1 Chemical Shift Chemical shift for a given molecule: • Number of signals = nonequivalent nuclei molecular symmetry • Relative intensity = number of nuclei • Position in the spectrum = shielding/chemical shift electronic structure • Multiplicity = connectivity of atoms and groups 2 Nuclear Magnetic Shielding  Basic physical phenomenon: Nuclear Magnetic Shielding  For diamagnetic samples, the nuclear magnetic shielding can be expressed as correction to the Zeeman splitting: E =  ħ B0(1 – ) =  ħ shielding constant  • In solution, the nuclear magnetic shielding constant  is a scalar quantity • In solids,  is a tensor (3 x 3 = 9, only 6 measurable) 3 Faraday's Law Changes in the magnetic flux through a coil of wire induce a voltage (emf) in the coil 4 Lenz's Law •A voltage is generated by a change in magnetic flux •The polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it •The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. 5 Nuclear Magnetic Shielding 6 Nuclear Magnetic Shielding  s-electrons spherically symmetric precess in the applied magnetic field = circulating electron is an electric current, producing a magnetic field at the nucleus which opposes the external field the resonant condition - the applied field must be increased - diamagnetic shift (shielding) all atoms have diamagnetic shifts p,d,f-electrons no spherical symmetry, and produce large magnetic fields at the nucleus - paramagnetic shifts (deshielding) 7 Bnucl = B0 – Bshield Bshield = B0  Bnucl = = B0 – B0  = B0(1 – )  =  Bnucl = B0(1 – ) Lenz’s rule B = the magnetic flux density or magnetic induction (T) H = the magnetic field (strength) (A/m) B =  H Two different nuclei Nuclear Magnetic Shielding  8 Nuclear Magnetic Shielding  Bo Bo(1-a) Bo(1-b) Bo  =  Bnucl = B0(1 – ) 9 Absolute Magnetic Shielding the absolute value of the nuclear magnetic shielding constant cannot be measured experimentally by NMR, difficult to measure, but can be done for atoms or small molecules MHz vs. Hz 1:106 Relative Magnetic Shielding Requires measurement of differences of resonance frequencies between a sample and a standard (much more easily done)  Internal standard - a reference compound is in the same sample preferred from spectroscopic point of view, may cause chemical problems  External standard - in a different sample tube 10 Absolute Chemical Shieldings 11 Chemical Shift Strength of Field: B0 = 1.41 T B0 = 2.35 T Operating Frequency, : 60 MHz 100 MHz Shift From TMS: 162 Hz 270 Hz  value: 2.70 ppm 2.70 ppm    MHz Hzrefs 0     The  scale (or ppm scale) is independent of the instrument used to obtain the spectrum 12 Chemical Shift 13 The relative shielding of the sample can be expressed as: Absolute Magnetic Shielding (-scale):  = 106 (nucl – s ) / nucl nucl = absolute resonance frequency of the atom s = absolute resonance frequency of the signal Chemical Shift (-scale):  = 106 (s – ref ) / ref ref = resonance frequency of the standard Conversion between both scales:  = (ref – s ) / (1 – ref ) ~ (ref – s ) ref = absolute magnetic shielding value of the standard  (H3PO4) = 0  (H3PO4) = 320 14 Magnetic field Magnetic Shielding Chemical shift Frequency Nuclei in electron poor environments Nuclei in electron rich environments Deshielded Shielded Downfield Upfield Low frequencyHigh frequency Positive Negative Convention: High frequency positive 15 Chemical Shift References 1H ppm SiMe4 0 DSS 0 Me3Si-CH2-CH2-CH2-SO3Na TSP 0 Me3Si-CD2-CD2-COONa 19F ppm CFCl3 0 CF3COOH 78.5 C6F6 162.9 HF 198.4 F2 422.9 129Xe (I = ½ , 26.4 %) 131Xe (I = 3/2 , 21.1 %) Xenon in freon Liquid XeOF4 16 Chemical Shift References 19F, ppm Be careful with literature data Sometimes C6F6 = 0 17 