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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 NMR History 1937 1946 1953 1966 1975 1985 Rabi predicts and observes nuclear magnetic resonance Bloch, Purcell first nuclear magnetic resonance of bulk sample Overhauser NOE (nuclear Overhauser effect) Ernst, Anderson Fourier transform NMR Jeener, Ernst 2D NMR 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 First NMR Spectra on Water 1H NMR spectra of water Bloch, F.; Hansen, W. W.; Packard, M. The nuclear induction experiment. Physical Review (1946), 70 474-85. NMR History First Observation of the Chemical Shift 1H NMR spectra ethanol Modern ethanol spectra Arnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., 1951. 19: p. 507. O 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 O O NH O O OH O OH HO O O O O O Taxol (natural product) NMR Structure of MMP-13 complexed to a ligand Each NMR Observable Nuclei Yields a Peak in the Spectra “fingerprint” of the structure 2-phenyl-1,3-dioxep-5-ene 1H NMR spectra 13C NMR spectra 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 B.) Theory of NMR: 1. Quantum Description i. Nuclear Spin (think electron spin) a) Nucleus rotates about its axis (spin) b) Nuclei with spin have angular momentum (p) 1) quantized, spin quantum number I l 2) 2I + 1 states: I, I-1, I-2, …, -I 3) identical energies in absence of external magnetic field c) NMR “active” Nuclear Spin (I) = ½: 1H, 13C, 15N, 19F, 31P biological and chemical relevance Odd atomic mass I = +½ & -½ NMR “inactive” Nuclear Spin (I) = 0: 12C, 16O Even atomic mass & number Quadrupole Nuclei Nuclear Spin (I) > ½: 14N, 2H, 10B Even atomic mass & odd number I = +1, 0 & -1 Information in a NMR Spectra g-rays x-rays UV VIS 1) Energy E = hu h is Planck constant u is NMR resonance frequency 10-10 Observable Name 10-8 IR m-wave radio 10-6 10-4 10-2 wavelength (cm) Quantitative 100 102 Information d(ppm) = uobs –uref/uref (Hz) chemical (electronic) environment of nucleus peak separation (intensity ratios) neighboring nuclei (torsion angles) Peak position Chemical shifts (d) Peak Splitting Coupling Constant (J) Hz Peak Intensity Integral unitless (ratio) relative height of integral curve nuclear count (ratio) T1 dependent Peak Shape Line width Du = 1/pT2 peak half-height molecular motion chemical exchange uncertainty principal uncertainty in energy ii. Magnetic Moment (m) a) spinning charged nucleus creates a magnetic field Magnetic moment Similar to magnetic field created by electric current flowing in a coil b) magnetic moment (m) is created along axis of the nuclear spin m = gp where: p – angular momentum g – gyromagnetic ratio (different value for each type of nucleus) c) magnetic moment is quantized (m) m = I, I-1, I-2, …, -I for common nuclei of interest: m = +½ & -½ Magnetic alignment = g h / 4p Bo In the absence of external field, each nuclei is energetically degenerate Add a strong external field (Bo). and the nuclear magnetic moment: aligns with (low energy) against (high-energy) iii. Energy Levels in a Magnetic Field a) Zeeman Effect -Magnetic moments are oriented in one of two directions in magnetic field b) Difference in energy between the two states is given by: DE = g h Bo / 2p where: Bo – external magnetic field units:Tesla (Kg s-2 A-1) h – Planck’s constant 6.6260 x 10-34 Js g – gyromagnetic ratio unique value per nucleus 1H: 26.7519 x 107 rad T-1 s2p (observed NMR frequency) c) Frequency of absorption: n = g Bo / d) From Boltzmann equation: Nj/No = exp(-ghBo/2pkT) 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 Frequency of absorption: n = g Bo / 2p 2. Classical Description i. Spinning particle precesses around an applied magnetic field a) Angular velocity of this motion is given by: wo = gBo where the frequency of precession or Larmor frequency is: n = gBo/2p Same as quantum mechanical description ii. Net Magnetization z z Classic View: - Nuclei either align with or against external magnetic field along the z-axis. - Since more nuclei align with field, net magnetization (Mo) exists parallel to external magnetic field Mo x y x y Bo Bo Quantum Description: - Nuclei either populate low energy (a, aligned with field) or high energy (b, aligned against field) - Net population in a energy level. - Absorption of radiofrequency promotes nuclear spins from a b. b DE = h n Bo > 0 a Bo An NMR Experiment We have a net magnetization precessing about Bo at a frequency of wo with a net population difference between aligned and unaligned spins. z z Mo x y x