Presentation on theme: "Nuclear Magnetic Resonance"— 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 statesNMR 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 Some NMR Web SitesThe Basics of NMR by J.P. Hornak Hypertext based NMR courseSpectral DataBase for Organic Compounds (SDBS)Educational NMR Software All kinds of NMR softwareNMR Knowledge Base A lot of useful NMR linksNMR Information Server News, Links, Conferences, JobsTechnical Tidbits Useful source for the art of shimmingNMR Wiki Sharing NMR know-how
4 Some More NMR Web SitesStructure Determination Using NMR by H. J. Reich Web based NMR courseeNMR NMR Periodic TableWeb Spectra Example NMR Structure ProblemsOrganic Structure Elucidation Another Work Book of UnknownsNMRShiftDB2 Predict NMR Chemical ShiftsChemDoodle Simulate NMR and MS SpectraNESG Wiki Another NMR Wiki Page, Emphasis in Protein NMR
5 NMR HistoryRabi predicts and observes nuclear magnetic resonance Bloch, Purcell first nuclear magnetic resonance of bulk sample1953 Overhauser NOE (nuclear Overhauser effect)1966 Ernst, Anderson Fourier transform NMR1975 Jeener, Ernst 2D NMR1985 Wüthrich first solution structure of a small protein (BPTI)from NOE derived distance restraintsD 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 relaxationTROSY (molecular weight > 100 kDa)Nobel prizes1944 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)
6 NMR History 1H NMR spectra of water First NMR Spectra on Water Bloch, F.; Hansen, W. W.; Packard, M. The nuclear induction experiment. Physical Review (1946),
7 NMR History 1H NMR spectra ethanol Modern ethanol spectra First Observation of the Chemical Shift1H NMR spectra ethanolModern ethanol spectraArnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., : 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 IR2.) 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> Polysaccharides4.) Drug Design> Structure Activity Relationships by NMR5) Medicine -MRITaxol (natural product)NMR Structure of MMP-13 complexed to a ligandMRI images of the Human Brain
9 Each NMR Observable Nuclei Yields a Peak in the Spectra “fingerprint” of the structure2-phenyl-1,3-dioxep-5-ene1H NMR spectra13C NMR spectra
10 Protein Structures from NMR 2D NOESY Spectra at 900 MHzLysozyme Ribbon Diagram
11 Information in a NMR Spectra Observable Name Quantitative InformationPeak position Chemical shifts (d) d(ppm) = uobs –uref/uref (Hz) chemical (electronic)environment of nucleusPeak 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 curve T1 dependentPeak Shape Line width Du = 1/pT molecular motionpeak half-height chemical exchangeuncertainty principaluncertainty in energy
12 A Direct Application to NMR A Basic Concept in ElectroMagnetic TheoryA Direct Application to NMRA perpendicular external magnetic field will induce an electric current in a closed loopAn electric current in a closed loop will create a perpendicular magnetic field
13 Theory of NMR l Quantum Description Nuclear Spin (think electron spin)Nucleus rotates about its axis (spin)Nuclei with spin have angular momentum (p)1) quantized, spin quantum number I2) 2I + 1 states: I, I-1, I-2, …, -I3) identical energies in absence of external magnetic fieldc) NMR “active” Nuclear Spin (I) = ½:1H, 13C, 15N, 19F, 31P Odd atomic massI = +½ & -½NMR “inactive” Nuclear Spin (I) = 0:12C, 16O Even atomic mass & numberQuadrupole Nuclei Nuclear Spin (I) > ½:14N, 2H, 10B Even atomic mass & odd numberI = +1, 0 & -1l
14 where: Magnetic Moment (m) spinning charged nucleus creates a magnetic fieldmagnetic moment (m) is created along axis of the nuclear spinm = gpwhere:p – angular momentumg – gyromagnetic ratio (different value for each type of nucleus)magnetic moment is quantized (m)m = I, I-1, I-2, …, -Ifor common nuclei of interest:m = +½ & -½Magnetic momentSimilar to magnetic field created by electric current flowing in a coil
15 Magnetic alignment = g h / 4p Bo Add a strong external field (Bo). and the nuclear magnetic moment:aligns with (low energy)against (high-energy)In the absence of external field,each nuclei is energetically degenerate
16 Energy Levels in a Magnetic Field Zeeman Effect -Magnetic moments are oriented in one of two directions in magnetic fieldDifference in energy between the two states is given by:DE = g h Bo / 2pwhere:Bo – external magnetic field units:Tesla (Kg s-2 A-1)h – Planck’s constant x Jsg – gyromagnetic ratio unique value per nucleus1H: x 107 rad T-1 s-Frequency of absorption: n = g Bo / 2p (observed NMR frequency)From Boltzmann equation: Nj/No = exp(-ghBo/2pkT)
