Further development and application of the ECS scaling theory: Non-linear molecules

The energy corrected sudden (ECS) scaling theory is applied to rotational energy transfer (RR,T) in the HeNH₃ system: one of the largest and most complex systems studied thus far. A test of the scaling and an accurate prediction of available cross sections required the development of two new results: (1) a scaling relation between properly symmetrized symmetric-top cross sections; and (2) a higher-order ECS adiabaticity correction factor than was previously available. The final scaling relation, through the incorporation of ortho—para symmetry effects, exhibits two interesting features: (1) the fundamental input to the scaling, used to generate both ortho and para results, consists of only ortho transitions; and (2) these ortho fundamentals divide into two distinct groups — one used to predict only Δk = 0 transitions and the other only Δk ?= 0 transitions. The scaling is tested using “exact” cross sections calculated on a short-range Gordon—Kim potential surface and on a more realistic, longer-range Hartee—Fock surface. Scaling predictions are in very good agreement in the short-range case with the kinetic-energy shift being the only adiabaic correction necessary. In the second, longer-range case, considerably more adiabatic behavior is encountered and the scaling results are in only moderately good agreement even with the incorporation of a higher-order adiabatic correction factor. These two systems serve to illustrate some of the virtues and limitations of the scaling approach.