NMR (nuclear Magnetic Resonance)

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Rawat DA Greatt

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NMR (nuclear Magnetic Resonance)

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1. Nuclear Magnetic Resonance (NMR) Spectroscopy By_ Saurav k. Rawat M.Sc. Chem. (Physical special) School of Chemical Science, St. John’s College, Agra 2. Definition of NMR Spectroscopy Nuclear Magnetic resonance spectroscopy: commonly referred to as NMR, is a technique which exploits the Magnetic properties of certain nuclei to study physical, chemical, and biological properties of matter Compared to mass spectrometry, larger amounts of sample are needed, but non-destructive 3. NMR History • 1937 Rabi’s prediction and observation of nuclear Magnetic resonance • 1945 First NMR of solution (Bloch et al for H2O) and solids (Purcell et al for parafin)! • 1953 Overhauser NOE (nuclear Overhauser effect) • 1966 Ernst, Anderson Fourier transform NMR • 1975 Jeener, Ernst 2D NMR • 1980 NMR protein structure by Wuthrich • 1990 3D and 1H/15N/13C Triple resonance • 1997 Ultra high field (~800 MHz) & TROSY(MW 100K) 4. Continuation of NMR History Nobel prizes 1944 Physics Rabi (Columbia) "for his resonance method for recording the Magnetic properties of atomic nuclei" 1991 Chemistry Ernst (ETH) 1952 Physics Bloch (Stanford), Purcell (Harvard) "for their development of new methods for nuclear Magnetic precision measurements and discoveries in connection therewith" "for his contributions to the development of the methodology of high resolution nuclear Magnetic resonance (NMR) spectroscopy" 5. Continuation of NMR History 2002 Chemistry Wüthrich (ETH) "for his development of nuclear Magnetic resonance spectroscopy for determining the three-dimensional structure of biological macromolecules in solution" 2003 Medicine Lauterbur (University of Illinois in Urbana ), Mansfield (University of Nottingham) "for their discoveries concerning Magnetic resonance imaging" 6. Spin of Nuclei Fermions : Odd mass nuclei with an odd number of nucleons have fractional spins. I = 1/2 ( 1H, 13C, 19F, 31P ), I = 3/2 ( 11B, 33S ) & I = 5/2 ( 17O ). Bosons : Even mass nuclei with odd numbers of protons and neutrons have integral spins. I = 1 ( 2H, 14N ) Even mass nuclei composed of even numbers of protons and neutrons have zero spin I = 0 (12C, and 16O, 32S) 7. Nuclear Magnetic Resonance (NMR) -the nuclei of some atoms spin: 1H, 13C, 19F, … -the nuclei of many atoms do not spin: 2H, 12C, 16O, … -moving charged particles generate a Magnetic field (?) -when placed between the poles of a powerful magnet, spinning nuclei will align with or against the applied field creating an energy difference. Using a fixed radio frequency, the Magnetic field is changed until the ?E = EEM. When the energies match, the nuclei can change spin states (resonate) and give off a Magnetic signal. ?E 8. Magnetic field = 14,092 gauss for 1H v = 60,000,000 Hz (60 MHz) NMR spectrum intensity Magnetic field ? 10 9 8 7 6 5 4 3 2 1 0 chemical shift (ppm) 9. 1H nuclei are shielded by the Magnetic field produced by the surrounding electrons. The higher the electron density around the nucleus, the higher the Magnetic field required to cause resonance. CH3Cl versus CH4 lower electron higher electron density density resonate at lower resonate at higher applied field applied field CHCCl3 ?? 10. Information from 1H-NMR spectra: 1. Number of signals: How many different types of hydrogens in the molecule. 2. Position of signals (chemical shift): What types of hydrogens. 3. Relative areas under signals (integration): How many hydrogens of each type. 4. Splitting pattern: How many neighboring hydrogens. 11. 1. Number of signals: How many different types of hydrogens in the molecule. Magnetically equivalent hydrogens resonate at the same applied field. Magnetically equivalent hydrogens are also chemically equivalent. # of signals? CH4 CH3CH3 12. H3C CH3 C C H3C CH3 CH3 CH3 one one one two number of signals? 13. CH3 Br H3C C CH3 CH3CH2-Br one two CH3CH2CH2-Br CH3CHCH3 Cl three two 14. CH3 CH2Cl CH3CHCH2CH3 Br Cl-CH2CH2CH2-Cl four two three 15. 2. Position of signals (chemical shift): what types of hydrogens. primary 0.9 ppm secondary 1.3 tertiary 1.5 aromatic 6-8.5 allyl 1.7 benzyl 2.2-3 chlorides 3-4 H-C-Cl bromides 2.5-4 H-C-Br iodides 2-4 H-C-I alcohols 3.4-4 H-C-O alcohols 1-5.5 H-O- (variable) Note: combinations may greatly influence chemical shifts. For example, the benzyl hydrogens in benzyl chloride are shifted to lower field by the chlorine and resonate at 4.5 ppm. 16. reference compound = tetramethylsilane (CH3)4Si @ 0.0 ppm remember: Magnetic field ? ? chemical shift convention: let most upfield signal = a, next most upfield = b, etc. … c b a tms 17. toluene CH3 b a b a 18. H3C CH3 C a a C H3C CH3 CH3 a b CH3 a a chemical shifts 19. CH3 Br H3C C a a b CH3 CH3CH2-Br CH3CH2CH2-Br CH3CHCH3 Cl a a a b c a b a 20. b d c a b a b CH3 CH2Cl CH3CHCH2CH3 Br Cl-CH2CH2CH2-Cl a b c 21. 3. Integration (relative areas under each signal): how many hydrogens of each type. a b c CH3CH2CH2Br a 3H a : b : c = 3 : 2 : 2 b 2H c 2H a b a CH3CHCH3 a 6H a : b = 6 : 1 Cl b 1H 22. H3C CH3 C a a C H3C CH3 CH3 a b CH3 a a a 12 H a 12 H a 6 H a 6 H b 4 H integration 23. CH3 Br H3C C a a b CH3 CH3CH2-Br a 9 H a 3 H b 2 H CH3CH2CH2-Br CH3CHCH3 Cl a a a b c a b a a 3 H b 2 H c 2 H a 6 H b 1 H 24. b d c a b a b CH3 CH2Cl CH3CHCH2CH3 Br Cl-CH2CH2CH2-Cl a b c a 3 H b 3 H c 2 H d 1 H a 2 H b 4 H a 3 H b 2 H c 4 H 25. c b a Integration: measure the height of each “step” in the integration and then calculate the lowest whole number ratio: a:b:c = 24 mm : 16 mm : 32 mm = 1.5 : 1.0 : 2.0 ? 3H : 2H : 4H 26. If the formula is known ( C8H9OF ), add up all of the “steps” and divide by the number of hydrogens = (24 + 16 + 32 mm) / 9H = 8.0 mm / Hydrogen. a = 24 mm / 8.0 mm/H ? 3 H; b = 16 mm/8.0 mm/H ? 2H; c = 32 mm/8.0 mm/H ? 4H. 27. 