NMR-CASTEP. Jonathan Yates. Cavendish Laboratory, Cambridge University. J-coupling cons. NMR-CASTEP York 2007 Jonathan Yates.

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Jonathan Yates Cavendish Laboratory, Cambridge University 2 2

[ppm] -43.8-47.4 "(31P) 29 "( Si1) -213.3-214.8 "(29Si2) -217.

6 "( Si3) J The effect of a perturbi constants must therefor

1 Jonathan Yates Cavendish Laboratory, Cambridge University N1a-N7b a hemical shift Experiment Calculation [ppm] [ppm] "(31P) 29 "( Si1) "(29Si2) "( Si3) J The effect of a perturbi constants must therefor present case, the j-cou P Si O NMR-CASTEP 4 J-coupling cons b Valid Comparing Guan J-co int hyd J-couplin

2 Overview Nuclear Magnetic Resonance Solid-state NMR 1st principles theory GIPAW Chemical shifts Electric Field Gradients

3 Nuclear Spin I=0 12 C, 16 O I=½ 1 H, 19 F, 29 Si, 31 P, 57 Fe 13 C, 15 N I>½ (net quadrupole moment) 14 N, 17 O, 35 Cl, 37 Cl

4 Nuclear Magnetic Resonance ωo = γ B

5 Magnetic Resonance Blocal = B0+Binduced Binduced = -σ B0 Chemical Shielding 1.Compute induced orbital current 2.Obtain chemical shielding via Biot- Savart Law Orbital Current induced by B-field in Porphyrin ring

6 13 C NMR δ iso = (ω ω ref) 10 6 ω ref chemical shift (ppm) Flurbiprofen

7 Solid-State NMR NMR power pattern Magic Angle Spinning (MAS) Increasing Spinning Freq

8 13 C NMR (MAS) Flurbiprofen MAS reduces broadening from: Chemical Shift Anisotropy Dipolar Interaction (eg 1 H- 1 H)

9 Cluster Approximation The only approach for quantum chemistry codes But you have to worry about making the cluster small terminating the cluster long range electrostatics

10 Pseudopotentials Pseudowavefunction Na All-electron wavefunctio r c Pseudopotential All-electron potential The core electrons are frozen and the valence orbitals smoothed within the core radius

11 A pseudopotential theory The core electrons contribution to the shielding must not be chemically sensitive We must fix up the wavefunction near the nucleus Projector augmented waves Φ = T Φ where T = 1 + n ( φ n φ n ) β n These break gauge invariance

12 GIPAW A theory for solid-state NMR NMR - CASTEP code: JRY + C. Pickard (St Andrews), F. Mauri (Paris) Density Functional Theory Planewave basis Pseudopotentials GIPAW - USP (ppm) (a) H C F Si P Gauge Including Projector Augmented Waves core properties with all-electron accuracy NMR-CASTEP vs Gaussian JRY, C. Pickard, F. Mauri PRB 76, (2007) GIPAW - USP (ppm) All Electron Shielding (ppm) (b) All Electron Shielding (ppm) H C F Si P

13 GIPAW - applications Porphyrins Pharmaceutical polymorphs 1H 13C 1H, 13C, 19F Amino acids Zirconates Tellurite glasses 17O 17O 31P 23Na 125Te 13C, 17O, 35Cl

14 Definitions Chemical shielding tensor B local = σb applied Principal components σ xx, σ yy, σ zz Isotropic chemical shielding σ iso = 1/3Tr[σ] = 1/3(σ xx + σ yy + σ zz ) Isotropic chemical shift δ iso = σ ref σ iso How to find the reference shielding? Compute reference compound (often liquids, so not recommended) Compute relative to similar compound (eg benzene for nanotube) Take value from previous calculations Plot computed shielding vs experimental shift

15 Calculations *.param file task : magres magres_task : shielding efg nmr chemical shift/shielding electric field gradient both Must use on-the-fly pseudopotentials Highly sensitive to geometry (optimise H X-ray positions) CONVERGE (basis cut-off & k-points)

16 *.castep File =========================================================== Chemical Shielding Tensor Nucleus Shielding tensor Species Ion Iso(ppm) Aniso(ppm) Asym H H H O O O O =========================================================== Anisotropy σ aniso = σ zz 1/2(σ xx σ yy ) Asymmetry η = 3(σ yy σ xx )/2σ aniso

17 *.magres File ============ Atom: O 1 ============ O 1 Coordinates A TOTAL Shielding Tensor O 1 Eigenvalue sigma_xx (ppm) O 1 Eigenvector sigma_xx O 1 Eigenvalue sigma_yy (ppm) O 1 Eigenvector sigma_yy O 1 Eigenvalue sigma_zz (ppm) O 1 Eigenvector sigma_zz O 1 Isotropic: (ppm) O 1 Anisotropy: (ppm) O 1 Asymmetry:

18 Crystal Structure X-ray, Neutron diffraction Cambridge Structural Database C C H Calculate forces refine structure 311.0ppm Calculate chemical shifts 316.9ppm

19 Maltose 13 C axis 1 H axis Experiments: Steven Brown (Warwick) MAS-J-HMQC

20 Maltose 13 C axis 1 H axis Dispersion in 1 H shifts due to weak CH--O hydrogen bonds Yates et-al J. Am. Chem. Soc (2005) x - first principles

21 Oxygen-17 NMR 17 O has a quadrupole moment This interacts with an electric field gradient from the charge density G Rβ (r) ) E R (r) r β - Eigenvalues of G V xx, V yy, V zz V zz > V yy > V xx Quadrupolar Coupling Asymmetry C Q = eqv zz h η Q = V xx V yy V zz 17 O MAS Glutamic Acid. HCl

22 Oxygen-17 NMR 17 O has a quadrupole moment This interacts with an electric field gradient from the charge density G Rβ (r) ) E R (r) r β - Eigenvalues of G V xx, V yy, V zz V zz > V yy > V xx Quadrupolar Coupling Asymmetry C Q = eqv zz h η Q = V xx V yy V zz 17 O MAS Glutamic Acid. HCl

23 Glutamic Acid Polymorphs We find correlations between NMR parameters and hydrogen-bond strength Yates et al J.Phys. Chem. A (2004) Chemical Shift Quadrupolar Coupling Asymmetry

24 GIPAW Theory Getting more information Pickard & Mauri, "All-electron magnetic response with pseudopotentials: NMR chemical shifts", Phys. Rev. B, 63, (2001) Yates, Pickard & Mauri, Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials Phys. Rev. B, 76, (2007) Solid-State NMR Introduction to Solid State NMR Spectroscopy - Melinda Duer (pub. Blackwell) Applications Look at publication list of Chris J. Pickard

GIPAW: A solid-state theory for NMR

GIPAW: A solid-state theory for NMR Jonathan Yates jonathan.yates@materials.ox.ac.uk Materials Modelling Laboratory, Oxford Materials NMR parameters we will focus on non-metallic, diamagnetic materials