Einstein coefficients for diatomic molecules

Abstract

Re-examination of current semiempirical methods for computing Einstein coefficients for diatomic molecules has resulted in the development of a new technique for predicting infrared transition probabilities. The method uses a nonlinear transformation of existing polynomial dipole expressions with the subsequent application of appropriate boundary conditions to arrive at improved dipole curves. The transition probabilities predicted for HF are found to yield the most consistent agreement with the available experimental data when compared with existing results. Reanalysis of experimental data by the use of the new transition probabilities yields an HF(v) distribution for the reaction, H + F2 → HF(v) + F, 0 ≤ v ≤ 9, that is in better agreement with independent theoretical predictions than the uncorrected distribution. The method has also been used to compute the Einstein A coefficients of DF, HCl, and DCl.

A Review of Recent Experiments and Calculations Relevant to the Kinetics of the HF Laser

“…The Einstein coefficients used by most HF CFD codes are based on the values found in the Handbook of Chemical Lasers 7 ͑which are in turn, based on the empirical calculations of Herbelin and Emanuel͒, 8 and have not been updated in over 25 years. Table 1 gives a representative sample of the Handbook's HF vibration-rotational Einstein emission coefficients as well as the more recent ͑and preferred͒ results of Setser and co-workers, 9 see below.…”

“…10 Because the data are limited, it is generally necessary to extrapolate (R) for R values that are not observed experimentally. Typically, semiempirical techniques, such as the Padé expansion of Herbelin and Emanuel, 8 have been used to perform this extrapolation. In 1991, Zemke 11 and co-workers published a potential surface based on the spectroscopically determined potential of Coxon and Hajigeorgiou, 12 adjusted to reproduce the proper long-range behavior by including both dispersion and exchange effects.…”

“…Most experimental measurements, particularly those of Polanyi, 17 Jonathan, 18 and Tardy, 19 analyzed their data using Einstein coefficients that have since been shown to be inaccurate. 8,20,21 Hence, corrected distributions using the recommended set of A coefficients 9 are shown in parentheses in Table 5.…”

Direct Detection of the Product Vibrational-State Distribution in the Associative Detachment ReactionCl−+H→HCl(v)+Zwier1, Maricq2, Simpson3 et al. 1980Phys. Rev. Lett.31020View full textAdd to dashboardCite

“…; = 2, and A 21 and A 10 are the Einstein coefficients for spontaneous emission for the v = 2 -v = 1 and v = l-~v = 0 bands in HC1 (A 21 /A 10 = 1.72). 23 Gas-phase and wall deactivation were found to be negligible, under large variations of CC1 4 , H-atom, H 2 , and He flows. Since the measurements are made 1 msec downstream from the initial H-atom introduction, a small correction for radiative cascading must be included in the final N v=2 /N v=1 ratio.…”

Evaluation of State-Resolved Reaction Probabilities and Their Application in Population Models for He, H, and H2

“…For optically allowed spontaneous (dipole) transitions, this operator is equivalent to the dipole transition moment. Together with an appropriate prefactor, the transition probability (Einstein coefficient) of dipole transitions is equal to the overlap of two vibrational wave functions, convoluted with the dipole transition moment [45].…”