Jonathan Yates Cavendish Laboratory, Cambridge University 2 2 1 3 2 N1a-N7b a hemical shift Experiment Calculation [ppm] [ppm] -43.8-47.4 "(31P) 29 "( Si1) -213.3-214.8 "(29Si2) -217.0-218.7 29-119.1-128.6 "( 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
Overview Nuclear Magnetic Resonance Solid-state NMR 1st principles theory GIPAW Chemical shifts Electric Field Gradients
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
Nuclear Magnetic Resonance ωo = γ B
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
13 C NMR δ iso = (ω ω ref) 10 6 ω ref chemical shift (ppm) Flurbiprofen
Solid-State NMR NMR power pattern Magic Angle Spinning (MAS) Increasing Spinning Freq
13 C NMR (MAS) Flurbiprofen MAS reduces broadening from: Chemical Shift Anisotropy Dipolar Interaction (eg 1 H- 1 H)
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
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
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
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) 800 600 400 200 0-200 35 30 25 20 20 25 30 35 (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, 024401 (2007) GIPAW - USP (ppm) -400-400 -200 0 200 400 600 800 All Electron Shielding (ppm) 800 600 400 200 0-200 35 30 25 20 20 25 30 35 (b) -400-400 -200 0 200 400 600 800 All Electron Shielding (ppm) H C F Si P
GIPAW - applications Porphyrins Pharmaceutical polymorphs 1H 13C 1H, 13C, 19F Amino acids Zirconates Tellurite glasses 17O 17O 31P 23Na 125Te 13C, 17O, 35Cl
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
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)
*.castep File =========================================================== Chemical Shielding Tensor --------------------------------------------------------- Nucleus Shielding tensor Species Ion Iso(ppm) Aniso(ppm) Asym H 1 23.81 5.27 0.40 H 2 24.75-3.35 0.85 H 3 27.30-5.79 0.90 O 5-43.73 504.95 0.47 O 6-63.53 620.75 0.53 O 7-43.73 504.95 0.47 O 8-63.53 620.75 0.53 =========================================================== Anisotropy σ aniso = σ zz 1/2(σ xx σ yy ) Asymmetry η = 3(σ yy σ xx )/2σ aniso
*.magres File ============ Atom: O 1 ============ O 1 Coordinates 1.641 1.522 5.785 A TOTAL Shielding Tensor 218.1858 12.1357-25.7690 13.4699 191.6972-7.2419-25.9178-6.5205 216.3180 O 1 Eigenvalue sigma_xx 185.6127 (ppm) O 1 Eigenvector sigma_xx 0.5250-0.8103 0.2603 O 1 Eigenvalue sigma_yy 193.8979 (ppm) O 1 Eigenvector sigma_yy 0.4702 0.5310 0.7049 O 1 Eigenvalue sigma_zz 246.6904 (ppm) O 1 Eigenvector sigma_zz -0.7094-0.2477 0.6598 O 1 Isotropic: 208.7337 (ppm) O 1 Anisotropy: 56.9351 (ppm) O 1 Asymmetry: 0.2183
Crystal Structure X-ray, Neutron diffraction Cambridge Structural Database C1-0.602-0.537 6.384 C2 0.135 0.622 5.689 H1 0.257 0.361 4.639... Calculate forces refine structure 311.0ppm Calculate chemical shifts 316.9ppm
Maltose 13 C axis 1 H axis Experiments: Steven Brown (Warwick) MAS-J-HMQC
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. 127 10216 (2005) x - first principles
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
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
Glutamic Acid Polymorphs We find correlations between NMR parameters and hydrogen-bond strength Yates et al J.Phys. Chem. A 108 6032 (2004) Chemical Shift Quadrupolar Coupling Asymmetry
GIPAW Theory Getting more information Pickard & Mauri, "All-electron magnetic response with pseudopotentials: NMR chemical shifts", Phys. Rev. B, 63, 245101 (2001) Yates, Pickard & Mauri, Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials Phys. Rev. B, 76, 024401 (2007) Solid-State NMR Introduction to Solid State NMR Spectroscopy - Melinda Duer (pub. Blackwell) Applications Look at publication list of Chris J. Pickard