Quasi-classical trajectory calculations on a fast analytic potential energy surface for the C(1D)+H2 reaction

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.

Quantum Dynamics Study of the C(1D) + HD Reaction on the ã1A' and b̃1A″ Potential Energy Surfaces

We present an in-depth theoretical study of the C(¹D) + HD (v = 0, j = 0) → CD (CH) (v', j') + H (D) reaction using a time-dependent wave packet method with full Coriolis coupling on the Zhang-Ma-Bian potential energy surfaces (PESs) recently constructed by our group. The integral cross sections (ICS), differential cross sections, CD/CH branching ratios, and product state distributions are calculated over a wide range of collision energies. We find that the vibrational branching ratio defined as ICS(v'=1)/ICS(v'=0) obtained from the b̃¹A″ PES is much smaller than that from the ã¹A' PES for both product channels, which may be attributed to the dynamical effects of the conical intersection regulated (CI-R) intermediate on the b̃¹A″ PES. The collision energy dependence of CD/CH branching ratios displays oscillatory structures, which may be caused by the resonance states supported by the wells on the PESs. The high-temperature rate coefficients are also obtained and compared with previous results. The role of the excited-state PESs is also discussed.

Conical intersection-regulated intermediates in bimolecular reactions: Insights from C(1D) + HD dynamics

The importance of conical intersections (CIs) in electronically nonadiabatic processes is well known, but their influence on adiabatic dynamics has been underestimated. Here, through combined experimental and theoretical studies, we show that CIs induce a barrier and regulate conversion from a precursor metastable intermediate (CI-R) to a deep well one. This results in bond-selective activation, influencing the adiabatic dynamics markedly in the C(1D) + HD reaction. Theory is validated by experiment; quantum dynamics calculations on highly accurate ab initio potential energy surfaces yield rate coefficients and product branching ratios in excellent agreement with the experiment. Quasi-classical trajectory calculations reveal that the CI-R intermediate leads to unusual reaction mechanisms (designated as C─H activation complex conversion and cyclic complex), which are responsible for large branching ratios. We also reveal that CI-R intermediates exist in other reactive systems, and the dynamical effects uncovered here may have general significance.

Dynamical importance of van der Waals saddle and excited potential surface in C(1D)+D2 complex-forming reaction

Encouraged by recent advances in revealing significant effects of van der Waals wells on reaction dynamics, many people assume that van der Waals wells are inevitable in chemical reactions. Here we find that the weak long-range forces cause van der Waals saddles in the prototypical C(¹D)+D₂ complex-forming reaction that have very different dynamical effects from van der Waals wells at low collision energies. Accurate quantum dynamics calculations on our highly accurate ab initio potential energy surfaces with van der Waals saddles yield cross-sections in close agreement with crossed-beam experiments, whereas the same calculations on an earlier surface with van der Waals wells produce much smaller cross-sections at low energies. Further trajectory calculations reveal that the van der Waals saddle leads to a torsion then sideways insertion reaction mechanism, whereas the well suppresses reactivity. Quantum diffraction oscillations and sharp resonances are also predicted based on our ground- and excited-state potential energy surfaces.

It is commonly held that van der Waals wells are inevitable in chemical reactions. Here, the authors show that weak van der Waals forces in the entrance channel of a prototypical complex-forming reaction cause a van der Waals saddle instead, with different dynamical effects from a well at low collision energies.

Quasiclassical trajectory study of the C(1D) + HD reaction

Isotopic branching ratios are investigated by detailed quasiclassical trajectory calculations on our recent singlet ground and excited potential energy surfaces.

