Prediction of NMR parameters in the solidstate

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1 1J PO Prediction of NMR parameters in the solidstate Jonathan Yates Materials Modelling Laboratory, Oxford Materials 2J PSi 1
2 Nuclear Magnetic Resonance Applied Field Zero Field B Population differences! NMR signal is proportional to population difference For 1H in a 9.4 T field at 298 K 1 For H in 9.4T at 298K ω= γ B magnetogyric ratio fundamental nuclear constant! "E = 2.65 # J nupper/nlower = exp ( "E / kt) nupper/nlower = Sensitivity is an issue! Need Large γ and/or B Populations differences in NMR are very small sensitivity is alway
3 Common Isotopes Isotope Spin ϒ 10 7 T 1 rad s 1 Freq 9.4T Abundance % 1 H 1/ C 1/ Si 1/ P 1/
4 Common Isotopes Isotope Spin ϒ Freq 10 7 T 1 rad s T Abundance % 1 H 1/ C 1/ Si 1/ P 1/ O 5/ Ti 7/
5 Superconducting magnets SolidState NMR Spectrometers 600 MHz 14.1 T ~ 800,000 Image courtesy Sharon Ashbrook (St Andrews) 400 MHz 9.4 T ~ 300,000
6 Magnetic Shielding Flurbiprofen nonsteriodal antiinflamatory δ iso = (ω ω ref) 10 6 ω ref chemical shift (ppm) δ iso = σ ref σ iso Each distinct C atom experiences a different magnetic field and resonates at a unique frequency. Measure the change wrt a standard (for 13 C this is liquid tetramethylsilane) magnetic shielding (from calc)
7 Induced Current To compute the chemical shifts we just need to calculate the current induced by the external magnetic field BiotSavart B in (r) = 1 c d 3 r j(r ) r r r r 3. Obtain current within perturbation theory (linear response) O = O (0) + O (1) + O(B 2 ) Bin = σ B0 note: σ is a rank 2 tensor
8 Planewaves and Pseudopotentials To simulate periodic systems planewaves are a convenient choice: however describing the tightly bound core states, and oscillatory part of the valence states close to the nucleus are prohibitively expensive. We must approximate... Frozen Core Approximation Core electrons taken from free atom fixed during calculation Pseudopotential Approximation Valence electrons experience weak effective potential in the core region Note: Typically these two approximations are used together. But this does not have to be the case. Some codes can employ ʻselfconsistentʼ pseudopotentials which allow the core states to ʻrelaxʼ to their specific environment.
9 Atomic States Si
10 Approximations Overcoming the previous approximations Frozen Core Approximation Contribution of core electrons to shielding is not chemically sensitive 1s states in Carbon contribute ~200ppm in diamond, benzene, proteins ie core states contribute to shielding  but not shift. Pseudopotential Approximation Use PAW method to fixup valence wavefunction in the core region
11 pseudo = T, Projector Augmented Waves = T allelectron T = 1 + R,n[ φ R,n φ R,n ] p R,n T φ R,n φ R,n  + pseudo = allelectron GIPAW GaugeIncluding Projector Augmented Waves Modification of PAW by Pickard and Mauri for systems in an external magnetic field  plays a role similar to GIAO in quantum chemistry techniques
12 GIPAW vs Gaussian test on small molecules n.b. v. big Gaussian basis sets JRY, C. Pickard, F. Mauri PRB 76, (2007) Convergence of shielding with #planewaves GIPAW A theory for solidstate NMR with GIPAW using uncorrected valence GIPAW  USP (ppm) GIPAW  USP (ppm) (a) All Electron Shielding (ppm) (b) All Electron Shielding (ppm) H C F Si P H C F Si P
13 Firstprinciples NMR Crystal Structure Xray, Neutron diffraction Cambridge Structural Database C C H Calculate forces refine structure 311.0ppm Calculate chemical shifts 316.9ppm
14 Examples Steven Brown (Warwick) Maltose sugar used in brewing 13 C axis 1 H axis MASJHMQC
15 Examples Maltose sugar used in brewing 13 C x xx x x x 1 H axis xx x x x MASJHMQC x x  first principles
16 Examples 13 C axis 1 H axis Molecule to solid variation due to intermolecular interactions (weak hydrogen bonds) x  first principles J. Am. Chem. Soc (2005)
17 NMR Interactions Chemical Shift orbital currents Quadrupolar coupling (EFG) nuclei I>1/2 interact with local electric field gradients Function of charge density spinspin coupling (eg Jcoupling) splitting of resonance due to nucleusnucleus interaction hard to observe in solids...
18 EFG Eigenvalues V αβ (r) = d 3 r Electric Field Gradients Function of the charge density  ie groundstate property. Also computed by allelectron codes such as Wien2k, Crystal charge density n(r) r r 3 V xx, V yy, V zz V zz > V yy > V xx [ δ αβ 3 (r α r α )(r β r β ) r r 2 ] Quadrupolar Coupling Asymmetry C Q = eqv zz h η Q = V xx V yy V zz Note: The quadrupolar moment, Q, is a nuclear property. Most recent values given in Year2008 Standard Values of Nuclear Quadrupole Moments : P. Pyykkö, Mol. Phys. 106, (2008) But note Q appears as a simple scaling factor 17 O MAS Glutamic Acid. HCl
19 Jcoupling Electronmediated interaction of nuclear spins Nucleus A causes a magnetic field at nucleus B (and vice versa) A B No Jcoupling with Jcoupling J In solids J is rarely revealed in splitting of peaks in 1D spectra (anisotropic interactions broaden peaks) parallel antiparallel Increasing use of techniques, eg those using spinecho modulation, to measure J in solids.
