Quantum mechanical and quasiclassical simulations of molecular beam experiments for the F+H2→HF+H reaction on two ab initio potential energy surfaces

Reactant-Product Decoupling Technique Using the Intermediate Coordinate Method

Although the reactant-product decoupling (RPD) technique was proposed over two decades ago, it remains an efficient approach for calculating product state-resolved information on some simple direct reactions using the quantum wave packet method. In the past, usually the RPD technique employed the collocation method to transform the wave function between reactant and product arrangements, which requires quite large computational efforts. In this work, the intermediate coordinate (IC) method is employed to realize the RPD technique. Numerical examples demonstrate that this new IC RPD (IRPD) technique has superior computational efficiency compared with the original method employing the collocation method. Especially, the new IRPD technique significantly saves disk space and computer memory. To illustrate the features of our new method, the total reaction probabilities of the H + H2, H + Br2, and F + H2 reactions with J = 0 and the differential cross sections of the H + H2 and F + H2 reactions at a series of collision energy are calculated and presented. With this efficient and effective new RPD technique, the Li + HF reaction, which involves sharp resonances with long-range wave functions in the van der Waals wells in both the reactant and product arrangements, is also calculated with several J at the product state-resolved level to reveal the ability of the RPD technique for describing resonance wave functions. With these numerical examples, it is found that, for the reaction with resonances, the RPD approach should be applied carefully. Otherwise, it is very possible that the resonances could disappear with the application of the RPD technique.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H₂/D₂ reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H₂ and D₂) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H₂ and F + D₂ reactions are presented along with previous theoretical and experimental results.

INVESTIGATION OF THE CONTRIBUTION FOR THE NONCOLLINEAR CHANNEL OF THE F(2P3/2,2P1/2) + H2/D2 REACTIONS ON FOUR DIABATIC POTENTIAL ENERGY SURFACES

We performed the nonadiabatic time-dependent wave packet calculation on the four diabatic potential energy surfaces, which have the different barrier height, to investigate the contribution of the noncollinear channel for the F (2P) + H2/D2 (v = j = 0) reactions. The reaction probabilities, integral cross-sections, and rate constants are presented. The results indicate that the probabilities as the function of the collision energy have an obvious translation. The reactive activity of the reactions comes from the noncollinear reactive channel. The bent barrier height would decrease the reactive activity. The integral cross-sections are in the order of AWS < LWA-5 < LWA-78 ≈ MASW, which is opposite to that of the bent barrier height. At the lower temperature, the difference of the rate constants is unambiguous. As the temperature increases, the difference reduces. At the higher temperature, the rate constants computed on the four potential energy surfaces are close.

A STATE-TO-STATE QUANTUM DYNAMICAL STUDY OF THE H + HBr REACTION

The time-dependent wave packet method was used to calculate the state-to-state differential cross sections for abstraction and exchange processes in the title reaction on the Kurosaki–Takayanagi potential energy surface [Kurosaki Y, Takayanagi T, J Chem Phys119:7838, 2003], with the reactant HBr initially in the ground rovibrational state. It is found that the trend in the product distributions is similar for abstraction and exchange processes, but the differential cross sections are very different. For the exchange reaction, the product is mainly scattered in the backward hemisphere for collision energy up to 2.0 eV, although forward scattering gradually shows up in high collision energies. While for abstraction reaction, the differential cross section changes substantially with the collision energy, moving from predominantly backward peaked at low collision energy to predominantly forward peaked at high collision energy. The rovibrational state resolved differential cross section at collision energy of 2.0 eV exhibits two peaks for the abstraction reaction, one is around the angle of 50°, and the other at 0°. It is found that the peaks around 50°, are below the corresponding maximum j' lines provided by the kinematic constraint model, while the forward-scattered peaks straddle both sides of the kinematic limit, and are likely contributed from both the direct and the migratory reaction mechanisms as proposed by Zare and coworkers.

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.

