Accuracy of the energy-corrected sudden (ECS) scaling procedure for rotational excitation of CO by collisions with Ar

We examine the question, given a set of state-to-state rate constants k( j=0 → j'‖T) for collision-induced rotational transitions in a diatomic molecule, where j and j' are initial and final rotational quantum numbers and T is the translational temperature, can one use scaling analyses to predict a full set of j → j' rate constants? To answer this we consider a rigid rotator model of CO in a bath of Ar at 500 K, and we calculate accurate quasiclassical k( j → j'‖T) for j=0, 10, and 20 and j'=0-29. These are used to test the energy sudden (ES) and energy-corrected sudden (ECS) scaling procedures. Both procedures are used to predict the j=10 and j=20 rate constants from the j=0 values. The ES procedure, which has no adjustable parameters, overestimates the rates out of excited states by a factor of about 1.5 with a rms error of about 60%. The ECS procedure, in contrast, when the one parameter b_c (a critical impact parameter) is about 1.75-2.0 Å, yields excellent excited-state rates on the average and has a rms error of less than 20%. The value of b_c can be estimated by a weighted average impact parameter leading to inelastic collisions from a j=0 initial state.