, which could be optimized separately. In this way, an extremely long grid can be used to accommodate the characteristic long de Broglie wavelengths in the scattering coordinate. The better numerical scaling laws of the WP approach have the potential for handling larger nonadiabatic reactive systems at low temperatures in the future.

Dynamics studies of the H + HBr reaction: Based on a new potential energy surface

The initial state specific quantum wave packet dynamics studies of the H + HBr (v₀ = 0, j₀ = 0-2) reaction were performed using a new global potential energy surface (PES) of the ground state of the BrH₂ system for the collision energy ranging from 0.01 to 2.0 eV. The PES was constructed using the permutation invariant polynomial neural network method based on approximately 63 000 ab initio points, which were calculated by the multireference configuration interaction method with AVTZ and AVQZ basis sets. To improve the accuracy of the PES, Davidson's correction and spin-orbit coupling effects were considered in the ab initio calculation and the basis set was extrapolated to complete basis set limit. The new PES was compared with the previous ones and also the available experimental data, which suggests that the new PES is more accurate. The state-to-state quantum wave packet dynamics was carried out using the reactant-coordinate based approach. The reaction probabilities, integral and differential cross sections, rovibrational state distributions of product and rate constants, etc., were compared with the available theoretical and experimental studies. In general, the present work is in better agreement with the available experimental data. The quantum dynamics studies suggest that the rotational excitation of HBr has little effect on the reaction.

A new ab initio potential energy surface of LiClH (1A') system and quantum dynamics calculation for Li + HCl (v = 0, j = 0-2) → LiCl + H reaction

A new ab initio potential energy surface (PES) for the ground state of Li + HCl reactive system has been constructed by three-dimensional cubic spline interpolation of 36 654 ab initio points computed at the MRCI+Q/aug-cc-pV5Z level of theory. The title reaction is found to be exothermic by 5.63 kcal/mol (9 kcal/mol with zero point energy corrections), which is very close to the experimental data. The barrier height, which is 2.99 kcal/mol (0.93 kcal/mol for the vibrationally adiabatic barrier height), and the depth of van der Waals minimum located near the entrance channel are also in excellent agreement with the experimental findings. This study also identified two more van der Waals minima. The integral cross sections, rate constants, and their dependence on initial rotational states are calculated using an exact quantum wave packet method on the new PES. They are also in excellent agreement with the experimental measurements.

Quantum and quasi-classical calculations for the S⁺ + H₂(v,j) → SH⁺(v',j') + H reactive collisions

State-to-state cross-sections for the S(+) + H2(v,j) → SH(+)(v',j') + H endothermic reaction are obtained using quantum wave packet (WP) and quasi-classical (QCT) methods for different initial ro-vibrational H2(v,j) over a wide range of translation energies. The final state distribution as a function of the initial quantum number is obtained and discussed. Additionally, the effect of the internal excitation of H2 on the reactivity is carefully studied. It appears that energy transfer among modes is very inefficient that vibrational energy is the most favorable for the reaction, and rotational excitation significantly enhances the reactivity when vibrational energy is sufficient to reach the product. Special attention is also paid to an unusual discrepancy between classical and quantum dynamics for low rotational levels while agreement improves with rotational excitation of H2. An interesting resonant behaviour found in WP calculations is also discussed and associated with the existence of roaming classical trajectories that enhance the reactivity of the title reaction. Finally, a comparison with the experimental results of Stowe et al. for S(+) + HD and S(+) + D2 reactions exhibits a reasonably good agreement with those results.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

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.

EFFECTS ON THE CHEMICAL STEREODYNAMICS OF THE INITIAL VIBRATIONAL EXCITATION IN THE F + LiH (v = 0-2, j = 0) → LiF + H REACTION

In this work, the product polarization characteristics are reported for the reaction F + LiH (v = 0 - 2, j = 0) → LiF + H at the collision energy of 35 kcal/mol, by using the QCT method on the Aguado–Paniagua-potential energy surface (see Aguado et al.). The distribution of P(θr) which represents the K (reagent relative velocity vector) and J′ (product rotational angular momentum vector) correlation, the dihedral angle distribution of K-K′ (product relative velocity vector)-J′ P(φr), the angular distribution P(θr, φr) and the four polarization-dependent differential cross sections (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), (2π/σ)(dσ21-/dωt) in each initial state are presented and discussed.