Factors Influencing Chemical Shifts (1) The physical state of the sample (solid, liquid, solution or gas) (2) For solutions, the solvent and the concentration of solute (3) The nature of the reference procedure, e.g. internal, external (coaxial tubes or substitution), absolute frequency (4) The reference compound and, if used internal to a solution, its concentration (5) The temperature and pressure of the sample (6) Whether oxygen and other gases have been removed from the sample (7) Any chemical present in the sample, in addition to the compound under investigation and any reference compound 18 Factors Influencing Chemical Shifts (1) Intramolecular factors Diamagnetic contribution Paramagnetic contribution Magnetic anisotropy Ring currents van der Waals repulsion (2) Intermolecular factors Volume susceptibility van der Waals forces Induced electric field Collision complexes 19 Fundamental Contributions to the Magnetic Shielding Constant  =  dia +  para +   nonloc  dia - Interaction of electrons of nucleus A with the external magnetic field B0 induces a diamagnetic current density. This produces an induced field at the nucleus A which is proportional to B0 and opposite in sign SHIELDING CONTRIBUTION The substraction of the internal field from the applied field causes nuclei A to resonate at a high applied field 20 Fundamental Contributions to the Magnetic Shielding Constant  para - Interaction of B0 with electrons with non-vanishing orbital moments induces a polarisation of the electron distribution. This produces an additional induced field at the nucleus A which is proportional to B0 and equal in sign DESHIELDING CONTRIBUTION The addition of the internal field to the applied field causes nuclei to resonate at a low applied field −  =  dia +  para +   nonloc 21 Fundamental Contributions to the Magnetic Shielding Constant   nonloc - Electrons localized at distant nuclei B may contribute to the shielding at nucleus A (ring currents in aromatic molecules, solvent influences, shielding anisotropy of carbonyl groups) SHIELDING or DESHIELDING CONTRIBUTION Generally lower in magnitude than dia or para.  =  dia +  para +   nonloc 22 Magnetic Shielding Which Electrons contribute to and ?dia para dia para Core Electrons Valence s-Electrons Valence p,d,f-Electrons Total orbital magnetic moment for closed shells : = 0l = 0l = 1,2,3l + + + – – + para = 0 for spherical closed-shell atoms or ions (F )– 23 Magnetic Shielding Magnetic Shielding Contributions for Different Elements s-Block Elements valence p-orbitals absent (H) or hardly occupied (group 1, 2 metals) diamagnetic term dominates large non-local contributions (up to 20% for H)1   p,d-Block Elements valence p,d-orbitals involved in bonding term dominates non-local contributions mostly not important (but may become important for nuclei with lone pairs) paramagnetic  24 The Diamagnetic Contribution to the Magnetic Shielding Constant Bnucl = B0 – Binduced = B0 – B0  Bnucl = B0(1 – )  =  Bnucl = B0(1 – ) 25 The Diamagnetic Contribution to the Magnetic Shielding Constant  = d,is + d d,is Shielding Constant for an isolated atom (LAMB, easily computed from first principles, electron in a spherical orbit) 010 2 0, || 4   r m e e isd    0 = vawefunction of the ground state 0 = 4π 107 N A2 permeability of free space me = electron mass r = electron radius 26 The Diamagnetic Contribution to the Magnetic Shielding Constant  = d,is + d d Correction for Atoms in Molecules (Approximation by FLYGARE) Shielding increases when •element number Zi of the ligands increases •coordination number of the observed atom increases •bond distance ri decreases   lignads i i lignads i i e d r Z k r