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

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 HoIII and ErIII 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 LnIII 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
LnIII ion. Calculations indicate that the CF ground states
of the HoIII centers in 1-Ho are predominantly
comprised of contributions from small MJ, while those of the ErIII 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.