Dong H. Zhang

Full-dimensional time-dependent treatment for diatom-diatom reactions: The H2+OH reaction

Extending our previous studies for the H2+OH reaction in five mathematical dimensions (5D) [J. Chem. Phys. 99, 5615 (1993); 100, 2697 (1994)], we present in this paper a full‐dimensional (6D) dynamics study for the title reaction. The 6D treatment uses the time‐dependent wave‐packet approach and employs discrete variable representations for three radial coordinates and coupled angular momentum basis functions for three angular coordinates. The present 6D study employs an energy projection method to extract reaction probabilities for a whole range of energies from a single wave‐packet propagation, while previous studies produced only energy‐averaged reaction probability from a single wave‐packet propagation. The application of the energy‐projection method allows us to efficiently map out the energy dependence of the reaction probability on a fine grid which revealed surprisingly sharp resonancelike features at low collision energies on the Schatz–Elgersma potential surface. Our calculation shows that the potential‐averaged 5D treatment can produce reaction probabilities essentially indistinguishable from the full‐dimensional result. We also report initial state‐selected reaction cross sections and rate constants which are in good agreement with our previous calculations. The effect of OH vibration on H2+OH reaction is examined in the present study and our calculation shows that the OH vibration can enhance the rate constant by about a factor of 1.7 in good agreement with the experimental estimate of about 1.5.

Quantum reactive scattering with a deep well: Time‐dependent calculation for H+O2 reaction and bound state characterization for HO2

We show in this paper a time‐dependent (TD) quantum wave packet calculation for the combustion reaction H+O2 using the DMBE IV (double many‐body expansion) potential energy surface which has a deep well and supports long‐lived resonances. The reaction probabilities from the initial states of H+O2(3Σ−g) (v=0–3, j=1) for total angular momentum J=0 are obtained for scattering energies from threshold up to 2.5 eV, which show numerous resonance features. Our results show that, by carrying out the wave packet propagation to several picoseconds, one can resolve essentially all the resonance features for this reaction. The present TD results are in good agreement with other time‐independent calculations. A particular advantage of the time‐dependent approach to this reaction is that resonance structures—strong energy dependence of the reaction probability—can be mapped out in a single wave packet propagation without having to repeat scattering calculations for hundreds of energies. We also report calculations of s...

A six dimensional quantum study for atom–triatom reactions: The H+H2O→H2+OH reaction

A time‐dependent wave packet method has been developed to study atom–triatom ABC+D→AB+CD reactions in full six dimensions (6D). The approach employs a body‐fixed coupled angular momentum basis for three angular coordinates, and three 1D bases for three radial coordinates. It permits the calculation of diatom AB vibrational state resolved total reaction probability for an initial rovibrational state of the triatom ABC. The approach is applied to study the H+H2O→H2+OH reaction on the modified Schatz–Elgersman potential energy surface. Initial state‐selected total reaction probabilities are presented for initial ground and several vibrationally excited states of H2O for total angular momentum J=0, along with the final OH vibrational state distributions. We also report the cross sections for reaction from the initial ground vibrational and the first bending excited states of H2O. Comparisons are made between our results and those from other theoretical calculations and experiments.

Accurate quantum calculation for the benchmark reaction H2+OH→H2O +H in five‐dimensional space: Reaction probabilities for J=0

A time‐dependent wave packet method has been employed to compute initial state‐specific total reaction probabilities for the benchmark reaction H2+OH→H2O+H on the modified Schatz–Elgersman potential energy surface which is derived from ab initio data. In our quantum treatment, the OH bond length is fixed but the remaining five degrees of freedom are treated exactly in the wave packet calculation. Initial state‐specific total reaction probabilities for the title reaction are presented for total angular momentum J=0 and the effects of reagents rotation and H2 vibration on reaction are examined.

