Quantum statistical and wave packet studies of insertion reactions of S(D1) with H2, HD, and D2

Reaction dynamics of S(3P) with 1,3-butadiene and isoprene: crossed-beam scattering, low-temperature flow experiments, and high-level electronic structure calculations

Sulfur atoms serve as key players in diverse chemical processes, from astrochemistry at very low temperature to combustion at high temperature. Building upon our prior findings, showing cyclization to thiophenes following the reaction of ground-state sulfur atoms with dienes, we here extend this investigation to include many additional reaction products, guided by detailed theoretical predictions. The outcomes highlight the complex formation of products during intersystem crossing (ISC) to the singlet surfaces. Here, we employed crossed-beam velocity map imaging and high-level ab initio methods to explore the reaction of S(3P) with 1,3-butadiene and isoprene under single-collision conditions and in low-temperature flows. For the butadiene reaction, our experimental results show the formation of thiophene via H2 loss, a 2H-thiophenyl radical through H loss, and thioketene through ethene loss at a slightly higher collision energy compared to previous observations. Complementary Chirped-Pulse Fourier-Transform mmWave spectroscopy (CP-FTmmW) measurements in a uniform flow confirmed the formation of thioketene in the reaction at 20 K. For the isoprene reaction, we observed analogous products along with the 2H-thiophenyl radical arising from methyl loss and C3H4S (loss of ethene or H2 + acetylene). CP-FTmmW detected the formation of thioformaldehyde via loss of 1,3-butadiene, again in the 20 K flow. Coupled-cluster calculations on the pathways found by the automated kinetic workflow code KinBot support these findings and indicate ISC to the singlet surface, leading to the generation of various long-lived intermediates, including 5-membered heterocycles.

Reactions dynamics for X + H2 insertion reactions (X = C(1D), N(2D), O(1D), S(1D)) with Cayley propagator ring-polymer molecular dynamics

In this work, rate coefficients of four prototypical insertion reactions, X + H2 → H + XH (X = C(1D), N(2D), O(1D), S(1D)), and associated isotope reactions are calculated based on ring polymer molecular dynamics (RPMD) with Cayley propagator (Cayley-RPMD). The associated kinetic isotope effects are systematically studied too. The Cayley propagator used in this work increases the stability of numerical integration in RPMD calculations and also supports a larger evolution time interval, allowing us to reach both high accuracy and efficiency. So, our results do not only provide chemical kinetic data for the title reactions in an extended temperature range but also consist of experimental results, standard RPMD, and other theoretical methods. The results in this work also reflect that Cayley-RPMD has strong consistency and high reliability in its investigations of chemical dynamics for insertion reactions.

Sulfur (3P) Reaction with Conjugated Dienes Gives Cyclization to Thiophenes under Single Collision Conditions

We combine crossed-beam velocity map imaging with high-level ab initio/transition state theory modeling of the reaction of S(3P) with 1,3-butadiene and isoprene under single collision conditions. For the butadiene reaction, we detect both H and H2 loss from the initial adduct, and from reaction with isoprene, we see both H loss and methyl loss. Theoretical calculations confirm these arise following intersystem crossing to the singlet surface forming long-lived intermediates. For the butadiene reaction, these lose H2 to form thiophene as the dominant channel, H to form the detected 2H-thiophenyl radical, or ethene, giving thioketene. For isoprene, additional reaction products are suggested by theory, including the observed H and methyl loss radicals, but also methyl thiophene, thioformaldehyde, and thioketene. The results for S(3P) + 1,3-butadiene, showing direct cyclization to the aromatic product and yielding few bimolecular product channels, are in striking contrast to those for the analogous O(3P) reaction.

Universal behavior in complex-mediated reactions: Dynamics of S(1D) + o-D2 → D + SD at low collision energies

Reactive and elastic cross sections and rate coefficients have been calculated for the S(1D) + D2(v = 0, j = 0) reaction using a modified hyperspherical quantum reactive scattering method. The considered collision energy ranges from the ultracold regime, where only one partial wave is open, up to the Langevin regime, where many of them contribute. This work presents the extension of the quantum calculations, which in a previous study were compared with the experimental results, down to energies in the cold and ultracold domains. Results are analyzed and compared with the universal case of the quantum defect theory by Jachymski et al. [Phys. Rev. Lett. 110, 213202 (2013)]. State-to-state integral and differential cross sections are also shown covering the ranges of low-thermal, cold, and ultracold collision energy regimes. It is found that at E/kB < 1 K, there are substantial departures from the expected statistical behavior and that dynamical features become increasingly important with decreasing collision energy, leading to vibrational excitation.

