An Improved Potential Energy Surface for the H2Cl System and Its Use for Calculations of Rate Coefficients and Kinetic Isotope Effects

Development of the Time-Independent Methods for the Cl + H2/F + HD Reaction Using Hyper-Spherical Coordinates Including (Full) Spin-Orbit Characteristics

Recently, a combined study of high-resolution molecular crossed beam experiment and accurate full-dimensional time-dependent theory, including full spin-orbit characteristics on the effect of electronic spin and orbital angular momenta in the F + HD reaction, was reported by some of us, focusing on the partial wave resonance phenomenon (Science 2021, 371, 936-940). It revealed that the time-dependent theory could explain all of the details observed in the high-resolution experiment. Here, we develop two time-independent close-coupling methods using hyperspherical coordinates, including the two-state model, where only a part of the spin-orbit characteristics is considered, and the six-state model, where the full spin-orbit characteristics is considered. With these two newly developed theoretical models and the adiabatic theoretical model, the detailed reaction dynamics of the F + HD (v = 0, j = 0) reaction and the Cl + H2 (v = 0, j = 0) reaction are investigated and compared. Some of the results are compared with the time-dependent quantum wave packet theory and the experimental observations, and good agreements have been obtained, which suggests the validity of the pure-procession approximation in the six-state model using different theoretical methods. This work demonstrates the ability of the reactive scattering theory including full spin-orbit characteristics for describing the reactions of a halogen atom plus hydrogen molecule and its isotopologues.

Significant Isotope Effects from the Nonadiabatic Couplings in the Cl(2P) + HD(v = 0, j = 0) Reaction

The impact of non-Born-Oppenheimer couplings on the isotopic effects in the reaction of the Cl(2P) atom with the HD (v = 0, j = 0) molecule is investigated with our recently developed nonadiabatic time-independent quantum scattering methods, where the full open-shell characteristics are included in the six-state model, and also with the recently developed two-state model solving by time-independent methods, where part of the open-shell characteristic is included. The same reaction is also calculated with the simple adiabatic model using the lowest adiabatic potential energy surface. Compared with the results from different models, it is found that the reactivity of the Cl + HD → HCl + D channel is significantly overestimated in the adiabatic model. In contrast, the reactivity of the other channel agrees well with the nonadiabatic models. This is due to the van der Waals well in the reactant channel being changed a lot by including the nonadiabatic couplings. These quantum dynamics calculations suggest that sometimes the adiabatic model should be used with caution; otherwise, it may result in significant deviations for some reactions.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Transition states of spin-forbidden reactions

New approximation method for locating stationary points on lowest spin-coupled potential energy surface (PES) using density functional calculations.

Full-dimensional multi-state simulation of the photodissociation of thioanisole

The photodissociation of thioanisole is very interesting because the experiments of Lim and Kim provide evidence for mode-specific effects on the product distribution. They showed that, with a specific S-CH₃ stretching mode being excited as the reagent is excited to the S₁ electronic state, there is a sharp increase in the proportion of the ground-state product to the excited-state product. In the present work, we report 78 011 full-dimensional semiclassical multi-state trajectories of the photodissociation process using the coherent switching with decay of mixing dynamics method. The potential surfaces and couplings are based on electronic structure calculations that include dynamic correlation through second order perturbation theory. We report results for four sets of initial conditions, one corresponding roughly to 0-0 excitation and three corresponding to exciting one vibrational mode, to look for mode-specific effects. The simulations show no significant mode-specific effect on the product energy distributions, but they do show an effect on the distribution of minimum-energy gaps in the trajectories and on the lifetime for dissociation. In particular, excitation of the S-CH₃ stretching mode leads to trajectories passing closer to the S₁-S₂ conical intersection and to shorter lifetimes. This provides a possible explanation of why experimental results are different for excitation of this vibration.

