Application of the Pekeris approximation to the radial Frost-Musulin potential in diatomic molecules

Accurate modeling of diatomic molecular interactions requires potential functions that closely match experimental data. The radial Frost-Musulin (RFM) potential provides a realistic description of these interactions but lacks an exact analytical solution under the Schrödinger equation. Previous studies have typically employed the Greene-Aldrich approximation to make the RFM solvable, but this method introduces significant deviations from reference data such as Rydberg-Klein-Rees (RKR) results, limiting its predictive reliability. In this study, the Pekeris approximation scheme is applied to the RFM potential and the centrifugal barrier term of the Schrödinger equation, preserving the essential features of the interaction. By using the generalized fractional Nikiforov-Uvarov method, analytical expressions for the bound-state energy eigenvalues with fractional parameters are derived. The resulting Pekeris-approximated RFM potential and its corresponding energy eigenvalue equations are applied to several diatomic molecules, including BCl (X ¹ Σ ⁺ ), CO (X ¹ Σ ⁺ ), K ₂ (X ¹ Σ _g ⁺ ), ⁷ Li ₂ (1 ³ Δ _g ), Na ₂ (5 ¹ Δ _g ), and Na ₂ (C(2) ¹ Π _u ). The relative error in absolute percentage (REAP) obtained with the Pekeris-approximated RFM potential ranges from 0.0969% to 1.9476% compared to the exact RFM potential, while the derived energy eigenvalue equations achieve REAP values between 0.1239% and 1.5233% across the same species. These results demonstrate that the Pekeris approximation offers a more physically consistent and accurate framework for predicting bound-state energies in diatomic systems than previous approaches.