Shu Liu

Experimental and Theoretical Differential Cross Sections for a Four-Atom Reaction: HD + OH → H2O + D

A theoretical analysis of a four-atom reaction has a level of detail and accuracy previously restricted to three-atom systems. Quantum dynamical theories have progressed to the stage in which state-to-state differential cross sections can now be routinely computed with high accuracy for three-atom systems since the first such calculation was carried out more than 30 years ago for the H + H2 system. For reactions beyond three atoms, however, highly accurate quantum dynamical calculations of differential cross sections have not been feasible. We have recently developed a quantum wave packet method to compute full-dimensional differential cross sections for four-atom reactions. Here, we report benchmark calculations carried out for the prototypical HD + OH → H2O + D reaction on an accurate potential energy surface that yield differential cross sections in excellent agreement with those from a high-resolution, crossed–molecular beam experiment.

Depression of reactivity by the collision energy in the single barrier H +CD4 → HD+ CD3 reaction

Crossed molecular beam experiments and accurate quantum scattering calculations have been carried out for the polyatomic H + CD4 → HD + CD3 reaction. Unprecedented agreement has been achieved between theory and experiments on the energy dependence of the integral cross section in a wide collision energy region that first rises and then falls considerably as the collision energy increases far over the reaction barrier for this simple hydrogen abstraction reaction. Detailed theoretical analysis shows that at collision energies far above the barrier the incoming H-atom moves so quickly that the heavier D-atom on CD4 cannot concertedly follow it to form the HD product, resulting in the decline of reactivity with the increase of collision energy. We propose that this is also the very mechanism, operating in many abstraction reactions, which causes the differential cross section in the backward direction to decrease substantially or even vanish at collision energies far above the barrier height.

Time-dependent wave packet theory for state-to-state differential cross sections of four-atom reactions in full dimensions: Application to the HD + OH → H2O + D reaction

Time-dependent wave packet method has been developed to calculate differential cross section for four-atom reactions in full dimension, utilizing an improved version of reactant-product-decoupling scheme. Differential cross sections for the title reaction were calculated for collision energy up to 0.4 eV. It is found that the differential cross sections for the reaction are all peaked in the backward direction. The majority of H(2)O is produced in the first stretch excited state, with a large fraction of available energy for the reaction going into H(2)O internal motion. As compared in a previous report by Xiao et al. [Science 333, 440 (2011)], the differential cross section at E(c) = 0.3 eV and the differential cross section at the backward direction as a function of collision energy agree with experiment very well, indicating it is possible now to calculate complete dynamical information for some simple four-atom reactions, as have been done for three-atom reactions in the past decades.

Communication: A six-dimensional state-to-state quantum dynamics study of the H + CH4 → H2 + CH3 reaction (J = 0).

We report a quantum state-to-state reaction dynamics study for the title reaction. The calculation was based on an approximation that we introduced to the eight-dimensional model for the X + YCZ(3) → XY + CZ(3) type of reactions that restricts the non-reacting CZ(3) group in C(3V) symmetry proposed by Palma and Clary [J. Chem. Phys. 112, 1859 (2000)], by assuming that the CZ(3) group can rotate freely with respect to its C(3V) symmetry axis. With the CH bond length in group fixed at its equilibrium distance, the degree of freedom included in the calculation was reduced to six. Our calculation shows that the six-dimensional treatment can produce reaction probabilities essentially indistinguishable from the seven-dimensional (with CH bond length fixed in the original eight-dimensional model) results. The product vibrational/rotational state distributions and product energy partitioning information are presented for ground initial rovibrational state with the total angular momentum J = 0.

Communication: State-to-state quantum dynamics study of the OH + CO → H + CO2 reaction in full dimensions (J = 0)

A full dimensional state-to-state quantum dynamics study is carried out for the prototypical complex-formation OH + CO → H + CO(2) reaction in the ground rovibrational initial state on the Lakin-Troya-Schatz-Harding potential energy surface by using the reactant-product decoupling method. With three heavy atoms and deep wells on the reaction path, the reaction represents a huge challenge for accurate quantum dynamics study. This state-to-state calculation is the first such a study on a four-atom reaction other than the H(2) + OH ↔ H(2)O + H and its isotope analogies. The product CO(2) vibrational and rotational state distributions, and product energy partitioning information are presented for ground initial rovibrational state with the total angular momentum J = 0.