4. Splitting pattern: how many neighboring hydrogens. In general, n-equivalent neighboring hydrogens will split a 1H signal into an ( n + 1 ) Pascal pattern. “neighboring” – no more than three bonds away n n + 1 Pascal pattern: 0 1 1 singlet 1 2 1 1 doublet 2 3 1 2 1 triplet 3 4 1 3 3 1 quartet 4 5 1 4 6 4 1 quintet 28. note: n must be equivalent neighboring hydrogens to give rise to a Pascal splitting pattern. If the neighbors are not equivalent, then you will see a complex pattern (aka complex multiplet). note: the alcohol hydrogen –OH usually does not split neighboring hydrogen signals nor is it split. Normally a singlet of integration 1 between 1 – 5.5 ppm (variable). 29. H3C CH3 C a a C H3C CH3 a 12 H singlet a 12 H singlet CH3 a b CH3 a a a 6 H singlet a 6 H singlet b 4 H singlet splitting pattern? 30. CH3 Br H3C C a a b CH3 CH3CH2-Br a 9 H singlet a 3 H triplet b 2 H quartet CH3CH2CH2-Br CH3CHCH3 Cl a a a b c a b a a 3 H triplet b 2 H complex c 2 H triplet a 6 H doublet b 1 H septet 31. b d c a b a b CH3CHCH2CH3 CH3 CH2Cl Br Cl-CH2CH2CH2-Cl a b c a 3 H triplet b 3 H doublet c 2 H complex d 1 H complex a 2 H quintet b 4 H triplet a 3 H singlet b 2 H singlet c 4 H ~singlet a b c CH3CH2-OH a 3 H triplet b 2 H quartet c 1 H singlet 32. Information from 1H-NMR spectra: 1. Number of signals: How many different types of hydrogens in the molecule. 2. Position of signals (chemical shift): What types of hydrogens. 3. Relative areas under signals (integration): How many hydrogens of each type. 4. Splitting pattern: How many neighboring hydrogens. 33. cyclohexane a singlet 12H 34. 2,3-dimethyl-2-butene CH3 C H3C C H3C CH3 a singlet 12H 35. benzene a singlet 6H 36. p-xylene H3C CH3 a a b a singlet 6H b singlet 4H 37. tert-butyl bromide CH3 a singlet 9H H3C C CH3 Br 38. ethyl bromide a b CH3CH2-Br a triplet 3H b quartet 2H 39. 1-bromopropane a b c CH3CH2CH2-Br a triplet 3H b complex 2H c triplet 3H 40. isopropyl chloride a b a CH3CHCH3 Cl a doublet 6H b septet 1H 41. 2-bromobutane b d c a CH3CHCH2CH3 Br a triplet 3H b doublet 3H c complex 2H d complex 1H 42. o-methylbenzyl chloride CH3 CH2Cl a b c a singlet 3H b singlet 2H c ~ singlet 4H 43. ethanol a c b CH3CH2-OH a triplet 3H b singlet 1H c quartet 2H 44. ethylbenzene CH2CH3 c b a a triplet 3H b quartet 2H c ~singlet 5H 45. p-diethylbenzene a b c b a CH3CH2 CH2CH3 a triplet 6H b quartet 4H c singlet 4H 46. m-diethylbenzene 47. o-diethylbenzene 48. 2-bromo-2-methylbutane b CH3 b CH3CCH2CH3 a Br c a triplet 3H b singlet 6H c quartet overlap 2H b & c 49. di-n-propylether a b c c b a CH3CH2CH2-O-CH2CH2CH3 a triplet 6H b complex 4H c triplet 4H 50. 1-propanol a b d c CH3CH2CH2-OH a triplet 3H b complex 2H c singlet 1H d triplet 2H 51. C11H16 5H 2H 9H a 9H = 3CH3, no neighbors c 5H = monosubstituted benzene b 2H, no neighbors c b a CH2 CH3 C CH3 CH3 neopentylbenzene 52. C4H8Br2 6H a = 6H, two CH3 with no neighbors (CH3)2C— b = CH2, no neighbors & shifted downfield due to Br 2H CH3 H3C C CH2 Br Br 53. C7H8O 5H c = monosubst. benzene b = CH2 c = OH 2H 1H H2C OH 54. C4H9Br a doublet 1.04 ppm 6H b complex 1.95 ppm 1H c doublet 3.33 ppm 2H a = two equivalent CH3’s with one neighboring H (b?) c = CH2 with one neighbor H (also b) a CH3 a 6H doublet CH3CHCH2Br b 1H complex a b c c 2H doublet 55. C10H13Cl a singlet 1.57 ppm 6H b singlet 3.07 ppm 2H c singlet 7.27 ppm 5H a = two-equilalent CH3’s with no neighbors c = monosubstituted benzene ring b = CH2 b a c CH3 CH2C CH3 Cl a singlet 6H b singlet 2H c singlet 5H 56. 13C – NMR 13C ~ 1.1% of carbons 1) number of signals: how many different types of carbons 2) splitting: number of hydrogens on the carbon 3) chemical shift: hybridization of carbon sp, sp2, sp3 4) chemical shift: evironment 57. 2-bromobutane a c d b CH3CH2CHCH3 Br 13C-NMR 58. Angular Momentum A spinning charge generates a Magnetic field, the resulting spin-magnet has a Magnetic moment (?) proportional to the spin I mmaaggnneettiicc mmoommeenntt m == g pp wwhheerree g iiss tthhee ggyyrroommaaggnneettiicc rraattiioo,, aanndd iitt iiss aa ccoonnssttaanntt ffoorr aa ggiivveenn nnuucclleeuuss m =g p =g I (I +1)h / 2p When I=0, m=0 ** There is no spin for nuclei with I=0 ““Right HHaanndd RRuullee”” determines the direction of the Magnetic field around a current-carrying wire and vice-versa 59. Energy Differentiation In the presence of an external Magnetic field (B0), two spin states exist, +1/2 and -1/2 (For I=1/2). The Magnetic moment of the lower energy +1/2 state is aligned with the external field, and that of the higher energy -1/2 spin state is opposed to the external field. Aligned against the applied field Aligned with the applied field 60. Energy Differentiation Difference in energy between the two states is given by: DE = g h Bo / 2p where: Bo – external Magnetic field h – Planck’s constant g – gyroMagnetic ratio When the energy of the photon matches the energy difference between the two spin states , an absorption of energy occurs. We call that phenomenon Resonance DE = hu = ghBo / 2p So, u = g Bo / 2p 61. Larmor Precession Spinning particle precesses about the external field axis with an angular frequency known as the Larmor frequency wL = g Bo When radio frequency energy matching the Larmor frequency is introduced at a right angle to the external field, it would cause a transition between the two energy levels of the spin. In other world, the precessing nucleus will absorb energy and the Magnetic moment will flip to its I = _1/2 state 62. g- Values for some nuclei Isotope Net Spin g / MHz T-1 Abundance / % 1H 1/2 42.58 99.98 2H 1 6.54 0.015 3H 1/2 45.41 0.0 31P 1/2 17.25 100.0 23Na 3/2 11.27 100.0 14N 1 3.08 99.63 15N 1/2 4.31 0.37 13C 1/2 10.71 1.108 19F 1/2 40.08 100.0 63. Schematic NMR Spectrometer 64. Fourier transformation and the NMR spectrum Fourier RF Pulse transform The Fourier transform (FT) is a computational method for analyzing the frequencies present in an oscillating signal The NMR spectrum 65. 