The Non-local Contribution to the Magnetic Shielding Constant  = dia + para +  nonloc magnetic anisotropy of neighboring groups temperature isotope shift solvent effects ASIS, SIIS H-bonding concentration effects local 1 Magnetic Anisotropy of Neighboring Groups Magnetic anisotropy of neighboring groups Remote shielding effects by electrons of non-spherically symmetric groups – (nearly all groups, but some strong) McConnell formula (cylindrical symmetry) group = (  ) 1  3 cos2 )/(3r3)    magnetic susceptibility 1  3 cos2  = 0 for  = 54.7º In a magnetic field, valence electrons are induced to circulate. This generates a secondary magnetic field that opposes/enhances the applied field near the nucleus A higher/lower field is needed to achieve resonance = shielding/deshielding effect 2 Magnetic Anisotropy  is the angle between the vector r and the symmetry axis A ( - )the molar anisotropy of the bond  -  the susceptibilities parallel and perpendicular to the symmetry axis H = measured nucleus Z = anisotropic neighboring groups McConnel formula (cylindrical symmetry, group Z approximated as a magnetic dipole) group = (  ) 1  3 cos2 )/(3r3) 3 Groups with Magnetic Anisotropy + shielding  deshielding 4 Ring Current in Aromatic Rings  electrons in aromatic rings are induced to circulate in a magnetic field Diatropic ring current •induces magnetic field aligned with the applied field in the vicinity of the aryl protons (causing deshielding = downfield shift) •opposes the applied field at protons above and below the ring (causing shielding = upfield shift) 5 Ring Current in Aromatic Rings shielding surfaces 0.1 ppm in yellow, at 0.5 ppm in green, at 1 ppm in green-blue, at 2 ppm in cyan, and 5 ppm in blue deshielding surface at 0.1 ppm in red Ring current = measure of cyclic delocalization of  electrons in aromatic rings Shielding strong Deshielding weak 6 Magnetic Anisotropy mult 7.1 ppm singlet 4.2 ppm Octamethyl-[2, 2]-metacyclophane 8 Me groups on C-C bridges not shown 7 Ring Current in Aromatic Rings H2C CH2 H2C H2C H2 C H2 C CH2 CH2 2.6 ppm 0.3 ppm1 H NMR 8 Ring Current in Aromatic Rings 1,6-methano[10]annulene 1H NMR 9 Magnetic Anisotropy N Me Me N Me Me Me Me N Me Me N H H H H 11.75 14.26 1H NMR 10 Magnetic Anisotropy 1H NMR[18]annulene 11 Magnetic Anisotropy S Si F S S Si F 3  (19 F) 160.6  (19 F) 5.3 12 Ring Current in Antiaromatic Rings Ring systems of antiaromatic character with [4n] π-electrons exhibit a reversed anisotropy effect of decreased intensity – paratropic ring current •a deshielding area above and below the plane of the ring system •a shielding area in the plane of the ring system pentalene shielding surfaces 0.1 ppm in yellow 0.5 ppm in green 1 ppm in green-blue 2 ppm in cyan 5 ppm in blue deshielding surface at 0.1 ppm in red 13 Ring Current in Aromatic/Antiaromatic Rings NICS Nucleus independent chemical shift • absolute shielding calculated in the center of a molecule • measures aromaticity / antiaromaticity Negative NICS = shielded = diatropic = aromatic Positive NICS = deshileded = paratropic = antiaromatic 14 NICS Nucleus independent chemical shift 15 Negative NICS = aromatic Positive NICS = antiaromatic   NICSs (ppm) aromatic stabilization energies (ASEs, kcal/mol) Spherical aromaticity: closo-B12H12 2- (NICS = 34.4 ppm) NICS Nucleus independent chemical shift 16 -aromatic (benzene) and antiaromatic (cyclobutadiene) Negative NICS = aromatic Positive NICS = antiaromatic NICS(0) (computed in the ring center) nonzero NICS for nonaromatic, saturated, and unsaturated hydrocarbon rings NICS(1) (1 Å above the ring center) the local contributions are diminished relative to the ring current effects Aromatic/Antiaromatic Rings Trans-15,16-dimethyl-15,16-dihydropyrene aromatic [4n+2] π-electrons Trans-15,16-dimethyl-15,16-dihydropyrene dianion antiaromatic [4n] π-electrons CH3 CH3 CH3 CH3 2-4.25 ppm 21.0 ppm 1H NMR 17 Aromatic/Antiaromatic Rings [18] annulene aromatic [4n+2] π-electrons Diatropic ring current [18] annulene dianions antiaromatic [4n] π-electrons Paratropic ring current Low temp. 1H NMR H H 2- 9.28 ppm -3.0 ppm H H-1.1 ppm 20.8 29.5 ppm 2- K 18 Kekulene Kekulene is extremely insoluble. 