Nonadiabatic state-to-state reactive collisions among open shell reactants with conical intersections: the OH((2)Pi) + F((2)P) example

Accurate wave packet calculations on the OH((2)Pi) + F((2)P) → O((3)P) + HF((1)Sigma(+)) reactive collisions are performed using a recently proposed coupled diabatic states. Adiabatic and nonadiabatic dynamics are compared in detail, analyzing the final state distribution of products. It is found that with the new surfaces a significant increase of the rate constant is obtained, with noticeable nonadiabatic effects. The inclusion of the spin-orbit splittings for the calculation of the electronic partition function produces an important increase of the reaction rate constants, yielding a rather good agreement with the experimental results. It is also concluded that spin-orbit couplings are also necessary in the entrance channel to describe this reaction.

Potential energy surface and reactive collisions for the Au+H(2) system

A global potential energy surface is obtained for the ground state of the endoergic Au((2)S)+H(2)(X (1)Sigma(g) (+))-->AuH((1)Sigma(+))+H((2)S) reaction. The global potential is obtained by fitting highly correlated ab initio calculations on the system, using relativistic pseudopotential for the gold atom. Several electronic states are calculated correlating with Au((2)S)+H(2), Au((2)D)+H(2), and H(2), Au((2)P)+H(2) asymptotes. These states show several conical intersections and curve crossings along the minimum energy reaction path which are analyzed in detail. One of them gives rise to an insertion well in which there are important contributions from the Au((2)D) and Au((2)P) states of gold, which is interesting because it is analog to the deep chemisorption well appearing in larger gold clusters. Quantum wave packet and quasiclassical trajectory dynamical calculations performed for the reaction at zero total angular momentum are in good agreement, provided that a Gaussian binning method is used to account for the zero-point energy of products. Finally, integral and differential cross sections are calculated for the reaction with quasiclassical trajectories. Two different reaction mechanisms are found, one direct and the second indirect, in which the Au atom inserts in between the two hydrogen atoms because of the existence of the insertion well discussed above.

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.

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.

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.

Collisional and photoinitiated reaction dynamics in the ground electronic state of Ca-HCl

Ca+HCl(upsilon,j) reactive collisions were studied for different rovibrational states of the HCl reactant using wave-packet calculations in reactant Jacobi coordinates. A recently proposed potential-energy surface was used with a barrier of approximately 0.4 eV followed by a deep well. The possibility of an insertion mechanism due to this last well has been analyzed and it was found that once the wave packet passes over the barrier most of it goes directly to CaCl+H products, which shows that the reaction dynamics is essentially direct. It was also found that there is no significant change in the reaction efficiency as a function of the initial HCl rovibrational state, because CaHCl at the barrier has an only little elongated HCl bond. Near the threshold for reaction with HCl(upsilon=0), however, the reaction shows significant steric effects for j > 0. In a complementary study, the infrared excitation from the Ca-HCl van der Waals well was simulated. The spectrum thus obtained shows several series of resonances which correspond to quasibound states correlating to excited HCl(upsilon) vibrations. The Ca-HCl binding energies of these quasibound states increase dramatically with upsilon, from 75 to 650 cm(-1), because the wave function spreads increasingly over larger HCl bond lengths. Thus it explores the region of the barrier saddle point and the deep insertion well. Although also the charge-transfer contribution increases with upsilon, the reaction probability for resonances of the upsilon=2 manifold, which are well above the reaction threshold, is still negligible. This explains the relatively long lifetimes of these upsilon=2 resonances. The reaction probability becomes significant at upsilon=3. Our simulations have shown that an experimental study of this type will allow a gradual spectroscopic probing of the barrier for the reaction.

Effect of rotational energy on the reaction Li+HF(υ=0,j)→LiF+H: An experimental and computational study

In a crossed molecular-beam study we have measured angular and time-of-flight distributions of the product LiF from the reaction Li + HF(upsilon = 0)-->LiF + H at various collision energies ranging from 97 to 363 meV for three markedly different rotational state distributions of HF obtained at nozzle temperatures close to 315, 510, and 850 K. Particularly, for the low and intermediate collision energies we observe significant effects of the varying j-state populations on the shape of the product angular distributions. At 315 K an additional feature appears in the angular distributions which is interpreted as being due to scattering from HF dimers. The experimental data are compared with simulations of the monomer reaction based on extensive quasiclassical trajectory calculations on a new state-of-the-art ab initio potential energy surface. We find an overall good agreement between the theoretical simulations and the experimental data for the title reaction, especially at the highest HF nozzle temperature.