1H NMR and 13C NMR Spectrum 1H NMR spectra d ppm 13C NMR spectra d ppm Down field High field 66. Chemical Shift-d When an atom is placed in a Magnetic field, its electrons circulate about the direction of the applied Magnetic field. This circulation causes a small Magnetic field at the nucleus which opposes the externally applied field The Magnetic field at the nucleus (the effective field) is therefore generally less than the applied field by a fraction : B = B0 (1-s), So u = g B0 (1-s) / 2p 67. Chemical Shift-d The electron density around each nucleus in a molecule varies according to the types of nuclei and bonds in the molecule. The opposing field and therefore the effective field at each nucleus will vary. This is called the chemical shift pAhse wnoem ceanno tnel.l from n = g B0 (1-s) / 2p , the greater the value of Bo, the greater the frequency difference. This relationship could make it difficult to compare NMR spectra taken on spectrometers operating at different field strengths. The term chemical shift was developed to avoid this problem. The chemical shift of a nucleus is the difference between the resonance frequency of the nucleus and a standard, relative to the standard. This quantity is reported in ppm and given the symbol delta. d = (n - nref) x106 / nref 68. Standard for Chemical Shift In NMR spectroscopy, the standard is often tetramethylsilane, Si(CH3)4, abbreviated TMS. Tetramethyl silane (TMS) is used as reference because it is soluble in most organic solvents, is inert, volatile, and has 12 equivalent 1H and 4 equivalent 13C. TMS signal is set to 0 69. Shielding and Deshielding A nucleus is said to be shielded when electrons around the nucleus circulates in a Magnetic field and create a secondary induced Magnetic field which opposes the applied field . Trends in chemical shift are explained based on the degree of shielding or deshielding , e.g. of deshielding effect 70. Chemical Shift-d Chemical shift depends on : • Electronegativity of nearby atoms • Hybridization of adjacent atoms • diaMagnetic effects • paraMagnetic effects • solvent effect 71. Spin-Spin Coupling Spin-spin coupling: The coupling of the intrinsic angular momentum of different particles. Such coupling between pairs of nuclear spins is an important feature of nuclear Magnetic resonance (NMR) spectroscopy as it can provide detailed information about the structure and conformation of molecules. Spin-spin coupling between nuclear spin and electronic spin is responsible for hyperfine structure in atomic spectra. 72. J-Coupling J-coupling: also called indirect spin-spin coupling, is the coupling between two nuclear spins due to the influence of bonding electrons on the Magnetic field running between the two nuclei. J-coupling provides information about dihedral angles, which can be estimated using the Karplus equation. It is an important observable effect in 1D NMR spectroscopy. The coupling constant, J (usually in frequency units, Hz) is a measure of the interaction between a pair of nuclei 73. 1H-NMR • 1H experiencing the same chemical environment or chemical shift are called equivalent hydrogens. • 1H experiencing different environment or having different chemical shifts are nonequivalent hydrogens. 74. Chemical Shift - 1H-NMR 75. 1H Chemical shifts (CH3 ) 4 Si RCH3 RCH2 R R3 CH R2 C=CRCHR2 RC CH ArCH3 ArCH2 R ROH RCH2 OH RCH2 OR R2 NH O O RCCH3 RCCH2 R O RCOCH3 O RCOCH2 R RCH2 I RCH2 Br RCH2 Cl RCH2 F ArOH R2 C=CH2 R2 C=CHR ArH O O RCH RCOH 3.7-3.9 4.1-4.7 3.1-3.3 3.4-3.6 3.6-3.8 4.4-4.5 4.5-4.7 6.5-8.5 9.5-10.1 Type of Hydrogen 0 (by definition) Type of Hydrogen Chemical Shift (d) 0.8-1.0 1.2-1.4 1.4-1.7 1.6-2.6 2.0-3.0 2.2-2.5 2.3-2.8 0.5-6.0 3.4-4.0 2.1-2.3 2.2-2.6 Chemical Shift (d) 3.3-4.0 0.5-5.0 4.6-5.0 5.0-5.7 10-13 76. Factors to Affect 1H Chemical Shift Chemical shift : (1) electronegativity of nearby atoms, (2) hybridization of adjacent atoms, and (3) diaMagnetic effects Electronegativity CH3 -X CH3F CH3OH CH3Cl CH3Br CH3 I (CH3 ) 4C (CH3 ) 4Si Electroneg-ativity of X Chemical Shift (d) 4.0 3.5 3.1 2.8 2.5 2.1 1.8 4.26 3.47 3.05 2.68 2.16 0.86 0.00 77. Hybridization of adjacent atoms RCH3 , R2CH2 , R3CH R2C=C(R)CHR2 RC CH R2C=CHR, R2C=CH2 RCHO Allylic Type of Hydrogen (R = alkyl) Name of Hydrogen Chemical Shift (d) Alkyl Acetylenic Vinylic Aldehydic 0.8 - 1.7 1.6 - 2.6 2.0 - 3.0 4.6 - 5.7 9.5-10.1 78. Carbon-Carbon Triple Bond Effect A carbon-carbon triple bond shields an acetylenic hydrogen and shifts its signal to lower frequency (to the right) to a smaller value Type of H Name RCH3 R2C=CH2 RC CH Alkyl Acetylenic Vinylic Chemical Shift (d) 0.8- 1.0 2.0 - 3.0 4.6 - 5.7 79. Carbon-Carbon Double Bond Effect Magnetic induction in the p bond of a carbon-carbon double bond deshields vinylic hydrogens and shifts their signal higher frequency 80. Aromatic Effect The Magnetic field induced by circulation of p electrons in an aromatic ring deshields the hydrogens on the ring and shifts their signal to higher frequency 81. Signal Splitting for 1H Peak: The units into which an NMR signal is split; doublet, triplet, quartet, multiplet, etc. Signal splitting: Splitting of an NMR signal into a set of peaks by the influence of neighboring nonequivalent hydrogens. (n + 1) rule: If a hydrogen has n hydrogens nonequivalent to it but equivalent among themselves on the same or adjacent atom(s), its 1H-NMR signal is split into (n + 1) peaks. 82. Pascal’s triangle The relative peak intensities for multiplet peaks arising from J-coupling of a 1H to N equivalent 1H can be determined using Pascal’s triangle: 83. Coupling constant Coupling constant (J): The separation on an NMR spectrum (in hertz) between adjacent peaks in a multiplet. 84. 13C-NMR Spectroscopy Organic compounds contain carbon. Unfortunately, the C-12 nucleus does not have a nuclear spin, but the C-13 nucleus does due to the presence of an unpaired neucarbon-1tron. C-13 nuclei make up approximately 1% of the carbon nuclei on earth. Therefore, 13C NMR will be much less sensitive than 1HNMR NMR 85. 13C-NMR Spectroscopy The presence of spin-spin coupling between a 13C nucleus and the nuclei of 1H atoms bonded to the 13C, splits the carbon-13 peaks and causes an even poorer signal-to-noise ratio Each nonequivalent 13C gives a different signal A 13C signal is split by the 1H bonded to it according to the (n + 1) rule. Coupling constants of 100-250 Hz are common, which means that there is often significant overlap between signals, and splitting patterns can be very difficult to determine. The most common mode of operation of a 13C-NMR spectrometer is a proton-decoupled mode. 86. Decoupling proton-decoupled mode, a sample is irradiated with two different radiofrequencies. One to excite all 13C nuclei, a second to cause all protons in the molecule to undergo rapid transitions between their nuclear spin states. On the time scale of a 13C-NMR spectrum, each proton is in an average or effectively constant nuclear spin state, with the result that 1H-13C spin-spin interactions are not observed and they are decoupled. 