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

Abstract

Articles you may be interested inSpin-orbit coupling in O 2 ( v ) + O 2 collisions. II. Quantum scattering calculations on dimer states involving the X Σ g − 3 , a Δ g 1 , and b Σ g + 1 states of O 2 A reliable ab initio potential energy surface and vibrational states for the ground electronic state of HgH 2 ( X Σ g + 1 )This work describes an extension of the Reproducing Kernel Hilbert Space ͑RKHS͒ 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 1 ⌺ g ϩ and a 3 ⌺ u ϩ of the sodium dimer using rovibrational spectral measurements. The exchange interaction of Na 2 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 1 ⌺ g ϩ dissociation energy 6022.025 (Ϯ0.049͒ cm Ϫ1 of Na 2 agrees within the experimental errors with the most recent experimental value ͓6022.0286 (Ϯ0.0053͒ cm Ϫ1 , Jones et al., Phys. Rev. A 54, R1006 ͑1996͔͒. The well depth of the a 3 ⌺ u ϩ state is determined to be 174.96 (Ϯ1.18͒ cm Ϫ1 , compared to the Rydberg-Klein-Rees ͑RKR͒ value of 174.45 (Ϯ0.36͒ cm Ϫ1 ͓Li et al., J. Chem. Phys. 82, 1178 ͑1985͔͒. Moreover, the equilibrium positions of both RKHS potential curves, 3.0796 (Ϯ0.0010͒ Å for the X 1 ⌺ g ϩ state and 5.089 (Ϯ0.062͒ Å for the a 3 ⌺ u ϩ state, are in excellent agreement with previously determined RKR results of 3.079 53 Å ͓Babaky and Hussein, Can. J. Phys. 67, 912 ͑1989͔͒ and 5.0911 Å ͑Li et al.͒, respectively. The experimentally determined values of the equilibrium position and well depth for the a 3 ⌺ u ϩ state differ from recent theoretical values of 5.192 Å and 177.7 cm Ϫ1 obtained by highly accurate ab initio calculations ͓Gutowski, J. Chem. Phys. 110, 4695 ͑1999͔͒. Finally, both RKHS potential curves at large distances reproduce very recent theoretical dispersion coefficients within 1.0ϫ10 Ϫ5 percentage errors.

New experimental data on the K2 state analyzed with the multi-parameter approach

“…Earlier [9], we observed similar discrepancies in the Na 2 a 3 R þ u state which led us to the revision of this state potential function [10]. One of the results of [10] was an explanation of the contradiction [32,33] between the experimental and theoretical values of R e .…”

Excited state potential energy surfaces from the inversion of absorption spectra: Removal of a global singularity

“…The conventional approach to inversion of Eq. ͑7͒ for determining the excited state V f (x) would involve least squares minimization with Tikhonov regularization; [19][20][21][22] below we show that in this case there is an underlying difficulty with this approach.…”

Two-color photoassociation spectroscopy of the lowest triplet potential of Na2

“…Good potentials have been obtained over the last twenty years, [9][10][11][12][13] and were recently improved further by Tiemann and co-workers. [1][2][3] All 64 vibrational states of X 1 ⌺ g ϩ have now been observed.…”

“…RKR potential curves for a 3 ⌺ u ϩ were generated by Friedman-Hill and Field 16 12 also generated a new a 3 ⌺ u ϩ potential from the data of Ref. 15 using a modified inverse perturbation analysis.…”