The binding affinities of [18]crown-6 and La3+, Nd3+, Gd3+, and Yb3+ have been reproduced in MeOH with Monte Carlo free-energy perturbation calculations which used newly derived Lennard-Lones parameters for the Ln3+ ions. The figure shows the complex of a lanthanide ion and the crown ether.
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Veggel et al. (1999) studied this question.
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