COMPUTATIONAL STUDY OF THE ACCURACY OF THE R-CENTROID APPROXIMATION

Author Institution: Department of Computer Science, York UniversityThe r-centroid approximation is used in the analysis of intensity measurements of electronic band spectra of diatomic molecules. The r-centroid approximation allows a separation of the band strength (and other related electronic transition probability parameters) into a pure vibrational term (the Franck-Condon factor $q_{v{^{\prime}}v{^{\prime\prime}}}$) and an electronic term (the electronic transition moment Re(r)). The r-centroid approximation is known to have limits to its applicability. However, no specific error limits or estimates have previously been given. A computational study has been performed using a wide number of molecules and analytic curve shapes to determine specific error limits which can be assigned to either a specific band strength, or in estimating the electronic transition moment using the r-centroid approximation. Other techniques suggested for avoiding the r-centroid approximation in the evaluation of Re(r) have also tested and the errors are compared with the use of the r-centroid approximation