Abstract
The results of accurate quantum reactive scattering calculations for the D + HD(v = 4, j = 0) D + HD(, ), D + HD(v = 4, j = 0) H + D2(, ) and H + D2(v = 4, j = 0) D + HD(, ) reactions are presented for collision energies between and . The ab initio BKMP2 PES for the ground electronic state of H3 is used and all values of total angular momentum between are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and total reaction rate coefficients are reported as a function of collision energy. Rotationally resolved differential cross sections are also reported as a function of collision energy and scattering angle. Large geometric phase effects appear in the ultracold reaction rate coefficients which result in a significant enhancement or suppression of the rate coefficient (up to 3 orders of magnitude) relative to calculations which ignore the geometric phase. The results are interpreted using a new quantum interference mechanism which is unique to ultracold collisions. Significant effects of the geometric phase also appear in the rotationally resolved differential cross sections which lead to a very different oscillatory structure in both energy and scattering angle. Several shape resonances occur in the 1– energy range and the geometric phase is shown to significantly alter the predicted resonance spectrum. The geometric phase effects and ultracold rate coefficients depend sensitively on the nuclear spin. Thus, experimentalists may be able to control the reaction by the selection of a particular nuclear spin state.
Highlights
For over 89 years, the Born-Oppenheimer [1] method has been the foundation for the quantum mechanical treatment of molecular structure, spectra, and scattering
If the ground electronic state becomes degenerate with an excited electronic state for some nuclear geometry, the real-valued ground state electronic wave function changes sign for any nuclear motion which encircles the degeneracy. [4, 5] This sign change occurs even though the degeneracy itself may lie very high in energy and is not energetically accessible for the given kinetic energy of the nuclear motion
Resolved, vibrationally resolved, and total reaction rate coefficients will be presented for several products states as a function of collision energy
Summary
For over 89 years, the Born-Oppenheimer [1] method has been the foundation for the quantum mechanical treatment of molecular structure, spectra, and scattering This methodology is based on a power series expansion of the molecular wave function and energies in terms of the small electron to nuclei mass ratio κ = (me/mnuc)1/4. Repeated solutions of the electronic structure are performed on a grid of nuclear geometries to construct an effective electronic potential energy surface (PES). The nuclear motion is governed by an effective electronic PES and by the presence of an effective magnetic field B = ∇ × A This magnetic field has the peculiar property of being zero everywhere except at the point of degeneracy where it exhibits a delta function singularity.
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