17 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) energyRFFrequency of absorption: n = g Bo / 2p
18 NMR Theory: Classical Description Spinning particle precesses around an applied magnetic fieldAngular velocity of this motion is given by:wo = gBowhere the frequency of precession or Larmor frequency is:n = gBo/2pSame as quantum mechanical description
19 Net Magnetization in a Magnetic Field MoyxzBoClassic View:- Nuclei either align with oragainst external magneticfield along the z-axis.- Since more nuclei align withfield, net magnetization (Mo)exists parallel to externalmagnetic fieldQuantum Description:Nuclei either populate lowenergy (a, aligned with field)or high energy (b, alignedagainst field)- Net population in a energylevel.- Absorption of radio-frequency promotes nuclearspins from a b.Bo > 0DE = h nabBo
20 An NMR ExperimentWe have a net magnetization precessing about Bo at a frequency of wo with a net population difference between aligned and unaligned spins.zzMoxxyyBoBoNow What?Perturbed the spin population or perform spin gymnasticsBasic principal of NMR experiments
21 The Basic 1D NMR Experiment Experimental details will effect the NMR spectra and the corresponding interpretation
22 An NMR Experimentresonant condition: frequency (w1) of B1 matches Larmor frequency (wo)energy is absorbed and population of a and b states are perturbed.zzMoB1 off…(or off-resonance)xxB1Mxyw1yyw1And/Or: Mo now precesses about B1 (similar to Bo) for as long as the B1 field is applied.Again, keep in mind that individual spins flipped up or down(a single quanta), but Mo can have a continuous variation.Right-hand rule
23 Classical Description Observe NMR SignalNeed to perturb system from equilibrium.B1 field (radio frequency pulse) with gBo/2p frequencyNet magnetization (Mo) now precesses about Bo and B1MX and MY are non-zeroMx and MY rotate at Larmor frequencySystem absorbs energy with transitions between aligned and unaligned statesPrecession about B1stops when B1 is turned offMzRF pulseB1 field perpendicular to B0Mxy
24 Absorption of RF Energy or NMR RF Pulse B1 off…(or off-resonance)MozxB1Mxyyw1Classic View:- Apply a radio-frequency (RF)pulse a long the y-axis- RF pulse viewed as a secondfield (B1), that the netmagnetization (Mo) willprecess about with anangular velocity of w1-- precession stops when B1turned offQuantum Description:- enough RF energy has beenabsorbed, such that thepopulation in a/b are nowequal- No net magnetization alongthe z-axis90o pulsew1 = gB1DE = h nabBo > 0Please Note: A whole variety of pulse widths are possible, not quantized dealing with bulk magnetization
25 An NMR Experiment NMR signal What Happens Next? The B1 field is turned off and Mxy continues to precess about Bo at frequency wo.zxwoMxyyReceiver coil (x) NMR signalFID – Free Induction DecayMxy is precessing about z-axis in the x-y planeTime (s)yyy
26 An NMR ExperimentThe oscillation of Mxy generates a fluctuating magnetic field which can be used to generate a current in a receiver coil to detect the NMR signal.NMR Probe (antenna)A magnetic field perpendicular to a circular loop will induce a current in the loop.
27 NMR Signal Detection - FID The FID reflects the change in the magnitude of Mxy asthe signal is changing relative to the receiver along the y-axisDetect signal along XRF pulse along YAgain, the signal is precessing about Bo at its Larmor Frequency (wo).
28 NMR Signal Detection - Fourier Transform So, the NMR signal is collected in the Time - domainBut, we prefer the frequency domain.Fourier Transform is a mathematical procedure thattransforms 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-axisT2 relaxationTwo types of relaxation processes, one in the x,y plane and one along the z-axisPeak shape also affected by magnetic field homogeneity or shimming
30 NMR Relaxation Mz = M0(1-exp(-t/T1)) No spontaneous reemission of photons to relax down to ground stateProbability too low cube of the frequencyTwo types of NMR relaxation processesspin-lattice or longitudinal relaxation (T1)i. transfer of energy to the lattice or solvent materialii. coupling of nuclei magnetic field with magnetic fields createdby the ensemble of vibrational and rotational motion of thelattice or solvent.iii. results in a minimal temperature increase in sampleMz = M0(1-exp(-t/T1))Recycle Delay: General practice is to wait 5xT1 for the system to have fully relaxed.
