Quasi-Quantum Treatment Of Rotationally Inelastic NO(X)-He Scattering

Rotationally inelastic scattering is one of the fundamental collision-induced energy transferprocesses that underlie intermolecular energy flow in chemically reacting systems such asatmospheric, combustion, thermal, cold and ultra-cold chemistry. The measurement of the fullyquantum state-to-state resolved angular distribution of the scattered products, characterized asthe differential cross sections （DCSs）, represents one of the most fundamental quantities ofinelastic scattering. It provides valuable information with different angular distributioncorresponding to regimes of different dynamics. The collision of the NO（X） molecule onto a Heatom is particularly interesting; due to the unpaired electron in the open-shell NO moleculeallows the energy transfer into the excited rotational levels of its upper spin-orbit state.Moreover such a collision may also alter its Λ-doublet and hyperfine states. The NO（X）-raregas atom collision system is a paradigm for what happens in a molecular collision involvingmore than one Born-Oppenheimer potential energy surface （PES）.The quasi-quantum treatment （QQT）（Gijsbertsen et al., JACS2006,128,8777） employs aFeynman path integration over angular variables in the kinematic apse frame to avoid thetraditional quantum mechanical （QM） partial wave expansion approach, while requiring muchless computational effort. QQT provides a physically compelling framework for the evaluationof rotationally inelastic scattering, including both DCSs and integral cross sections （ICSs）. Inthis thesis, we have made a series of efforts to improve and extend QQT method. The mainaccomplishments are:1. The QQT theory has been extended from spin-orbit state conserving transitions to thespin-orbit state changing transitions. This became possible by the introduction of anadditional angular variable, the dihedral angle ⅹ_R, between the plane of the NO-axis and its1Π open shell orbital lobe with respect to the plane of the NO axis and the He atom. Subsequently,the regular two dimensional PES V_sum（R,γ_R）was extended to a effective three dimensionalPES V （R,γ_R,Ⅹ_R）. The quantum state-to-state resolved DCSs and ICSs for collision of NO（X）with He, obtained from QQT theory and CC QM methods have been investigated employingboth in both spin-orbit conserving and changing transitions. This extension of the QQT modelpromises to provide a tool acquire insight into the underlying mechanism that brings aboutthe spin orbit excitation or purely rotationally inelastic excitation and as such offers a focusfor future work.2. A modified Quasi-Quantum Treatment （QQT） of the rotationally inelastic scattering hasbeen developed to study the integral and differential cross sections of NO （X²） with Heat the collision energy of508cm-1, which are compared with previous regular QQT andrigorous Quantum Mechanical （QM） calculations. The rigid shell potential energy surface（PES） defined as the contour V_sum（R, γ_R） Ecol, a basic assumption of regular QQT, results amore backwards scattered rotationally inelastic differential cross sections than thoseobtained by the exact QM solution on the complete ab initio PES. To improve on the rigidhard shell approximation, this paper presents the modified QQT, in which treatment, themodified hard shell PES contour V_sum（R,γ_R） E_col. cos²β is set equal to the fraction of thecollision energy provided by the incoming momentum vector directed anti-parallel to thesurface normal. In our example of He-NO（X）, indeed modified QQT results more forwardscattering especially for its parity changing rotationally inelastic transitions, compared toregular QQT but still less compared to exact QM. Tentatively this may be ascribed to thesteep repulsive core of the He-NO（X） V_sumPES. A more distinct forward trend formodified QQT is possible for collision systems with an appreciable softer core, as forexample the Alkali atom-NO（X） collision systems.3. QQT framework is extended to treat the DCS in the classically forbidden region as well asthe classically allowed region. Moreover, the QQT is applied to the collision energydependence of the angular distributions of these DCSs, and a new analytical formalism isderived that reveals a scaling relationship between the DCS calculated at a particular collision energy and the DCS at other collision energies. This scaling is shown to be exactalso for QM calculated or experimental DCSs if the magnitude of scattering amplitudedepends solely on the projection of the incoming momentum vector onto the kinematicapse vector. The QM DCSs of the NO（X）-He collision system were found to obey thisscaling law nearly perfectly for energies above63meV, that is, the DCSs at a collisionenergy of E_col^L=63meV can be accurately reconstructed from the correspondingNO（X）+He DCSs at E_col^H=147meV. This implies that there is no need to carry outadditional expensive close-coupled calculations to obtain the scattering angle dependenceof the quantum state resolved DCSs at collision energies between E_col^L=63meV andE_col^H=147meV. The mathematical derivation is accompanied by mechanistic description ofthe Feynman paths that contribute to the scattering amplitude in the classically allowed andforbidden regions, and the nature of the momentum transfer during the collision process.The successful application of the QQT collision energy scaling formalism reinforces theevidence that the He-NO rotationally inelastic DCSs depend very sensitive on theanisotropy of the repulsive part of the PES. This scaling relationship highlights the natureof （and limits to） the information that is obtainable from the collision-energy dependence ofthe DCS, and allows a description of the relevant angular range of the DCSs that embodiesthis information.