Date of Award

Summer 2017

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Babikov, Dmitri

Second Advisor

Huang, Jier

Third Advisor

Steinmetz, Mark


This thesis presents developments and applications of the mixed quantum/classical theory (MQCT) for inelastic scattering. In this approach, translational motion of collision partners is treated classically, while the internal degrees of freedom – rotational and/or vibrational motion – are treated quantum mechanically. Within this framework calculations of rotationally inelastic cross sections are carried out in a broad range of collision energies and results are compared against the exact full quantum data for several real systems. For CO +He, N2 + Na and H2 + He the agreement is excellent through six orders of magnitude range of cross sections values and for energies 1 < E < 10000 cm-1. Elastic and differential cross section for N2 + Na are described very accurately. For ro-vibrational transitions in CO + He and H2 +He MQCT reproduces full quantum results even for highly excited rotational states. For H2O + He it is found that at lower energies the typical errors for cross sections are on the order of 10%, which is acceptable. It is showed that computational cost of the fully-coupled MQCT scales as n2- 3, where n is the number of channels which is far more favorable in comparison with full quantum scaling n5-6. This enables calculations on larger molecules and at higher collision energies, than was possible using the standard approach. The largest system ever considered for rotational scattering, HCOOCH3 + He, is also treated by MQCT. At energies where quantum results are available (≤ 30 cm-1) the agreement is found very good. Then MQCT calculations for this system are extended up to E = 1000 cm-1. Finally, theoretical framework for treatment of molecule + molecule scattering is developed and applied to H2+H2 and N2+H2 systems where excellent agreement with exact quantum results is found. We also apply MQCT method to H2O + H2O rotationally inelastic scattering and obtain the first and only data for this process in a broad range of collisional energies. Success of MQCT makes this theory a practical tool for obtaining the state-to-state transition rates for astrochemical modeling and other applications.