Indirect “No-Bond” ³¹P···³¹P Spin–Spin Couplings in P,P‑[3]Ferrocenophanes: Insights from Solid-State NMR Spectroscopy and DFT Calculations

No-bond ³¹P–³¹P indirect dipolar couplings, which arise from the transmission of nuclear spin polarization through interaction of proximal nonbonded electron pairs have been investigated in the solid state for a series of closely related substituted P,P-[3]­ferrocenophanes and model systems. Through variation and combination of ligands (phenyl, cyclohexyl, isopropyl) at the two phosphorus sites, the P···P distances in these compounds can be varied from 3.49 to 4.06 Å. Thus, the distance dependence of the indirect no-bond coupling constant J_nb can be studied in a series of closely related compounds. One- and two-dimensional solid-state NMR experiments serve to establish the character of these couplings and to measure the isotropic coupling constants J_iso, which were found to range between 12 and 250 Hz. To develop an understanding of the magnitude of J_nb in terms of molecular structure, their dependences on intramolecular internuclear distances and relative orbital orientations is discussed by DFT-calculations on suitable models. In agreement with the literature the dependence of J_nb on the P···P distance is found to be exponential; however, the steepness of this curve is highly dependent on the internuclear equilibrium distance. For a quantitative description, the off-diagonal elements of the expectation value of the Kohn–Sham–Fock operator in the LMO basis for the LMOs of the two phosphorus lone-pairs is proposed. This parameter correlates linearly with the calculated J_nb values and possesses the same distance-dependence. In addition, the simulations indicate a distinct dependence of J_nb on the dihedral angle defined by the two C–P bonds providing ligation to the molecular backbone. For disordered materials or those featuring multiple sites, conformers, and/or polymorphism, a new double-quantum NMR method termed DQ-DRENAR can be used to conveniently measure internuclear ³¹P–³¹P distances. If conducted on compounds with known P···P distances, such measurements can also serve to estimate the magnitude of the anisotropy ΔJ of these no-bond indirect spin–spin couplings. The DFT results suggest that in the present series of compounds the magnitude of ΔJ is strongly correlated with that of the isotropic component, as both parameters have analogous distance dependences. While our studies indicate a sizable J-anisotropy for the model compound 1,8-bis­(diphenylphosphino)­napthalene (ΔJ ∼ −70 Hz), the corresponding values for the P,P-[3]­ferrocenophanes are significantly smaller, affecting their DQ-DRENAR curves only in a minor way. Based on the above insights, the structural aspects of conformational disorder and polymorphism observed in some of the P,P-[3]­ferrocenophanes are discussed.