y Bo Bo Now What? Perturbed the spin population or perform spin gymnastics Basic principal of NMR experiments An NMR Experiment resonant condition: frequency (w1) of B1 matches Larmor frequency (wo) energy is absorbed and population of a and b states are perturbed. z Mo B1 w1 z x B1 off… x (or off-resonance) y y Mxy w 1 And/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 Classical Description • Observe NMR Signal Need to perturb system from equilibrium. Net magnetization (Mo) now precesses about Bo and B1 B1 field (radio frequency pulse) with gBo/2p frequency MX and MY are non-zero Mx and MY rotate at Larmor frequency System absorbs energy with transitions between aligned and unaligned states Precession about B1stops when B1 is turned off Mz RF pulse B1 field perpendicular to B0 Mxy iii. Absorption of RF Energy or NMR RF Pulse z Classic View: 90o pulse - Apply a radio-frequency (RF) pulse a long the y-axis - RF pulse viewed as a second field (B1), that the net magnetization (Mo) will precess about with an angular velocity of w1 -- z Mo B1 w1 x B1 off… x (or off-resonance) y w1 = gB1 precession stops when B1 turned off Mxy w 1 y b Quantum Description: - enough RF energy has been absorbed, such that the population in a/b are now equal - No net magnetization along the z-axis DE = h n a Bo > 0 Please Note: A whole variety of pulse widths are possible, not quantized dealing with bulk magnetization An NMR Experiment What Happens Next? The B1 field is turned off and Mxy continues to precess about Bo at frequency wo. z x y Mxy Receiver coil (x) wo NMR signal FID – Free Induction Decay Mxy is precessing about z-axis in the x-y plane y Time (s) y y An NMR Experiment The 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. A magnetic field perpendicular to a circular loop will induce a current in the loop. NMR Probe (antenna) 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 Detect signal along X RF pulse along Y Again, the signal is precessing about Bo at its Larmor Frequency (wo). 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 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 T2 relaxation Two types of relaxation processes, one in the x,y plane and one along the z-axis iv. NMR Relaxation a) No spontaneous reemission of photons to relax down to ground state 1) Probability too low cube of the frequency b) Two types of NMR relaxation processes 1) spin-lattice or longitudinal relaxation 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 iv. Relaxation time (T1) exponential decay Mz = M0(1-exp(-t/T1)) Please Note: General practice is to wait 5xT1 for the system to have fully relaxed. 2) spin-spin or transverse relaxation 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 iv. relaxation time (T2) Mx = My = M0 exp(-t/T2) (derived from Heisenberg uncertainty principal) Please Note: Line shape is also affected by the magnetic fields homogeneity NMR Sensitivity The applied magnetic field causes an energy difference between aligned(a) and unaligned(b) nuclei b Low energy gap DE = h n Bo > 0 a Bo = 0 The population (N) difference can be determined from Boltzmman distribution: Na / Nb = e DE / kT The DE for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol Na / Nb = 1.000064 Very Small ! ~64 excess spins per million in lower state NMR Sensitivity NMR signal depends on: signal (s) % g4Bo2NB1g(u)/T 1) 2) 3) 4) 5) 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 strength DE = g h Bo / 2p Na / Nb = e DE / kT Increase energy gap -> Increase population difference -> Increase NMR signal DE ≡ Bo ≡ g g - Intrinsic property of nucleus can not be changed. (gH/gC)3 1H for 13C is 64x (gH/gN)3 for 15N is 1000x 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 !! NMR Sensitivity • Relative sensitivity of 1H, 13C, 15N and other nuclei NMR spectra depend on Gyromagnetic ratio (g) Natural abundance of the isotope g - Intrinsic property of nucleus can not be changed. (gH/gC)3 1H for 13C is 64x (gH/gN)3 for 15N is 1000x 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 caffeine 8 scans ~12 secs 13C NMR spectra of caffeine 8 scans ~12 secs 13C NMR spectra of caffeine 10,000 scans ~4.2 hours NMR Sensitivity Increase in Magnet Strength is a Major Means to Increase Sensitivity NMR Sensitivity But at a significant cost! ~$800,000 ~$2,00,000 ~$4,500,000 Chemical Shift Up 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 interesting The 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 v. Chemical Shift a) Small local magnetic fields (Bloc) are generated by electrons as they circulate nuclei. 