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Nuclear Magnetic Resonance A.) Introduction : Nuclear Magnetic Resonance (NMR) measures the absorption of electromagnetic radiation in the radio-frequency.

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Presentation on theme: "Nuclear Magnetic Resonance A.) Introduction : Nuclear Magnetic Resonance (NMR) measures the absorption of electromagnetic radiation in the radio-frequency."— Presentation transcript:

1 Nuclear Magnetic Resonance A.) Introduction : Nuclear Magnetic Resonance (NMR) measures the absorption of electromagnetic radiation in the radio-frequency region (~4-900 MHz) - nuclei (instead of outer electrons) are involved in absorption process - sample needs to be placed in magnetic field to cause different energy states NMR was first experimentally observed by Bloch and Purcell in 1946 (received Nobel Prize in 1952) and quickly became commercially available and widely used. Probe the Composition, Structure, Dynamics and Function of the Complete Range of Chemical Entities: from small organic molecules to large molecular weight polymers and proteins. NMR is routinely and widely used as the preferred technique to rapidly elucidate the chemical structure of most organic compounds. One of the MOST Routinely used Analytical Techniques

2 Some Suggested NMR References “Spin Dynamics – Basics of Nuclear Magnetic Resonance” M. H. Levitt “Tables of Spectral Data for Structure Determination of Organic Compounds” Pretsch, Clerc, Seibl and Simon “Spectrometric Identification of Organic Compounds” Silverstein, Bassler and Morrill “Organic Structure Determination Using 2-D NMR Spectroscopy: A Problem-Based Approach” Jeffrey H. Simpson “Essential Practical NMR for Organic Chemistry” Stephen A. Richards & John C. Hollerton “Basic One- and Two-Dimensional NMR Spectroscopy” Horst Friebolin “Modern NMR Techniques for Chemistry Research” Andrew E. Derome “Nuclear Magnetic Resonance Spectroscopy” R. K Harris “Experimental Pulse NMR. A Nuts and Bolts Approach” Eiichi Fukushima & Steve B.W. Roeder “Two-Dimensional Nuclear Magnetic Resonance in Liquids”, Ad Bax

3 The Basics of NMR by J.P. Hornak Hypertext based NMR course The Basics of NMR by J.P. Hornak Hypertext based NMR course Spectral DataBase for Organic Compounds (SDBS) Educational NMR Software All kinds of NMR software NMR Knowledge Base A lot of useful NMR links NMR Information ServerNews, Links, Conferences, Jobs Technical Tidbits Useful source for the art of shimming NMR WikiSharing NMR know-how Some NMR Web Sites

4 Some More NMR Web Sites Structure Determination Using NMR by H. J. Reich Web based NMR course Structure Determination Using NMR by H. J. Reich Web based NMR course eNMRNMR Periodic Table Web SpectraExample NMR Structure Problems Organic Structure ElucidationAnother Work Book of Unknowns NMRShiftDB2Predict NMR Chemical Shifts ChemDoodle Simulate NMR and MS Spectra NESG Wiki Another NMR Wiki Page, Emphasis in Protein NMR

5 1937 Rabi predicts and observes nuclear magnetic resonance 1946 Bloch, Purcell first nuclear magnetic resonance of bulk sample 1953 Overhauser NOE (nuclear Overhauser effect) 1966 Ernst, Anderson Fourier transform NMR 1975 Jeener, Ernst 2D NMR 1985 Wüthrich first solution structure of a small protein (BPTI) from NOE derived distance restraints 1987 3D NMR + 13C, 15N isotope labeling of recombinant proteins (resolution) 1990 pulsed field gradients (artifact suppression) 1996/7 new long range structural parameters: - residual dipolar couplings from partial alignment in liquid crystalline media - projection angle restraints from cross-correlated relaxation TROSY (molecular weight > 100 kDa) Nobel prizes 1944 Physics Rabi (Columbia) 1952 Physics Bloch (Stanford), Purcell (Harvard) 1991 Chemistry Ernst (ETH) 2002 Chemistry Wüthrich (ETH) 2003 Medicine Lauterbur (University of Illinois in Urbana ), Mansfield (University of Nottingham) NMR History

6 First NMR Spectra on Water Bloch, F.; Hansen, W. W.; Packard, M. The nuclear induction experiment. Physical Review (1946), 70 474-85. 1 H NMR spectra of water

7 NMR History First Observation of the Chemical Shift 1 H NMR spectra ethanol Modern ethanol spectra Arnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., 1951. 19: p. 507.