An experimental and theoretical investigation of the C(1D) + D2 reaction

Rate constants derived from ring polymer molecular dynamics calculations confirm the validity of this method for studying low-temperature complex-forming reactions

Ring-Polymer Molecular Dynamics for the Prediction of Low-Temperature Rates: An Investigation of the C((1)D) + H2 Reaction

Quantum mechanical calculations are important tools for predicting the rates of elementary reactions, particularly for those involving hydrogen and at low temperatures where quantum effects become increasingly important. These approaches are computationally expensive, however, particularly when applied to complex polyatomic systems or processes characterized by deep potential wells. While several approximate techniques exist, many of these have issues with reliability. The ring-polymer molecular dynamics method was recently proposed as an accurate and efficient alternative. Here, we test this technique at low temperatures (300-50 K) by analyzing the behavior of the barrierless C((1)D) + H2 reaction over the two lowest singlet potential energy surfaces. To validate the theory, rate coefficients were measured using a supersonic flow reactor down to 50 K. The experimental and theoretical rates are in excellent agreement, supporting the future application of this method for determining the kinetics and dynamics of a wide range of low-temperature reactions.

Global analytical ab initio ground-state potential energy surface for the C((1)D)+H2 reactive system

A new global ab initio potential energy surface (called ZMB-a) for the 1(1)A' state of the C((1)D)+H2 reactive system has been constructed. This is based upon ab initio calculations using the internally contracted multireference configuration interaction approach with the aug-cc-pVQZ basis set, performed at about 6300 symmetry unique geometries. Accurate analytical fits are generated using many-body expansions with the permutationally invariant polynomials, except that the fit of the deep well region is taken from our previous fit. The ZMB-a surface is unique in the accurate description of the regions around conical intersections (CIs) and of van der Waals (vdW) interactions. The CIs between the 1(1)A' and 2(1)A' states cause two kinds of barriers on the ZMB-a surface: one is in the linear H-CH dissociation direction with a barrier height of 9.07 kcal/mol, which is much higher than those on the surfaces reported before; the other is in the C((1)D) collinearly attacking H2 direction with a barrier height of 12.39 kcal/mol. The ZMB-a surface basically reproduces our ab initio calculations in the vdW interaction regions, and supports a linear C-HH vdW complex in the entrance channel, and two vdW complexes in the exit channel, at linear CH-H and HC-H geometries, respectively.

Effect of vibrational and rotational excitation on the stereodynamics of the C(1D) + H2 (v, j) → CH + H reaction

The stereodynamics of the title reaction on the ab initio1A′ potential energy surface (PES) (B. Bussery-Honvault, P. Honvault, and J.-M. Launay. 2001. J. Chem. Phys. 115: 10701) at a collision energy of 16 kJ/mol have been studied using quasi-classical trajectory (QCT) method. Vector properties including angular momentum alignment parameters and four polarization-dependent differential cross sections (PDDCS) of the product CH are presented. Furthermore, the influence of reagent vibrational and rotational excitations on the product vector properties have also been studied in the present work. The calculated results indicate that the angle distributions of the CH product are mainly dominated by backward–forward scattering.

Born-Oppenheimer quantum dynamics of the C((1)D)+H(2) reaction on the CH(2) ã (1)A(1) and b (1)B(1) surfaces

We present the Born-Oppenheimer coupled-channel dynamics of the reaction (12)C((1)D)+(1)H(2)(X (1)Sigma(g) (+))-->CH(X (2)Pi)+H((2)S), considering the uncoupled CH(2) states ã (1)A(1) and b (1)B(1), the permutation-inversion symmetry, and Coriolis interactions. Using accurate MRCI potential energy surfaces (PESs), we obtain initial-state-resolved reaction probabilities, cross sections, and rate constants through the time-dependent, real wavepacket (WP) and flux methods, taking into account the proton-spin statistics for both electronic species. Comparing results on both PESs, we point out the role of the b (1)B(1) upper state on the initial-state-resolved dynamics and on the thermal kinetic rate. WP probabilities at J=0 and cross sections at E(col)=0.080 eV agree quite well with quantum-mechanical time-independent findings. Probabilities and WP snapshots show the different reaction mechanisms on the PESs, i.e., an ã (1)A(1) indirect perpendicular insertion and a b (1)B(1) direct sideways collision, associated with many and few sharp resonances, respectively. All cross sections are very large at low E(col), decrease at high energies, and that of the lowest reactant state presents some weak resonances. As the temperature increases from 100 to 400 K, the ã (1)A(1) rate constant increases slightly from 1.37x10(-10) to 1.43x10(-10) cm(3) s(-1), whereas the b (1)B(1) one decreases from 1.30x10(-10) to 0.98x10(-10) cm(3) s(-1). In this temperature range, the b (1)B(1) contribution to the total rate constant thus decreases from 49% to 41%. At 300 K, the WP and experimental rates are equal to (2.45+/-0.08)x10(-10) and (2.0+/-0.6)x10(-10) cm(3) s(-1), respectively.

