Jesus F. Castillo

ABC: a quantum reactive scattering program

Abstract This article describes a quantum mechanical reactive scattering program for atom–diatom chemical reactions that we have written during the past several years. The program uses a coupled-channel hyperspherical coordinate method to solve the Schrodinger equation for the motion of the three nuclei on a single Born–Oppenheimer potential energy surface. It has been tested for all possible deuterium-substituted isotopomers of the H + H 2 , F + H 2 , and Cl + H 2 reactions, and tried and tested potential energy surfaces for these reactions are included within the program as Fortran subroutines.

Quantum mechanical angular distributions for the F+H2 reaction

Quantum mechanical integral and differential cross sections have been calculated for the title reaction at the three collision energies studied in the 1985 molecular beam experiment of Lee and co‐workers, using the new ab initio potential energy surface of Stark and Werner (preceding paper). Although the overall agreement between the calculated and experimental center‐of‐mass frame angular distributions is satisfactory, there are still some noticeable differences. In particular, the forward scattering of HF(v′=3) is more pronounced in the present calculations than it is in the experiment and the calculations also predict some forward scattering of HF(v′=2). A comparison with the quasiclassical trajectory results of Aoiz and co‐workers on the same potential energy surface shows that the forward scattering is largely a quantum mechanical effect in both cases, being dominated by high orbital angular momenta in the tunneling region where the combined centrifugal and potential energy barrier prevents classical...

Using quantum rotational polarization moments to describe the stereodynamics of the H+D2(v=0,j=0)→HD(v′,j′)+D reaction

We present results of quantum calculations we have performed on the title reaction in order to study its stereodynamics at collision energies of 0.54 and 1.29 eV. Our theoretical model is based on a representation where directional properties are expressed in terms of real rotational polarization moments instead of magnetic quantum numbers. We analyze the physical meaning of rotational polarization moments and show that, when defined as in the present work, these quantities directly describe the reaction stereodynamics in terms of intuitive chemical concepts related to preferences in the reaction mechanism for particular planes and senses of molecular rotation. Using this interpretation, we identify two distinct regimes for the stereodynamics of the title reaction, observed when HD is formed with low or high rotational excitation. We also identify relevant characteristics of both regimes: (i) the existence and location of preferred planes and senses of molecular rotation, (ii) correlations between these p...

The dynamics of the hydrogen exchange reaction at 2.20 eV collision energy: Comparison of experimental and theoretical differential cross sections

The H+D2(v=0,j=0)→HD(v′,j′)+D isotopic variant of the hydrogen atom exchange reaction has been studied in a crossed molecular beam experiment at a collision energy of 2.20 eV. Kinetic energy spectra of the nascent D atoms were obtained by using the Rydberg atom time-of-flight technique. The extensive set of spectra collected has permitted the derivation of rovibrationally state-resolved differential cross sections in the center-of-mass frame for most of the internal states of the HD product molecules, allowing a direct comparison with theoretical predictions. Accurate 3D quantum mechanical calculations have been carried out on the refined version of the latest Boothroyd–Keogh–Martin–Peterson potential energy surface, yielding an excellent agreement with the experimentally determined differential cross sections. The comparison of the results from quasi-classical trajectory calculations on the same potential surface reveals some discrepancies with the measured data, but shows a good global accordance. The t...

The O(1D)+H2 reaction at 56 meV collision energy: A comparison between quantum mechanical, quasiclassical trajectory, and crossed beam results

Quantum mechanical and quasiclassical trajectory reactive scattering calculations have been performed for the O(1D)+H2 (v=0,j=0) reaction on the Dobbyn–Knowles ab initio 1u200a1A′ and 1u200a1A″ potential energy surfaces (PES) at the mean collision energy Ecol=56u2009meV (1.3 kcal/mol) of a crossed beam experimental study based on H-atom Rydberg “tagging” time-of-flight detection. Novel data from this latter experiment are presented and compared with the theoretical results at the level of state-resolved integral and differential cross sections and product recoil energy distributions. A good overall agreement with small discrepancies is found between the experimental data and the results of the two theoretical approaches. The main conclusion of the present work is that the contribution of the ground state 1u200a1A′ PES to the global reactivity accounts for the experimental observations and that, at the title collision energy, the participation of the 1u200a1A″ PES in the reaction is negligible for all practical purposes.

Cl+HD(v=1; J=1,2) reaction dynamics: Comparison between theory and experiment

Vibrationally state-resolved differential cross sections (DCS) and product rotational distributions have been measured for the Cl+HD(v=1,u200aJ=1)→HCl(DCl)+D(H) reaction at a mean collision energy of 0.065 eV using a photoinitiated reaction (“photoloc”) technique. The effect of HD reagent rotational alignment in the Cl+HD(v=1,u200aJ=2) reaction has also been investigated. The experimental results have been compared with exact quantum mechanical and quasiclassical trajectory calculations performed on the G3 potential energy surface of Allison et al. [J. Phys. Chem. 100, 13575 (1996)]. The experimental measurements reveal that the products are predominantly backward and sideways scattered for HCl(v′=0) and HCl(v′=1), with no forward scattering at the collision energies studied, in quantitative agreement with theoretical predictions. The experimental product rotational distribution for HCl(v′=1) also shows excellent agreement with quantum-mechanical calculations, but the measured DCl+H to HCl+D branching ratio is ne...