Signature of shape resonances on the differential cross sections of the S(1D)+H2 reaction

Shape resonances appear when the system is trapped in an internuclear potential well after tunneling through a barrier. They manifest as peaks in the collision energy dependence of the cross section (excitation function), and in many cases, their presence can be observed experimentally. High-resolution crossed-beam experiments on the S(¹D) + H₂(j = 0) reaction in the 0.81-8.5 meV collision energy range reaction revealed non-monotonic behavior and the presence of oscillations in the reaction cross section as a function of the collision energy, as predicted by quantum mechanical (QM) calculations. In this work, we have analyzed the effect of shape resonances on the differential cross sections for this insertion reaction by performing additional QM calculations. We have found that, in some cases, the resonance gives rise to a large enhancement of extreme backward scattering for specific final states. Our results also show that, in order to yield a significant change in the state-resolved differential cross section, the resonance has to be associated with constructive interference between groups of partial waves, which requires not getting blurred by the participation of many product helicity states.

Quantum dynamics studies of isotope effects in the Mg+(3p) + HD → MgH+/MgD+ + D/H insertion reaction

The time-dependent wave packet quantum dynamics studies for the Mg+(3p) + HD → MgH+/MgD+ + D/H diabatic reaction are carried out for the first time on recently developed diabatic YHWCH potential energy surfaces [Phys. Chem. Chem. Phys., 2018, 20, 6638-6647]. The results of reaction probabilities and total integral cross sections show a dramatic preference to the formation of MgD+ over MgH+ owing to the insertion reaction mechanism in the title reaction. The MgD+/MgH+ branching ratio witnesses a monotonic decrease from 10.58 to 3.88 at collision energy range of 0.01 to 0.20  eV, and at the collision energy of 0.114  eV, it is close to the experimental value of 5. The rovibrational state-resolved ICSs of the two channels show the products MgD+ have higher vibrational excitation and hotter rotational state distributions. The opacity function P(J) suggests that the MgH+ + D channel and MgD+ + H channel are dominated by high-b and low-b collisions, respectively. Both forward and backward scattering peaks are found in the differential cross section curves, whereas the angle distributions of products are not strictly forward-backward symmetric because of the short lifetime of the complex in the reaction.

Dynamics study on the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction: insertion-abstraction mechanism

Time-dependent wave packet calculations are carried out for two reaction channels of the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction. The potential well on the excited state potential energy surface makes the reaction preferable to proceed through the insertion reaction path. The dominance of the NaD + H reaction channel and product rotational state distributions are found to be in agreement with the characteristics of typical adiabatic insertion reactions. However, significant forward scattering peaks in the differential cross sections (DCS) are found to be inconsistent with the forward-backward symmetric scattering characteristic of typical adiabatic insertion reactions, which indicate that the Na(3p) + HD reaction is dominated by a direct reaction mechanism. The comparison between adiabatic and non-adiabatic calculated DCSs reveals that the non-adiabatic couplings in the reaction could reduce the lifetime of the intermediate complex. Finally, the insertion-abstraction mechanism is put forward for the non-adiabatic Na(3p) + HD reaction.

Theoretical Study of Barrierless Chemical Reactions Involving Nearly Elastic Rebound: The Case of S(1D) + X2, X = H, D

For some values of the total angular momentum consistent with reaction, the title processes involve nonreactive trajectories proceeding through a single rebound mechanism during which the internal motion of the reagent diatom is nearly unperturbed. When such paths are in a significant amount, the classical reaction probability is found to be markedly lower than the quantum mechanical one. This finding was recently attributed to an unusual quantum effect called diffraction-mediated trapping, and a semiclassical correction was proposed in order to take into account this effect in the classical trajectory method. In the present work, we apply the resulting approach to the calculation of opacity functions as well as total and state-resolved integral cross sections (ICSs) and compare the values obtained with exact quantum ones, most of which are new. As the title reactions proceed through a deep insertion well, mean potential statistical calculations are also presented. Seven values of the collision energy, ranging from 30 to 1127 K, are considered. Two remarkable facts stand out: (i) The corrected classical treatment strongly improves the accuracy of the opacity function as compared to the usual classical treatment. When the entrance transition state is tight, however, those trajectories crossing it with a bending vibrational energy below the zero point energy must be discarded. (ii) The quantum opacity function, particularly its cutoff, is finely reproduced by the statistical approach. Consequently, the total ICS is also very well described by the two previous approximate methods. These, however, do not predict state-resolved ICSs with the same accuracy, proving thereby that (i) one or several genuine quantum effects involved in the dynamics are missed by the corrected classical treatment and (ii) the dynamics are not fully statistical.