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.

Potential energy surface intersections in the C(D1)H2 reactive system

Potential energy surface (PES) intersection seams of two or more electronic states from the 1 1A', 2 1A', 3 1A', 1 1A", and 2 1A" states in the C(1D)H2 reactive system are investigated using the internally contracted multireference configuration interaction method and the aug-cc-pVQZ basis set. Intersection seams with energies less than 20 kcal/mol relative to the C(1D) + H2 asymptote are searched systematically, and finally several seam lines (at the linear H-C-H, linear C-H-H, and C(2v), geometries, respectively) and a seam surface (at Cs geometries) are discovered and determined. The minimum energy crossing points on these seams are reported and the influences of the PES intersections, in particular, conical intersections, on the CH2 spectroscopy and the C(1D) + H2 reaction dynamics are discussed. In addition, geometries and energies of the 1 1A2 and 1 1B2 states of methylene biradical CH2 are reported in detail for the first time.

Dynamical Study of H2 and D2 Desorbing from a Cu(111) Surface

A theoretical study of H(2) and D(2) desorbing from Cu(111) is reported. The study makes use of the LEPS PES of Dai and Zhang [J. Chem. Phys. 1995, 102, 6280]. The LEPS parameters have been modified in order to lower the barrier threshold in conformity with accurate ab initio electronic structure calculations. The topological study of the modified PES by the CHAIN method reveals unambiguously that the transition state (TS) is located at the top of a unique early barrier along the desorption path. The adsorbed H atoms are supposed to be in thermal equilibrium with the metal surface. Batches of classical trajectories (CT) are then carried out from the TS onto the products with their initial conditions canonically distributed and the effect of their possible recrossing of the TS taken into account according to Keck's method [Discuss. Faraday Soc. 1962, 33, 173]. Product state distributions are then calculated using the Gaussian weighting procedure [Chem. Phys. Lett. 2004, 397, 106] to account for the quantization of the vibration motion of the desorbed diatom. These distributions are in overall good agreement with experimental measurements. On average, the early barrier to desorption results in a significant vibrational excitation of the final diatom and a strong deexcitation of its rotational angular momentum J from the TS onto the products. Moreover, the orientation of the rotation plane is roughly random for low values of J (both cartwheel and helicopter motions are observed) while it is more likely parallel to the metal surface for large values of J (predominance for helicopter motion). These findings are analyzed in some details.

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.

Resonances of CH2(ãA11) and their roles in unimolecular and bimolecular reactions

Low-lying resonances of the CH2(a 1A1) system (J=0) in an accurate ab initio potential energy surface are studied using a filter-diagonalization method. The width of these resonances fluctuates by more than two orders of magnitude and on average increases with the energy. Analysis of the resonance states concludes that the unimolecular decay of the excited molecular system near the dissociation threshold is neither mode specific nor statistical state specific. This is apparently due to remnant regularity embedded in the largely chaotic classical phase space, as evidenced by periodic orbit analysis. As a result, the Rice-Ramsperger-Kassel-Marcus and statistical adiabatic channel models overestimate the average unimolecular decay rate. The implications of the resonances for the bimolecular C(1D)+H2 reaction are also discussed.

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.

A wave packet based statistical approach to complex-forming reactions

A wave packet based statistical model is suggested for complex-forming reactions. This model assumes statistical formation and decay of the long-lived reaction complex and computes reaction cross sections and their energy dependence from capture probabilities. This model is very efficient and reasonably accurate for reactions dominated by long-lived resonances, as confirmed by its application to the C((1)D)+H(2) reaction.