Quantum calculations for rotational energy transfer in nitrogen molecule collisions

Abstract

Rotational energy transfer in collisions of nitrogen molecules has been studied theoretically, using the N2–N2 rigid-rotor potential of van der Avoird et al. [J. Chem. Phys. 84, 1629 (1986)]. For benchmarking purposes, converged close coupling (CC) calculations have been carried out to a total energy of about 200 cm−1. Coupled states (CS) approximation calculations have been carried out to a total energy of 680 cm−1, and infinite order sudden (IOS) approximation calculations have also been carried out. The CC and CS cross sections have been obtained both with and without identical molecule exchange symmetry, whereas exchange was neglected in the IOS calculations. The CS results track the CC cross sections rather well: between 113–219 cm−1 the average deviation is 14%, with accuracy improving at higher energy. Comparison between the CS and IOS cross sections at the high energy end of the CS calculations, 500–680 cm−1, shows that IOS is sensitive to the amount of inelasticity and the results for large ΔJ transitions are subject to larger errors. State-to-state cross sections with even and odd exchange symmetry agree to better than 2% and are well represented as a sum of direct and exchange cross sections for distinguishable molecules, an indication of the applicability of a classical treatment for this system. This result, however, does not apply to partial cross sections for given total J, but arises from a near cancellation of the interference terms between even and odd exchange symmetries on summing over partial waves. In order to compare with experimental data for rotational excitation rates of N2 in the n=1 excited vibrational level colliding with ground vibrational level (n=0) bath N2 molecules, it is assumed that exchange scattering between molecules in different vibrational levels is negligible and direct scattering is independent of n so that distinguishable molecule rigid rotor rates may be used. With these assumptions good agreement is obtained. Although the IOS approximation itself is found to provide only moderately accurate values for rate constants, IOS/ECS scaling methods, especially if based on fundamental rates obtained from coupled channel results, are found to provide generally good accuracy.