8 Typical Applications of NMR: 1.) Structural (chemical) elucidation > Natural product chemistry > Synthetic organic chemistry - analytical tool of choice of synthetic chemists - used in conjunction with MS and IR 2.) Study of dynamic processes > reaction kinetics > study of equilibrium (chemical or structural) 3.) Structural (three-dimensional) studies > Proteins, Protein-ligand complexes > DNA, RNA, Protein/DNA complexes > Polysaccharides 4.) Drug Design > Structure Activity Relationships by NMR 5) Medicine -MRI MRI images of the Human Brain NMR Structure of MMP-13 complexed to a ligand Taxol (natural product)

9 2-phenyl-1,3-dioxep-5-ene 13 C NMR spectra 1 H NMR spectra Each NMR Observable Nuclei Yields a Peak in the Spectra “fingerprint” of the structure

10 Protein Structures from NMR 2D NOESY Spectra at 900 MHz Lysozyme Ribbon Diagram

11 Information in a NMR Spectra Observable Name QuantitativeInformation Peak position Chemical shifts (  )  (ppm) =  obs –  ref /  ref (Hz) chemical (electronic) environment of nucleus Peak Splitting Coupling Constant (J) Hz peak separation neighboring nuclei (intensity ratios) (torsion angles) Peak Intensity Integral unitless (ratio) nuclear count (ratio) relative height of integral curveT 1 dependent Peak Shape Line width  = 1/  T 2 molecular motion peak half-height chemical exchange uncertainty principal uncertainty in energy

12 A Basic Concept in ElectroMagnetic Theory A Direct Application to NMR A perpendicular external magnetic field will induce an electric current in a closed loop An electric current in a closed loop will create a perpendicular magnetic field

13 Theory of NMR Quantum Description Nuclear Spin (think electron spin) a) a)Nucleus rotates about its axis (spin) a) a)Nuclei with spin have angular momentum (p) 1) quantized, spin quantum number I 2) 2 I + 1 states: I, I-1, I-2, …, -I 3) identical energies in absence of external magnetic field c) NMR “active” Nuclear Spin (I) = ½: 1 H, 13 C, 15 N, 19 F, 31 P  Odd atomic mass I = +½ & -½ NMR “inactive” Nuclear Spin (I) = 0: 12 C, 16 O  Even atomic mass & number Quadrupole Nuclei Nuclear Spin (I) > ½: 14 N, 2 H, 10 B  Even atomic mass & odd number I = +1, 0 & -1 l

14 Magnetic Moment (  ) a) a)spinning charged nucleus creates a magnetic field b) b)magnetic moment (  ) is created along axis of the nuclear spin  =  p where: p – angular momentum  – gyromagnetic ratio (different value for each type of nucleus) c) c)magnetic moment is quantized (m) m = I, I-1, I-2, …, -I for common nuclei of interest: m = +½ & -½ Similar to magnetic field created by electric current flowing in a coil Magnetic moment

15 BoBo =  h / 4  Magnetic alignment In the absence of external field, each nuclei is energetically degenerate Add a strong external field (B o ). and the nuclear magnetic moment: aligns with (low energy) against (high-energy)

16 Energy Levels in a Magnetic Field a) a)Zeeman Effect -Magnetic moments are oriented in one of two directions in magnetic field b) b)Difference in energy between the two states is given by:  E =  h B o / 2  where: B o – external magnetic field  units:Tesla (Kg s -2 A -1 ) h – Planck’s constant  6.6260 x 10 -34 Js  – gyromagnetic ratio  unique value per nucleus 1 H: 26.7519 x 10 7 rad T -1 s - c) c)Frequency of absorption: =  B o / 2  (observed NMR frequency) d) d)From Boltzmann equation:N j /N o = exp(-  hB o /2  kT)

17 Frequency of absorption: =  B o / 2  Energy Levels in a Magnetic Field Transition from the low energy to high energy spin state occurs through an absorption of a photon of radio-frequency (RF) energy RF

18 NMR Theory: Classical Description Spinning particle precesses around an applied magnetic field a) a)Angular velocity of this motion is given by:  o =  B o where the frequency of precession or Larmor frequency is: =  B o /2  Same as quantum mechanical description

19 Net Magnetization in a Magnetic Field MoMo y x z x y z BoBo BoBo B o > 0  E = h   BoBo Classic View: - Nuclei either align with or against external magnetic field along the z-axis. - Since more nuclei align with field, net magnetization (M o ) exists parallel to external magnetic field Quantum Description: - - Nuclei either populate low energy ( , aligned with field) or high energy ( , aligned against field) - Net population in  energy level. - Absorption of radio- frequency promotes nuclear spins from   .