A Time-Dependent Quantum Dynamical Study of the H + HBr Reaction

Time-dependent wave packet calculations were carried out to study the exchange and abstraction processes in the title reaction on the Kurosaki-Takayanagi potential energy surface (Kurosaki, Y.; Takayanagi, T. J. Chem. Phys. 2003, 119, 7838). Total reaction probabilities and integral cross sections were calculated for the reactant HBr initially in the ground state, first rotationally excited state, and first vibrationally excited state for both the exchange and abstraction reactions. At low collision energy, only the abstraction reaction occurs because of its low barrier height. Once the collision energy exceeds the barrier height of the exchange reaction, the exchange process quickly becomes the dominant process presumably due to its larger acceptance cone. It is found that initial vibrational excitation of HBr enhances both processes, while initial rotational excitation of HBr from j(0) = 0 to 1 has essentially no effect on both processes. For the abstraction reaction, the theoretical cross section at E(c) = 1.6 eV is 1.06 A(2), which is smaller than the experimental result of 3 +/- 1 A(2) by a factor of 2-3. On the other hand, the theoretical rate constant is larger than the experimental results by about a factor of 2 in the temperature region between 220 and 550 K. It is also found that the present quantum rate constant is larger than the TST result by a factor of 2 at 200 K. However, the agreement between the present quantum rate constant and the TST result improves as the temperature increases.

Spin-orbit relaxation of Cl(P1∕22) and F(P1∕22) in a gas of H2

The authors present quantum scattering calculations of rate coefficients for the spin-orbit relaxation of F(2P1/2) atoms in a gas of H2 molecules and Cl(2P1/2) atoms in a gas of H2 and D2 molecules. Their calculation of the thermally averaged rate coefficient for the electronic relaxation of chlorine in H2 agrees very well with an experimental measurement at room temperature. It is found that the spin-orbit relaxation of chlorine atoms in collisions with hydrogen molecules in the rotationally excited state j=2 is dominated by the near-resonant electronic-to-rotational energy transfer accompanied by rotational excitation of the molecules. The rate of the spin-orbit relaxation in collisions with D2 molecules increases to a great extent with the rotational excitation of the molecules. They have found that the H2/D2 isotope effect in the relaxation of Cl(2P1/2) is very sensitive to temperature due to the significant role of molecular rotations in the nonadiabatic transitions. Their calculation yields a rate ratio of 10 for the electronic relaxation in H2 and D2 at room temperature, in qualitative agreement with the experimental measurement of the isotope ratio of about 5. The isotope effect becomes less significant at higher temperatures.

Recent advances in crossed-beam studies of bimolecular reactions

A critical overview of the recent progress in crossed-beam reactive scattering is presented. This review is not intended to be an exhaustive nor a comprehensive one, but rather a critical assessment of what we have been learning about bimolecular reaction dynamics using crossed molecular beams since year 2000. Particular emphasis is placed on the information content encoded in the product angular distribution-the trait of a typical molecular beam scattering experiment-and how the information can help in answering fundamental questions about chemical reactivity. We will start with simple reactions by highlighting a few benchmark three-atom reactions, and then move on progressively to the more complex chemical systems and with more sophisticated types of measurements. Understanding what cause the experimental observations is more than computationally simulating the results. The give and take between experiment and theory in unraveling the physical picture of the underlying dynamics is illustrated throughout this review.

Transition-State Energy and Geometry, Exothermicity, and van der Waals Wells on the F + H2 → FH + H Ground-State Surface Calculated at the r12-ACPF-2 Level

Explicitly correlated averaged coupled-pair functional methods have been used to compute the ground-state Born-Oppenheimer potential energy surface for the F + HH' --> FH + H' reaction at the F + HH' and FH + H' asymptotes, the F...HH', and FH...H van der Waals wells, the reaction transition state, and at points along the intrinsic reaction coordinate connecting all of these stationary points. To these energies, corrections for spin-orbit coupling and scalar relativistic effects were added to produce total electronic energies whose accuracy is demonstrated to be very high (e.g., 0.1 kcal mol(-1)). The final data are used to refine the two-body parts of the currently best three-dimensional potential energy surface for this reaction, to predict several spectroscopic parameters of the species involved, and to offer accurate estimates of the title reaction's exothermicity (32.0 kcal mol(-1)) and activation barrier (1.8 kcal mol(-1)) as well as the geometry of the transition state.