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Perchlorate formation on Mars through surface radiolysis-initiated atmospheric chemistry: A potential mechanism

Recent observations of the Martian surface by the Phoenix lander and the Sample Analysis at Mars indicate the presence of perchlorate (ClO₄^-). The abundance and isotopic composition of these perchlorates suggest that the mechanisms responsible for their formation in the Martian environment may be unique in our solar system. With this in mind, we propose a potential mechanism for the production of Martian perchlorate: the radiolysis of the Martian surface by galactic cosmic rays, followed by the sublimation of chlorine oxides into the atmosphere and their subsequent synthesis to form perchloric acid (HClO₄) in the atmosphere, and the surface deposition and subsequent mineralization of HClO₄ in the regolith to form surface perchlorates. To evaluate the viability of this mechanism, we employ a one-dimensional chemical model, examining chlorine chemistry in the context of Martian atmospheric chemistry. Considering the chlorine oxide, OClO, we find that an OClO flux as low as 3.2 × 10⁷ molecules cm^-2 s^-1 sublimated into the atmosphere from the surface could produce sufficient HClO₄ to explain the perchlorate concentration on Mars, assuming an accumulation depth of 30 cm and integrated over the Amazonian period. Radiolysis provides an efficient pathway for the oxidation of chlorine, bypassing the efficient Cl/HCl recycling mechanism that characterizes HClO₄ formation mechanisms proposed for the Earth but not Mars.

Reaction dynamics and mechanism of the Cl + HD(v = 1) reaction: a quantum mechanical study

Time-independent quantum mechanical calculations have been performed in order to characterize the dynamics and stereodynamics of Cl + HD reactive collisions. Calculations have been carried out at two different total energy values and for various initial states using the adiabatic potential energy surface by Bian and Werner [J. Chem. Phys. 2000, 112, 220]. Special attention has been paid to the reaction with HD(v = 1) for which integral and differential cross-sections have been calculated and the effect of vibrational vs translational energy on the reactivity has been examined. In addition, the reactant polarization parameters and polarization-dependent differential cross-sections have been determined. From these results, the spatial preferences of the reaction and the extent of the control of the cross sections achievable through a suitable preparation of the reactants have been also studied. The directional requirements are tighter for the HCl channel than for the DCl one. Formation of the products takes place preferentially when the rotational angular momentum of the HD molecule is perpendicular to the reactants approach direction. Cross-sections and polarization moments computed from the scattering calculations have been compared with experimental results by Kandel et al. [J. Chem. Phys. 2000, 112, 670] for the reaction with HD(v = 1) produced by stimulated Raman pumping. The agreement so obtained is good, and it improves the accordance found in previous calculations with other methodologies and potential energy surfaces.

STEREODYNAMICS STUDY OF THE ABSTRACTION REACTION H + CD4 → HD + CD3

A new London–Eyring–Polanyi–Sato (LEPS) potential energy surface (PES) is employed in this work to study the stereo properties for the abstraction reaction of hydrogen with methane at its rovibrationally ground state using the quasiclassical trajectory method (QCT). A "quasi-triatomic" approximation is used to treat the CD3 group of CD4 as a pseudoatom. The calculated excitation function of the title reaction can give a good agreement to most experimental and theoretical data at collision energies (Ec =1.5 ~ 2.5 eV ). Further investigation of the product HD in reaction H + CD4 (v = 0, j = 0) → HD + CD3 and D + CH4 (v = 0, j = 0) → HD + CH3 shows the dependence of the product rotational polarization on collision energies and mass factor, but P(θr) is not sensitive to both the collision energies and the mass factor.

Combined Self-Consistent-Field and Spin-Flip Tamm-Dancoff Density Functional Approach to Potential Energy Surfaces for Photochemistry

We present a new approach to calculating potential energy surfaces for photochemical reactions by combining self-consistent-field calculations for single-reference ground and excited states with symmetry-corrected spin-flip Tamm-Dancoff approximation calculations for multireference electronic states. The method is illustrated by an application with the M05-2X exchange-correlation functional to cis-trans isomerization of the penta-2,4-dieniminium cation, which is a model (with three conjugated double bonds) of the protonated Schiff base of retinal. We find good agreement with multireference configuration interaction-plus-quadruples (MRCISD+Q) wave function calculations along three key paths in the strong-interaction region of the ground and first excited singlet states.

