5 tional online material. For the convenience of the reader we also made fits us- ing the MLR potential description from [29], which might allow for defining the potential by a lower number of pa- rameters. It has the mathematical form with the long-range function and the exponential function where Three mapping functions y a b are defined as where the placeholder a can either be ’ e ’ for the equi- librium radius R$_{e}$ or ’ ref ’ for R$_{ref}$ and the exponent b can either be p or q . R$_{ref}$ is an expansion point at an internuclear distance larger than R$_{e}$ . The β$_{i}$ , C$_{i}$ , R$_{e}$ , and the dissociation energy D$_{e}$ are the fit parameters, while the parameter R$_{ref}$ and the exponents p and q are man- ually chosen to optimize the potential description with a minimum number of coefficients and to get the proper long range behavior. The potential coefficients for the MLR description are given in table III, the normalized standard deviation is σ = 0 . 80 as for the description given in table I. Thus there is no significant difference in the quality of the de- scription of the data set. The clear advantage of the potential description from table III compared to the po- tential description from table I is the lower number of potential coefficients necessary (14 β$_{i}$ instead of 20 a$_{i}$ ) and the fact that it is indefinitely continuously differen- tiable at all points which is not the case for the poten- tial of table I at the points R$_{i}$ and R$_{a}$ . Disadvantages are the much more complex formula with three mapping functions instead of one and a much stronger correlation of the long range coefficients C$_{i}$ with the potential co- efficients β$_{i}$ (see eqn (5)). For the potential description from table I the correlation between the C$_{i}$ and the a$_{i}$ is only due to the integration of the wave functions over the full potential region. Thus we applied the recommended C$_{i}$ values from table II for the fit of the MLR potential. The dissociation energy obtained in the MLR approach TABLE II: Comparison of the long range coefficients derived from fits of freely varying parameters with the recommended values applying a fixed C$_{8}$ value and with theoretical long range coefficients published in recent years. For the details on evaluation procedure and uncertainty estimates see text. TABLE III: The coefficients of the MLR potential description for the ground state X $^{1}$Σ+ g . The potential energy is calculated with respect to the potential minimum, the dispersion coeffi- cients were taken from table II. freely var. recommended [12] [13] [25] [26] [27] C$_{6}$ [10 $^{7}$cm − 1 ˚ A $^{6}$] 1.527(33) 1.525(5) 1.566 1.495(3) 1.5481 1.528(94) 1.509(20) C$_{8}$ [10 $^{8}$cm − 1 ˚ A $^{8}$] 5.1(15) (5.159)[28] 5.201 5.118(4) C$_{10}$ [10 $^{10}$cm − 1 ˚ A $^{10}$] 2.0(13) 1.91(27) 1.61 1.593 β$_{0}$ -1.458760592449 β$_{1}$ -0.031511799120 β$_{2}$ -0.912033020316 β$_{3}$ -0.033913017557 β$_{4}$ -0.465124882150 β$_{5}$ 0.287008644909 β$_{6}$ -0.585285048765 β$_{7}$ 2.490073196261 β$_{8}$ 3.065232204927 β$_{9}$ -8.521057394373 β$_{10}$ -0.771989570637 β$_{11}$ 17.679758812808 β$_{12}$ -11.143746759192 β$_{13}$ -1.704727367184 C$_{6}$ 1.525 × 10 7 cm − 1 ˚ A 6 C$_{8}$ 5.159 × 10 8 cm − 1 ˚ A 8 C$_{10}$ 1.910 × 10 cm − 1 ˚ A 10 D$_{e}$ 1081.6352 cm − 1 R$_{e}$ 4.6719032 ˚ A R$_{ref}$ 5.5 ˚ A p 5 q 3 V$_{MLR}$ ( R ) = D$_{e}$ [ 1 − U$_{LR}$ ( R ) U$_{LR}$ ( R$_{e}$ ) e − β ( y ref p ) × y e $_{p}$( R ) ] 2 (5) U$_{LR}$ ( R ) = C$_{6}$ R 6 + C$_{8}$ R 8 + C$_{10}$ R 10 (6) β = y ref p ( R ) β$_{∞}$ + [ 1 − y ref p ( R ) ] N ∑ i =0 β$_{i}$y ref q ( r ) i , (7) β$_{∞}$ = ln [ 2 D$_{e}$ U$_{LR}$ ( R$_{e}$ ) ] . (8) y a b = R b − R b a R b + R b a . (9)