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The experimental determination of the usual long range parameters $C5,C6,C8,\dots$ of diatomic molecules, is difficult and lacks precision due to strong correlations. Nevertheless their precise determination is particularly useful since it can allow in principle the calculation of the related parameters of the other molecular electronic states with the same configuration. From Fourier Transform high resolution spectra using corrected extrapolations from Le Roy's theory and calculations from RKR potential curves it is possible to obtain determinations which are mutually consistent. Comparison of these results with ab initio calculations have been made in the cases of $Li2$ and $I2$.