Orientation effects in Cl + H2 inelastic collisions: characterization of the mechanisms

Based on quantum mechanical scattering (QM) calculations, we have analyzed the polarization of the product hydrogen molecule in Cl + H(2) (v = 0, j = 0) inelastic collisions. The spatial arrangements adopted by the rotational angular momentum and internuclear axis of the departing molecule have been characterized and used to prove that two distinct mechanisms, corresponding to different dynamical regimes, are responsible for the inelastic collisions. Such mechanisms, named as low-b and high-b, correlate with well defined ranges of impact parameter values, add in an essentially incoherent way, and can be clearly differentiated through the quantum mechanical polarization moment that measures the orientation of the products rotational angular momentum with respect to the scattering plane. Other directional effects turn out to fail when it comes to distinguishing the mechanisms. Quasiclassical trajectories (QCT) calculations have been used as a supplement to the purely quantum mechanical analysis. By combining QM and QCT results, which are in very good agreement, we have succeeded in obtaining a clear and meaningful picture of how the two types of collisions take place.

Dynamical regimes on the Cl + H2 collisions: inelastic rainbow scattering

While Cl + H(2) reactive collisions have been a subject of numerous experimental and theoretical studies, inelastic collisions leading to rotational energy transfer and/or vibrational excitation have been largely ignored. In this work, extensive quantum mechanical calculations covering the 0.5-1.5 eV total energy range and various initial rovibrational states have been carried out and used to perform a joint study of inelastic and reactive Cl + H(2) collisions. Quasiclassical trajectories calculations complement the quantum mechanical results. The analysis of the inelastic transition probabilities has revealed the existence of two distinct dynamical regimes that correlate with low and high impact parameters, b, and are neatly separated by glory scattering. It has been found that while high-b collisions are mainly responsible for |Δj| = 2 transitions which dominate the inelastic scattering, they are very inefficient in promoting higher |Δj| transitions. The effectiveness of this type of collision also drops with rotational excitation of H(2). In contrast, reactive scattering, that competes with |Δj| > 2 inelastic transitions, is exclusively caused by low-b collisions, and it is greatly favored when the reactants get rotationally excited. Previous studies focusing on the reactivity of the Cl + H(2) system established that the van der Waals well located in the entrance channel play a key role in determining the mechanism of the collisions. Our results prove this to be also a case for inelastic processes, where the origin of the double dynamical regime can be traced back to the influence exerted by this well that shapes the topology of the entrance channel of the Cl-H(2) system.

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.

Laser Spectroscopic Excitation Function and Reaction Threshold Studies of the H + DCl → HCl + D Gas-Phase Isotope Exchange Reaction

The dynamics of the gas-phase hydrogen atom exchange reaction H + DCl --> HCl + D were studied using the pulsed laser photolysis/laser induced fluorescence "pump-and-probe" method. Laser photolysis of H2S at 222 nm was used to generate nonequilibrium distributions of translationally excited hydrogen atoms at high dilution in a flowing moderator gas (Ar)/reagent (DCl) mixture. H and D atoms were detected with sub-Doppler resolution via Lyman-alpha laser induced fluorescence spectroscopy, which allowed the measurement of the line shapes of the moderated H atom Doppler profiles as well as the concentration of the D atoms produced in the H + DCl --> HCl + D reaction. From the measured H atom Doppler profiles, the time evolution of the initially generated nascent nonequilibrium H atom speed distribution toward its room-temperature thermal equilibrium form was determined. In this way, the excitation function and the reaction threshold (E0 = 0.65 +/- 0.13 eV) for the H + DCl --> HCl + D reaction could be determined from the measured nonequilibrium D atom formation rates and single collision absolute reaction cross-section values of 0.12 +/- 0.04 A2 and 0.45 +/- 0.11 A2 measured at reagent collision energies of 1.0 and 1.4 eV, respectively.