31 NMR Relaxation Mx = My = M0 exp(-t/T2) spin-spin or transverse relaxation (T2)i. exchange of energy between excited nucleus and low energystate nucleusii. randomization of spins or magnetic moment in x,y-planeiii. related to NMR peak line-widthMx = My = M0 exp(-t/T2)(derived from Heisenberg uncertainty principal)Please Note: Line shape is also affected by the magnetic fields homogeneity
32 NMR Sensitivity The applied magnetic field causes an energy difference between aligned(a) and unaligned(b) nucleibLow energy gapBo > 0DE = h naBo = 0The population (N) difference can be determined fromBoltzmman distribution:Na / Nb = e DE / kTThe DE for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / molVery Small !~64 excess spins per million in lower stateNa / Nb =
33 NMR Sensitivity DE ≡ Bo ≡ g g NMR signal depends on: Number of Nuclei (N) (limited to field homogeneity and filling factor)Gyromagnetic ratio (in practice g3)Inversely to temperature (T)External magnetic field (Bo2/3, in practice, homogeneity)B12 exciting field strengthsignal (s) ~ g4Bo2NB1g(u)/TNa / Nb = e DE / kTDE = g h Bo / 2pIncrease energy gap -> Increase population difference -> Increase NMR signalDE≡Bo≡gg- Intrinsic property of nucleus can not be changed.
34 NMR Sensitivity g (gH/gC)3 for 13C is 64x (gH/gN)3 for 15N is 1000x Relative sensitivity of 1H, 13C, 15N and other nuclei NMR spectra depend onGyromagnetic ratio (g)Natural abundance of the isotopeg- Intrinsic property of nucleus can not be changed.(gH/gC)3 for 13C is 64x(gH/gN)3 for 15N is 1000x1H is ~ 64x as sensitive as 13C and 1000x as sensitive as 15N !Consider that the natural abundance of 13C is 1.1% and 15N is 0.37%relative sensitivity increases to ~6,400x and ~2.7x105x !!1H NMR spectra of caffeine8 scans ~12 secs13C NMR spectra of caffeine8 scans ~12 secs13C NMR spectra of caffeine10,000 scans ~4.2 hours
35 NMR SensitivityIncrease in Magnet Strength is a Major Means to Increase Sensitivity
36 But at a significant cost! NMR SensitivityBut at a significant cost!~$800,000~$2,000,000~$4,500,000
37 Chemical ShiftUp to this point, we have been treating nuclei in general terms.Simply comparing 1H, 13C, 15N etc.If all 1H resonate at 500MHz at a field strength of 11.7T,NMR would not be very interestingThe chemical environment for each nuclei results in a unique local magnetic field (Bloc) for each nuclei:Beff = Bo - Bloc Beff = Bo( 1 - s )s is the magnetic shielding of the nucleus
38 Chemical Shift Beff = Bo - Bloc --- Beff = Bo( 1 - s ) Small local magnetic fields (Bloc) are generated by electrons as they circulate nuclei.Current in a circular coil generates a magnetic fieldThese local magnetic fields can either oppose or augment the external magnetic fieldTypically oppose external magnetic fieldNuclei “see” an effective magnetic field (Beff) smaller then the external fields – magnetic shielding or screening constanti. depends on electron densityii. depends on the structure of the compoundBeff = Bo - Bloc Beff = Bo( 1 - s )
39 Chemical Shift Beff = Bo - Bloc --- Beff = Bo( 1 - s ) HO-CH2-CH3 s – reason why observe three distinct NMR peaks instead of one based on strength of B0n = gBo/2pde-shielding high shieldingShielding – local field opposes Bo
40 Chemical Shift Effect of Magnetic Anisotropy 1) external field induces a flow (current) of electrons in p system – ring current effect2) ring current induces a local magnetic field with shielding (decreased chemical shift) and deshielding (increased chemical shifts)Decrease in chemical shiftsIncrease in chemical shifts
41 The NMR scale (d, ppm) n - nref Bo >> Bloc -- MHz compared to Hz Comparing small changes in the context of a large number is cumbersomen - nrefd = ppm (parts per million)nrefInstead use a relative scale, and refer all signals (n) in the spectrum to the signal of a particular compound (nref).IMPORTANT: absolute frequency is field dependent (n = g Bo / 2p)CH3Tetramethyl silane (TMS) is a common reference chemicalH3CSiCH3CH3