87. Chemical Shift - 13C-NMR Characteristic Carbon NMR Chemical Shifts (ppm) (CH3)4Si = TMS = 0.00 ppm (singlet) CDCl3 (solvent) = 77.0 ppm (triplet) RCH3 0 – 40 RCH2Cl 35 – 80 benzene ring 110 – 160 RCH2R 15 – 55 R3COH 40 – 80 C=O ester 160 – 180 R3CH 20 – 60 R3COR 40 - 80 C=O amide 165 – 180 RCH2I 0 – 40 RCºCR 65 – 85 C=O carboxylic acid 175 – 185 RCH2Br 25 - 65 R2C=CR2 100 - 150 C=O aldehyde, ketone 180 – 210 Trends •RCH3 < R2CH2 < R3CH •Electronegative atoms cause downfield shift •Pi bonds cause downfield shift •C=O 160-210 ppm 88. 13C-NMR: Integration 1H-NMR: Integration reveals relative number of hydrogens per signal 13C-NMR: Integration reveals relative number of carbons per signal •Rarely useful due to slow relaxation time for 13C time for nucleus to relax from excited spin state to ground state 89. Interpreting NMR Spectra Alkanes 1H-NMR signals appear in the range of 0.8-1.7. 13C-NMR signals appear in the considerably wider range of 10-60. Alkenes 1H-NMR signals appear in the range 4.6-5.7. 1H-NMR coupling constants are generally larger for trans-vinylic hydrogens (J= 11-18 Hz) compared with cis-vinylic hydrogens (J= 5-10 Hz). 13C-NMR signals for sp2 hybridized carbons appear in the range 100-160, which is to higher frequency from the signals of sp3 hybridized carbons. 90. Interpreting NMR Spectra Alcohols 1H-NMR O-H chemical shift often appears in the range 3.0-4.0, but may be as low as 0.5. 1H-NMR chemical shifts of hydrogens on the carbon bearing the -OH group are deshielded by the electron-withdrawing inductive effect of the oxygen and appear in the range 3.0-4.0. Ethers A distinctive feature in the 1H-NMR spectra of ethers is the chemical shift, 3.3-4.0, of hydrogens on the carbons bonded to the ether oxygen. 91. a a b b 92. Interpreting NMR Spectra Aldehydes and ketones 1H-NMR: aldehyde hydrogens appear at 9.5-10.1. 1H-NMR: a-hydrogens of aldehydes and ketones appear at 2.2-2.6. 13C-NMR: carbonyl carbons appear at 180-215. Amines 1H-NMR: amine hydrogens appear at 0.5-5.0 depending on conditions. 93. 1H NMR isobutyraldehyde a b c c b a 1H NMR Methyl ethyl ketone a a b c c b 94. Interpreting NMR Spectra CCaarrbbooxxyylliicc aacciiddss 1H-NMR: carboxyl hydrogens appear at 10-13 ppm, higher than most other types of hydrogens. 13C-NMR: carboxyl carbons in acids and esters appear at 160-180 ppm. c b a c b a 95. NMR = Nuclear Magnetic Resonance Physical Principles: Some (but not all) nuclei, such as 1H, 13C, 19F, 31P have nuclear spin. A spinning charge creates a Magnetic moment, so these nuclei can be thought of as tiny magnets. If we place these nuclei in a Magnetic field, they can line up with or against the field by spinning clockwise or counter clockwise. N N S a- spin state, favorable, lower energy S A spinning nucleus with it's Magnetic field aligned with the Magnetic field of a magnet N S b- spin state, N unfavorable, higher energy S A spinning nucleus with it's Magnetic field aligned against the Magnetic field of a magnet Alignment with the Magnetic field (called a) is lower energy than against the Magnetic field (called b). How much lower it is depends on the strength of the Magnetic field Note that for nuclei that don’t have spin, such as 12C, there is no difference in energy between alignments in a Magnetic field since they are not magnets. As such, we can’t do NMR spectroscopy on 12C. 96. NMR: Basic Experimental Principles Imagine placing a molecule, for example, CH4, in a Magnetic field. We can probe the energy difference of the a- and b- state of the protons by irradiating them with EM radiation of just the right energy. In a magnet of 7.05 Tesla, it takes EM radiation of about 300 MHz (radio waves). So, if we bombard the molecule with 300 MHz radio waves, the protons will absorb that energy and we can measure that absorbance. In a magnet of 11.75 Tesla, it takes EM radiation of about 500 MHz (stronger magnet means greater energy difference between the a- and b- state of the protons) E b proton spin state (higher energy) at no Magnetic field, there is no difference beteen a- and b- states. DE = h x 300 MHz DE = h x 500 MHz 7.05 T 11.75 T Bo a proton spin state (lower energy) Graphical relationship between Magnetic field (B o) and frequency ( n) for 1H NMR absorptions 0 T But there’s a problem. If two researchers want to compare their data using magnets of different strengths, they have to adjust for that difference. That’s a pain, so, data is instead reported using the “chemical shift” scale as described on the next slide. 97. The Chemical Shift (Also Called d) Scale Here’s how it works. We decide on a sample we’ll use to standardize our instruments. We take an NMR of that standard and measure its absorbance frequency. We then measure the frequency of our sample and subtract its frequency from that of the standard. We then then divide by the frequency of the standard. This gives a number called the “chemical shift,” also called d, which does not depend on the Magnetic field strength. Why not? Let’s look at two examples. Imagine that we have a magnet where our standard absorbs at 300,000,000 Hz (300 megahertz), and our sample absorbs at 300,000,300 Hz. The difference is 300 Hz, so we take 300/300,000,000 = 1/1,000,000 and call that 1 part per million (or 1 PPM). Now lets examine the same sample in a stronger Magnetic field where the reference comes at 500,000,000 Hz, or 500 megahertz. The frequency of our sample will increase proportionally, and will come at 500,000,500 Hz. The difference is now 500 Hz, but we divide by 500,000,000 (500/500,000,000 = 1/1,000,000, = 1 PPM). It’s brilliant. Of course, we don’t do any of this, it’s all done automatically by the NMR machine. Even more brilliant. 