How Reactants Polarization Can Be Used to Change and Unravel Chemical Reactivity

This article presents theoretical methods for the description of the directional effect of reactant rotation on the reactivity of atom-diatom systems and suggests an experiment that could be used to test theoretical predictions. The theory can be used in conjunction with both quantum reactive scattering and quasiclassical trajectory calculations, and is stated in general terms, which allows it to deal with arbitrary reactant polarizations. The illustrative results obtained for the benchmark H + D2 reaction are also presented and show that under experimentally achievable conditions one can largely control reactive cross sections and product state distributions, while at the same time gaining valuable and at times surprising information on the reaction mechanism.

Heavy atom tunneling in chemical reactions: Study of H+LiF collisions

The H+LiF(X (1)sigma(+),upsilon=0-2,j=0)-->HF(X (1)sigma(+),upsilon',j')+Li(2S) bimolecular process is investigated by means of quantum scattering calculations on the chemically accurate X 2A' LiHF potential energy surface of Aguado et al. [A. Aguado, M. Paniagua, C. Sanz, and J. Roncero, J. Chem. Phys. 119, 10088 (2003)]. Calculations have been performed for zero total angular momentum for translational energies from 10(-7) to 10(-1) eV. Initial-state selected reaction probabilities and cross sections are characterized by resonances originating from the decay of metastable states of the H...F-Li and Li...F-H van der Waals complexes. Extensive assignment of the resonances has been carried out by performing quasibound states calculations in the entrance and exit channel wells. Chemical reactivity is found to be significantly enhanced by vibrational excitation at low temperatures, although reactivity appears much less favorable than nonreactive processes due to the inefficient tunneling of the relatively heavy fluorine atom strongly bound in van der Waals complexes.

Quantum dynamics of the Li+HF→H+LiF reaction at ultralow temperatures

Quantum-mechanical calculations are reported for the Li+HF(v=0,1,j=0)-->H+LiF(v',j') bimolecular scattering process at low and ultralow temperatures. Calculations have been performed for zero total angular momentum using a recent high-accuracy potential-energy surface for the X2A' electronic ground state. For Li+HF(v=0,j=0), the reaction is dominated by resonances due to the decay of metastable states of the Li cdots,...F-H van der Waals complex. Assignment of these resonances has been carried out by calculating the eigenenergies of the quasibound states. We also find that while chemical reactivity is greatly enhanced by vibrational excitation, the resonances get mostly washed out in the reaction of vibrationally excited HF with Li atoms. In addition, we find that at low energies, the reaction is significantly suppressed due to the less-efficient tunneling of the relatively heavy fluorine atom.

Direct versus resonances mediated F+OH collisions on a new 3A″ potential energy surface

A theoretical study of the F(2P) + OH(2Pi) --> HF(1Sigma+) + O(3P) reactive collisions is carried out on a new global potential energy surface (PES) of the ground 3A" adiabatic electronic state. The ab initio calculations are based on multireference configuration interaction calculations, using the aug-cc-pVTZ extended basis sets of Dunning et al. A functional representation of the PES shows no nominal barrier to reaction, contrary to previous results by others. Wave packet and quasiclassical trajectory calculations have been performed for this PES to study the F + OH(v = 0,j) reactive collision. The comparison was performed at fixed and constant values of the total angular momentum from 0 to 110 and relative translational energy up to 0.8 eV. The reaction presents a dynamical barrier, essentially due to the zero-point energy for the bending vibration near the saddle point. This determines two different reaction mechanisms. At energies higher than approximately 0.125 eV the reaction is direct, while below that value it is indirect and mediated by heavy-light-heavy resonances. Such resonances, also found in the simulations of the photodetachment spectrum of the triatomic anion, manifest themselves in the quasiclassical simulations, too, where they are associated to periodic orbits.

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.