Quantum state‐to‐state reaction probabilities for the H+H2O→H2+OH reaction in six dimensions

A time‐dependent wave packet method has been employed to calculate the state‐to‐state reaction probability for the H+H2O(0,0,0)→H2(v1,j1)+OH(v2,j2) reaction for J=0 and initial nonrotating H2O on the modified Schatz–Elgersman potential energy surface in full six dimensions (6D). Starting from a wave packet for an atom–triatom asymptotic state in atom–triatom Jacobi coordinates, we transfer the wave packet to diatom–diatom Jacobi coordinates after the wave packet moves into the interaction region. Propagation is then carried out in the diatom–diatom Jacobi coordinates until the reaction flux measured in the diatom–diatom asymptotic region is converged.

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.

CUMULATIVE REACTION PROBABILITY VIA TRANSITION STATE WAVE PACKETS

A new time‐dependent approach to the cumulative reaction probability, N(E), has been developed based on the famous formulation given by Miller and co‐workers [J. Chem. Phys. 79, 4889 (1983)], N(E)=[(2π)2/2] tr[δ(E−H)Fδ(E−H)F]. Taking advantage of the fact that the flux operator has only two nonzero eigenvalues, we evaluate the trace efficiently in a direct product basis of the first flux operator eigenstates and the Hamiltonian eigenstates on the dividing surface (internal states). Because the microcanonical density operator, δ(E−H), will eliminate contributions to N(E) from an internal state with the energy much higher than the total energy E, we can minimize the number of internal states required by choosing a dividing surface with the lowest density of internal states. If the dividing surface is located in an asymptotic region, one just needs to include all the open channels, i.e., with internal energy lower than the total energy. Utilizing the Fourier transform for δ(E−H), we can obtain the informatio...

Breakdown of the Born-Oppenheimer approximation in the F+ o-D2 -> DF + D reaction.

The reaction of F with H2 and its isotopomers is the paradigm for an exothermic triatomic abstraction reaction. In a crossed-beam scattering experiment, we determined relative integral and differential cross sections for reaction of the ground F(2P3/2) and excited F*(2P1/2) spin-orbit states with D2 for collision energies of 0.25 to 1.2 kilocalorie/mole. At the lowest collision energy, F* is ∼1.6 times more reactive than F, although reaction of F* is forbidden within the Born-Oppenheimer (BO) approximation. As the collision energy increases, the BO-allowed reaction rapidly dominates. We found excellent agreement between multistate, quantum reactive scattering calculations and both the measured energy dependence of the F*/F reactivity ratio and the differential cross sections. This agreement confirms the fundamental understanding of the factors controlling electronic nonadiabaticity in abstraction reactions.

A seven-dimensional quantum study of the H+CH4 reaction

The initial state selected time-dependent wave packet method has been developed to study the H+CH4 reaction in seven dimensions by employing the model developed by Palma and Clary [J. Chem. Phys. 112, 1859 (2000)]. The latter eight-dimensional model only assumes that the nonreacting CH3 group keeps a C3V symmetry in reaction. The CH bond lengths in the nonreacting CH3 group were fixed in the study to reduce the number of degrees of freedom to seven. Our calculations reveal that it is very important to accurately deal with the umbrella motion of the CH3 group while studying this reaction. We investigated the effects of the fundamental vibrational excitations of CH4 on the reaction. Finally, we compare our rate constant for the ground rovibrational initial state with available experimental and other theoretical results.

Accurate quantum calculations for H2+OH→H2O+H: Reaction probabilities, cross sections, and rate constants

Following a previous Communication [J. Chem. Phys. 99, 5615 (1993)], which reported several initial state‐selected total reaction probabilities for the title reaction for J=0, we present in this paper the methodologies of the previous calculation and show results of new calculations. In particular, the present calculations are extended to all angular momentum J≳0 and obtained reaction cross sections for a range of energies using the centrifugal sudden (CS) approximation. The computed cross sections are used to obtain the state‐specific thermal rate constants for both the ground and the excited vibrations of H2. The dynamics calculation, in which the nonreactive OH bond is frozen, includes explicitly five degrees of freedom in the time‐dependent quantum dynamics treatment. The comparison of the present accurate cross sections with other approximate theoretical calculations shows discrepancies. The computed rate constants (from the ground rotation state) are larger than experimental measurements at low temp...