98. The Chemical Shift of Different Protons NMR would not be very valuable if all protons absorbed at the same frequency. You’d see a signal that indicates the presence of hydrogens in your sample, but any fool knows there’s hydrogen in organic molecules. What makes it useful is that different protons usually appear at different chemical shifts (d). So, we can distinguish one kind of proton from another. Why do different protons appear at different d? There are several reasons, one of which is shielding. The electrons in a bond shield the nuclei from the Magnetic field. So, if there is more electron density around a proton, it sees a slightly lower Magnetic field, less electron density means it sees a higher Magnetic field: C H Z This represents the electron density of a C-H bond. How much electron density is on the proton depends on what else is attached to the carbon. If Z is an elelctronegative atom, the carbon becomes electron deficient and pulls some of the electron density away from the H. if Z is an electron donating group, more electron density ends up on the H. How do the electrons shield the Magnetic field? By moving. A moving charge creates a Magnetic field, and the field created by the moving electrons opposes the Magnetic field of our NMR machine. It’s not a huge effect, but it’s enough to enable us to distinguish between different protons in our sample. 99. The Hard Part - Interpreting Spectra Learning how an NMR machine works is straightforward. What is less straightforward is learning how to use the data we get from an NMR machine (the spectrum of ethyl acetate is shown below). That’s because each NMR spectrum is a puzzle, and there’s no single fact that you simply have to memorize to solve these spectra. You have to consider lots of pieces of data and come up with a structure that fits all the data. What kinds of data do we get from NMR spectra? For 1H NMR, there are three kinds each of which we will consider each of these separately: 1) Chemical shift data - tells us what kinds of protons we have. 2) Integrals - tells us the ratio of each kind of proton in our sample. 3) 1H - 1H coupling - tells us about protons that are near other protons. 100. Chemical Shift Data As previously mentioned, different kinds of protons typically come at different chemical shifts. Shown below is a chart of where some common kinds of protons appear in the d scale. Note that most protons appear between 0 and 10 ppm. The reference, tetramethylsilane (TMS) appears at 0 ppm, and aldehydes appear near 10 ppm. There is a page in your lab handout with more precise values for this chart. Note that these are typical values and that there are lots of exceptions! d ppm Me TMS R H O R NR2 CH3 CH3 (R) HO CH3 O R OCH3 CH3 R R R H O R H H Ph CH3 Cl CH3 Ph OH OH R NH R Upfield region of the spectrum Downfield region of the spectrum TMS = Me Si Me Me 10 9 8 7 6 5 4 3 2 1 0 101. Integrals Integrals tell us the ratio of each kind of proton. They are lines, the heights of which are proportional to the intensity of the signal. Consider ethyl acetate. There are three kinds of protons in this molecule, the CH3 next to the carbonyl, the CH2 next to the O and the CH3 next to the CH2. The ratio of the signals arising from each of these kinds of protons should be 3 to 2 to 3, respectively. So, if we look at the height of the integrals they should be 3 to 2 to 3. With this information, we can know which is the CH2 signal (it’s the smallest one), but to distinguish the other two, we have to be able to predict their chemical shifts. The chart on the previous page allows us to make that assignment (the CH3 next to the C=O should appear at ~ 2 PPM, while the other CH3 should be at ~ 1 PPM). 3H'S 3H'S 2 H'S O O H H O O CH3 H3C O O 102. 1H - 1H Coupling You’ll notice in the spectra that we’ve seen that the signals don’t appear as single lines, sometimes they appear as multiple lines. This is due to 1H - 1H coupling (also called spin-spin splitting or J-coupling). Here’s how it works: Imagine we have a molecule which contains a proton (let’s call it HA) attached to a carbon, and that this carbon is attached to another carbon which also contains a proton (let’s call it HB). It turns out that HA feels the presence of HB. Recall that these protons are tiny little magnets, that can be oriented either with or against the Magnetic field of the NMR machine. When the field created by HB reinforces the Magnetic field of the NMR machine (B0 ) HA feels a slightly stronger field, but when the field created by HB opposes B0, HA feels a slightly weaker field. So, we see two signals for HA depending on the alignment of HB. The same is true for HB, it can feel either a slightly stronger or weaker field due to HA’s presence. So, rather than see a single line for each of these protons, we see two lines for each. HA HB C C HA HB HA is sp lit into two lines b ecause it feels the Magnetic field of HB. HB is sp lit into two lines b ecause it feels the Magnetic field of HA. For this line, HB is lined up with the Magnetic field (adds to the overall Magnetic field, so the line comes at higher frequency) For this line, HB is lined up against the Magnetic field (sub tracts from the overall Magnetic field, so the line comes at lower frequency) 103. More 1H - 1H Coupling What happens when there is more than one proton splitting a neighboring proton? We get more lines. Consider the molecule below where we have two protons on one carbon and one proton on another. HA HB C C Note that the signal p roduced b y HA + HA ' is twice the size HA' HA + HA' HB HA and HA ' app ear at the same chemical shift b ecause they are in identical environments They are also sp lit into two lines (called a doub let) b ecause they feel the Magnetic field of HB. HB is sp lit into three lines because it feels the Magnetic field of HA and HA ' of that p roduced b y HB 104. Why are There Three Lines for HB? HB feels the splitting of both HA and HA’. So, let’s imagine starting with HB as a single line, then let’s “turn on” the coupling from HA and HA’ one at a time: HB If uncoupled, H B would appear as a singlet where the dashed line indicates the chemical shift of the singlet. Now, let's "turn on" HB - HA coupling. This splits the single line into two lines Now, let's "turn on" HB - HA' coupling. This splits each of the two new lines into two lines, but notice how the two lines in the middle overlap. Overall, we then have three lines. HA HB C C HA' Because the two lines in the middle overlap, that line is twice as big as the lines on the outside. More neighboring protons leads to more lines as shown on the next slide. 