Algebraic vs. numerical methods for analysing diatomic spectral data: a resolution of discrepancies

Resolution of a convergence problem in direct-potential-fit data analyses: Applications to GaH(X1Σ+) and ArH+(X1Σ+)

“…This agreement further confirms the validity of DPF methods, by confirming that all methods so far considered for implementing it can yield exactly the same results if proper convergence techniques are applied [7].…”

“…It has been shown that this ''direct-potentialfit'' (DPF) approach can represent large, multi-state, multi-isotopologue data sets to within the full accuracy of the data, while requiring much smaller sets of empirical parameters than do traditional fits to analytic expressions for the level energies. Apparent differences between results of this type obtained using algebraic rather than direct numerical methods to solve the relevant radial Schrö dinger equation [1][2][3][4][5][6] have been shown to be due to an internal convergence problem in some implementations of the algebraic method [7], and possible questions about the reliability of the DPF approach to diatomic data analysis had apparently been resolved.…”

Application of direct potential fitting to line position data for the and states of Li2

“…Around the time of our first work [12], other groups [18,19] had also begun to explore the advantage of direct least squares determination of potential energy functions having full quantum mechanical significance, albeit with the use of derived energy levels, rather than the line positions, as input data. Several recent studies by Le Roy and co-workers [10,[20][21][22] also provide a strong impetus for the implementation of the DPF approach.…”

Isotopically invariant analysis of vibration–rotation transitions of HBr and its isotopologues

“…It is possible to calculate vibrational energies E v , rotational constants B v , and the set of centrifugal distortion constants from those parameters, if necessary. Le Roy [16] reviewed this method in detail. Although the procedure is more complicated, the ''direct potential fits'' method requires smaller numbers of parameters and has a better ability to predict transition frequencies outside the range analyzed.…”