1H NMR spectrum taken at 200° C in deuterated tetrachlorobenzene 2 annulenes or 6 benzene rings[4n+2] π-electrons 19 Magnetic Anisotropy Acetylenic H Acidic but shielded 20 Magnetic Anisotropy Ethylenic H 21 Magnetic Anisotropy of Ethylene C = grey, H = black) 0.1 ppm deshielding isosurface = yellow 0.1 ppm shielding isosurface = magenta 22 Magnetic Anisotropy + shielding  deshielding 23 Magnetic Anisotropy + shielding  deshielding 24 Magnetic Anisotropy Hax Heq The equatorial protons are deshielded by 0.48 ppm wrt the axial 25 Magnetic Anisotropy of C60 Diatropic ring current 7.0 ppm Paratropic ring current +5.4 ppm antiaromatic aromatic 26 Magnetic Anisotropy 3He @ C60 3He @ C70 3He + C60/ C70 650 ºC 3000 bar  (3He) 6.3 ppm  (3He) 28.8 ppm 27 Magnetic Anisotropy 3He @ C60  (3He) 6.3 ppm  (3He) 49.2 ppm 3He @ C60 6shifted to high field = higher aromatic character 6-MRs and 5-MRs of the fullerene cage of C60 6- show diamagnetic ring currents 28 Magnetic Anisotropy  (3He) 28.8 ppm  (3He) +8.2 ppm shifted to low field = a reduction in aromaticity 3He @ C70 3He @ C70 6- 29 Magnetic Anisotropy 1H NMR spectra H2 in liquids ∼4 ppm H2@C60 in 1,2-dichlorobenzene-d4 1.5 ppm 30 Ortho- and Parahydrogen 31 Magnetic Anisotropy The 1H NMR spectrum of 2 in pyridine-d5 - A singlet at δ 32.18 (16 H) characteristic of a C8H8 ligand bound to uranium(IV) - Two signals at δ +4.49 (8 H) and +1.96 (12 H) due to a single NEt4 + group 32 Solvent Effects • Chemical shift – considerable influence • Coupling constants – very small changes • Relaxation – higher viscosity reduces T1 and T2 of small molecules Van der Waals forces 0.1 – 0.2 ppm in 1H NMR Magnetic anisotropy of solvent – benzene, aromatics (solvent/solute orientation not averaged to zero) Hydrogen bonding 33 1H Chemical Shifts of Methanol in Selected Solvents Solvent CDCl3 CD3COCD3 CD3SOCD3 CD3C≡N CH3 3.40 3.31 3.16 3.28 O–H 1.10 3.12 4.01 2.16 34 Hydrogen Bonding Increasing concentration More extensive H-bonding Deshielding of OH signal 35 Hydrogen Bonding  (17O) water liquid 0.0 ppm gas 36.1 ppm 36 Hydrogen Bonding Ar = mesityl CH3 H3C CH3 B N CH3 CH3 CH3 Ar Ar Ha Hb F The methylene hydrogens are diastereotopic – steric congestion two H signals at 3.69 and 4.81 ppm B N CH3 CH3 CH3 Ar Ar O3S-CF3 Ha Hb H-F hydrogen bonding Ha 6.50 ppm – deshielding coupling to F nucleus doublet of doublets 1JH-F = 9.2 Hz 2JH-H = 12.9 Hz The peaks marked by *correspond to mesityl CH resonances 37 Temperature Effects Anharmonic potential Occupation of vibrational levels changes with temperature Changes in effective distance between atoms Chemical shift is a weighted average of the individual vibrational states 38 Temperature in NMR Temperature dependent NMR parameters •Chemical shift •Number of signals – dynamic NMR spectroscopy •Kinetics of exchange processes •Equilibrium – reaction, tautomers, conformers •Relaxation – T1 and T2 depend on molecular tumbling •Dipolar and scalar coupling – exchange •Molecular diffusion coefficient D – Stokes-Einstein •Equilibrium magnetization M0 Thermocouple position wrt sample Temperature gradients within the sample Sample heating by decoupling power 39 Methanol Thermometer 40 Methanol (neat) Temperature range: 178 – 330 K Peaks used: -CH3 and -OH Equation: T [K] = 409.0 - 36.54  - 21.85 ()2 C. Amman, P. Meier and A. E. Merbach, J. Magn. Reson. 1982, 46, 319-321. Ethylene glycol (neat) Temperature range: 273 – 416 K Peaks used: -CH2- and -OH Equation: T [K] = 466.5 - 102.00  C. Amman, P. Meier and A. E. Merbach, J. Magn. Reson. 1982, 46, 319-321. CCl4 and (CD3)2CO (50/50 vol% mixture) Temperature range: 190 – 360 K Peaks used: CD3-CO-CD3 and CCl4 Equation: T [K] = 5802.3 - 50.73  J. J. Led, S. B. Petersen, J. Magn. Reson. 