We report accurate coupled-channel quantum calculations of state-to-state and degeneracy-averaged differential cross sections for the rotationally inelastic collision Ar + HF(V i ) 0, j i ) 0, m i ) 0) f Ar + HF(V f ) 0, j f , m f ), where V i , j i , m i and V f , j f , m f are initial and final vibrational, rotational, and helicity quantum numbers, respectively. The calculations have been performed at eight collision energies and assume that HF is a rigid rotator. Structure in the differential cross sections is analyzed using the unrestricted version of nearsidefarside (NF) theory. The NF theory decomposes the partial wave series (PWS) for the helicity scattering amplitude into two subamplitudes, one N, the other F. This is the first application of NF theory to an atomheteronuclear molecule inelastic collision. It is demonstrated that the NF technique provides a clear physical interpretation of the angular scattering, except sometimes for scattering angles, θ, close to 0°and 180°. It is also shown that a resummation of the PWS can improve the usefulness of the NF technique, when the N and F cross sections possess small oscillations. The resummation procedure exploits recurrence properties of reduced rotation matrix elements to extract a factor (R + βcos θ) -1 from the PWS, where R and β are constants. Criteria for choosing R and β so as to obtain a physically meaningful NF decomposition are discussed.
Articles you may be interested inRotating full-and reduced-dimensional quantum chemical models of molecules
We present converged quantum scattering results for the Cl + HCl f ClH + Cl reaction in which the three electronic states that correlate asymptotically to the ground state of Cl( 2 P) + HCl ( 1 Σ + ) are included in the dynamical calculations. The potential energy surfaces are taken from recent restricted open-shell coupledcluster singles doubles with perturbative triples and multireference configuration interaction ab initio computations of A. J. Dobbyn, J. N. L. Connor, N. A. Besley, P. J. Knowles, and G. C. Schatz [Phys. Chem. Chem. Phys. 1999, 1, 957], as refined by T. W. J. Whiteley, A. J. Dobbyn, J. N. L. Connor, and G. C. Schatz [Phys. Chem. Chem. Phys. 2000, 2, 549]. The long-range van der Waals portions of the potential surfaces are derived from multisurface empirical potentials due to M.-L. Dubernet and J. M. Hutson [J. Phys. Chem. 1994, 98, 5844]. Spin-orbit coupling has been included using a spin-orbit parameter that is assumed to be independent of nuclear geometry, and Coriolis interactions are calculated accurately. Reactive scattering calculations have been performed for total angular momentum quantum number J ) 1 / 2 using a hypersphericalcoordinate coupled-channel method in full dimensionality. The scattering calculations are used to study the influence of the spin-orbit coupling parameter λ on the fine-structure-resolved cumulative reaction probabilities and transition-state resonance energies with λ varying from -150% to +150% of the true Cl value. The results show the expected dominance of the 2 P 3/2 state to overall reactivity for λ close to the true Cl value and the dominance of the 2 P 1/2 state for λ close to -1 times the true Cl value. Between these two limits, the fine-structure-resolved cumulative reaction probabilities show oscillations as λ varies, statistical behavior being recovered for λ ) 0. We present a two-state model that roughly matches these oscillations and which suggests that the reactivity oscillations are due to coherent mixing of the Ω j ) 1 / 2 components of the 2 Σ and 2 Π states that are derived from the 2 P states in the van der Waals regions of the potential surfaces. This mixing leads to inverted spin-orbit propensities (i.e., the upper spin-orbit state is more reactive than the lower one) for certain values of λ. Our analysis of resonance energies indicates significant variation in resonance stability with the value of λ, a general trend being that narrower resonances occur when |λ| is smaller than about 50% of the absolute value of the true Cl value, suggesting that narrow resonances occur when there is significant coherent mixing. In addition, we find evidence for Stueckelberg interference oscillations in the total cumulative reaction probabilities due to a conical intersection between the 1 2 A′ and 2 2 A′ potential surfaces.
The model we have termed quantum constrained kinematics and found to give an accurate account of atom-diatom inelastic scattering is tested by application to elementary atom-molecule reactive collisions. The approach emphasizes the disposal of initial relative momentum into rotational angular momentum of the product diatomic via vector relations that are constrained by the internal quantum structure of the product diatomic. We introduce the concept of vibrational momentum of the atoms in a diatomic molecule in order to treat vibrational and rotational excitation of the product species. This representation is valuable in providing a realistic picture of the motion in a heteronuclear diatomic and also indicates how the enthalpy of a reaction may be disposed in momentum terms. It may also provide criteria for assessing the likelihood of particular reaction mechanisms. Comparison of results calculated using the quantum constrained kinematic model with experimental data indicates a number of simple, transferable rule-of-thumb guides to the outcome of reactive collisions. Most probable j values and distributions are accurately predicted using readily available data in parameter-free calculations. It is found that in reactive collisions, initial velocity distributions are mapped onto those of product rotational states via an effective impact parameter distribution that is sharply peaked around the half bond length of the product diatomic molecule.
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