42 The NMR scale (d, ppm)Chemical shift (d) is a relative scale so it is independent of Bo. Same chemical shift at 100 MHz vs. 900 MHz magnetIMPORTANT: absolute frequency is field dependent (n = g Bo / 2p)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 TMSCHCl3ppmincreasing d decreasing dlow field high fielddown field up fieldhigh frequency (u) low frequencyde-shielding high shieldingParamagnetic diamagnetic600 MHz150 MHz92 MHz1H13C2HIncreasing field (Bo)Increasing frequency (u)Increasing gIncreasing energy (E, consistent with UV/IR)
44 Chemical Shift Trends For protons, ~ 15 ppm: For carbon, ~ 220 ppm: Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)
45 Chemical Shift Trends Alcohols, protons a to ketones Aromatics Amides AcidsAldehydesOlefinsAliphaticppm1510752TMSAromatics,conjugated alkenesC=O inketonesAliphatic CH3,CH2, CHOlefinsppm2101501008050TMSC=O of Acids,aldehydes, estersCarbons adjacent toalcohols, ketones
46 CHARACTERISTIC PROTON CHEMICAL SHIFTS Type of ProtonStructureChemical Shift, ppmCyclopropaneC3H60.2PrimaryR-CH30.9SecondaryR2-CH21.3TertiaryR3-C-H1.5VinylicC=C-HAcetylenictriple bond,CC-H2-3AromaticAr-H6-8.5BenzylicAr-C-H2.2-3AllylicC=C-CH31.7FluoridesH-C-F4-4.5ChloridesH-C-Cl3-4BromidesH-C-Br2.5-4IodidesH-C-I2-4AlcoholsH-C-OH3.4-4EthersH-C-OR3.3-4EstersRCOO-C-HH-C-COOR2-2.2AcidsH-C-COOH2-2.6Carbonyl CompoundsH-C-C=O2-2.7AldehydicR-(H-)C=O9-10HydroxylicR-C-OH1-5.5PhenolicAr-OH4-12EnolicC=C-OH15-17CarboxylicRCOOHAminoRNH21-5Common Chemical Shift RangesCarbon 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 identifiedSee:“Tables of Spectral Data for Structure Determination ofOrganic Compounds” Pretsch, Clerc, Seibl and Simon“Spectrometric Identification of Organic Compounds”Silverstein, Bassler and MorrillSpectral Databases:Aldrich/ACD Library of FT NMR SpectraSadtler/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 :135–69
48 Predicting Chemical Shift Assignments Empirical Chemical Shift Trends (Databases) Have Been Incorporated Into A Variety of Software ApplicationsExample: ChemDrawProgram that allows you to generate a 2D sketch of any compoundcan also predict 1H and 13C chemical shiftsmatches sub-fragments of structure to structures in database
49 Predicting Chemical Shift Assignments How Does the Predicted Results Compare to Experimental Data?Parameter Experimental ( ppm) Predicted (ppm) D(A)D(B)D(C)Typical accuracyA number of factors can affect prediction:Similarity of structures in reference databaseSolventTemperaturestructure/conformationadditive 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 SpectraExample: nmrdb.org NMR Predictor (http://www.nmrdb.org/new_predictor)Program that allows you to generate a 2D sketch of any compoundPredicts 1H chemical shifts
52 Coupling Constantsthrough-bond interaction that results in the splitting of a single peak into multiple peaks of various intensitiesThe spacing in hertz (hz) between the peaks is a constanti. coupling constant (J)bonding electrons convey spin states of bonded nucleispin states of nuclei are “coupled”alignment of spin states of bonded nuclei affects energy of the ground (a) and excited states (b) of observed nucleiCoupling pattern and intensity follows Pascal’s triangle
53 Coupling Constants bb I S ab ba S I I S aa Energy level of a nuclei are affected by covalently-bonded neighbors spin-states1H1H1Hthree-bond13Cone-bondSpin-States of covalently-bonded nuclei want to be aligned.+J/4J (Hz)bbISabba-J/4SII S+J/4aaThe magnitude of the separation is called coupling constant (J) and has units of Hz.