1978, 32, 1-17. TeMe2 (neat) Temperature range: Peaks used: 125Te high field shift 0.128 ppm K-1 41 Ideal Thermometer Nonreactive and stable/ internal thermometer Intramolecular effect / one compound added, no concentration, solvent dependency Wide range of temperatures Linear response Strong response Δ/ ∆T Solvent independent 42 Chemical Shift Thermometer H 13C SiMe3 SiMe3 SiMe3 13C Enriched 43 Paramagnetic Compounds • Organic radicals, transition metal complexes • Unpaired electron = large fluctuating magnetic field • Relaxation – unpaired electron reduces T1 and T2 = extremely broad lines • Coupling of nuclear and electron spins • The paramagnetic center induces additional paramagnetic shift • Chemical shift 1H NMR very large range 200 ppm 13C NMR range 1000 ppm 44 Paramagnetic Compounds iso Isotropic shift (isotropic part of the tensor) orbital Ramsay (diamagnetic + paramagnetic), the difference between the chemical shielding of a reference compound and the orbital contribution to the shielding tensor of the investigated paramagnetic molecule, temperature independent, approximated by the NMR shift of a diamagnetic analogue or experimentally the temperature-(in)-dependent parts can be separated by a least-squares fit (1/T dependence) of NMR spectra measured at different temperatures FC Fermi contact shift – delocalized e = through bond, vanishes relatively quickly as the number of chemical bonds from the paramagnetic metal center with the spin density localized in the metal d-orbitals, increases PC Pseudocontact – dipolar = through space, an inverse distance dependence (1/r3), temperature-dependent, obeys the Curie law (in the absence of zero-field splitting (ZFS) and when the (2S + 1) degenerate ground state is well-separated from excited energy levels) PCFC orbitaliso   45 Paramagnetic Compounds FC Fermi contact shift – μe = the Bohr magneton, γ = the gyromagnetic ratio of nucleus , kT = the thermal energy, (2S + 1) = the multiplicity of the ground state, giso is the isotropic part of the g tensor, Aiso is the isotropic part of the hyperfine coupling tensor isoisoeFC Ag kT SS    3 )1(   )( 9 )1( dipolaraniePC AgTr kT SS      PC Pseudocontact – where gani = the g-tensor anisotropy, Adipolar = the dipolar part of the hyperfine coupling tensor the dipolar interaction between an averaged electron magnetic moment (typically centered on the metal center) and the magnetic moment of the nucleus 46 Paramagnetic Compounds For small molecules, 1D NMR spectra measured at various temperatures, the temperature-independent (orbital) and temperature-dependent (paramagnetic) contributions are determined from a Curie plot: NMR chemical shifts versus reciprocal absolute temperature (1/T) the monotonic dependence in the Curie plots is obtained only for systems obeying the Curie law, i.e., for doublet or higher multiplets when the zero-field splitting effects are negligible for systems with non-negligible zero-field splitting the NMR temperature dependence becomes more complicated PCFC orbitalparamagorbitaliso   47 Paramagnetic Compounds R = CN paramagorbitaliso   48 Paramagnetic Compounds PCFC orbitaliso   49 Pseudocontact Shift The anisotropic magnetic susceptibility affects the Larmor frequencies of nearby nuclei the through-space “dipolar” or “pseudocontact” shift 9 H along the Fe-C bond vector are shifted downfield (the addition of the internal field to the applied field causes them to resonate at a low applied field) H along the yz plane (perpendicular to the Fe-C bond vector) are shifted upfield An analogy is the diamagnetic “ring current” in aromatics, which gives downfield shifts of protons in the plane of the electron circulation and upfield shifts of protons normal to the plane of the electron circulation 50 Pseudocontact Shift The paramagnetic current in the iron compounds shifts H in the yz plane upfield those normal to the yz plane downfield The dominance of the pseudocontact shift is anomalous for paramagnetic complexes, for which the chemical shifts typically are dominated by the through-bond “contact” shift. 51 Pseudocontact Shift 52 Lanthanide-Induced Shifts (LIS) 53 Lanthanide-Induced Shifts (LIS) 54 Lanthanide-Induced Shifts (LIS) 55