20 An NMR Experiment MoMo y x z x y z BoBo BoBo We have a net magnetization precessing about B o at a frequency of  o with a net population difference between aligned and unaligned spins. Now What? Perturbed the spin population or perform spin gymnastics Basic principal of NMR experiments

21 The Basic 1D NMR Experiment Experimental details will effect the NMR spectra and the corresponding interpretation

22 B 1 off… (or off-resonance) MoMo z x B1B1 z x M xy yy 11 11 Right-hand rule resonant condition: frequency (  1 ) of B 1 matches Larmor frequency (  o ) energy is absorbed and population of  and  states are perturbed. An NMR Experiment And/Or: And/Or: M o now precesses about B 1 (similar to B o ) for as long as the B 1 field is applied. Again, keep in mind that individual spins flipped up or down (a single quanta), but M o can have a continuous variation.

23 RF pulse B 1 field perpendicular to B 0 M xy MzMz Classical Description Observe NMR Signal   Need to perturb system from equilibrium.   B 1 field (radio frequency pulse) with  B o /2  frequency   Net magnetization (M o ) now precesses about B o and B 1   M X and M Y are non-zero   M x and M Y rotate at Larmor frequency   System absorbs energy with transitions between aligned and unaligned states   Precession about B 1 stops when B 1 is turned off

24 Classic View: - Apply a radio-frequency (RF) pulse a long the y-axis - RF pulse viewed as a second field (B 1 ), that the net magnetization (M o ) will precess about with an angular velocity of  1 - - precession stops when B 1 turned off Quantum Description: - enough RF energy has been absorbed, such that the population in  /  are now equal - No net magnetization along the z-axis B 1 off… (or off-resonance) MoMo z x B1B1 z x M xy yy 11 11  1 =  B 1 90 o pulse B o > 0  E = h   Please Note: A whole variety of pulse widths are possible, not quantized dealing with bulk magnetization Absorption of RF Energy or NMR RF Pulse

25 An NMR Experiment What Happens Next? The B 1 field is turned off and M xy continues to precess about B o at frequency  o. z x M xy Receiver coil (x) y  NMR signal oo FID – Free Induction Decay yyy Mxy is precessing about z-axis in the x-y plane Time (s)

26 The oscillation of M xy generates a fluctuating magnetic field which can be used to generate a current in a receiver coil to detect the NMR signal. An NMR Experiment A magnetic field perpendicular to a circular loop will induce a current in the loop. NMR Probe (antenna)

27 NMR Signal Detection - FID The FID reflects the change in the magnitude of Mxy as the signal is changing relative to the receiver along the y-axis Again, the signal is precessing about B o at its Larmor Frequency (  o ). RF pulse along Y Detect signal along X

28 NMR Signal Detection - Fourier Transform So, the NMR signal is collected in the Time - domain But, we prefer the frequency domain. Fourier Transform is a mathematical procedure that transforms time domain data into frequency domain

29 NMR Signal Detection - Fourier Transform After the NMR Signal is Generated and the B1 Field is Removed, the Net Magnetization Will Relax Back to Equilibrium Aligned Along the Z-axis T 2 relaxation Two types of relaxation processes, one in the x,y plane and one along the z-axis Peak shape also affected by magnetic field homogeneity or shimming

30 NMR Relaxation a) a)No spontaneous reemission of photons to relax down to ground state Probability too low  cube of the frequency b) b)Two types of NMR relaxation processes spin-lattice or longitudinal relaxation (T 1 ) i. transfer of energy to the lattice or solvent material ii. coupling of nuclei magnetic field with magnetic fields created by the ensemble of vibrational and rotational motion of the lattice or solvent. iii. results in a minimal temperature increase in sample M z = M 0 (1-exp(-t/T 1 )) Recycle Delay: General practice is to wait 5xT 1 for the system to have fully relaxed.

31 NMR Relaxation spin-spin or transverse relaxation (T 2 ) i. exchange of energy between excited nucleus and low energy state nucleus ii. randomization of spins or magnetic moment in x,y-plane iii. related to NMR peak line-width M x = M y = M 0 exp(-t/T 2 ) ( derived from Heisenberg uncertainty principal) Please Note: Line shape is also affected by the magnetic fields homogeneity

32 NMR Sensitivity B o = 0 B o > 0  E = h   N  / N  = e  E / kT Boltzmman distribution: The applied magnetic field causes an energy difference between aligned(  ) and unaligned(  ) nuclei The population (N) difference can be determined from The  E for 1 H at 400 MHz (B o = 9.5 T) is 3.8 x 10 -5 Kcal / mol      Very Small ! ~64 excess spins per million in lower state Low energy gap