105. Splitting Patterns with Multiple Neighboring no. of neighbors relative intensities pattern 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 0 1 2 3 4 5 6 singlet (s) doublet (d) triplet (t) quartet (q) pentet sextet septet example H H C C H H C C H H H C C H H H H C C C H H H H H H C C C H H H H H C C C H H H H H Protons If a proton has n neighboring protons that are equivalent, that proton will be split into n+1 lines. So, if we have four equivalent neighbors, we will have five lines, six equivalent neighbors… well, you can do the math. The lines will not be of equal intensity, rather their intensity will be given by Pascal’s triangle as shown below. We keep emphasizing that this pattern only holds for when the neighboring protons are equivalent. Why is that? The answer is two slides away. 106. More About Coupling Earlier we said that protons couple to each other because they feel the Magnetic field of the neighboring protons. While this is true, the mechanism by which they feel this field is complicated and is beyond the scope of this class (they don’t just feel it through space, it’s transmitted through the electrons in the bonds). It turns out that when two protons appear at the same chemical shift, they do not split each other. So, in EtBr, we have a CHnext to a CH, and each proton of the CHgroup is 3 23 only coupled to the protons of the CHgroup, not the other CHprotons 2 3 because all the CHprotons come at H the H same chemical shift. 3 C C H H H Br The blue protons all come at the same chemical shift and do not split each other The red protons both come at the same chemical shift and do not split each other H H C C H H H Br H H C C H H H Br 107. Not all Couplings are Equal When protons couple to each other, they do so with a certain intensity. This is called the “coupling constant.” Coupling constants can vary from 0 Hz (which means that the protons are not coupled, even though they are neighbors) to 16 Hz. Typically, they are around 7 Hz, but many molecules contain coupling constants that vary significantly from that. So, what happens when a molecule contains a proton which is coupled to two different protons with different coupling constants? We get a different pattern as described in the diagram below. So, if the protons are not equivalent, they can have different coupling constants and the resulting pattern will not be a triplet, but a “doublet of doublets.” Sometimes, nonequivalent protons can be on the same carbon as described on the next slide. 108. Coupling Constants in Alkenes Coupling constants in alkenes can also differ depending on whether the protons are cis or trans to each other. Note that in a terminal alkene (i.e., an alkene at the end of a carbon chain), the cis and trans protons are NOT equivalent. One is on the same side as the substituent, the other is on the opposite side. The coupling of trans protons to each other is typically very large, around 16 Hz, while the coupling of cis protons, while still large, is a little smaller, around 12 Hz. This leads to the pattern shown below, and an example of a molecule with this splitting pattern is shown HA on the next slide. If uncoupled, HA would appear as a singlet where the dashed line indicates Now, let's "turn on" HA - HX coupling. This splits the single line into two lines that are 16 Hz appart Now, let's "turn on" HA - HM coupling. This splits each of the two new lines into two lines that are 12 Hz appart for a total of four lines 16 Hz 12 Hz 12 Hz HA HM HX 12Hz coupling 16 Hz coupling There are other times when protons on the same carbon are nonequivalent, which we’ll see later. 109. HO HO H H CH3 HO HO CH3 A molecule with a terminal alkene HO H H H HO H H H HO H H H OH Me OH Me Me OH Me H A molecule with a nine line splitting pattern Me OH Me Me OH Me H H Nine lines, you just can't see two of them because they are so small. 110. 3. Nuclear Magnetic Resonance - NMR results from resonant absorption of electroMagnetic energy by a nucleus (mostly protons) changing its spin orientation - The resonance frequency depends on the chemical environment of the nucleus giving a specific finger print of particular groups (NMR spectroscopy) - NMR is nondestructive and contact free - Modern variants of NMR provide 3D structural resolution of (not too large) proteins in solution - NMR tomography (Magnetic resonance imaging, MRI) is the most advanced and powerful imaging tool 112 111. 113 Some history of NMR 1946 Principle of solid state NMR (Bloch, Purcell) 1950 Resonance frequency depends on chemical environment (Proctor, Yu) 1953 Overhauser effect 1956 First NMR spectra of protein (Ribonuclease) 1965 Fourier Transform spectroscopy (Ernst) 112. 114 1973 Imaging tomography (Mansfield) 1985 First protein structure (bovine pancreatic trypsin inhibitor) in solution (Wüthrich) 113. 115 By now: More than 150 protein structures (M < 60 000) BPTI Bound water Protein dynamics 114. 116 Functional MRI 115. 