Globally Accurate Potential Energy Surface for HCS(A2A″) by Extrapolation to the Complete Basis Set Limit

A global potential energy surface (PES) representation of the C(³P) + SH(X ²Π) → H(²S) + CS(a ³Π) system is developed by fitting plenty of precise energies obtained through the ab initio calculation with aug-cc-pV QZ and aug-cc-pV5Z basis sets via extrapolation to the complete basis set limit. The topographical characteristics of the PES are examined in detail, and it is found that they agree well with previous calculations available in the literature. By utilizing the PES of HCS(A²A″), the corresponding reaction is investigated using the quasi-classical trajectory (QCT) method in the collision energy range of 0.08-1.0 eV. The minimum energy paths (MEPs) calculated on the basis of the present PES indicate that the C(³P) + SH(X ²Π) → H(²S) + CS(a ³Π) reaction is exothermic, with the exothermicity ∼0.204 eV. The calculation for the capture time indicates that the reaction is mainly governed by the indirect mechanism at the lower collision energy, while, for higher collision energy, the direct mechanism is in coexistence with the indirect mechanism, and the latter one plays a dominant role.

An Empirical Dynamical Barrier for Statistical Theory of Low-Energy Reactive S(1D) + HD(j = 0), H2(j = 0) Collisions

A simple model potential is proposed to describe the dynamical barrier in the mean interaction potential at small distances between the reactants in S(¹D) + HD(¹Σ, v = 0, j = 0) reaction. The statistical theory of collision complex formation and complex decay is applied to calculate the total reaction cross sections and the cross sections for SH and SD productions in the range of low collision energies E_c = (0.4-60) meV. The results are compared with measured cross sections and results of hyperspherical close coupling calculations. As a check of consistency the same comparisons are presented for the case of S(¹D) + H₂(¹Σ, v = 0, j = 0) reaction.

Globally accurate potential energy surface for the ground-state HCS(X2A') and its use in reaction dynamics

A globally accurate many-body expansion potential energy surface is reported for HCS(X²A') by fitting a wealth of accurate ab initio energies calculated at the multireference configuration interaction level using aug-cc-pVQZ and aug-cc-pV5Z basis sets via extrapolation to the complete basis set limit. The topographical features of the present potential energy surface are examined in detail and is in good agreement with the raw ab initio results, as well as other theoretical results available in literatures. By utilizing the potential energy surface of HCS(X²A'), the dynamic studies of the C(³P) + SH(X²Π) → H(²S) + CS(X¹∑⁺) reaction has been carried out using quasi-classical trajectory method.

A new potential energy surface for the H2S system and dynamics study on the S((1)D) + H2(X(1)Σg(+)) reaction

We constructed a new global potential energy surface (PES) for the electronic ground state ((1)A') of H2S based on 21,300 accurate ab initio energy points over a large configuration space. The ab initio energies are obtained from multireference configuration interaction calculations with a Davidson correction using basis sets of quadruple zeta quality. The neural network method is applied to fit the PES, and the root mean square error of fitting is small (1.68 meV). Time-dependent wave packet studies for the S((1)D) + H2(X(1)Σg(+)) → H((2)S) + SH(X(2)Π) reaction on the new PES are conducted to study the reaction dynamics. The calculated integral cross sections decrease with increasing collision energy and remain fairly constant within the high collision energy range. Both forward and backward scatterings can be observed as expected for a barrierless reaction with a deep well on the PES. The calculated integral cross sections and differential cross sections are in good agreement with the experimental results.

INVESTIGATION OF THE EXCHANGE REACTION H + H′S → HS + H′ ON THE 1A′ STATE POTENTIAL ENERGY SURFACE

The quantum time dependent wave packet (TDWP) and quasiclassical trajectory (QCT) calculations were carried out to study the exchange reaction H(2S) + H′S(2Π) → HS(2Π) + H′(2S) on the 1A′ potential energy surface (PES). The integral cross sections of the H + H′S (v = j = 0) → HS + H′ reaction calculated by the two methods were presented. The results reveal that the integral cross sections (ICS) decrease with the collision energy increasing. The result of the QCT calculations is reasonably consistent with the time-dependent wave packet. Moreover, the differential cross sections (DCS) were calculated by the QCT method at the four different collision energies, which display a forward–backward symmetry. A long-lifetime H2S intermediate complex of the exchange reaction was found according to the trajectories. In the stereodynamics investigation, the polar and dihedral angle distribution functions were calculated, which have the distinct oscillations. The oscillations could be attributed to the deep well on the 1A′ PES. However, based on the polar-angle and dihedral angle distribution functions, it could be predicted that the main product rotational angular momentum preferentially point to the positive or negative direction of y-axes.