Quasiclassical Trajectory Study of the F + CH4 Reaction Dynamics on a Dual-Level Interpolated Potential Energy Surface

An ab initio interpolated potential energy surface (PES) for the F + CH4 reactive system has been constructed using the interpolation method of Collins and co-workers. The ab initio calculations have been performed using second-order Möller-Plesset (MP2) perturbation theory to build the initial PES. Scaling all correlation (SAC) methodology has been employed to improve the ab initio calculations and to construct a dual-level PES. Using this PES, a detailed quasiclassical trajectory study of integral and differential cross sections, product rovibrational populations and internal energy distributions has been carried out for the F + CH4 and F + CD4 reactions and the theoretical results have been compared with the available experimental data.

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%.

Theoretical study of transition state structure and reaction enthalpy of the F+H2→HF+H reaction by a diffusion quantum Monte Carlo approach

Ab initio calculations of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction has been carried out by the fixed-node diffusion quantum Monte Carlo method in this study. The Monte Carlo sampling is based on the Ornstein-Uhlenbeck random walks guided by a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculated barrier height of 1.09(16) kcal/mol is consistent with the experimental values, 0.86(10)/1.18(10) kcal/mol, and the calculated value from the multireference-type coupled-cluster (MRCC) calculation with the aug-cc-pVQZ(F)/cc-pVQZ(H) basis set, 1.11 kcal/mol. The Monte Carlo-based calculation also gives a similar value of the reaction enthalpy, -32.00(4) kcal/mol, compared with the experimental value, -32.06(17) kcal/mol, and the calculated value from a MRCC/aug-cc-pVQZ(F)/cc-pVQZ(H) calculation, -31.94 kcal/mol. This study clearly indicates a further application of the random-walk-based approach in the field of quantum chemical calculation.

Comparison of experimental time-of-flight spectra of the HF products from the F+H2 reaction with exact quantum mechanical calculations

High resolution HF product time-of-flight spectra measured for the reactive scattering of F atoms from n-H2(p-H2) molecules at collision energies between 69 and 81 meV are compared with exact coupled-channel quantum mechanical calculations based on the Stark-Werner ab initio ground state potential energy surface. Excellent agreement between the experimental and computed rotational distributions is found for the HF product vibrational states v'=1 and v'=2. For the v'=3 vibrational state the agreement, however, is less satisfactory, especially for the reaction with p-H2. The results for v'=1 and v'=2 confirm that the reaction dynamics for these product states is accurately described by the ground electronic state 1 (2)A' potential energy surface. The deviations for HF(v'=3, j' > or =2) are attributed to an enhancement of the reaction resulting from the 25% fraction of excited ((2)P(12)) fluorine atoms in the reactant beam.

A resonance-mediated non-adiabatic reaction: F*(2P1/2) + HD --> HF(v' = 3) + D

The reaction of F(2P3/2,1/2) + HD --> HF(v' = 3) + D was investigated in a rotating-source, crossed-beam machine. The high translational energy resolution afforded by the Doppler-selected time-of-flight technique enabled us to distinguish the differential attributes of the HF(v' = 3) + D products of the ground state (2P3/2) reaction from those due to the spin-orbit excited (2P1/2) one. It was found that the F*(2P1/2) reactivity is significantly smaller than that for F(2P3/2), and the two state-to-state angular distributions exhibit remarkable similarities, though some differences were noted. Comparing the results with those concluded previously, we assert that both the adiabatic (F(2P3/2) + HD) and, in particular, the non-adiabatic (F*(2P1/2) + HD) reactions are predominantly mediated by a resonance mechanism for the formation of the HF(v' = 3) + D channel.