Experimental and theoretical differential cross sections for the reactions Cl+H2/D2

Experimental and theoretical differential cross sections for the reactions between Cl atoms and two isotopic variants of molecular hydrogen (H2 and D2) are presented. The experimental results have been obtained by using the crossed molecular beam method with mass spectrometric detection. The theoretical results have been computed using both the quasiclassical trajectory and quantum mechanical (QM) methods. The potential energy surface employed for the calculations is the ab initio BW2 surface by Bian and Werner [J. Chem. Phys. 112, 220 (2000)]. The theoretical results have been directly compared to the experiments in the laboratory frame at a collision energy (Ec) of 4.25 and 5.85 kcal/mol for the Cl+H2 reaction and of 4.9 and 6.3 kcal/mol for the Cl+D2 reaction. The agreement between QM results and experiment is quite satisfactory for the Cl+D2 reaction, especially for the low collision energy, while for Cl+H2 is less good, especially when considering data at the lower Ec.

Disagreement between theory and experiment in the simplest chemical reaction: Collision energy dependent rotational distributions for H+D2→HD(ν′=3,j′)+D

We present experimental rotational distributions for the reaction H + D2 --> HD(nu = 3,j) + D at eight different collision energies between 1.49 and 1.85 eV. We combine a previous measurement of the state-resolved excitation function for this reaction [Ayers et al., J. Chem. Phys. 119, 4662 (2003)] with the current data to produce a map of the relative reactive cross section as a function of both collision energy and rotational quantum number (an E-j plot). To compare with the experimental data, we also present E-j plots resulting from both time-dependent and time-independent quantum mechanical calculations carried out on the BKMP2 surface. The two calculations agree well with each other, but they produce rotational distributions significantly colder than the experiment, with the difference being more pronounced at higher collision energies. Disagreement between theory and experiment might be regarded as surprising considering the simplicity of this system; potential causes of this discrepancy are discussed.

Nearside–farside analysis of state-selected differential cross sections for reactive molecular collisions

The usual theoretical procedure for evaluating the differential cross section (DCS) of a molecular collision consists of numerically summing a partial wave series (PWS) for the scattering amplitude. The PWS typically has many numerically significant terms making it difficult (or impossible) to gain physical insight into the origin of structure in a DCS. A nearside–farside (NF) analysis of a DCS decomposes the PWS scattering amplitude into two subamplitudes: one nearside, the other farside. This decomposition is successful if the magnitudes of the two subamplitudes are never much greater than that of the scattering amplitude itself. It is then often possible to gain a clear physical picture of the origin of structure in a DCS, and hence obtain information on the collision dynamics. A new NF theory called the restricted NF decomposition is described. We present the first application of this NF decomposition to reactive molecular collisions whose PWS are expanded in a basis set of reduced rotation matrix elements. The reactions whose DCSs we NF analyze are: F+H2→FH+H, F+HD→FH+D (or FD+H) and H+D2→HD+D. Exact quantum scattering matrix elements are employed as input to the NF analyses. DCSs are also computed using a simple semiclassical optical model. We demonstrate that the restricted NF decomposition provides valuable physical insights into the structured angular distributions of these three chemical reactions. Applications of NF methods to elastic and inelastic molecular angular scattering are also described.

Quantum mechanical angular distributions for the F+HD reaction

Quantum-mechanical integral and differential cross-sections have been calculated for the title reaction at the two collision energies (Ecoll=1.35 and 1.98 kcal mol-1) studied in the 1985 molecular beam experiment of Lee and co-workers, using the new abinitio potential-energy surface of Stark and Werner. The DF+H product channel is found to behave essentially classically: the present quantum-mechanical angular distributions for this channel are in good agreement with both the earlier quasi-classical trajectory results of Aoiz and co-workers on the same potential-energy surface and the results of the molecular beam experiment. However, the HF+D product channel in which the light H atom is transferred between two heavier atoms is inherently more quantum-mechanical: our computed angular distributions for this channel differ significantly from the quasi-classical trajectory results and agree better with the results of the experiment (especially at the higher of the two experimental collision energies). The main quantum-mechanical effect that is identified in the calculations is a reactive scattering resonance that gives rise to a pronounced forward-scattering peak in the calculated F+HD(v=0, j=0)→HF(v′=3)+D differential cross-section. The influence of this resonance on the reaction dynamics is discussed in some detail, together with the implications of our results at the lower of the two collision energies for an improvement to the Stark–Werner potential-energy surface.