Rate coefficients from quantum and quasi-classical cumulative reaction probabilities for the S(1D) + H2 reaction

Cumulative reaction probabilities (CRPs) at various total angular momenta have been calculated for the barrierless reaction S((1)D) + H(2) → SH + H at total energies up to 1.2 eV using three different theoretical approaches: time-independent quantum mechanics (QM), quasiclassical trajectories (QCT), and statistical quasiclassical trajectories (SQCT). The calculations have been carried out on the widely used potential energy surface (PES) by Ho et al. [J. Chem. Phys. 116, 4124 (2002)] as well as on the recent PES developed by Song et al. [J. Phys. Chem. A 113, 9213 (2009)]. The results show that the differences between these two PES are relatively minor and mostly related to the different topologies of the well. In addition, the agreement between the three theoretical methodologies is good, even for the highest total angular momenta and energies. In particular, the good accordance between the CRPs obtained with dynamical methods (QM and QCT) and the statistical model (SQCT) indicates that the reaction can be considered statistical in the whole range of energies in contrast with the findings for other prototypical barrierless reactions. In addition, total CRPs and rate coefficients in the range of 20-1000 K have been calculated using the QCT and SQCT methods and have been found somewhat smaller than the experimental total removal rates of S((1)D).

Dynamics of the S(1D2)+HD(j=0) reaction at collision energies approaching the cold regime: a stringent test for theory

We report integral cross sections for the S(1D2)+HD(j=0)→DS+H and HS+D reaction channels obtained through crossed-beam experiments reaching collision energies as low as 0.46 meV and from adiabatic time-independent quantum-mechanical calculations. While good overall agreement with experiment at energies above 10 meV is observed, neither the product channel branching ratio nor the low-energy resonancelike features in the HS+D channel can be theoretically reproduced. A nonadiabatic treatment employing highly accurate singlet and triplet potential energy surfaces is clearly needed to resolve the complex nature of the reaction dynamics.

Mean potential phase space theory of chemical reactions

A nonconventional application of phase space theory to the insertion reactions A+H(2), with A=C((1)D) and S((1)D), is presented. Instead of approximating the potential energies of interaction between separated fragments by their isotropic long-range contributions, as in the original theory, the latter are replaced by the accurate potential energies averaged with respect to Jacobi angles. The integral and differential cross sections obtained from this mean potential phase space theory (MPPST) turn out to be in very satisfying agreement with the benchmark predictions of the time-independent and time-dependent statistical quantum methods. The formal and numerical simplicity of MPPST with respect to any approach combining statistical assumptions and dynamical calculations makes it a promising tool for studying indirect polyatomic reactions.

Significant Nonadiabatic Effects in the S(1D) + HD Reaction

A nonadiabatic quantum dynamics calculation involving four coupled potential energy surfaces (two degenerate 3A' ', one 3A', and one 1A') and the spin-orbit coupling matrix for these states is reported for the title reaction. The results show that the important discrepancy between theoretically calculated and experimentally measured intramolecular isotope effects can at least in part be attributed to significant nonadiabatic effects.

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.

Dynamics of insertion reactions of H2 molecules with excited atoms

Recent progress in the study of insertion reactions of hydrogen molecules with excited atoms is reviewed in this article. In particular, the dynamics of the reaction of O(1D), N(2D), C(1D), and S(1D) with H2 and its isotopomers, which have received a great deal of attention over the past decade, are examined in detail. All of these systems have in common the existence of several potential energy surfaces (PES) correlating with the reagents' states, and consequently, they can give rise to reaction following different adiabatic and nonadiabatic pathways. The main contribution, however, arises from their ground singlet PESs which feature the existence of deep wells with small or null barriers for insertion. Accordingly, these reactions proceed mainly via formation of relatively long-lived collision complexes and display an overall nearly statistical behavior. In spite of their similarities, the various reactions have peculiar characteristics caused by important differences of their respective PESs. The contribution of excited PES to the global reactivity, which has also become an important issue and a challenge both for theory and experiment, is also examined. The different theoretical approaches are discussed in the text, along with the experimental results obtained by a variety of techniques. The recent exact quantum treatments of these reactive systems together with the development of a rigorous statistical model have contributed to a very accurate description which in many cases matches very well the detailed measurements. The quasi-classical trajectory (QCT) method has also provided a fairly accurate description of the reaction dynamics for these systems. In particular, the analysis in terms of collision times has yielded interesting clues about the reaction mechanisms.