3.1 Principle of Nuclear Magnetic Resonance Many (but not all) nuclei have a spin (I). Quantum mechanically I can have 2I+1 orientations in an external Magnetic field B. 117 This spin is associated with a Magnetic moment gI: nuclear g-factor 116. Since biomatter is made of H,C,N and O, these are the most relevant nuclei for biological NMR 118 117. Larmor precession around B1 119 Mechanical (classical) model Spinning top with Magnetic B0 || z moment mL and angular momentum I precesses with frequency wL under torque D B1 x y a Larmor precession of mL around B0 Torque on Magnetic moment mL in B0 The precession frequency is independent of a and equals the Larmor frequency Application of a horizontal Magnetic field B1 which rotates at wL: In the frame rotating with mL the orientation of B1 relative to mL is constant Additional precession of mL around B1 at frequency 118. Quantum mechanical description The Magnetic moment orients in a Magnetic field B0. Different orientations correspond to different energies 120 B0 I = 1/2 mI = 1/2 mI = - 1/2 E B0 1H, 13C, 31P B0 I = 1 mI = 1 - 1 E B0 2H, 14N, 0 I = 3/2 mI = 3/2 B0 1/2 - 3/2 E B0 23Na, -1/2 gI = 5.58 When photons with frequency wL are absorbed a transition from the lower to the upper level occurs. Selection rule DmI = 1 g = 42.576 MHz/T 119. Bulk magnetization A sample contains many nuclei (typically N ~ 1017 or higher). In zero field all spin orientations are equivalent. The bulk magnetization (I.e. is the sum of all m’s) is very small and fluctuates around M=0. At finite fields B0 (and finite temperature) the occupation of states at different energies E obeys Boltzmann statistics exp(- E/kBT) – thermal equilibrium is assumed. For I=1/2 the spin state “parallel” to B0 has lower energy E1 than the “ antiparallel” state with energy E2. Therefore there is a net magnetization along the z-axis. However since DE = E2 – E1 is much smaller than kBT the magnetization is far from saturation. 121 120. 122 The number of spins in state 1,2 is Thus the population imbalance is Which yields a bulk magnetization with The average magnetization in x,y vanishes because the precessions of individual spins are uncorrelated. 121. The application of a pulse of duration t changes the average angle of the magnetization by a certain angle (c.f. the mechanical model or a change in population densities), given by: 123 J J ( ) 1 t B g = Thus a pulse of duration t =2p/4 w1 gives a change in angle of p/2 – pulse I.e. the magnetization is flipped into the xy plane. Mx and My now oscillate with wL. If M is flipped out of equilibrium (out of the z-direction) by a B1- pulse, it will relax back to Mz into thermal equilibrium. This occurs because of Magnetic interaction of m with the environment (atoms, eventually in crystalline lattice) and is characterized by the so–called longitudinal (or spin-lattice) relaxation time T1. 122. This relaxation is described by a set of rate equations for the transitions between the states 124 dn W n n W n n dt dn 0 0 = - - - ( ) ( ) 0 0 W n n W n n = - - - ( ) ( ) a dt b b a a b a a b b Which yields a simple exponential relaxation of the magnetization in the z-direction 123. 125 The amplitudes of Mx and My decay with another relaxation time T2 called spin-spin relaxation time. This relaxation originates from inhomogeneity of B0 . It is described by another phenomenological equation y x y x Immediately after p/2 pulse later 124. To be complete, the precession in the static field has to be taken into account as well, which is described by the Bloch equations 126 One can detect the transverse magnetization Mx or My by a pick up coil where a current I(t) is induced by the oscillating transverse magnetization. The width of the FT of I(t) provides a measurement of T2 (Method of free induction decay) 125. 127 3.2 Classical NMR experiments Absorption signal 126. High frequency NMR spectrometers require very strong Magnetic fields, which are produced using super-cooled coils (T = 4.2K, liquid He). The superconducting coils are surrounded by a giant vessel containing liquid N2. 128 600 MHz Proton NMR Spectrometer B0 k He B1 N2 127. 3.3 Chemical shift The external field B0 is changed (reduced in amplitude) due to local field -sB0 generated by the diaMagnetic currents induced by B0 in the electron system near the nucleus. s is the shielding constant (diaMagnetic susceptibility) 129 The shielding depends on the orientation of B0 with respect to the molecules (e.g. benzene ring) near the nucleus. s is a tensor. If the rotational motion of the molecules is fast compared to 1/wL the precessing spin I sees an effective (time averaged ) field Bloc. If the rotation is free (like in most simple liquids) the anisotropy of the shielding is averaged out, s becomes a number. The NMR lines are very narrow. NB. In solids or large proteins in viscous environment where motions are strongly hindered or slowed down, the NMR lines are significantly broader. Motional narrowing! 13C NMR spectrum of liquid benzene 128. 130 Usual measure: Frequency shift of sample (1) relative to some reference sample (2); unit: ppm Origin of chemical shift: = shielding of B0 129. 131 Benzene C6H6 Toluene C6H5-CH3 All 6 carbons are identical same chemical shift, one line 5 different types of C-atoms, 5 lines Examples: 13C NMR 130. 1H-NMR of ethyl alcohol, CH3CH2OH Three types of protons CH3 OH CH2 131. 133 132. Typical chemical shifts Reference Tetramethylsilane Si (CH3) 4 Has very narrow line Chemical shifts are frequently used in chemistry and biology to determine amount of specific groups in sample (quantitative spectroscopy) 134 133. 135 134. 136 3.4 Pulsed NMR More efficient than classical (frequency or B) scans Study the free induction decay (FID) “Ideal” FID = one precession frequency Pick up coil 135. “Real” FID = several precession frequencies because of several nuclei with different chemical shifts 31P NMR 137 FT 136. 138 Spin echo 90 degree flip Evolution = spreading (dephasing) in x,y plane 180 degree flip = mirror image relative to x Refocusing = spin echo t p/2 p t1 t1 My - echo after 2 t1 FID T2 T1 137. 139 Spin-Spin Interactions give rise to relaxation of the magnetization Scalar or J – coupling (through bond) Most bonds are characterized by antiparallel orientation of electron spins (bonding orbital) The nuclear spins are oriented antiparallel to “ their “ bond electron A B The nuclear spins mA and mB are coupled, independent of the direction of the external field; Interaction energy: DE = a mA . mB Energy to flip eg spin B A B NB: In polyatomic molecules the J-coupling can also be promoted by -C-bonds or other bonds ( A – C – B ). It is short ranged (max. 2 or 3 bond lengths) eg H2 138. 140 J- coupling results in additional splitting of (chemically shifted) lines The Magnetic dipoles of the CH3 group protons interact with the aldehyde proton spin and vice versa. Parallel orientations have higher energies. NB: the spin-spin coupling constant J also depends on the bond angle -> info on conformation 139. 