Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in spacefixed and bodyfixed reference frames
Abstract
We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the spacefixed and second in the bodyfixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the statetostate transition matrix is complexvalued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the statetostate transitions are driven by realvalued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the spacefixed formulation can serve as a test of the bodyfixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.
 Publication:

Journal of Chemical Physics
 Pub Date:
 November 2013
 DOI:
 10.1063/1.4827256
 Bibcode:
 2013JChPh.139q4108S
 Keywords:

 atommolecule collisions;
 quantum theory;
 rotational states;
 sparse matrices;
 vibrational states;
 34.50.s;
 33.20.Sn;
 31.15.X;
 33.20.Tp;
 Scattering of atoms and molecules;
 Rotational analysis;
 Alternative approaches;
 Vibrational analysis