Large-scale solid-state 7Li and 31P pNMR shift calculationsincluding g-tensor and zero-field splitting contributions for a seriesof lithium vanadium phosphate battery materials.

Calculations of NMR shifts for paramagnetic periodic solids using CP2K, with applications to Li-ion battery materials

Prof. Dr. Martin Kaupp, Arobendo Mondal, Tech-nische Universität Berlin, Institut für Chemie, Theo-retische Chemie/Quantenchemie, Sekr. C7, Strassedes 17. Juni 135, D-10623 Berlin, Germany

In Short

• Development and application of modern pNMRtheory for solids using NMR/EPR parameters ob-tained with the CP2K code

Solid-state paramagnetic nuclear magnetic reso-nance (“pNMR”) is still an underdeveloped discipline,both experimentally and in terms of its interpreta-tion by quantitative electronic-structure calculations.Accurate calculations of pNMR shifts are as compli-cated as determining and assigning chemical shiftexperimentally. In the past decade significant devel-opments in experimental techniques and instrumen-tation for acquisition of pNMR shifts for solids havebeen made. The development of ab initio quantum-mechanical calculation of nuclear magnetic reso-nance (NMR) is still lagging behind but is slowlybecoming important in the field. In our previousproject proposal the main goal was to develop andvalidate a computational approach for paramagneticsolid-state NMR chemical shift computations.

Figure 1: Supercell of nasicon-like lithium transition-metal phos-phates Li3V2(PO4)3 having 320 atoms used for hyperfine tensorcalculations. There are total 48 individual lithium atoms having 3distinct Li sites.

Figure 2: Molecular models of the two distinct vanadium centersof Li3V2(PO4)3 solids, where the terminal oxygens have beensaturated with hydrogen atoms. Model A and B has 4 and 3lithium atoms respectively.

The powerful and efficient Gaussian-augmented-plane-wave implementation of the CP2K code hasenabled us to perform large-scale computations ofNMR shifts for extended paramagnetic solids us-ing hybrid functionals with an efficiency previouscomputations have lacked. It has also given ac-cess to contact, pseudo-contact, as well as orbitalshift contributions to pNMR shifts by combining hy-perfine couplings obtained with hybrid functionalswith g-tensors and orbital shieldings computed usinggradient-corrected functionals. The study of sev-eral materials with large unit cells has now beenmade possible with extended Gaussian basis setsdue to the highly efficient and parallel performanceof CP2K. The validation for various ingredients topNMR shifts has been performed in comparison withtypical quantum-chemical codes for molecules in alarge super-cell. This has then been followed bydetailed studies of g-tensors for Li3V2(PO4)3 and de-tailed lithium pNMR shift computations for the samematerial, for which detailed experimental data areavailable. In addition to full periodic g-tensor calcula-tions we also tested an incremental scheme in whichthe g-tensors for molecular cluster models cut fromthe solid-state structure have been computed. Thatis, we built and tested molecular models for the vana-

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Figure 3: 7Li chemical shifts of three different lithium sites Lia,Lib and Lic for the Li3V2(PO4)3 material. The variation of totalchemical shifts with respect to the use of different functionalsfor hyperfine couplings is been presented for each Li site. Com-parison of calculated total chemical shift using cluster-modelsolid-phase g-tensor with respect to the full periodic g-tensorcalculation. Comparison of computed shifts based on XRD andoptimized (OPT) structures. The g-tensor and orbital shieldinghave been calculated using the PBE functional.

dium sites in the solid material of interest (Figure 2)to perform molecular g-tensor calculations and com-bined them according to the orientation of the spincenters in the super-cell to produce g-tensors forthe simulation cell. The difference between the g-tensors obtained from such a cluster approach andperiodic calculations is very small. The comparisonof calculated chemical shifts using the periodic g-tensor and the "incremental cluster-model" g-tensorare shown in the Figure 3, where the difference be-tween 7Li chemical shifts is negligible for all the threekinds of Li atoms. The advantage of the incrementalmodel for our future work is, that it should allow us togo beyond GGA functionals, and in fact beyond DFT,e.g. using multi-reference approaches, needed forexample for the Co or Ni systems we also study. Thisextensive study, including molecular super-cell andsolid-state tests on simpler models for the variousingredients of pNMR shifts with CP2K. We note inpassing that, within the EU Initial Training Networkthrough which this study has been funded, we havebeen involved also in a parallel study with somewhatdifferent codes and approaches in collaboration withour partners in Cambridge.4

Having now available methods that also allow in-clusion of g-tensors (and zero-field splittings, ZFS)for several spin centers in the simulation cell, our

next step is to investigate and analyze the behaviorof g-tensors and ZFS tensor contributions by sam-pling periodic solids having various spin centers withvariable spin states. Notably, both the g-tensor andthe ZFS contribute to additional terms in the modernpNMR shift formalisms we use. It is evident that non-identical spin centers will break the symmetry of theunit cell, which will be reflected in the anisotropy ofthe EPR and NMR data. The increased anisotropywill have a significant influence on calculations ofpseudo-contact shifts, which arise from the com-bined effect of the anisotropic part of the hyperfine,g- and ZFS tensors (in other words the interactionof hyperfine anisotropy with the magnetic anisotropyaround the spin-carrying metal sites).

To this end we focus on a larger set of ternarylithium vanadium phosphate materials with variablelithium content. This allows us to compare systemsthat are on one side structurally closely related buton the other side feature different spin states andother details. Due to the availability of a wide rangeof experimental EPR and pNMR data, these sys-tems are perfectly suitable to extend our develop-ment and validation of novel methodology in pNMRshift computations for extended solids. In this exten-sion application we want to start this by exploratorycalculations on two materials (the Li1V2(PO4)3 andLi2V2(PO4)3 systems).

WWWhttp://www.ens-lyon.fr/crmn/pnmr/fellows/arobendo-mondal/

More Information

[1] M. Kaupp, M. Bühl, and V. G. Malkin Calcu-lations of NMR and EPR Parameters: Theoryand Applications (Wiley-VCH, Weinheim, 2004)

[2] T.O. Pennanen and J. Vaara Phys. Rev. Lett.100, 133002 (2008).

[3] Yin, S.-C., Strobel, P. S., Grondey, H., Nazar, L.F. Chem. Mater. 16, 1456 (2004).

[4] Pigliapochi, R., Pell, A. J., Seymour, I. D., Grey,C. P., Ceresoli, D., Kaupp, M. Phys. Rev. B 95,054412 (2017).

Project PartnersClare Grey (University of Cambridge)

Funding

EU, The pNMR project is an Initial Training Net-work (ITN) providing fellowships for researchers.It receives funding from the People Programme(Marie Curie Actions) of the European Union’s Sev-enth Framework Programme (FP7/2007-2013) underREA grant agreement n317127.

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