TABLE I: The potential coefficients and derived molecular constants for the ground state X $^{1}$Σ+ g . The potential energy is calculated with respect to the asymptote, the dispersion co- efficients are the recommended values from the third column of table II. a 1 -6.50 × 10 − 2 cm − 1 a 2 1.5939056 × 10 4 cm − 1 a 3 -2.9646778 × 10 4 cm − 1 a 4 -6.269777 × 10 3 cm − 1 a 5 4.4952358 × 10 4 cm − 1 a 6 8.709016 × 10 3 cm − 1 a 7 -1.0054929 × 10 5 cm − 1 a 8 5.94784152 × 10 5 cm − 1 a 9 -9.95239126 × 10 5 cm − 1 a 10 -1.14496717 × 10 7 cm − 1 a 11 4.606463055 × 10 7 cm − 1 a 12 3.74666573 × 10 7 cm − 1 a 13 -5.439157146 × 10 8 cm − 1 a 14 9.364833940 × 10 8 cm − 1 a 15 1.387879748 × 10 9 cm − 1 a 16 -8.4009054730 × 10 9 cm − 1 a 17 1.5781752106 × 10 cm − 1 a 18 -1.5721037673 × 10 cm − 1 a 19 8.376043061 × 10 9 cm − 1 a 20 -1.88984880 × 10 9 cm − 1 b -0.17 R m 4.6719018 ˚ A T m -1081.6384 cm − 1 R i 3.963 ˚ A n 12.362 A -1.3328825 × 10 3 cm − 1 B 3.321662099 × 10 cm − 1 ˚ A n R a 10.5 ˚ A C 6 1.525 × 10 7 cm − 1 ˚ A 6 C 8 5.159 × 10 8 cm − 1 ˚ A 8 C 10 1.91 × 10 cm − 1 ˚ A 10 derived constants: D e 1081.64(2) cm − 1 D 0 1061.58(1) cm − 1 R e 4.6720(1) ˚ A spite the precision of the energies of the levels v ′′ = 62, J ′′ = 0 and J ′′ = 2 from [15] incorporated in the fit, the set of coefficients is still significantly correlated. While the C$_{6}$ coefficient is quite well fixed the coefficients C$_{8}$ or C$_{10}$ can be varied over a larger range of values without a significant reduction in the quality of the description of the data set, if all other coefficients are adjusted ac- cordingly. To estimate uncertainties for the long range coefficients different potential fits were done where each time the C$_{8}$ coefficient was held fixed at a different value within its range as given in the second column of table II. The results shown for the other C$_{i}$ coefficients are av- eraged values from the series of fits and their uncertainty bounds represent an increase of the sum of the weighted squared residuals by 2%, which is a quite safe limit, since only 113 of the 6077 energy levels included in the fit are directly affected by this change. Because the derived uncertainty for the C$_{8}$ coefficient is significantly larger than the uncertainty claimed for the theoretically calculated coefficient by [13] (see the fifth column of table II) and also larger than the dif- ference between the two available theoretical C$_{8}$ coeffi- cients [12, 13], additional potential fits were done, where each time the C$_{8}$ coefficient was held fixed at a value taken from [12] or [13] or the average of both. Such a procedure was also tried with the theoretical C$_{6}$ coeffi- cients, but those resulting potentials gave a significantly less convincing description of the data set and also the re- sulting coefficients C$_{8}$ and C$_{10}$ showed strong deviations to the theoretical values. Additional fits were done for different numbers of potential coefficients a$_{j}$ and differ- ent connection radii R$_{i}$ and R$_{a}$ . For a few fits R$_{a}$ was set to values as large as 13 ˚ A, which led to significantly less well determined long range coefficients with higher cor- relation without obtaining a significant improvement in the description of the data. The resulting C$_{i}$ coefficients of all the fits using either the C$_{8}$ coefficient from [12] or from [13] or its mean value were averaged to obtain the recommended values, which are listed in the third col- umn of the table II. The uncertainties are 1 σ standard deviations of the averaged values. Table II compares the dispersion parameters derived with freely varied C$_{i}$ coefficients and the recommended values with the published theoretical long range coeffi- cients from recent years. As one can see, the values in the second column are in good agreement with all the other values, while the recommended values do deviate from the most precise theoretical coefficient set from [13] more than one would expect considering the given un- certainties, there. This could be due to different reasons. The paper [13] used the lifetime of the atomic $^{1}$S—$^{1}$P transition from [14], which was calculated from the C$_{3}$ coefficient of the state 2 $^{1}$Σ+ u fitted to photoassociation data. In [14] line broadenings of the PA resonances are mentioned, which could indicate predissociation due to the coupling to the continuum of electronic states from lower asymptotes and could lead to a systematic shift of these asymptotic levels of the state 2 $^{1}$Σ+ $_{u}$. Another rea- son could be that the presently derived uncertainties are underestimated because of a too low number of differ- ent potential descriptions used for averaging. The com- puting effort of testing the long range correlation by a Monte Carlo study would be enormous for the presently employed analytical type of potential description and the available hard and software. A pointwise representation of the potential derived from the parameters in table I and the analytical po- tential description for the best fitting values obtained by freely varying C$_{i}$ coefficients can be found in the addi- 4