33 NMR Sensitivity  E  h  B o /  2  NMR signal depends on: 1) 1)Number of Nuclei (N) (limited to field homogeneity and filling factor) 2) 2)Gyromagnetic ratio (in practice  3 ) 3) 3)Inversely to temperature (T) 4) 4)External magnetic field (B o 2/3, in practice, homogeneity) 5) 5)B 1 2 exciting field strength N  / N  = e  E / kT Increase energy gap -> Increase population difference -> Increase NMR signal EE ≡ BoBo ≡   - Intrinsic property of nucleus can not be changed.  4 B o 2 NB 1 g(  )/T signal (s) ~  4 B o 2 NB 1 g(  )/T

34  - Intrinsic property of nucleus can not be changed.    C ) 3 for 13 C is 64x    N ) 3 for 15 N is 1000x 1 H is ~ 64x as sensitive as 13 C and 1000x as sensitive as 15 N ! Consider that the natural abundance of 13 C is 1.1% and 15 N is 0.37% relative sensitivity increases to ~6,400x and ~2.7x10 5 x !! NMR Sensitivity Relative sensitivity of 1 H, 13 C, 15 N and other nuclei NMR spectra depend on  Gyromagnetic ratio (  )  Natural abundance of the isotope 1 H NMR spectra of caffeine 8 scans ~12 secs 13 C NMR spectra of caffeine 8 scans ~12 secs 13 C NMR spectra of caffeine 10,000 scans ~4.2 hours

35 NMR Sensitivity Increase in Magnet Strength is a Major Means to Increase Sensitivity

36 NMR Sensitivity But at a significant cost! ~$800,000 ~$2,000,000~$4,500,000

37 Chemical Shift Up to this point, we have been treating nuclei in general terms. Simply comparing 1 H, 13 C, 15 N etc. If all 1 H resonate at 500MHz at a field strength of 11.7T, NMR would not be very interesting B eff = B o - B loc --- B eff = B o ( 1 -  )  is the magnetic shielding of the nucleus The chemical environment for each nuclei results in a unique local magnetic field (B loc ) for each nuclei:

38 Chemical Shift a) a)Small local magnetic fields (B loc ) are generated by electrons as they circulate nuclei. Current in a circular coil generates a magnetic field b) b)These local magnetic fields can either oppose or augment the external magnetic field Typically oppose external magnetic field Nuclei “see” an effective magnetic field (B eff ) smaller then the external field  – magnetic shielding or screening constant i. depends on electron density ii. depends on the structure of the compound B eff = B o - B loc --- B eff = B o ( 1 -  )

39 Chemical Shift B eff = B o - B loc --- B eff = B o ( 1 -  ) HO-CH 2 -CH 3 de-shielding high shielding Shielding – local field opposes B o =  B o /2   – reason why observe three distinct NMR peaks instead of one based on strength of B 0

40 Effect of Magnetic Anisotropy 1) external field induces a flow (current) of electrons in  system – ring current effect 2) ring current induces a local magnetic field with shielding (decreased chemical shift) and deshielding (increased chemical shifts) Decrease in chemical shifts Increase in chemical shifts Chemical Shift

41 The NMR scale ( , ppm) - ref  = ppm (parts per million) ref Instead use a relative scale, and refer all signals ( ) in the spectrum to the signal of a particular compound ( ref ). B o >> B loc -- MHz compared to Hz Comparing small changes in the context of a large number is cumbersome Tetramethyl silane (TMS) is a common reference chemical H 3 C Si CH 3 CH 3 CH 3 IMPORTANT: absolute frequency is field dependent ( =  B o / 2  )

42 The NMR scale ( , ppm) Chemical shift  is a relative scale so it is independent of B o. Same chemical shift at 100 MHz vs. 900 MHz magnet IMPORTANT: absolute frequency is field dependent ( =  B o / 2  ) At higher magnetic fields an NMR spectra will exhibit the same chemical shifts but with higher resolution because of the higher frequency range.

43 NMR Spectra Terminology Increasing field (B o ) Increasing frequency (  ) Increasing  Increasing energy (E, consistent with UV/IR) 1H1H 13 C 2H2H 600 MHz150 MHz92 MHz TMS CHCl 3 7.27 0 ppm increasing  decreasing  low field high field down field up field high frequency (  ) low frequency de-shielding high shielding Paramagnetic diamagnetic

44 Chemical Shift Trends Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm) For protons, ~ 15 ppm: For carbon, ~ 220 ppm:

45 Chemical Shift Trends 0 TMS ppm 2107515 Aliphatic Alcohols, protons  to ketones Olefins Aromatics Amides Acids Aldehydes ppm 5015010080210 Aliphatic CH 3, CH 2, CH Carbons adjacent to alcohols, ketones Olefins Aromatics, conjugated alkenes C=O of Acids, aldehydes, esters 0 TMS C=O in ketones

