Reaction dynamics of S([sup 1]D)+H[sub 2]/D[sub 2] on a new ab initio potential surface

The vibronic state dependent predissociation of H2S: determination of all fragmentation processes

Photochemistry plays a significant role in shaping the chemical reaction network in the solar nebula and interstellar clouds. However, even in a simple triatomic molecule photodissociation, determination of all fragmentation processes is yet to be achieved. In this work, we present a comprehensive study of the photochemistry of H₂S, derived from cutting-edge translational spectroscopy measurements of the H, S(¹D) and S(¹S) atom products formed by photolysis at wavelengths across the range 155-120 nm. The results provide detailed insights into the energy disposal in the SH(X), SH(A) and H₂ co-fragments, and the atomisation routes leading to two H atoms along with S(³P) and S(¹D) atoms. Theoretical calculations allow the dynamics of all fragmentation processes, especially the bimodal internal energy distributions in the diatomic products, to be rationalised in terms of non-adiabatic transitions between potential energy surfaces of both ¹A' and ¹A'' symmetry. The comprehensive picture of the wavelength-dependent (or vibronic state-dependent) photofragmentation behaviour of H₂S will serve as a text-book example illustrating the importance of non-Born-Oppenheimer effects in molecular photochemistry, and the findings should be incorporated in future astrochemical modelling.

Rotational and nuclear-spin level dependent photodissociation dynamics of H2S

The detailed features of molecular photochemistry are key to understanding chemical processes enabled by non-adiabatic transitions between potential energy surfaces. But even in a small molecule like hydrogen sulphide (H₂S), the influence of non-adiabatic transitions is not yet well understood. Here we report high resolution translational spectroscopy measurements of the H and S(¹D) photoproducts formed following excitation of H₂S to selected quantum levels of a Rydberg state with ¹B₁ electronic symmetry at wavelengths λ ~ 139.1 nm, revealing rich photofragmentation dynamics. Analysis reveals formation of SH(X), SH(A), S(³P) and H₂ co-fragments, and in the diatomic products, inverted internal state population distributions. These nuclear dynamics are rationalised in terms of vibronic and rotational dependent predissociations, with relative probabilities depending on the parent quantum level. The study suggests likely formation routes for the S atoms attributed to solar photolysis of H₂S in the coma of comets like C/1995 O1 and C/2014 Q2.

The photodissociation dynamics of small molecules in the vacuum ultraviolet range can have key implications for astrochemical modelling, but revealing such dynamical details is a challenging task. Here the authors, combining high resolution experimental techniques, provide a detailed description of the fragmentation dynamics of selected rotational levels of a predissociated Rydberg state of H₂S.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

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.

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).

Kinetics and dynamics of the S(1D2) + H2 → SH + H reaction at very low temperatures and collision energies

We report combined studies on the prototypical S(1D2) + H2 insertion reaction. Kinetics and crossed-beam experiments are performed in experimental conditions approaching the cold energy regime, yielding absolute rate coefficients down to 5.8 K and relative integral cross sections to collision energies as low as 0.68 meV. They are supported by quantum calculations on a potential energy surface treating long-range interactions accurately. All results are consistent and the excitation function behavior is explained in terms of the cumulative contribution of various partial waves.

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.

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.

Experimental and Theoretical Differential Cross Sections for the N(2D) + H2 Reaction

In this paper, we report a combined experimental and theoretical study on the dynamics of the N(2D) + H2 insertion reaction at a collision energy of 15.9 kJ mol(-1). Product angular and velocity distributions have been obtained in crossed beam experiments and simulated by using the results of quantum mechanical (QM) scattering calculations on the accurate ab initio potential energy surface (PES) of Pederson et al. (J. Chem. Phys. 1999, 110, 9091). Since the QM calculations indicate that there is a significant coupling between the product angular and translational energy distributions, such a coupling has been explicitly included in the simulation of the experimental results. The very good agreement between experiment and QM calculations sustains the accuracy of the NH2 ab initio ground state PES. We also take the opportunity to compare the accurate QM differential cross sections with those obtained by two approximate methods, namely, the widely used quasiclassical trajectory calculations and a rigorous statistical method based on the coupled-channel theory.

