A litmus test for the balanced description of dispersion interactions and coordination chemistry of lanthanoids

The influence of long-range interactions on the structure of complexes of Eu(III) with four 9-hydroxy-phenalen-1-one ligands (HPLN) and one alkaline earth metal dication [Eu(PLN)$_{4}$AE]$^{+}$ (AE: Mg, Ca, Sr, and Ba) is analyzed. Through the [Eu(PLN)$_{4}$Ca]$^{+}$ complex, which is a charged complex with two metals—one of them a lanthanoid—and with four relatively fluxional π-ligands, the difficulties of describing such systems are identified. The inclusion of the D3(BJ) or D4 corrections to different density functionals introduces significant changes in the structure, which are shown to stem from the interaction between pairs of PLN ligands. This interaction is studied further with a variety of density functionals, wave-function based methods, and by means of the random phase approximation. By comparing the computed results with those from experimental evidence of gas-phase photoluminescence and ion mobility measurements it is concluded that the inclusion of dispersion corrections does not always yield structures that are in agreement with the experimental findings.