55 singlet doublet triplet quartet pentet 1:1 1:2:1 1:3:3:1 1:4:6:4:1 Common NMR Splitting Patternssinglet doublet triplet quartet pentet1: :2: :3:3: :4:6:4:1Multiplets consist of 2nI + 1 linesI is the nuclear spin quantum number (usually 1/2) andn is the number of neighboring spins.Coupling Rules:equivalent nuclei do not interactcoupling constants decreases with separation ( typically # 3 bonds)multiplicity given by number of attached equivalent protons (n+1)multiple spin systems multiplicity (na+1)(nb+1)Relative peak heights/area follows Pascal’s triangleCoupling constant are independent of applied field strengthIMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.
58 Example: The proton NMR spectrum is for a compound of empirical formula C4H8O. Identify the compound Strong singlet at ~2.25 ppmmethyl next to carbonylAbsence of peak at ~9.7 ppmeliminates aldehyde groupAnd suggests ketoneTriplet at ~1.2 ppm suggests a methyl group coupled to a methylene groupQuartet at ~2.5 ppm suggests a methylene next to a carbonyl coupled to a methyl
59 Nuclear Overhauser Effect (NOE) Interaction between nuclear spins mediated through empty space (#5Å) like ordinary bar magnetsImportant: effect is time-averagedGives rise to dipolar relaxation (T1 and T2) and specially to cross-relaxationPerturb 1H spin populationaffects 13C spin populationNOE effect
60 Nuclear Overhauser Effect (NOE) Nuclear Overhauser Effect (NOE, h) – 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)hi = (I-Io)/Iowhere Io is thermal equilibrium intensityirradiateN-dbbAXNabNbaXN+daaAObserved signals only occur from single-quantum transitionsPopulations and energy levels of a homonuclear AX system (large chemical shift difference)
61 Nuclear Overhauser Effect (NOE) Saturated(equal population)N-½dsaturatebbSIN-½dN+½dabbaIN+½daaSSaturated(equal population)Observed signals only occur from single-quantum transitionsPopulations and energy levels immediately following saturation of the S transitionsN-½dbbW1AW1XRelaxation back to equilibrium can occur through:Zero-quantum transitions (W0)Single quantum transitions (W1)Double quantum transitions (W2)W2N-½dN+½dabbaW0W1XW1AaaN+½dThe observed NOE will depend on the “rate” of these relaxation pathways
62 Important: the effect is time-averaged! Nuclear Overhauser Effect (NOE)Mechanism for RelaxationDipolar coupling between nucleilocal field at one nucleus is due to the presence of the otherdepends on orientation of the whole moleculeDipolar coupling, T1 and NOE are related through rotational correlation time (tc)rotational correlation is the time it takes a molecule to rotate one radian (360o/2p).Relaxation or energy transfers only occurs if some frequencies of motion match the frequency of the energy of transitionthe available frequencies for a molecule undergoing Brownian tumbling depends on tcNOE is dependent on the distance (1/r6) separating the two dipole coupled nucleiImportant: the effect is time-averaged!
