Carbonate-Bridged Lanthanoid Triangles: Single-Molecule Magnet Behavior, Inelastic Neutron Scattering, and Ab Initio...

Optimization of literature synthetic procedures has afforded, in moderate yield, homogeneous and crystalline samples of the five analogues Na11[{RE(OH2)}3CO3(PW9O34)2] (1-RE; RE = Y, Tb, Dy, Ho, and Er). Phase-transfer methods have allowed isolation of the mixed salts (Et4N)9Na2[{RE(OH2)}3CO3(PW9O34)2] (2-RE; RE = Y and Er). The isostructural polyanions in these compounds are comprised of a triangular arrangement of trivalent rare-earth ions bridged by a μ3-carbonate ligand and sandwiched between two trilacunary Keggin {PW9O34} polyoxometalate ligands. Alternating-current (ac) magnetic susceptibility studies of 1-Dy, 1-Er, and 2-Er reveal the onset of frequency dependence for the out-of-phase susceptibility in the presence of an applied magnetic field at the lowest measured temperatures. Inelastic neutron scattering (INS) spectra of 1-Ho and 1-Er exhibit transitions between the lowest-lying crystal-field (CF) split states of the respective J = 8 and (15)/2 ground-state spin-orbit multiplets of the Ho(III) and Er(III) ions. Complementary ab initio calculations performed for these two analogues allow excellent reproduction of the experimental magnetic susceptibility and low-temperature magnetization data and are in reasonable agreement with the experimental INS data. The ab initio calculations reveal that the slight difference in coordination environments of the three Ln(III) ions in each complex gives rise to differences in the CF splitting that are not insignificant. This theoretical result is consistent with the observation of multiple relaxation processes by ac magnetic susceptibility and the broadness of the measured INS peaks. The ab initio calculations also indicate substantial mixing of the MJ contributions to the CF split energy levels of each Ln(III) ion. Calculations indicate that the CF ground states of the Ho(III) centers in 1-Ho are predominantly comprised of contributions from small MJ, while those of the Er(III) centers in 1-Er are predominantly comprised of contributions from large MJ, giving rise to slow magnetic relaxation. Although no direct evidence for intramolecular RE···RE magnetic coupling is observed in either magnetic or INS studies, on the basis of the ab initio calculations, we find noncollinear magnetic axes in 1-Er that are coplanar with the erbium triangle and radially arranged with respect to the triangle's centroid; thus, we argue that the absence of magnetic coupling in this system arises from dipolar and antiferromagnetic superexchange interactions that cancel each other out.