Dynamics of the C(D1)+D2 reaction: A comparison of crossed molecular-beam experiments with quasiclassical trajectory and accurate statistical calculations

In this paper we report a combined experimental and theoretical study on the dynamics of the insertion reaction C((1)D)+D(2) at 15.5 kJ mol(-1) collision energy. Product angular and velocity distributions have been obtained in crossed beam experiments and quasiclassical trajectory (QCT) and rigorous statistical calculations have been performed on the recent and accurate ab initio potential energy surface of Bussery-Honvault, Honvault, and Launay at the energy of the experiment. The molecular-beam results have been simulated using the theoretical calculations. Good agreement between experiment and both QCT and statistical predictions is found.

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

A thorough theoretical investigation of the reactions between S(1D) and various hydrogen isotopomers (H2, D2, and HD) has been carried out using a recent ab initio potential energy surface. State-resolved integral and differential cross sections, thermal rate constants, and their dependence on energy or temperature were obtained from quantum mechanical capture probabilities within a statistical model. For comparison, the J=0 reaction probabilities were also computed using an exact wave packet method. The statistical results are in excellent agreement with available exact differential and integral cross sections. The comparison with experimental results shows that the agreement is reasonably good in general, but some significant differences exist, particularly for the SD/SH branching ratio in the S(1D)+HD reaction.

Determination of the internal state distribution of the SD product from the S(1D)+D2 reaction

The S(1D)+D2-->SD+D reaction has been studied through a photolysis-probe experiment in a cell. S(1D) reagent was prepared by 193 nm photolysis of CS2, and the SD(X 2Pi) product was detected by laser fluorescence excitation. The nascent rotational/fine-structure state distribution of the SD(X 2Pi) product was determined. This reaction, previously studied theoretically and in a crossed molecular beam experiment, is known to proceed through formation and decay of a long-lived collision complex involving the deep well in the H2S ground electronic state. The determined SD rotational state distribution in the v=0 vibrational level was found to be approximately statistical, with a small preference for formation of the F1 (Omega=3/2) fine-structure manifold over F2 (Omega=1/2). The branching into the Lambda doublet levels was also investigated, and essentially equal populations of levels of A' and A" symmetry were found. The present results are compared with previous investigations of this reaction and the analogous O(1D)+D2 reaction.

Reactions of C(1D) with H2 and its deuterated isotopomers, a wave packet study

Using a Chebyshev wave packet method, total and state-resolved reaction probabilities (J=0) were calculated for the reactions of C(1D) with various hydrogen isotopomers (H2, D2, and HD, nu i=0, j i=0) on a recent ab initio potential energy surface. For all the isotopic variants, it was found that the initial state specified reaction probabilities have no energy threshold and are strongly oscillatory, indicative of the involvement of long-lived resonances in this barrierless reaction. The J=0 product vibrational and rotational distributions for all three isotopic reactions, and the CH/CD branching ratio for the C+HD reaction, show strong dependence on the collision energy, further underscoring the important role played by the resonances. The generally decaying vibrational distributions and highly excited rotational distributions, which corroborate an insertion mechanism, and the dominance of the CD+H channel in the C+HD reaction are consistent with existing experimental observations. Initial state specified integral cross sections and rate constants were estimated using a capture model. The estimated rate constants were found to be close and in the order kHD>kH2>kD2. Finally, a method to calculate branching ratio in the C+HD reaction is proposed.

Quantum effects in the differential cross Ssctions for the insertion reaction N(2D) + H2

The quantum (QM) scattering theory has been difficult to apply to the family of insertion reactions and the approximate quasiclassical trajectory (QCT) method or statistical calculations were mostly applied. In this Letter, we compare the experimental differential cross sections for the title insertion reaction with the results of QM and QCT calculations on an ab initio potential energy surface. The QM results reproduce well the crossed beam experiment, while a small, but significant, difference in the QCT ones points to quantum effects, possibly the occurrence of tunneling through the combined potential and centrifugal barrier.