Effect of spin–orbit corrections on the F+D2 → DF+D reaction
Introduction
The F+H2 → HF+H reaction has been extensively studied both theoretically and experimentally for more than 20 years. One crucial step has marked the history of this prototype reaction: the crossed molecular beam experiments of Lee and co-workers 1, 2which gave the first vibrationally resolved differential cross-sections of this system. Several quasi-classical trajectory (QCT) 3, 4and quantum-mechanical (QM) 5, 6, 7, 8studies based on different potential energy surfaces 9, 10, 11, 12, 13have followed. The best agreement between the experimental and theoretical results 14, 15, 16, 17, 18, 19has been obtained with the fully ab initio potential energy surface of Stark and Werner [20], the so-called SW PES (which corresponds to the electronic ground state without spin–orbit corrections). Recent experiments 21, 22, 23have furnished rotationally resolved differential cross-sections and have stimulated new QCT and QM [24]calculations.
The isotopic variant F+D2 → DF+D reaction has been less studied, but recently several theoretical studies 25, 26, 27, 28, 29appeared after the high resolution molecular beam experiments performed in Göttingen at 90, 110, 140, 180 and 240 meV collision energies 30, 31, 32, 33, 34. The related QCT, coupled states (CS) (at 90 meV) and accurate QM calculations used the previous SW PES. Semi-quantitative agreement between the theoretical and experimental integral cross-sections (ICS) and differential cross-sections (DCS) has been found. However, for these two isotopic reactions, discrepancies still remain, especially for absolute values. Recently, Hartke and Werner computed another potential energy surface [35], the so-called HSW PES, in which spin–orbit corrections are added. Their effect is to lower the F(P)+H2 entrance arrangement of the SW PES by one third of the P3/2–P1/2 fine structure splitting, which results in an increase of the barrier height by 16.5 meV, with a total height of 83 meV. Hartke and Werner [35]showed that spin–orbit corrections were necessary to bring the peaks in the photoelectron spectra of FH2− to their correct positions.
It is expected that the effect of spin–orbit corrections should be important at low energies. It is therefore interesting to consider their influence on the collision energy threshold. The QCT excitation function shows a threshold at around 40 meV with the SW PES [16]. However, a CS calculation [17]using this same PES predicts no threshold for the F+D2 reaction (nor for F+H2). This absence of an energy threshold is attributed to a too small barrier height of the SW PES. An enhancement of the barrier height (for instance by spin–orbit corrections) should give rise to a threshold. We have therefore examined the effect of the spin–orbit corrections on the F+D2 → DF+D reaction by using an accurate quantum-mechanical method and the HSW PES, in order to clarify these points.
Section snippets
Results and discussion
Quantum-dynamical calculations were performed with the hyperspherical method, using the same convergence parameters and basis sets as in our previous study with the SW PES [29]. The basis sets include two closed vibrational manifolds in each arrangement (v=5,6 for DF and v=1,2 for D2). We took into account all states with ( is the projection of the total angular momentum on the axis of least inertia). All partial waves with total angular momentum J⩽25 at 90 meV and J⩽40 at 240 meV have
Conclusion
Quantum-mechanical dynamical calculations performed on the HSW PES with spin–orbit corrections added in the entrance channel of the SW PES do not really improve the comparison with experiments. At 90 meV, in general the agreement between QM and experimental DCS and ICS is even worse than with the SW PES. However, for v′=4 it gets better since no rotational bimodality is found in QM rotational DCS obtained with the HSW PES, as in the experiments. At 240 meV, where the effect of spin–orbit is
Acknowledgements
We would like to thank B. Hartke and H.-J. Werner for an early access to the HSW potential energy surface.
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