63 2D NOESY (Nuclear Overhauser Effect) Relative magnitude of the cross-peak is related to the distance (1/r6) between the protons (≥ 5Ǻ).NOE is a relaxation factor that builds-up duringThe “mixing-time (tm)
64 NMR Structure Determination NOE Data Is the Fundamental Piece of Information to Determine Any Structure (DNA, RNA, Protein, small molecule)2D NOESY Spectra at 900 MHzLysozyme Ribbon Diagram
66 Superconducting Magnet solenoid wound from superconducting niobium/tin or niobium/titanium wirekept at liquid helium temperature (4K), outer liquid N2 dewarnear zero resistance minimal current lose magnet stays at field for years without external power sourceCross-section of magnetmagnetspinnersample liftNMR TubeRF coilscryoshimsshimcoilsProbeSuperconducting solenoidUse up to 190 miles of wire!Liquid N2Liquid He
68 Lock System Corrects for magnetic field drift c) NMR probes contains an additional transmitter coil tuned to deuterium frequencychanges in the intensity of the reference absorption signal controls a feedback circuit; a frequency generator provides a fixed reference frequency for the lock signalif 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 resonanceLock Feedback CircuitLock Changes FromOff-resonance to On-resonance
69 Superconducting Magnet Problems:Field is not constant over sample (spatial variation)Again:n = gBo/2p
70 Magnetic Field Homogeneity Frequency of absorption: n = g Bo / 2pPoor Homogeneity multiple peaks at different effective BoResonance depends on position in NMR sampleGood Homogeneity single peak with frequency dependent on Bo
71 Shim System Corrects for magnetic inhomogeneity Spatial arrangement of 20 or more coilschange current in each coil to “patch” differences in field and fix distortions in peak shapeactual shim coilsSketch of shim coils
72 Shim CoilsOptimize shims by i) minimizing line-width, ii) maximizing lock signal or iii) maximizing FIDExamples of poor line-shapes due to shimming errors
73 Tune and Match SystemTune- corrects the differences between observed and desired frequencyMatch – correct impedance difference between resonant circuit and transmission line (should be 50W )Power submitted to transmitter and receiver is maximizedAdjust two capacitors until the tuning and desired frequency match and you obtain a nullAffects:signal-to-noiseaccuracy of 90o pulsesample heatingchemical shift accuracy
74 The Analog to Digital Converter (ADC) has a maximum range of integers Receiver GainAmplifies the radio frequency FID signal from the probeSet to maximize signal-to-noiseSignal is dependent on sample concentrationThe Analog to Digital Converter (ADC) has a maximum range of integersClipped FidClipped FIDDynamic Range Problem
75 Continuous Wave (CW) vs. Pulse/Fourier Transform NMR Sensitivity IssueA 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 * = NMR Pulse tp Pulse length (time, tp) FT a) In FT-NMR, how are all the individual nuclei excited simultaneously?b) RF pulses are typically short-duration (msecs)- produces bandwidth (1/4t) centered around single frequency- shorter pulse width broader frequency bandwidth1H 6 ms 90o pulse ±41666 Hz ±69.4 ppm at 600 MHzHeisenberg Uncertainty Principal: Du.Dt ~ 1/2p*=tpPulse length (time, tp)A radiofrequency pulse is a combination of a wave (cosine) of frequency wo and a step functionFTThe Fourier transform indicates the pulse covers a range of frequencies
77 NMR Pulse tp qt = g * tp * B1 NMR pulse length or Tip angle (tp) qt Mo zzqtMotpxxB1Mxyyyqt = g * tp * B1The length of time the B1 field is on => torque on bulk magnetization (B1)A measured quantity – instrument and sample dependent.
78 NMR Pulse p / 2 p Some useful common pulses 90o pulse Mo zz90o pulseMop / 2Maximizes signal in x,y-planewhere NMR signal detectedxxMxy90oyyzz180o pulseInverts the spin-population.No NMR signal detectedMopxx180o-MoyyCan generate just about any pulse width desired.
79 NMR Data Detection and Processing Fourier Transform NMRIncrease signal-to-noise (S/N) by collecting multiple copies of FID and averaging signal.But, total experiment time is proportional to the number of scansexp. time ~ (number of scans) x (recycle delay)
80 Proper Spectral WidthNeeds to be large enough to capture all the NMR resonancesCorrect SpectraSpectra with carrier offset resulting in peak folding or aliasingSweep Width(range of radio-frequencies monitored for nuclei absorptions)
81 Quadrature detectiona) Frequency of B1 (carrier) is set to the center of the spectra.- Small pulse length to excite the entire spectrum- Minimizes folded noiseb) How to differentiate between peaks upfield and downfield from carrier?- observed peak frequencies are all relative to the carrier frequencyc) If carrier at edge of spectra, peaks are all positive or negative relative to carrier- Excite twice as much noise, decrease S/NHow to differentiate between magnetization that precesses clockwise and counter clockwise?
82 Quadrature detection carrier same frequency relative to the carrier, but opposite sign.
83 Quadrature detection PH = 0 B Use two detectors 90o out of phase. w (B1)BFPH = 0PH = 90SUse two detectors 90o out of phase.Phase of Peaksare different.
