Computation of NMR Shifts for Paramagnetic Solids Including Zero-Field-Splitting and Beyond-DFT Approaches. Application to LiMPO₄ (M = Mn, Fe, Co, Ni) and MPO₄ (M = Fe, Co)

A protocol for the computation of NMR shifts of paramagnetic spin-coupled solids is described and applied to the olivine-type lithium-ion battery cathode materials LiMPO 4 (M = Mn, Fe, Co, Ni) and to the related binary phosphates MPO 4 (M = Fe, Co). The computational approach includes Fermi-contact (FC), pseudocontact (PC), as well as orbital contributions to the shifts and combines periodic density functional computations with multireference post-Hartree–Fock methods. A shift formalism based on EPR spin-Hamiltonian parameters corrected for residual spin couplings within the Curie–Weiss regime is used. Orbital shieldings as well as hyperfine couplings (HFCs) are obtained at DFT levels for large simulation cells using the CP2K code, taking advantage of hybrid functionals for the HFCs. g-Tensors and zero-field-splitting tensors are computed within an incremental cluster model, using CASSCF and NEVPT2 approaches, providing thus the first post-Hartree–Fock treatments of these properties for extended solids. Comparison with DFT approaches indicates improved accuracy, particularly for the Co and Ni systems. Spin–orbit-induced PC shifts are shown to be significant in several cases for 7 Li shifts, when FC contributions are moderate. This holds in particular for LiCoPO 4, where the PC contributions dominate, but 7 Li PC and orbital shifts are also non-negligible for LiFePO 4 and LiNiPO 4 . Isotropic 31 P shifts are dominated clearly by FC contributions. Here the present computations nevertheless tend to be more accurate than previous computational studies, due to the use of hybrid DFT methods with extended Gaussian-type basis sets. Spin–orbit effects influence the FC shifts via deviations of the isotropic g-value from g e . 7 Li and 31 P shift tensors for all materials are predicted as guidelines for further experimental studies. Notably, the 31 P shift anisotropies may also be influenced substantially by spin–orbit-induced terms.