Quantum study of the Li+HF→LiF+H reaction

New ab initio potential energy surface of NaFH (1A') system and quantum dynamics studies for the Na + HF (v, j) → NaF + H reaction

A global potential energy surface (PES) for the electronic ground state of the Na + HF reactive system is constructed by three-dimensional cubic spline interpolation of 37 000 ab initio points obtained using the multireference configuration interaction method including the Davidson's correction (MRCI + Q) with auc-cc-pV5Z basis set. The endoergicity, well depth and properties of the separated diatomic molecules are in good agreement with experimental estimations. Quantum dynamics calculations have been performed and compared with those of the previous MRCI PES as well as experimental values. The better agreement between theory and experiment indicates the accuracy of the new PES.

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 classical dynamics of H + CaCl(X (2)Σ(+)) → HCl + Ca((1)S) reaction and vibrational energy levels of the HCaCl complex

We carried out accurate quantum wave packet as well as quasi-classical trajectory (QCT) calculations for H + CaCl (νi = 0, ji = 0) reaction occurring on an adiabatic ground state using the recent ab initio potential energy surface to obtain the quantum and QCT reaction probabilities for several partial waves (J = 0, 10, and 20) as well as state resolved QCT integral and differential cross sections. The complete list of vibrational energy levels supported by the intermediate HCaCl complex is also obtained using the Lanczos algorithm. The QCT reaction probabilities show excellent agreement with the quantum ones except for the failure in reproducing the highly oscillatory resonance structure. Despite the fact that the reaction is exothermic and the existence of a barrier that is energetically lower than the bottom of the reactant valley, the reaction probability for J = 0 shows threshold-like behavior and the reactivity all through the energies is very low (<0.1). The dynamical features at two different energy regions (<0.35 eV and >0.35 eV) are found to be different drastically from each other. The analyses of these results suggest that the reaction is governed by one of the two different types of reaction mechanism, one is the direct mechanism at the high energy region and the other is the indirect mechanism at the low energy region by which the reaction proceeds through the long-lived intermediate complex followed by a statistical dissociation into asymptotic channels.

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.

QUASICLASSICAL TRAJECTORY STUDY OF STEREODYNAMICS FOR THE REACTIONS Li+HF/DF/TF

Stereodynamics of the reaction Li + HF (v = 0,j = 0) → LiF + H and its isotopic variants on the ground electronic state (12A′) potential energy surface (PES) are studied by employing the quasiclassical trajectory (QCT) method. At a collision energy of 2.2 kcal/mol, product rotational angular momentum distributions, P(θr) and P(ϕr), are calculated in the center-of-mass (CM) frame. The results demonstrate that the product rotational angular momentum j′ is not only aligned along the direction perpendicular to the reagent relative velocity vector k, but also oriented along the negative y-axis. The four generalized polarization-dependent differential cross sections (PDDCSs) are also computed. The PDDCS00 distribution shows a sideways scattering for the reaction Li + HF and a strongly backward scattering for the reaction Li + DF . However, it displays both the forward and backward scatterings for the reaction Li + TF . These features demonstrate that the Li + HF and Li + DF reactions proceed predominantly through the direct reaction mechanism. However, the Li + TF reaction undergoes both the direct and indirect reaction mechanisms. The PDDCS21- distribution indicates that the product angular distributions are anisotropic.

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.

INFLUENCE OF THE COLLISION ENERGY ON STEREODYNAMICS OF THE F + LiH (v = 0, j = 0) → LiF + H REACTION

The stereodynamics of the title reaction based on the ground 2A′ potential energy surface (PES) has been investigated using the method of the quasi-classical trajectory (QCT) at different collision energies (23 kcal/mol, 35 kcal/mol and 46 kcal/mol). The vector properties of the angular momentum (described by the distribution of K - J′P(θr), the dihedral angle distribution of K - K′ - J′P(φr) and the angular distribution P(θr, ϕr)) and the four PDDCSs [(2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), (2π/σ)(dσ21-/dωt)] of the product LiF at each collision energy have been presented, respectively. Further, the collision energy effects on the behavior of the product LiF have been discussed and studied.

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.

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.

Transition-state spectroscopy of the photoinduced Ca + CH3F reaction. 3. Reaction following the local excitation to Ca(4s3d 1D)

The Ca* + CH3F --> CaF* + CH3 reaction was studied both experimentally and theoretically. The reaction was photoinduced in Ca...CH3F complexes, which were illuminated by a tunable laser in the range 18 000-24 000 cm-1. The absorption band that leads to the reaction extends between 19 000 and 23 000 cm-1. It is formed of three broad overlapping structures corresponding to the excitation of different electronic states of the complex. The two structures of lowest energy were considered in detail. They are associated with two series of respectively 2 and 3 molecular states correlating to Ca(4s3d 1D) + CH3F at infinite separation between Ca and CH3F. The assignment of these structures to specific electronic transitions of the complex stemmed from theoretical calculations where the Ca...CH3F complex is described by a linear Ca-F-C backbone. 2D potential energy surfaces were calculated by associating a pseudopotential description of the [Ca2+] and [F7+] cores, a core polarization operator on calcium, an extensive Gaussian basis, and a treatment of the electronic problem at the CI-MRCI level. All the excited levels correlating to the 4s2 1S, 4s3d 1D, and 4s4p 1P levels of Ca in the Ca + CH3F channel were documented in a calculation that explored the rearrangement channels where either Ca + CH3F or CaF + CH3 are formed. Then, wavepacket calculations on the 2D-PES's allowed one to simulate the absorption spectrum of the complex, in an approximation where the various electronic states of the complex are not coupled together. The assignment above stemmed from this. The second outcome of the calculation was that whatever the excited level of the complex that is considered, the reaction has to proceed through energy barriers. The electronic excitation of the complex on the red side of the absorption band does not seem to deposit enough energy in the system to overcome these barriers (even the lowest one) or to stimulate tunneling reactions. An alternative reaction mechanism involving a transfer to triplet PES's is proposed.

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.

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.

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.

Ab initiopotential-energy surface for the reaction Ca+HCl→CaCl+H

The potential-energy surface of the ground electronic state of CaHCl has been obtained from 6400 ab initio points calculated at the multireference configuration-interaction level and represented by a global analytical fit. The Ca+HCl-->CaCl+H reaction is endothermic by 5100 cm(-1) with a barrier of 4470 cm(-1) at bent geometry, taking the zero energy in the Ca+HCl asymptote. On both sides of this barrier are potential wells at linear geometries, a shallow one due to van der Waals interactions in the entrance channel, and a deep one attributed to the H(-)Ca(++)Cl(-) ionic configuration. The accuracy of the van der Waals well depth, approximately 200 cm(-1), was checked by means of additional calculations at the coupled-cluster singles and doubles with perturbative triples level and it was concluded that previous empirical estimates are unrealistic. Also, the electric dipole function was calculated, analytically fitted in the regions of the two wells, and used to analyze the charge shifts along the reaction path. In the insertion well, 16,800 cm(-1) deep, the electric dipole function confirmed the ionic structure of the HCaCl complex and served to estimate effective atomic charges. Finally, bound rovibrational levels were computed both in the van der Waals well and in the insertion well, and the infrared-absorption spectrum of the insertion complex was simulated in order to facilitate its detection.

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.