Reproducing kernel technique for extracting accurate potentials from spectral data: Potential curves of the two lowest states X ¹Σ⁺_g and a ³Σ⁺_u of the sodium dimer

This work describes an extension of the Reproducing Kernel Hilbert Space (RKHS) method, in conjunction with the Tikhonov regularization, for constructing potential energy surfaces, with correct asymptotic forms, from high quality experimental measurements. The method is applied to the construction of new, global potential energy curves of the two lowest states X ¹Σ⁺_g and a ³Σ⁺_u of the sodium dimer using rovibrational spectral measurements. The exchange interaction of Na₂ at intermediate and long ranges is accordingly derived and adopted for determining the ionization energy of the corresponding valence electron. It is found that the resulting ground-state X ¹Σ⁺_g dissociation energy 6022.025 (±0.049) cm^-1 of Na₂ agrees within the experimental errors with the most recent experimental value [6022.0286 (±0.0053) cm^-1, Jones et al., Phys. Rev. A 54, R1006 (1996)]. The well depth of the a ³Σ⁺_u state is determined to be 174.96 (± 1.18) cm^-1, compared to the Rydberg-Klein-Rees (RKR) value of 174.45 (±0.36) cm^-1 [Li et al., J. Chem. Phys. 82, 1178 (1985)]. Moreover, the equilibrium positions of both RKHS potential curves, 3.0796 (±0.0010) Å for the X ¹Σ⁺_g state and 5.089 (±0.062) Å a ³Σ⁺_u state, are in excellent agreement with previously determined RKR results of 3.07953 Å [Babaky and Hussein, Can. J. Phys. 67, 912 (1989)] and 5.0911 Å (Li et al.), respectively. The experimentally determined values of the equilibrium position and well depth for the a ³Σ⁺_u state differ from recent theoretical values of 5.192 Å and 177.7 cm^-1 obtained by highly accurate ab initio calculations [Gutowski, J. Chem. Phys. 110, 4695 (1999)]. Finally, both RKHS potential curves at large distances reproduce very recent theoretical dispersion coefficients within 1.0×10^-5 percentage errors.