Angular distributions for the F+H2→HF+H reaction: The role of the F spin-orbit excited state and comparison with molecular beam experiments

We report quantum mechanical calculations of center-of-mass differential cross sections (DCS) for the F+H(2)-->HF+H reaction performed on the multistate [Alexander-Stark-Werner (ASW)] potential energy surfaces (PES) that describe the open-shell character of this reaction. For comparison, we repeat single-state calculations with the Stark-Werner (SW) and Hartke-Stark-Werner (HSW) PESs. The ASW DCSs differ from those predicted for the SW and HSW PES in the backward direction. These differences arise from nonadiabatic coupling between several electronic states. The DCSs are then used in forward simulations of the laboratory-frame angular distributions (ADs) measured by Lee, Neumark, and co-workers [J. Chem. Phys. 82, 3045 (1985)]. The simulations are scaled to match experiment over the range 12 degrees <Theta(lab)<80 degrees. As a natural consequence of the reduced backward scattering, the ASW ADs are more forward and sideways scattered than predicted by the HSW PES. At the two higher collision energies (2.74 and 3.42 kcal/mol) the enhanced sideways scattering of HF v(')=2 products bring the ASW ADs in very good agreement with the experiment. At the lowest collision energy (1.84 kcal/mol), the simulations, for all three sets of PESs consistently underestimate the sideways scattering. The residual disagreements, particularly at the lowest collision energy, may be due to the known deficiencies in the PESs.

Role of the F spin-orbit excited state in the F+HD reaction: Contributions to the dynamical resonance

We report quantum mechanical calculations of excitation functions (relative reaction cross sections) for the F+HD reaction. We include three potential energy surfaces and an accurate treatment of all couplings (non-adiabatic, spin-orbit, and Coriolis). Comparison with experimental results [Dong, Lee, and Liu, J. Chem. Phys., 113, 3633 (2000)] show excellent agreement for the DF product channel and an improved but not perfect agreement for the HF product channel. In the former case, when weighted by the (16%) fractional population of the spin-orbit excited state (F(*)) in the beam, the overall reactivity of the F(*) is small (approximately 5%). For the HF product channel and with the same (16%) fractional weight, F(*) reactivity makes a contribution of approximately 12% in the high-energy tail of the resonance peak. As a result, averaging over the population of F spin-orbit states in the beam changes the shape of the resonance. The greater the fraction of F(*) in the beam, the less pronounced will be the resonance modulation of the reaction excitation function.

The investigation of spin–orbit effect for the F(2P)+HD reaction

In this paper, we employ the time-dependent quantum wave packet method to study the reaction of F((2)P(3/2), (2)P(1/2)) with HD on the Alexander-Stark-Werner potential energy surface. The reaction probabilities and total integral cross sections of the spin-orbit ground and excited states for the two possible products of the system are calculated. Because the reaction channel of the excited spin-orbit state is closed at the resonance energy, the resonance feature does not appear in the reaction probabilities and cross section for the F((2)P(1/2))+HD(v=j=0)-->HF+D reaction, in contrast with that found for the ground spin--orbit state. We also compare the average cross sections of the two possible products with the experimental measurement. The resonance peak in the present average cross section for the HF+D product is slightly larger than the experimental result, but much smaller than that of the single-state calculations on the potential energy surface of Stark and Werner. It seems that the spin--orbit coupling would play a relatively important role in this reaction. Moreover, the isotope effects of the ground and excited spin--orbit states and the reactivity of the two product channels from the excited spin--orbit state are presented.

Simulation of the reactive scattering of F+D2 on a model family of potential energy surfaces with various topographies: the correlation approach

The connection between the salient features of the potential energy surface (PES) and the dynamical characteristics of the elementary collision process is studied using a correlation approach based on quasiclassical trajectory simulations. The method is demonstrated for the reaction F + D2 --> D + DF for which the scattering characteristics were calculated on a model family of PES's based on a London-Eyring-Polanyi-Sato-type five-parameter equation. The correlations between the reactive cross section and the vibrational and rotational quantum numbers and the scattering angle of the DF product, and the various parameters of the collinear and noncollinear PES's, such as the location and height of the minimal barrier and the Sato coefficients, are reported. Although usually correlations between two variables suffice, in some cases coefficients of correlation among three variables are required. The role of nonlinear parameter dependencies in computing the correlation coefficients is also considered. The correlation approach makes it possible to examine a large set of potential surfaces without intermediate human control and obtain quantitative information.

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.