20 Jcoupling Orbital Dipole induces orbital motion of electrons (due to electron charge) This creates a localised magnetic field similar mechanism to NMR shielding Orbital Current Spin Dipole induces spin density (relative displacement of and electrons) This creates induced field via: FermiContact (ʻsʼ like density at nucleus) Spindipolar (nonspherical distribution of spin) similar mechanism to EPRhyperfine & Knightshift Induced Spin density: C2H2 Total J = Orbital + Spin H ve C C H +ve ve
21 Jcoupling Guanosine selfassembles into ribbons molecular electronics (FET) a 2h JN7a,N1b a 2h JN7b,N1a = 6.2±0.4 Hz (expt) 6.5 Hz (calc) 2h JN7a,N1b = 7.4±0.4 Hz (expt) 7.7 Hz (calc) J. Am. Chem. Soc. 130, (2008) b b 2h JN7b,N1a
22 Practical Details *.param file task : magres magres_task : shielding efg nmr chemical shift/shielding electric field gradient both Must use onthefly pseudopotentials Highly sensitive to geometry (optimise H Xray positions) CONVERGE (basis cutoff & kpoints)
23 *.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
24 *.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: Note: shielding tensor has a symmetric and an antisymmetric component. Typical NMR experiments are only sensitive to the symmetric part. Therefore we only diagonalise the symmetric part of the shielding tensor
25 Practical Things Some practical things to keep in mind Structure NMR is very sensitive to structure! XRD atom positions are often not sufficient for accurate simulation of NMR parameters Dynamics Atoms move  spectra are recorded at finite T. How to account for that in (static) calculations? Accuracy How good are our present (approximate) density functionals?
26 Structure Anomeric Carbon Crystallises as: 80% αmaltose 20% βmaltose Compute spectra for both structures separately and superimpose
27 Structure Anomeric Carbon After relaxing neighbouring atom O1ʼ which had large force / thermal ellipsoid
28 Dynamics MLF peptide 13 C rms error Static relaxed structure abinitio MD classical MD 4.2ppm 3.3ppm 3.0ppm 2 pm 5 μm J. Am. Chem. Soc. 132, 3993 (2010) Abinitio MD Captures large (20ppm) fluctuations on fs timescale Classical MD Samples rotomeric states half of sites have errors <1ppm  limitations of PBE
29 Magnetic Resonance File Format Aim Provide a complete archival format for a first principles calculation of NMR parameters Visualisation Abinitio Abinit, CASTEP QE, Wien2k etc fileformat Spinsimulation Database
30 Jmol viewer Opensource Crystalviewer Multiplatform (Java) Can embed in website New developments display selected values on structure convert shielding to chemical shift switch isotopes visualization of tensors (D, J, σ, EFG) relative orientations (Euler angles) select spin system for export
31 Database Abinitio calculations provide NMR parameters for all atoms in the system Papers often report only selected results Store full information as abinitio nmr fileformat in a database Allows later retrieval and processing of data Establish structural trends
32 Consultation Draft specification and examples Feedback and Comments to by 19th October 2012
33 Getting more information NMR Books Good Introduction Nuclear Magnetic Resonance (Oxford Chemistry Primers) P. J. Hore More advanced Spin Dynamics: Basics of Nuclear Magnetic Resonance Malcolm H. Levitt Solid state NMR SolidState NMR: Basic Principles and Practice David Apperley, Robin Harris, Paul Hodgkinson Useful survey of applications Multinuclear SolidState Nuclear Magnetic Resonance of Inorganic Materials Kenneth J.D. MacKenzie, M.E. Smith Recent Review Articles Recent advances in solidstate NMR spectroscopy of spin I = 1/2 nuclei Anne Lesage, Phys. Chem. Chem. Phys., 2009, 11, 6876 Recent advances in solidstate NMR spectroscopy of quadrupolar nuclei Sharon E. Ashbrook, Phys. Chem. Chem. Phys., 2009, 11, 6892
34 Getting more information GIPAW Theory A more in depth introduction to the theory ( JRY for a copy) Computations of Magnetic Resonance Parameters for Crystalline Systems: Principles Jonathan R. Yates, Chris J. Pickard Encyclopedia of Magnetic Resonance (2008) doi: / emrstm1009 Exhaustive (and exhausting!) review of applications and theory ( JRY for a copy) FirstPrinciple Calculation of NMR Parameters Using the GIPAW (Gauge Including Projector Augmented Wave) Method: a Chemist's Point of View Bonhomme, Gervais, Babonneau, Coelho, Pourpoint, Azais, Ashbrook, Griffin, Yates, Mauri, Pickard, Chemical Reviews (in press 2012) Original Theory Papers: Allelectron magnetic response with pseudopotentials: NMR chemical shifts, Chris J. Pickard, and Francesco Mauri. Phys. Rev. B, 63, (2001) Calculation of NMR Chemical Shifts for extended systems using Ultrasoft Pseudopotentials Jonathan R. Yates, Chris J. Pickard, and Francesco Mauri. Physical Review B 76, (2007) A First Principles Theory of Nuclear Magnetic Resonance JCoupling in solidstate systems Sian A. Joyce, Jonathan R. Yates, Chris J. Pickard, Francesco Mauri J. Chem. Phys. 127, (2007)
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