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Calculations of NMR chemical shifts in solids

Calculations of NMR chemical shifts in solids. Peter Blaha Institute of Materials Chemistry TU Vienna, Austria. NMR spectroscopy. NMR Hamiltonian. perturbation. Indirect spin-spin coupling. electric quadrupole interaction (EFG). direct dipolar coupling. Zeeman Hamiltonian.

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Calculations of NMR chemical shifts in solids

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  1. Calculations of NMR chemical shifts in solids Peter Blaha Institute of Materials Chemistry TU Vienna, Austria

  2. NMR spectroscopy

  3. NMR Hamiltonian perturbation Indirect spin-spin coupling electric quadrupole interaction (EFG) direct dipolar coupling Zeeman Hamiltonian magnetic shielding

  4. NMR Hamiltonian quadrupole interaction Zeeman Hamiltonian magnetic shielding

  5. NMR shielding, chemical shift: • s(R)istheshieldingtensoratthenucleusR • chemicalshift:

  6. Biot - Savart law The induced magnetic field (Bind) is derived from the induced current (jind) using a standard formula: in DFT the current density j(r) will be: perturbedw.f. Y 1 is obtained from perturbation theory diamagn. paramagn. sum over all empty states magnetic field

  7. sum over ALL empty states • standard APW basis set ul(r,El) only good near linearization El • adding additional LOs at high energies (up to 1000 Ry !!!) • H(1) contains the  operator, so we need to represent the radial derivative of ul(r,El) at l±1 • adding “NMR-los” • x_nmr -mode in1 [-focus nmr_atom] will set that up automatically

  8. practical calculation • run normal scf cycle • x_nmr_lapw -mode in1 [-focus O ] • view the resulting *in1c_nmr file • x_nmr_lapw [-p] • creates several directories (“nmr_q0, nmr_pqx, nmr_mqx, nmr_pqy, ..) and performs lapw1/2 steps for several k-meshes (k ± q) • creates the current • integrates the current • tail case.outputnmr_integ • for analysis one can calculate the shift from certain bands (energy range) only • x_nm_lapw [-p] -noinit -emin xx [-emax yy]

  9. Test of accuracy: Ar atom • the current j and chemical shielding s of a spherical atom can be calculated “exactly” from the density r(r) (no perturbation theory) by:

  10. Induced current in LAPW Induced current field for BaO (fcc) , Bext in (001)

  11. NMR shifts for F, O, Br, Cl F O Br Cl

  12. Interpretation of 19F NMR shielding in alkali fluorides • band wise analysis • character analysis (s,p,d) of the wave function of occupied and unoccupied states

  13. DOS of alkali fluorides (CsF) metal-p F-p band D varies between 5 eV for CsF to 20 eV for NaF D

  14. Band wise analysis of the isotropic shielding in MF F

  15. Decomposition of NMR shift • decomposition of NMR shift according tos, p, d - character andatom • Y0 = SatSlmRat,lmYlm • decompositionaccordingtogroundstateYo(0) andperturbedstatesYo(1) • Yo(1)

  16. metal-p band contribution Yo(0)|F, l=1 Yo(1)|F, l=1

  17. F-p band contribution Yo(1)|F, l=2 Yo(0)|F, l=1 Yo(1)|F, l=1

  18. metal p band F-p band Yo(1)|F, l=2 Yo(0)|F, l=1 Yo(0)|F, l=1 Yo(1)|F, l=1 Yo(1)|F, l=1 the only important ground state contribution the only important ground state contribution Yo(0)|F, l=1 positive, increasing contribution within the series negative, decreasing contribution within the series Yo(1)|F, l=1 constant contribution within the series Yo(1)|F, l=2

  19. bonding / antibonding F-p / Me-p interaction Re[Y] at X-point of CsF • F-p band, anti-bonding character of the Cs-p and F-p orbitals, • negative contribution to the shielding • Cs-p band, bonding character between Cs-p and F-p orbitals, • positive contribution to the shielding.

  20. metal-p band contribution

  21. Interactions relevant for NMR chemical shifts in alkali fluorides DEd DEp

  22. A, B interactions: coupling to the metal-d states, due to F-p – metal-p hybridization d-band position

  23. Effect of bond distance on the shielding • decreasing volume leads to stronger Me-p F-p interaction and to more negative shielding (Li does not have “Li-p band”)

  24. Effect of position of metal-d band on the F shielding • LDA+U acting on Cs-d (NaF) CsF

  25. The “slope” - problem exp. d vs. theoretical s: The slope must be ONE PBE: slope is too big PBE+U (metal d-states): with one U value it is not possible to fix oxygen AND fluorine CS.

  26. the slope - problem • hybrid-DFT is the standard method in CS calculations of molecules (Gaussian) • for (ionic) solids YS-PBE0 (HSE) gives a much toolarge correction (smaller mixing ??)

  27. the slope - problem BJ-potential (OEP) seems quite reasonable for ionic compounds

  28. Summary: NMR chemical shifts: • shielding of anions in solids determined by: • strength of metal-p -- F-p hybridization • distance of metal-p band from anion-p band • bond distance, number of neighbors • position of empty metal-d states

  29. Acknowledgement Robert Laskowski (TU Vienna) NMR: PRB 85, 035132 (2012) PRB 85, 245117 (2012) Thank you for your attention !

  30. How is | Yo(1) > constructed ? = which states contribute to ? what is their effect on j(r) ? We decompose the integral into spatial contributions (atomic spheres, interstital) and according to angular momentum components of Ye(0) Ye(0)|F, l=L

  31. F-p band contribution

  32. WIEN2k vs. CASTEP comparison s s

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