46 CHARACTERISTIC PROTON CHEMICAL SHIFTS Type of ProtonStructureChemical Shift, ppm CyclopropaneC3H6C3H6 0.2 PrimaryR-CH 3 0.9 SecondaryR 2 -CH 2 1.3 TertiaryR 3 -C-H1.5 VinylicC=C-H4.6-5.9 Acetylenictriple bond,CC-H2-3 AromaticAr-H6-8.5 BenzylicAr-C-H2.2-3 AllylicC=C-CH 3 1.7 FluoridesH-C-F4-4.5 ChloridesH-C-Cl3-4 BromidesH-C-Br2.5-4 IodidesH-C-I2-4 AlcoholsH-C-OH3.4-4 EthersH-C-OR3.3-4 EstersRCOO-C-H3.7-4.1 EstersH-C-COOR2-2.2 AcidsH-C-COOH2-2.6 Carbonyl CompoundsH-C-C=O2-2.7 AldehydicR-(H-)C=O9-10 HydroxylicR-C-OH1-5.5 PhenolicAr-OH4-12 EnolicC=C-OH15-17 CarboxylicRCOOH10.5-12 AminoRNH 2 1-5 Common Chemical Shift Ranges Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)

47 Predicting Chemical Shift Assignments Numerous Experimental NMR Data has been compiled and general trends identified See: See:  “Tables of Spectral Data for Structure Determination of Organic Compounds” Pretsch, Clerc, Seibl and Simon Organic Compounds” Pretsch, Clerc, Seibl and Simon  “Spectrometric Identification of Organic Compounds” Silverstein, Bassler and Morrill Silverstein, Bassler and Morrill Spectral Databases: Spectral Databases:  Aldrich/ACD Library of FT NMR Spectra  Sadtler/Spectroscopy (UV/Vis, IR, MS, GC and NMR)  Ongoing effort to predict chemical shifts from first principals (quantum mechanical description of factors contributing to chemical shifts) See: Cynthia J. Jameson, “Understanding NMR Chemical Shifts”, Annu. Rev. Phys. Chem. 1996. 47:135–69

48 Predicting Chemical Shift Assignments Empirical Chemical Shift Trends (Databases) Have Been Incorporated Into A Variety of Software Applications Example: ChemDraw Program that allows you to generate a 2D sketch of any compound can also predict 1 H and 13 C chemical shifts   matches sub-fragments of structure to structures in database

49 Predicting Chemical Shift Assignments How Does the Predicted Results Compare to Experimental Data? ParameterExperimental ( ppm)Predicted (ppm) D(A) 6.22 6.44 D(B) 6.536.44 D(C) 5.855.22 Typical accuracy A number of factors can affect prediction:   Similarity of structures in reference database   Solvent   Temperature   structure/conformation   additive nature of parts towards the whole

50 Predicting Chemical Shift Assignments Experimental NMR Data has also been used to Develop Web-Based Tools to Predict NMR Spectra Example: NMR Predictor ( Program that allows you to generate a 2D sketch of any compound Program that allows you to generate a 2D sketch of any compound Predicts 1 H chemical shifts Predicts 1 H chemical shifts

51 Demo of ChemDraw

52 Coupling Constants through-bond interaction that results in the splitting of a single peak into multiple peaks of various intensities 1) 1)The spacing in hertz (hz) between the peaks is a constant i. coupling constant (J) bonding electrons convey spin states of bonded nuclei 1) 1)spin states of nuclei are “coupled” 2) 2)alignment of spin states of bonded nuclei affects energy of the ground (  ) and excited states (  ) of observed nuclei 3) 3)Coupling pattern and intensity follows Pascal’s triangle

53 Coupling Constants Energy level of a nuclei are affected by covalently-bonded neighbors spin-states 13 C 1 H 1 H 1 H one-bond three-bond     I S S S I I J (Hz) Spin-States of covalently-bonded nuclei want to be aligned. The magnitude of the separation is called coupling constant (J) and has units of Hz. +J/4 -J/4 +J/4

54 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 1 7 21 35 35 21 7 1 Coupling Constants

55 singlet doublet triplet quartet pentet 1:1 1:2:1 1:3:3:1 1:4:6:4:1 Common NMR Splitting Patterns Coupling Rules: 1. 1.equivalent nuclei do not interact 2. 2.coupling constants decreases with separation ( typically # 3 bonds) 3. 3.multiplicity given by number of attached equivalent protons (n+1) 4. 4.multiple spin systems  multiplicity  (n a +1)(n b +1) 5. 5.Relative peak heights/area follows Pascal’s triangle 6. 6.Coupling constant are independent of applied field strength IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei. Multiplets consist of 2nI + 1 lines I is the nuclear spin quantum number (usually 1/2) and n is the number of neighboring spins.