Z m e    4 2 0 27 Diamagnetic Shifts for Isolated Atoms dia ppm 1H 18 13C 261 14/15N 325 17O 395 19F 471 21Ne 552 31P 961 33S 1050 83Kr 3246 127I 5502 129Xe 5642 195Pt 9396 207Pb 10061 Alkalides M 23Na 62 39K 105 87Rb 185 113Cs 280 Shielding increases when element number Z of the observed atom increases d ~ 0.319 104 Z 4/3 Large and heavy atoms have large diamagnetic shielding 28 Influence of Electronegativity 29 Compound, CH3X CH3F CH3OH CH3Cl CH3Br CH3I CH4 (CH3)4Si X F O Cl Br I H Si Elnegat of X 4.0 3.5 3.1 2.8 2.5 2.1 1.8 Chemical shift,  / ppm 4.26 3.4 3.05 2.68 2.16 0.23 0  (1H) ppm 30 Influence of Electronegativity Compound CHCl3 CH2Cl2 CH3Cl CH4  (1H) ppm 7.27    Influence of electronegative substituents : • increases with their increasing number • decreases with increasing distance 31 Influence of Electronegativity H3C C H3C H CH3 H2C C CH3 H C C HPh pKa ~55 44 28.8 (in DMSO) acidity of C increases % C-H s-character 25 33 50 electronegativity of C increases 32 Influence of Electronegativity Electronegativity C 2.5 H 2.1 33 Aromatic Proton Shifts Electrophilic substitution Meta directing Strongly deactivating Ortho, para directing Strongly activating 34 Aromatic Carbon Shifts 35 Aromatic Carbon Shifts Number of  electrons per C  (13C) ppm 36 The Paramagnetic Contribution to the Magnetic Shielding Constant Quantum chemical approach by RAMSEY: The electron polarization leading to para is described in terms of mixing of the wave functions of the molecular ground state with excited states under the influence of the magnetic field. Approximative expressions for para were given for main-group elements by KARPLUS and POPLE: para 2 Qibonds E –1 –3 r 2 ~~  – and for transition metals by GRIFFIN and ORGEL: para 2 E –1 –3 r 2 ~~ <(n-1)d> – < 0 L 0 > 2 | | 37 The Paramagnetic Contribution to the Magnetic Shielding Constant Nonspherical circulation of electrons under influence of B0 px py dxy dx2-y2 38 Paramagnetic Contribution to the Magnetic Shielding 3 p imbalance para rE P const    Average energy approximation 39 The Paramagnetic Contribution to the Magnetic Shielding Constant Characteristics of para : Magnitude of para (= deshielding) increases when • the mean electronic excitation energy decreases (para ~  E–1 ) HOMO-LUMO gap, O shielding is most susceptible to changes in  E–1 (1 eV = 30 ppm) least precisely known • the effective radius of the valence shell decreases (para ~ r–3 ) more electrons = more e-e repulsion = larger r • the imbalance of valence electrons increases (para = f(Qi /L2) ) increasing symmetry = decreasing imbalance higher bond order = shielding 3 p imbalance para rE P const    40 The Paramagnetic Contribution to the Magnetic Shielding Constant Contributions to para by individual valence electron pairs are anisotropic and may cancel out because of symmetry reasons ! Ag + NH3Ag AgH3N NH3 symm. unsymm. symm. para = 0 for spherical symmetry, closed shell atoms ( e.g. F) 41 Patterns of Chemical Shifts For p- and d-block elements, chemical shifts are dominated by the paramagnetic contribution to the magnetic shielding, para. The Karplus-Pople approach proves useful to rationalize some important general patterns of chemical shifts in terms of variations of Different total chemical shift ranges of different elements Correlation between chemical shifts and electronic transitions Comparable chemical shift patterns for electronically similar compounds of different elements –3 “radial term” E–1 “energy term” “orbital term” Q (L )i 2 42 Patterns of Chemical Shifts –3 “radial term” NH4 + NH3  (15N) 325.9 380.2 Positive charge = p orbital contraction, less e-e repulsion, radius decreases = deshielding CMe3 + HCMe3  (13C) 335.7 50 3 p imbalance para rE P const    43 Patterns of Chemical Shifts –3 “radial term” 129Xe Chemical Shift dependence on the oxidation state Xe(VIII) Xe(VI) Xe(IV) Xe(II) Xe(0) XeO6 2 XeO3 XeF4 XeF2 Xe 2077 217 253 1592 5331 XeOF4 Xe(OTeF5)4 Xe(OTeF5)2 0 637 2379 Higher oxidation state = more positive charge = smaller = deshielding 44 Patterns of Chemical Shifts 109Ag NMR Chemical Shift dependence on the oxidation state 45 Patterns of Chemical Shifts Chemists are interested in correlations between NMR chemical shifts and other molecular properties related to changes in molecular structures or reactivities. Some useful relations are found in particular for transition metal compounds: Chemical Shifts and the Spectrochemical Series of Ligands (o) Spectrochemical Series = increase in E(d-d) = energy term decreases Weak ligands = deshielding weak bonds para large Strong ligands = shielding strong bonds para small I < Br < S2 < NCS* < Cl < NO3  < F < OH < RCOO < ox < ONO* < H2O < SCN* < gly < edta < CH3CN < py < NH3 increases = radial term decreases –3 “radial term” F < H2O < NH3 < en < ox < SCN* < Cl < CN < Br < I Nephelauxetic effect increases = increases Electronegativity increases Ionic bonding Covalent bonding decreases increases Deshielding Shielding 3 p imbalance para rE P const    51 Patterns of Chemical Shifts Change of ligands induces usually changes of both the energy and radial terms –3 “radial term” Nephelauxetic effect Normal halogen dependence F Cl Br I E–1 “energy term” Spectrochemical Series Inverse halogen dependence I Br Cl F Deshielding with increasing electronegativity (similar to diamagnetic term) Shielding with increasing electronegativity Depending on which effect dominates, the variation of (M) with the electronegativity of X may follow completely different patterns. 52 Patterns of Chemical Shifts I. Normal Halogen (Ligand) Dependence (M) follows the nephelauxetic series of ligands, increases in the series I < Br < Cl < F Observed for many compounds of p-block elements many transition metal complexes with partly filled or filled d-shells II. Inverse Halogen (Ligand) Dependence (M) follows the spectrochemical series of ligands, increases in the series F < Cl < Br < I Observed for many transition metal complexes with d0, d10- configurations, alkali metals –3 “radial term” E–1 “energy term” 3 p imbalance para rE P const    53 Patterns of Chemical Shifts II. Inverse Halogen(Ligand) Dependence I. Normal Halogen(Ligand) Dependence -17,4 -36,1 -83 F Cl Br I 0 -20 -40 -60 -80 (29Si)(91Zr) 0 50 100 150 -50 -100 -150 -120 -66 2 Br 2 ICl, Br2 Cl 126 0 -49 ( Si) in H SiX29 3 ( Zr) in Cp ZrXY 91 2 54 51V NMR of Vanadyl derivatives VOBr3 VOCl3 VOF3 432 (neat) 0 (neat) 786 (CH3CN) Inverse Halogen (Ligand) Dependence para 2 E –1 –3 r 2 ~~ <(n-1)d> – < 0 L 0 > 2 | | 3 p imbalance para rE P const    55 51V NMR of Vanadatranes N V R N NR RN E 56 Patterns of Chemical Shifts III. Complicated Patterns Influence on and E-1 of similar magnitude Non-monotonous trend for (M) Observed for some compounds of p-group elements III. Complicated Patterns (31P) 0 50 100 150 200 250 F Cl Br I 97 220 227,4 178 ( P) in P 31 X3 57 Symmetry and Chemical Shifts PCl3 PCl4 + PCl5 PCl6   (31P) ppm 220 96 81 281 Increasing symmetry = lower imbalance = shielding “orbital term” Q (L )i 2 58 Coordination Number and Chemical Shifts Main group elements Higher CN = shielding Transition metals Higher CN = deshielding More  bonding = shielding More  bonding = deshielding 59 Coordination Number and Chemical Shifts Higher CN = shielding AlO4 AlO5 AlO6  (27Al) 60 Coordination Number and Chemical Shifts Higher CN = shielding  (27Al)