Inverse perturbation analysis: Improving the accuracy of potential energy curves

Uncertainty, Sensitivity, Convergence, and Rounding in Performing and Reporting Least-Squares Fits

“…5 In many cases the application of this procedure is quite straightforward, as the property of interest is an explicit analytic function of the parameters. For example, direct "Hamiltonian" fits of spectroscopic transition frequencies to analytic potential energy functions are becoming increasingly common (13)(14)(15)(16), and the potential parameters determined in this way can be readily used to predict the uncertainties in the resulting potential function in the extrapolation region beyond the range spanned by the data (27). However, this has rarely been done.…”

“…For fits to nonlinear models, such as near-dissociation expansions (NDE) expressions for the level energies (7)(8)(9)(10)(11)(12) or models for the potential energy function itself (13)(14)(15)(16), the situation can be particularly difficult. For example, an equivalent quality NDE fit to the same 9552-line data set for A state I 2 mentioned above requires only half as many parameters as the Dunham expansion fit (row 3 of Table 2) discussed above.…”

The Potential of the Ag2B− 11ΠuState

“…[ 6] lowest order molecular constants, Y 10 and Y 01 , agree to an accuracy of 1.2-6 1 10 05 with the theoretically expected Here, Y ik are the mass-independent Dunham coefficients and values given in the top row of Table 3 and Eq. [7].…”

New Vibrational Numbering and Potential Energy Curve for the 33ΠgElectronic State of the Li2Molecule

“…Such an error is sufficiently small that there is no need to revise the results of the present paper. However, more precise results for the potential function can be obtained by using the bound state IPA (Inverse Perturbation Approach) procedure (15). The third-order RKR procedure of (16) requires knowledge of 3 3 ⌸ g ro-vibrational term values of the two isotopomers in approximately the same region of energies and, hence, cannot be used here.…”