57 Karplus Equation – Coupling Constants Relates coupling constant to Torsional angle. Used to solve Structures! J = const. + 10Cos 

58 Example: The proton NMR spectrum is for a compound of empirical formula C 4 H 8 O. Identify the compound Strong singlet at ~2.25 ppm methyl next to carbonyl Absence of peak at ~9.7 ppm eliminates aldehyde group And suggests ketone Quartet at ~2.5 ppm suggests a methylene next to a carbonyl coupled to a methyl Triplet at ~1.2 ppm suggests a methyl group coupled to a methylene group

59 a) a)Interaction between nuclear spins mediated through empty space (#5Å)  like ordinary bar magnets b) b)Important: effect is time-averaged c) c)Gives rise to dipolar relaxation (T 1 and T 2 ) and specially to cross-relaxation Perturb 1 H spin population affects 13 C spin population NOE effect Nuclear Overhauser Effect (NOE)

60 Nuclear Overhauser Effect (NOE,  ) – the change in intensity of an NMR resonance when the transition of another are perturbed, usually by saturation. Saturation – elimination of a population difference between transitions (irradiating one transition with a weak RF field)  i = (I-I o )/I o where I o is thermal equilibrium intensity     N N N+  N-  X X A A irradiate Populations and energy levels of a homonuclear AX system (large chemical shift difference) Observed signals only occur from single-quantum transitions

61 Nuclear Overhauser Effect (NOE)     N+½  I I S S Populations and energy levels immediately following saturation of the S transitions N+½  N-½  Saturated (equal population) Saturated (equal population) saturate     W1AW1A W1AW1A W1XW1X W1XW1X W2W2 W0W0 Observed signals only occur from single-quantum transitions Relaxation back to equilibrium can occur through: Zero-quantum transitions (W 0 ) Single quantum transitions (W 1 ) Double quantum transitions (W 2 ) N-½  N+½  N-½  The observed NOE will depend on the “rate” of these relaxation pathways

62 Nuclear Overhauser Effect (NOE) Mechanism for Relaxation Dipolar coupling between nuclei – – local field at one nucleus is due to the presence of the other – – depends on orientation of the whole molecule Dipolar coupling, T 1 and NOE are related through rotational correlation time (  c ) – – rotational correlation is the time it takes a molecule to rotate one radian (360 o /2  ). Relaxation or energy transfers only occurs if some frequencies of motion match the frequency of the energy of transition – – the available frequencies for a molecule undergoing Brownian tumbling depends on tc NOE is dependent on the distance (1/r 6 ) separating the two dipole coupled nuclei Important: the effect is time-averaged!

63 2D NOESY (Nuclear Overhauser Effect) Relative magnitude of the cross-peak is related to the distance (1/r 6 ) between the protons (≥ 5Ǻ). NOE is a relaxation factor that builds-up during The “mixing-time (tm)

64 2D NOESY Spectra at 900 MHz Lysozyme Ribbon Diagram NMR Structure Determination NOE Data Is the Fundamental Piece of Information to Determine Any Structure (DNA, RNA, Protein, small molecule)

65 NMR Instrumentation (block diagram)

66 sample lift NMR Tube RF coils cryoshims shimcoils Probe Liquid He Liquid N 2 Superconducting Magnet a) a)solenoid wound from superconducting niobium/tin or niobium/titanium wire b) b)kept at liquid helium temperature (4K), outer liquid N 2 dewar near zero resistance  minimal current lose  magnet stays at field for years without external power source Cross-section of magnet Superconducting solenoid Use up to 190 miles of wire! spinner magnet

67 Superconducting Magnet Problems:Problems: −Field drifts (B 0 changes) Field Drift over 11 Hrs (~ 0.15Hz/hr =  B o /2  =  B o /2  Remember:

68 Lock System a) a)Corrects for magnetic field drift c) NMR probes contains an additional transmitter coil tuned to deuterium frequency changes in the intensity of the reference absorption signal controls a feedback circuit; a frequency generator provides a fixed reference frequency for the lock signal if the observed lock signal differs from the reference frequency, a small current change occurs in a room-temperature shim coil (Z0) to create a small magnetic field to augment the main field to place the lock-signal back into resonance Lock Feedback Circuit Lock Changes From Off-resonance to On- resonance

69 Superconducting Magnet Problems:Problems: −Field is not constant over sample (spatial variation) =  B o /2  =  B o /2  Again:

70 Magnetic Field Homogeneity Frequency of absorption: =  B o / 2  Poor Homogeneity  multiple peaks at different effective B o Resonance depends on position in NMR sample Good Homogeneity  single peak with frequency dependent on B o