84 Equal delay between points Digital Resolution – number of data pointsThe FID is digitizedEqual delay between points(dwell time)DT = 1 / (2 * SW)Want to maximize digital resolution,more data points increases acquisition time (AQ) and experimental time (ET):AQ = DT x NP ET = AQ x NSlarger spectral width (SW) requires more data points for the same resolution
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 DecaySinc WigglesTruncated FID
87 Zero Filling 4K data 16K zero-fill 4K FID 20K FID No zero-filling Improve digital resolution by adding zero data points at end of FID4K data16K zero-fill4K FID20K FIDNo zero-filling16K zero-filling
88 Window Functions Good stuff Mostly noise Resolution Sensitivity Emphasize the signal or decrease the noise by applying a mathematical function to the FID.Good stuffMostly noiseResolutionSensitivityF(t) = 1 * e - ( LB * t ) – line broadeningEffectively adds LB in Hz to peakLine-widths
89 Can either increase S/N or Resolution Not Both! LB = 5.0 HzLB = -1.0 HzIncrease SensitivityIncrease ResolutionFTFT
90 Baseline CorrectionNeed a flat baseline – prefer to fix experimentallyApply any number of mathematical functions:linearPolynomial (upwards of 6-orders)FID reconstructionPenalized parametric smoothingEtc.A number of factors lead to baseline distortions:Intense solvent or buffer peaksPhasing problemsErrors in first data points of FIDShort recycle tinesShort acquisition timesReceiver gainXi & Roche BMC Bioinformatics (2008) 9:234
91 Phase CorrectionNeed a flat baseline – phase all peaks to be pure absorptive in shapePhase is due to difference in actual time and the zero-time point of FID (sin + cosines)Improper phasing can cause severedistortions in the baselineXi & Roche BMC Bioinformatics (2008) 9:234
92 NMR Peak Integration or Peak Area The relative peak intensity or peak area is proportional to the number of protons associated with the observed peak.Means to determine relative concentrations of multiple species present in an NMR sample.Relative peak areas = Number of protons3Integral traceHO-CH2-CH321
93 Exchange Rates and NMR Time Scale NMR time scale refers to the chemical shift time scalea) remember – frequency units are in Hz (sec-1) time scaleb) exchange rate (k)c) differences in chemical shifts between species in exchange indicate theexchange rate.d) For systems in fast exchange, the observed chemical shift is the averageof the individual species chemical shifts.Time Scale Chem. Shift (d) Coupling Const. (J) T2 relaxationSlow k << dA- dB k << JA- JB k << 1/ T2,A- 1/ T2,BIntermediate k = dA - dB k = JA- JB k = 1/ T2,A- 1/ T2,BFast k >> dA - dB k >> JA- JB k >> 1/ T2,A- 1/ T2,BRange (Sec-1) 0 – –dobs = f1d1 + f2d2f1 +f2 =1where:f1, f2 – mole fraction of each speciesd1,d2 – chemical shift of each species
94 k = p Dno2 /2(he - ho) k = p Dno / 21/2 k = p (Dno2 - Dne2)1/2/21/2 ii. Effects of Exchange Rates on NMR datak = p Dno2 /2(he - ho)k = p Dno / 21/2k = p (Dno2 - Dne2)1/2/21/2k = p (he-ho)k – exchange rateh – peak-width at half-height– peak frequencye – with exchangeo – no exchange
96 Multidimensional NMR NMR pulse sequences a) composed of a series of RF pulses, delays, gradient pulses and phasesb) in a 1D NMR experiment, the FID acquisition time is the time domain (t1)c) more complex NMR experiments will use multiple “time-dimensional” toobtain data and simplify the analysis.d) Multidimensional NMR experiments may also use multiple nuclei (2D,13C,15N) in addition to 1H, but usually detect 1H)1D NMR Pulse Sequence
97 Creating Multiple Dimensions in NMR a) collect a series of FIDS incremented by a second time domain (t1)b) the normal acquisition time is t2.c) Fourier transformation occurs for both t1 and t2, creating a two-dimensional (2D) NMR spectraRelative appearance of each NMR spectra will be modulated by the t1 delay
98 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 peaksFourier Transform t2 obtain series of NMR spectra modulated by t1Collections of FIDs with t1 modulationsLooking down t1 axis, each point has characteristics of time domain FIDFourier Transform t1 obtain 2D NMR spectraPeaks along diagonal are normal 1D NMR spectraContour map (slice at certain threshold) of 3D representation of 2D NMR spectra. (peak intensity is third dimensionCross-peaks correlate two diagonal peaks by J-coupling or NOE interactions
99 2D 1H-13C HSQC Experiment Correlates all directly bonded 13C-1H pairs generally requires 13C-labeling (1.1% natural abundance)
100 2D 1H-1H TOCSY ExperimentCorrelates all 3-bonded 1H-1H pairs in a molecules