18s_analpertb

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Lecture # 18 Supplement Contents A. A Model for the Perturbations and Fine Structure of the States of CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 B. Factorization of Perturbation Parameters . . . . . . . . . . . . . . . . . 2 C. The Electronic Perturbation Parameters . . . . . . . . . . . . . . . . . 3 A. A Model for the Perturbations and Fine Structure of the States of CO This paper reports the results of an analysis of the numerous perturbations of the CO a 3 and A 1 states, which belong to the ( 1 s ) 2 ( 1 s ) 2 ( 2 s ) 2 ( 2 s ) 2 ( 2 p ) 4 ( 2 p ) ( 2 p ) electronic con- figuration (abbreviated ), by the a 3 + , e 3 , d 3 i , I 1 and D 1 states, which belong to the ( 1 s ) 2 ( 1 s ) 2 ( 2 s ) 2 ( 2 s ) 2 ( 2 p ) 3 ( 2 p ) 2 ( 2 p ) configuration (abbreviated 3 ). As many data as possible from the absorption, emission, and radio frequency spectra involving these states were combined in a uniform and systematic analysis. In several cases it was possible to use earlier data from the work of Ger o and Szabo[3] to augment the modern studies. The vibronic levels fitted are listed in Table I. The letters adjacent to each level indicate the sources of the data. The 47 horizontal rows contain the combinations of vibronic levels treated by degenerate perturbation theory. The choice of which levels to include in each of the groups was usually determined by selecting all of the nearest and strongest perturbers of a given a 3 or A 1 level. (The vibronic levels of the A and a states conveniently never occur at the same energy.) Therefore, the fitted a 3 and A 1 constants reported here should be regarded as fully deperturbed with respect to all of the nearest interacting levels. Extensive use was made of a nonlinear least squares fitting procedure which has been described earlier. The elements of the effective Hamiltonian matrix are given by Wicke et al .[2] 1 5.76 Lecture # 18 Supplement Page 2 The analysis of perturbations of the CO a 3 and A 1 states has led to two important conclusions. (i) For perturbations between vibronic levels belonging to a given pair of electronic states the perturbation matrix element is the product of a vibrational factor with a constant electronic factor. (ii) Simple, single-configuration arguments successfully predict the sign and relative magnitude of each of the electronic factors for perturbations between levels of each pair of electronic states. Thus all of the perturbations considered here can be related to two constants which are joint properties of the electronic configurations. It is now possible to calculate the interaction energy between any rovibronic...
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18s_analpertb - MIT OpenCourseWare http://ocw.mit.edu 5.80...

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