71 Shim System Corrects for magnetic inhomogeneityCorrects for magnetic inhomogeneity Spatial arrangement of 20 or more coilsSpatial arrangement of 20 or more coils change current in each coil to “patch” differences in field and fix distortions in peak shape Sketch of shim coils actual shim coils

72 Shim Coils Optimize shims by i) minimizing line-width, ii) maximizing lock signal or iii) maximizing FIDOptimize shims by i) minimizing line-width, ii) maximizing lock signal or iii) maximizing FID Examples of poor line-shapes due to shimming errors Examples of poor line-shapes due to shimming errors

73 Tune and Match System a) a)Tune- corrects the differences between observed and desired frequency c) c)Match – correct impedance difference between resonant circuit and transmission line (should be 50  ) d) d)Power submitted to transmitter and receiver is maximized Adjust two capacitors until the tuning and desired frequency match and you obtain a null Affects: signal-to-noise accuracy of 90 o pulse sample heating chemical shift accuracy

74 Receiver Gain a) a)Amplifies the radio frequency FID signal from the probe b) b)Set to maximize signal-to-noise c) c)Signal is dependent on sample concentration The Analog to Digital Converter (ADC) has a maximum range of integers Clipped Fid Dynamic Range Problem Clipped FID

75 Continuous Wave (CW) vs. Pulse/Fourier Transform NMR Sensitivity Issue A frequency sweep (CW) to identify resonance is very slow (1-10 min.) Step through each individual frequency. Pulsed/FT collect all frequencies at once in time domain, fast (N x 1-10 sec)

76 A radiofrequency pulse is a combination of a wave (cosine) of frequency w o and a step function NMR Pulse a) In FT-NMR, how are all the individual nuclei excited simultaneously? b) RF pulses are typically short-duration (  secs) - produces bandwidth (1/4  ) centered around single frequency - shorter pulse width  broader frequency bandwidth  1 H 6  s 90 o pulse  ±41666 Hz  ±69.4 ppm at 600 MHz Heisenberg Uncertainty Principal:  t  FT *= tptp Pulse length (time, t p ) The Fourier transform indicates the pulse covers a range of frequencies

77 NMR Pulse z x M xy y z x y MoMo B1B1 tt tptp  t =  * t p * B 1 NMR pulse length or Tip angle (t p ) The length of time the B 1 field is on => torque on bulk magnetization (B 1 ) A measured quantity – instrument and sample dependent.

78 NMR Pulse z x M xy y z x y MoMo  / 2 Some useful common pulses 90 o Maximizes signal in x,y-plane where NMR signal detected z x -M o y z x y MoMo  180 o 90 o pulse 180 o pulse Inverts the spin-population. No NMR signal detected Can generate just about any pulse width desired.

79 NMR Data Detection and Processing Fourier Transform NMR Increase signal-to-noise (S/N) by collecting multiple copies of FID and averaging signal. But, total experiment time is proportional to the number of scans exp. time ~ (number of scans) x (recycle delay)

80 Correct Spectra Spectra with carrier offset resulting in peak folding or aliasing Sweep Width (range of radio-frequencies monitored for nuclei absorptions) Proper Spectral Width Needs to be large enough to capture all the NMR resonances

81 Quadrature detection a) Frequency of B1 (carrier) is set to the center of the spectra. - Small pulse length to excite the entire spectrum - Minimizes folded noise b) How to differentiate between peaks upfield and downfield from carrier? - observed peak frequencies are all relative to the carrier frequency c) If carrier at edge of spectra, peaks are all positive or negative relative to carrier - Excite twice as much noise, decrease S/N How to differentiate between magnetization that precesses clockwise and counter clockwise?

82 carrier same frequency relative to the carrier, but opposite sign. Quadrature detection

83  (B 1 ) B F B F PH = 0 PH = 90 PH = 0 PH = 90 F F S S Use two detectors 90 o out of phase. Phase of Peaks are different. Quadrature detection

84 Digital Resolution – number of data points Want to maximize digital resolution, more data points increases acquisition time (AQ) and experimental time (ET): AQ = DT x NPET = AQ x NS larger spectral width (SW) requires more data points for the same resolution The FID is digitized Equal delay between points (dwell time) DT = 1 / (2 * SW)

85 Digital Resolution – number of data points Want to maximize digital resolution:

86 Proper Acquisition Time Needs to be long enough to allow FID to Completely Decay Sinc Wiggles Truncated FID

87 4K data16K zero-fill 4K FID20K FID No zero-filling 16K zero-filling Zero Filling Improve digital resolution by adding zero data points at end of FID

88 Window Functions Emphasize the signal or decrease the noise by applying a mathematical function to the FID. Good stuffMostly noise F(t) = 1 * e - ( LB * t ) – line broadening Effectively adds LB in Hz to peak Line-widths Sensitivity Resolution