A new ab initio potential-energy surface of HO2(X2A") and quantum studies of HO2 vibrational spectrum and rate constants for the H + O2 <--> O + OH reactions

A new global potential-energy surface for the ground electronic state of HO(2)(X(2)A(")) has been developed by three-dimensional cubic spline interpolation of more than 15 000 ab initio points, which were calculated at the multireference configuration-interaction level with Davidson correction using the augmented correlation-consistent polarized valence quadruple zeta basis set. Low-lying vibrational states were obtained in this new potential using the Lanczos method and assigned. The calculated vibrational frequencies are in much better agreement with the available experimental band origins than those obtained from a previous potential. In addition, rate constants for the H+O(2) <--> O + OH reactions were obtained using a wave-packet-based statistical model. Reasonably good agreement with experimental data was obtained. These results demonstrate the accuracy of the potential.

On the theory of complex-forming chemical reactions: effect of parity conservation on the polarization of differential cross sections

For complex-forming triatomic reactions such as the prototypical insertion reactions intensively studied in the last few years, quantum mechanical differential cross sections (DCS) present sharp forward/backward polarization peaks when the reagent rotational angular momentum quantum number j is zero. Moreover, the size of the peaks decreases rapidly with increasing j values so that for j = 3, they are no longer visible. In contrast, the polarization peaks are always missing in the classical mechanical DCSs. Apart from the peaks, however, the quantum and classical DCSs are usually in good agreement. In a recent rapid communication, we showed that the fundamental reason for the previous differences in the quantum and classical scenarios is that parity conservation leads in quantum mechanics to an angular momentum constraint without equivalent in classical mechanics. We also proposed a parity-restoring approximation leading to an accurate semi-classical description of the peaks. While only the main lines of the demonstration were given in the communication, we report here the whole developments. We also analyse why the peaks disappear when the reagent diatom is rotationally excited. As a by-product of the previous developments, we finally discuss the possibility of a general statistico-dynamical semiclassical approach.

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.

Exact quantum dynamics of N(D2)+H2→NH+H reaction: Cross-sections, rate constants, and dependence on reactant rotation

Using an exact Chebyshev wave packet method, initial state-specified (upsilon(i)=0, j(i)=0,2) integral cross-sections and rate constants are obtained for the title reaction on the latest ab initio potential energy surface. Reaction probabilities up to J=29 are dependent on the reactant rotation and show mild oscillations superimposed on a broad background. Due to a barrier in the entrance channel, the cross sections increase with energy with clear thresholds and the rate constants vary with temperature in the Arrhenius form. The calculated canonical rate constant is in good agreement with the experimental measurements. Our results also indicate that the quasiclassical trajectory method underestimates the rate due to the neglect of tunneling, while the quantum statistical approach overestimates because of the short lifetime of the reaction intermediate.

Parity conservation and polarization of differential cross sections in complex-forming chemical reactions

For complex-forming chemical reactions, such as atom-diatom insertion reactions, quantum scattering and quantum statistical calculations usually predict sharp forward/backward peaks in the Differential Cross Sections (DCS). Conversely, the corresponding classical calculations are unable to reproduce these peaks. We show here that the basic reason for such an intriguing failure is that parity conservation is ignored in classical mechanics. A by-product of the analysis is a simple parity-restoring approximation that might significantly increase the ability of classical mechanics to describe DCSs over the whole angular range for the title processes.

Time-Dependent Quantum Wave Packet Calculations of Three-Dimensional He - O2 Inelastic Scattering

We have studied a three-dimensional time-dependent quantum dynamics of He - O2 inelastic scattering by using a recently published ab initio potential energy surface. The state-to-state transition probabilities at zero total angular momentum have been calculated in the energy range of 0.12-0.59 eV, and the product rotational distributions are extracted. J-shifting approximation is used to estimate the probabilities for J > 0. The integral cross sections and thermal rate constants are then calculated.