The Solution Structure of Rhombic Lanthanide Complexes Analyzed with a Model-Free and Crystal-Field Independent Paramagnetic NMR Method:  Application to Nonaxial Trimetallic Complexes [Ln<i><sub>x</sub></i>Lu<sub>3</sub><sub>-</sub><i><sub>x</sub></i>(TACI-3H)<sub>2</sub>(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> (<i>x</i> = 1−3)

The model-free approach has been extended with the derivation of a novel three-nuclei crystal-field independent method for investigating isostructurality in nonaxial (i.e., rhombic) complexes along the lanthanide series. Application of this technique to the heterotrimetallic sandwich complexes [LnLu<sub>2</sub>(TACI-3H)<sub>2</sub>(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup>, which possess a single <i>C</i><sub>2</sub><i><sub>v</sub></i>-symmetrical paramagnetic center, unambiguously evidences isostructurality for Ln = Pr−Yb, while the variation of the second-rank crystal-field parameters and along the series prevents reliable structural analyses with the classical one-nucleus equation. Extension toward polymetallic magnetically noncoupled rhombic lanthanide complexes in [Ln<sub>2</sub>Lu(TACI-3H)<sub>2</sub>(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> (two paramagnetic centers with <i>C</i><i><sub>s</sub></i> microsymmetry) and [Ln<sub>3</sub>(TACI-3H)<sub>2</sub>(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> (three paramagnetic centers with <i>C</i><sub>2</sub><i><sub>v</sub></i> microsymmetry) requires only minor modifications of the original three-nuclei equation. Isostructurality characterizes [Ln<sub>2</sub>Lu(TACI-3H)<sub>2</sub>(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> (Ln = Pr−Yb), while [Ln<sub>3</sub>(TACI-3H)<sub>2</sub>(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> exhibit a structural change between Eu and Tb which results from the concomitant contraction of the three metallic centers. Particular attention has been focused on (i) the stepwise increase of contact (i.e., through-bond) and pseudocontact (i.e., through-space) contributions when the number of paramagnetic centers increases, (ii) the assignment of <sup>13</sup>C resonances in the strongly paramagnetic complexes [Ln<sub>3</sub>(TACI-3H)<sub>2</sub>(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> (Ln = Tb−Yb) for which reliable <i>T</i><sub>1</sub> measurements and {<sup>1</sup>H−<sup>13</sup>C} correlation spectra are not accessible, and (iii) the combination of crystal-field dependent and independent methods for analyzing the paramagnetic NMR spectra of axial and nonaxial lanthanide complexes.