Accuracy of the centrifugal sudden approximation in the H + CHD3 → H2 + CD3 reaction

The initial state selected time-dependent wave packet method has been extended to calculate the coupled-channel reaction probabilities with total angular momentum J(tot) > 0 for the title reaction with seven degrees of freedom included. Fully converged integral cross sections were obtained for the ground and a number of vibrational excited initial states on a new potential energy surface recently constructed by this group using neural network fitting. As found from a previous study with the centrifugal sudden (CS) approximation, all these initial vibrational excitations investigated in this study enhance the reactivity considerably at a given collision energy, in particular the CH stretch excited state. The energy initially deposited in CH stretch motion is more effective than translational energy on promoting the reaction in the entire energy region, while for CH bending or CD3 umbrella excitations only at the high collision energy the vibrational energy becomes more effective. Our calculations also revealed that the accuracy of the CS approximation considerably deteriorates with the increase of J(tot), in particular on the threshold energy. The CS approximation underestimates the integral cross sections for all these initial states, albeit not very severely. In general, it works better at high collision energies and for vibrationally excited initial states, with the increase of integral cross section.

An ab initio quasi-diabatic potential energy matrix for OH(2Σ) + H2

A diabatic potential energy matrix for three electronic states of OH(3) has been constructed by interpolation of multi-reference configuration interaction electronic structure data. The reactive, exchange and non-reactive quenching dynamics are investigated using surface hopping classical trajectories. Classical trajectory simulations show good agreement with cross molecular beam data for the OH((2)Σ) + D(2) → HOD + D reaction.

State-to-state quantum versus classical dynamics study of the OH + CO → H + CO2 reaction in full dimensions (J = 0): checking the validity of the quasi-classical trajectory method

AbstractWe report full-dimensional state-to-state quantum mechanical (QM) and quasi-classical trajectory (QCT) calculations on the title reaction for the ground rovibrational initial state with total angular momentum fixed at zero on the accurate potential energy (PES) constructed recently by using permutation-invariant polynomial–neural network method (Li et al. in J Chem Phys 140:044327, 2014), to check the validity of the QCT method for the reaction. It is found that the QM state-to-state results strongly depend on the resonance structures in reaction, but the collision energy-averaged results show a smooth change with the increase of collision energy. Overall, the agreement between collision energy-averaged QM and QCT state-to-state results is satisfactory, in particular at high collision energy region, indicating that the QCT method is rather accurate on describing dynamics of the reaction on the PES. On the other hand, because earlier studies revealed the QCT results on the PES do not agree very well with the experimental measurements available, more theoretical and experimental studies should be carried out to achieve a full understanding on the dynamics of this benchmark complex-forming reaction.

State-to-state differential cross sections for a four-atom reaction: H2 + OH → H2O + H in full dimensions

The time-dependent wave packet method has been employed to calculate state-to-state differential cross sections for the title reaction in full dimensions. It is found that the majority of H2O is produced in the first stretching excited states, with a large fraction of available energy for the reaction ending up as product internal motion. The differential cross sections for collision energy up to 0.4 eV are all peaked in the backward direction, but the width of the angular distribution increases considerably as the increase of collision energy. The isotope effect was also examined by comparing the scattering angular distribution for the title reaction with those for the HD + OH and D2 + OH reactions obtained in our previous work.

The dynamics of the D2 + OH --> HOD + D reaction: a combined theoretical and experimental study.

A combined theoretical and experimental study has been carried out to show the current status of comparison between experiment and theory on the title reaction. Differential cross sections and product relative translational energy distributions at collision energies of 0.25 and 0.34 eV, as well as the collision energy dependence of differential cross section in the backward direction have been measured by using crossed molecular beam experiment with D-atom Rydberg tagging technique. Theoretically, the time-dependent wave packet method has been employed to calculate state-to-state differential cross sections for the title reaction in full dimension. It is found that the experimental observations are in good accord with those of Davis and coworkers at the collision energy of 0.28 eV [Science, 290, 958 (2000)]. The overall agreement between theory and experiment on this benchmark four-atom reaction is good, but not perfect. Further studies, both theoretical and experimental, are called to bring a complete agreement between theory and experiment on the reaction.