141 1D NMR of macromolecules Alanine in D20 J-coupling Tryptophan in D20 J-coupling structure Lysozyme (129 amino acids) Assignment of lines ok Assignment too complicated NB: VERY high field NMR, in principle could solve resolution problem 140. Selection rule demands Gives rate equations of the type: dn W n n W n n W n n dt 142 Interactions between different spin-states Dm = ±1 1 = (1) ( D - D ) + (1) ( D - D ) + ( D - D ) s 2 1 I 3 1 2 4 1 141. Generalizing from before, we obtain the magnetizations of the two spin states and the population difference: D I = D n - D n + D n - D n D S = D n - D n + D n - D n I S n n n n 1 3 2 4 1 2 3 4 z z D = D - D - D + D 2 z z 1 3 2 4 Thus one obtains a rate equation for the magnetization: d D I = d D n - d D n + d D n - d D n z 1 3 2 4 dt dt dt dt dt Which is more useful written in terms of magnetizations: d D I = - W + W + W + W D I - W - W D S - W - W D I S dt 143 ( (1) ( 2) ) ( ) ( (1) ( 2) ) 2 0 2 0 z 2 I I z z I I z z Note selection rules demand W2 = W0 = 0 142. 144 The same game can be played for the other magnetization, giving an analogue equation, which cross correlate the different spins. 2D NMR of macromolecules makes use of these cross correlations FID A second 90O pulse in the same (x) direction as the first one flips all spins pointing into y back to z. The instant Mx stays unaffected. t Mxy t1 Mxy(n) has marker at n1 = 1/t1 143. 145 Protocol: Take FID’s at variable values of t1 1D (auto) peaks Cross peaks indicating spin-spin coupling 144. Through bond interaction 146 2D COSY spectrum of isoleucine C bewteen CaH and CbH aH Cross peaks give information on distance along the bond CbH CdH3 CgH2 145. 2D COSY spectrum of a heptapeptide Tyr-Glu-Arg-Gly- Asp-Ser-Pro (YGRGDSP) 147 146. Direct dipole-dipole interaction (through space) can take up a change of Dm = +/- 1, I.e. relax the selection rules. B-field generated by dipole m 148 2 4 3 0,2 6 , IS Transition rates go with the V : g W : g square of the interaction r r IS IS Related to the energy changes of A and B due to the induced fields at A and B: - mABB and - mBBA Strong dependence on distance between the different spin sites (r-6 due to dipole interaction) gives very sensitive spatial information about distances between spins down to 0.5 nm 147. Now take along the cross terms of the magnetizations gives the Solomon equation: æ æ - + ö æ - ö ç çè ø¸ - + èç + ø¸ - - - - ö ¸ = ç ¸ ç s - l - - l æ - + ö - l + æ - ö ¸ ç ç ¸ ç + ¸ - l ¸ è è ø è ø ø 149 æ · ç D I ö z ¸= æ - R - s öæ D I I z ö çç · ç ¸ç ¸ èD S ¸¸ - s - R øèD S z ø è S z ø ( ) ( ) ( ) ( ) ( ) æ D ö æ D = 0 ö èD ç ¸= ø èD ç = ¸ ø I t I t exp 0 z Lt z z z S t S t ( ) R R 1 exp l t R R 1 exp l t s exp l t exp l t ( ) ( ) ( ( ) ( ) ) 1 2 1 2 ( ( ) ( ) ) ( ) ( ) R R R 2 2 2 2 1 2 1 2 exp exp exp 1 exp 1 exp 2 2 2 2 S I I S I S S I Lt t t R R t R R t R R R Solved by: 148. æ - + - - - - ö ç ¸ = ç ¸ çç - - - - + - ¸¸ è ø 150 Simplify by assuming RI =RS: Lt R ( ) 1 exp exp exp exp ( ( t ) ( t ) ) ( ( t ) ( t ) ) 1 2 1 2 ( ( t ) ( t ) ) ( ( t ) ( t ) ) 1 2 1 2 exp 2 exp exp 1 exp exp 2 R l l s l l s l l l l This implies maximum mixing after a time scale tm Flip the spins S at that time to enhance contrast 149. For macromolecules, there are many interacting spins, thus a much more complicated set of equations would have to be solved 151 s · æ ö = ç ¸ ç ¸ çè ø¸ uur j n uur R s 1 1 1 1 1 I I D s O s D i in s R n nj n s Combine this (nuclear Overhauser) enhancement with the technique of 2D spectroscopy gives NOESY: The appearance of correlation peaks as a function of tmix gives information about the spatial properties (s) of the atoms 150. 152 Part of 2D NOESY spectrum of a YGRGDSP H H NOESY correlates all protons near in real space even if the are chemically distant Typical NOESY signatures 151. 153 Determination of protein structure from multi-dimensional NMR - data Starting structure (from chemical sequence) Random folding at start of simulation Heating to overcome local energy barriers Cooling under distance constraints from NMR Repeating for many starting structures Family of structures 152. 154 153. NMR solution structures of proteins Tyrosine Phosphatase Cytochrome 3 155 154. 3.5 MRI At much reduced spatial resolution, NMR can also be used as an imaging tool, where the spatial resolution is obtained by encoding space by a frequency (i.e. a field gradient) 156 155. 157 Mostly driven by T2 relaxations, apply a gradient field across the sample, which gives different Larmor frequencies for different positions (all done at H frequencies) Resonance condition only fulfilled at one specific position 156. 158 Now we have to also encode position in the x-y direction 157. 159 Apply a field gradient along the y-direction for a short time, which gives a phase shift to the different nuclei as a function of depth 158. 160 Finally apply a field gradient along the x-direction during readout, which gives a frequency shift of the FID precession 159. 161 Then you take a signal with a pickup coil as a function of FID time and time duration of the phase coding pulse, which you Fourier transform to obtain a proper image 160. 162 Since you have turned a spatial measurement into a spectroscopic one, the resolution is spectroscopically limited (or limited by the gradients you apply) Therefore fast scans (needed for functional studies have less resolution) 161. 163 Recap Sec. 3 NMR is a spectroscopic method given by the absorption of em radiation by nuclei The signals depend on the nuclei, the applied field and the chemical environment Using Fourier-transform methods, a fast characterization of different freqeuncy spectra is possible Sensitivity is enhanced by using cross correlations in 2D NMR 162. 164 More recap Dipole-Dipole interactions can be used to characterize spatial relationships Spin-Spin interactions are used to determine chemical bonds Gives atomic resolution for macromolecules including dynamics Using Magnetic field gradients, spatially resolved measurements are possible resulting in MRI 163. 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