89 FT LB = -1.0 HzLB = 5.0 Hz Can either increase S/N or Resolution Not Both! Increase SensitivityIncrease Resolution

90 Baseline Correction Need a flat baseline – prefer to fix experimentally Xi & Roche BMC Bioinformatics (2008) 9:234 Apply any number of mathematical functions: linear Polynomial (upwards of 6-orders) FID reconstruction Penalized parametric smoothing Etc. A number of factors lead to baseline distortions: Intense solvent or buffer peaks Phasing problems Errors in first data points of FID Short recycle tines Short acquisition times Receiver gain

91 Phase Correction Need a flat baseline – phase all peaks to be pure absorptive in shape Xi & Roche BMC Bioinformatics (2008) 9:234 Improper phasing can cause severe distortions in the baseline Phase is due to difference in actual time and the zero-time point of FID (sin + cosines)

92 NMR Peak Integration or Peak Area a) a)The relative peak intensity or peak area is proportional to the number of protons associated with the observed peak. b) b)Means to determine relative concentrations of multiple species present in an NMR sample. HO-CH 2 -CH 3 1 2 3 Relative peak areas = Number of protons Integral trace

93 i. i.NMR time scale refers to the chemical shift time scale a) remember – frequency units are in Hz (sec -1 )  time scale b) exchange rate (k) c) differences in chemical shifts between species in exchange indicate the exchange rate. d) For systems in fast exchange, the observed chemical shift is the average of the individual species chemical shifts. Time Scale Chem. Shift (  Coupling Const. (J) T 2 relaxation Slow k <<  A -  B k << J A - J B k << 1/ T 2,A- 1/ T 2,B Intermediate k =  A -  B k = J A - J B k = 1/ T 2,A- 1/ T 2,B Fast k >>  A -  B k >> J A - J B k >> 1/ T 2,A - 1/ T 2,B Range (Sec- 1 ) 0 – 1000 0 –12 1 - 20  obs = f 1  1 + f 2  2 f 1 + f 2 =1 where: f 1, f 2 – mole fraction of each species  1,  2 – chemical shift of each species Exchange Rates and NMR Time Scale

94 ii.Effects of Exchange Rates on NMR data k =  (h e -h o ) k =  (  o 2 -  e 2 ) 1/2 /2 1/2 k =   o / 2 1/2 k =  o 2 /2(h e - h o ) k – exchange rate h – peak-width at half-height – peak frequency e – with exchange o – no exchange

95 coalescence NMR Dynamics and Exchange k = 0.1 s -1 k = 5 s -1 k = 200 s -1 k = 88.8 s -1 k = 40 s -1 k = 20 s -1 k = 10 s -1 k = 400 s -1 k = 800 s -1 k = 10,000 s -1 40 Hz Increasing Exchange Rate slow fast No exchange: With exchange: Equal Population of Exchange Sites

96 Multidimensional NMR NMR pulse sequences a) composed of a series of RF pulses, delays, gradient pulses and phases b) in a 1D NMR experiment, the FID acquisition time is the time domain (t 1 ) c) more complex NMR experiments will use multiple “time-dimensional” to obtain data and simplify the analysis. d) Multidimensional NMR experiments may also use multiple nuclei ( 2 D, 13 C, 15 N) in addition to 1H, but usually detect 1 H) 1D NMR Pulse Sequence

97 Creating Multiple Dimensions in NMR a) collect a series of FIDS incremented by a second time domain (t 1 ) b) the normal acquisition time is t 2. c) Fourier transformation occurs for both t1 and t2, creating a two- dimensional (2D) NMR spectra Relative appearance of each NMR spectra will be modulated by the t 1 delay

98 Collections of FIDs with t 1 modulations Fourier Transform t 2 obtain series of NMR spectra modulated by t 1 Looking down t 1 axis, each point has characteristics of time domain FID Fourier Transform t 1 obtain 2D NMR spectra Peaks along diagonal are normal 1D NMR spectra Cross-peaks correlate two diagonal peaks by J-coupling or NOE interactions Contour map (slice at certain threshold) of 3D representation of 2D NMR spectra. (peak intensity is third dimension Creating Multiple Dimensions in NMR In 2D NMR spectra, diagonal peaks are normal 1D peaks, off-diagonal or cross- peaks indicate a correlation between the two diagonal peaks

99 2D 1 H- 13 C HSQC Experiment Correlates all directly bonded 13 C- 1 H pairs generally requires 13 C-labeling (1.1% natural abundance)

100 2D 1 H- 1 H TOCSY Experiment Correlates all 3-bonded 1 H- 1 H pairs in a molecules

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