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

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

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.

A Quantum Wave Packet Dynamical Study of the Electronic and Spin−Orbit Coupling Effects on the Resonances in Cl(2P) + H2 Scattering

Dynamical resonances in Cl(2P) + H2 scattering are investigated with the aid of a time-dependent wave packet approach using the Capecchi-Werner coupled ab initio potential energy surfaces [Phys. Chem. Chem. Phys. 2004, 6, 4975]. The resonances arising from the prereactive van der Waals well (approximately 0.5 kcal/mol) and the transition-state (TS) region of the 2Sigma(1/2) ground spin-orbit (SO) state of the Cl(2P) + H2 system are calculated and assigned by computing their eigenfunctions and lifetimes. The excitation of even quanta along the bending coordinate of the resonances is observed. The resonances exhibit an extended van der Waals progression, which can be attributed to the dissociative states of ClH2. Excitation of H2 vibration is also identified in the high-energy resonances. The effect of the excited 2P(1/2) SO state of Cl on these resonances is examined by considering the electronic and SO coupling in the dynamical simulations. While the electronic coupling has only a minor impact on the resonance structures, the SO coupling has significant effect on them. The nonadiabatic effect due to the SO coupling is stronger, and as a result, the spectrum becomes broad and diffuse particularly at high energies. We also report the photodetachment spectrum of ClD2- and compare the theoretical findings with the available experimental results.

Details and consequences of the nonadiabatic coupling in the Cl(2P) + H2reaction

In an investigation of nonadiabaticity in the Cl + H2 reaction we examine the various coupling terms responsible. By neglecting various of these terms, we show that the spin-orbit coupling in the Cl atom is primarily responsible for non Born-Oppenheimer effects in this reaction, and that the anisotropies in the contributing electronic potential energy surfaces as well as Coriolis terms, are considerably weaker in their effect. Neglect of all coupling except spin-orbit leads to little change in the calculated reaction probabilities both for the Born-Oppenheimer allowed [Cl(2P3/2) + H2] and Born-Oppenheimer forbidden [Cl(2P1/2) + H2] reactions. This implies that one can safely neglect the coupling between different values of the electronic projection quantum number omega. Consequently, the computational effort involved in an accurate quantum scattering treatment of this (and, hopefully, other similar reactions) can be substantially reduced.

Absolute rate calculations for atom abstractions by radicals: energetic, structural and electronic factors

We calculate transition-state energies of atom-transfer reactions from reaction energies, electrophilicity indices, bond lengths, and vibration frequencies of the reactive bonds. Our calculations do not involve adjustable parameters and uncover new patterns of reactivity. The generality of our model is demonstrated comparing the vibrationally adiabatic barriers obtained for 100 hydrogen-atom transfers with the corresponding experimental activation energies, after correction for the heat capacities of reactants and transition state. The rates of half of these reactions are calculated using the Transition-State Theory with the vibrationally adiabatic path of the Intersecting-State Model and the semiclassical correction for tunneling (ISM/scTST). The calculated rates are within an order of magnitude of the experimental ones at room temperature. The temperature dependencies and kinetic isotope effects of selected systems are also in good agreement with the available experimental data. Our model elucidates the roles of the reaction energy, electrophilicity, structural parameters, and tunneling in the reactivity of these systems and can be applied to make quantitative predictions for new systems.

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.

Theoretical study of the validity of the Born-Oppenheimer approximation in the Cl + H2 --> HCl + H reaction

Reactivity of the excited spin-orbit state of Cl with H2 to yield ground-state HCl products is forbidden by the Born-Oppenheimer (BO) approximation. We used new ab initio potential energy surfaces and exact quantum scattering calculations to explore the extent of electronic nonadiabaticity in this reaction. In direct contrast to recent experiments, we predict that the BO-allowed reaction of the ground spin-orbit state will be much more efficient than the BO-forbidden reaction of the excited spin-orbit state. Also, Coriolis coupling opens up an electronically nonadiabatic inelastic channel, which competes substantially with reaction.