1) Current in a circular coil generates a magnetic field b) These local magnetic fields can either oppose or augment the external magnetic field 1) Typically oppose external magnetic field 2) Nuclei “see” an effective magnetic field (Beff) smaller then the external field 3) s – magnetic shielding or screening constant i. depends on electron density ii. depends on the structure of the compound 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 B0 n = gBo/2p de-shielding high shielding Shielding – local field opposes Bo c) Effect of Magnetic Anisotropy 1) external field induces a flow (current) of electrons in p 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 The NMR scale (d, ppm) Bo >> Bloc -- MHz compared to Hz Comparing small changes in the context of a large number is cumbersome d= w - wref wref ppm (parts per million) Instead use a relative scale, and refer all signals (w) in the spectrum to the signal of a particular compound (wref ). IMPORTANT: absolute frequency is field dependent (n = g Bo / 2p) CH 3 Tetramethyl silane (TMS) is a common reference chemical H3C Si CH 3 CH 3 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 magnet IMPORTANT: 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. 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) Chemical Shift Trends Acids Aldehydes Alcohols, protons a to ketones Aromatics Amides Olefins Aliphatic ppm 15 C=O in ketones 10 7 5 Aromatics, conjugated alkenes Olefins 2 0 TMS Aliphatic CH3, CH2, CH ppm 210 150 C=O of Acids, aldehydes, esters 100 80 50 0 TMS Carbons adjacent to alcohols, ketones CHARACTERISTIC PROTON CHEMICAL SHIFTS Common Chemical Shift Ranges Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm) Type of Proton Structure Chemical Shift, ppm Cyclopropane C3H6 0.2 Primary R-CH3 0.9 Secondary R2-CH2 1.3 Tertiary R3-C-H 1.5 Vinylic C=C-H 4.6-5.9 Acetylenic triple bond,CC-H 2-3 Aromatic Ar-H 6-8.5 Benzylic Ar-C-H 2.2-3 Allylic C=C-CH3 1.7 Fluorides H-C-F 4-4.5 Chlorides H-C-Cl 3-4 Bromides H-C-Br 2.5-4 Iodides H-C-I 2-4 Alcohols H-C-OH 3.4-4 Ethers H-C-OR 3.3-4 Esters RCOO-C-H 3.7-4.1 Esters H-C-COOR 2-2.2 Acids H-C-COOH 2-2.6 Carbonyl Compounds H-C-C=O 2-2.7 Aldehydic R-(H-)C=O 9-10 Hydroxylic R-C-OH 1-5.5 Phenolic Ar-OH 4-12 Enolic C=C-OH 15-17 Carboxylic RCOOH 10.5-12 Amino RNH2 1-5 Coupling Constants Energy level of a nuclei are affected by covalently-bonded neighbors spin-states 1 H 13 1 1 H H three-bond C one-bond Spin-States of covalently-bonded nuclei want to be aligned. +J/4 I -J/4 bb S ab J (Hz) ba S +J/4 I aa I S The magnitude of the separation is called coupling constant (J) and has units of Hz. vi. 1 11 121 1331 14641 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 Spin-Spin Splitting (J-coupling) a) through-bond interaction that results in the splitting of a single peak into multiple peaks of various intensities 1) The spacing in hertz (hz) between the peaks is a constant i. coupling constant (J) b) bonding electrons convey spin states of bonded nuclei 1) spin states of nuclei are “coupled” 2) alignment of spin states of bonded nuclei affects energy of the ground (a) and excited states (b) of observed nuclei 3) Coupling pattern and intensity follows Pascal’s triangle Common NMR Splitting Patterns singlet doublet triplet quartet 1:1 1:2:1 1:3:3:1 pentet 1:4:6:4:1 Coupling Rules: 1. 2. 3. 4. 5. 6. equivalent nuclei do not interact coupling 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 triangle Coupling constant are independent of applied field strength IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei. Karplus Equation – Coupling Constants J = const. + 10Cosf Relates coupling constant to Torsional angle. Used to solve Structures! vii. Nuclear Overhauser Effect (NOE) a) Interaction between nuclear spins mediated through empty space (#5Å) like ordinary bar magnets b) Important: effect is time-averaged c) Gives rise to dipolar relaxation (T1 and T2) and specially to cross-relaxation Perturb 1H spin population affects 13C spin population NOE effect the 13C signals are enhanced by a factor 1 + h = 1 + 1/2 . g(1H)/g(13C) ~ max. of 2 Example 21: The proton NMR spectrum is for a compound of empirical formula C4H8O. Identify the compound Absence of peak at ~9.7 ppm eliminates aldehyde group And suggests ketone Triplet at ~1.2 ppm suggests a methyl group coupled to a methylene group Strong singlet at ~2.25 ppm methyl next to carbonyl Quartet at ~2.5 ppm suggests a methylene next to a carbonyl coupled to a methyl 3. NMR Instrumentation (block diagram) i. Superconducting Magnet a) solenoid wound from superconducting niobium/tin or niobium/titanium wire b) kept at liquid helium temperature (4K), outer liquid N2 dewar 1) near zero resistance minimal current lose magnet stays at field for years without external power source c) electric currents in the shim coils create small magnetic fields which compensate inhomogenieties Cross-section of magnet magnet spinner sample lift NMR Tube RF coils cryoshims shimcoils Probe Superconducting solenoid Use up to 190 miles of wire! Liquid N2 Liquid He ii. Lock System a) b) c) d) NMR magnetic field slowly drifts with time. Need to constantly correct for the field drift during data collection Deuterium NMR resonance of the solvent is continuously irradiated and monitored to maintain an on-resonance condition 1) changes in the intensity of the reference absorption signal controls a feedback circuit 2) a frequency generator provides a fixed reference frequency for the lock signal 3) 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 NMR probes contains an additional transmitter coil tuned to deuterium frequency Lock Feedback Circuit Field Drift over 11 Hrs (~ 0.15Hz/hr Lock Changes From Off-resonance to Onresonance iii. Sample Probe a) Holds the sample in a fixed position in the magnetic field b) Contains an air turbine to spin, insert and eject the sample c) Contains the coils for: 1) transmitting the RF pulse 2) detecting the NMR signal 3) observing the lock signal 4) creating magnetic field gradients d) Thermocouples and heaters to maintain a constant temperature iv. Pulse Generator & Receiver System a) Radio-frequency generators and frequency synthesizers produce a signal of essentially a single frequency. b) RF pulses are typically short-duration (msecs) 1) produces bandwidth (1/4t) centered around single frequency 2) shorter pulse width broader frequency bandwidth i. Heisenberg Uncertainty Principal: Du.Dt ~ 1/2p A radiofrequency pulse is a combination of a wave (cosine) of frequency w o and a step function * = tp Pulse length (time, tp) The Fourier transform indicates the pulse covers a range of frequencies FT iv. Pulse Generator & Receiver System c) A magnetic field perpendicular to a circular loop will induce a current in the loop. d) 90o NMR pulses places the net magnetization perpendicular to the probe’s receiver coil resulting in an induced current in the nanovolt to microvolt range e) preamp mounted in probe amplifies the current to 0 to 10 V f) no signal is observed if net magnetization is aligned along the Z or –Z axis 4. NMR Data Detection and Processing i. Fourier Transform NMR a) Instead of sequentially scanning through each individual frequency, simultaneously observe absorption of all frequencies. 1) frequency sweep (CW), step through each individual frequency is very slow (1-10 min) 2) short RF pulses result in bandwidth that cover entire frequency range 3) Fourier Transform NMR is fast (N x 1-10 sec) 4) Increase signal-to-noise (S/N) by collecting multiple copies of FID and averaging signal. b) c) S/N % rnumber of scans Observe each individual resonance as it precesses at its Larmor frequency (wo) in the X,Y plane. Monitor changes in the induced current in the receiver coil as a function of time. X y Detect signal along X RF pulse along Y n = gBo(1-s)/2p FID – Free Induction Decay i. Fourier Transform NMR d) Observed signal decays as a function of T2 relaxation 1) peak width at half-height (n½) is related to T2 e) NMR signal is collected in Time domain, but prefer frequency domain f) Transform from the time domain to the frequency domain using the Fourier function T2 relaxation Fourier Transform is a mathematical procedure that transforms time domain data into frequency domain ii. Sampling the Audio Signal a) Collect Digital data by periodically sampling signal voltage 1) ADC – analog to digital converter b) To correctly represent Cos/Sin wave, need to collect data at least twice as fast as the signal frequency c) If sampling is too slow, get folded or aliased peaks The Nyquist Theorem says that we have to sample at least twice as fast as the fastest (higher frequency) signal. Sample Rate - Correct rate, correct frequency SR = 1 / (2 * SW) -½ correct rate, ½ correct frequency Folded peaks! Wrong phase! SR – sampling rate Correct Spectra Spectra with carrier offset resulting in peak folding or aliasing Sweep Width (range of radio-frequencies monitored for nuclei absorptions) iii. Window Functions a) Emphasize the signal and decrease the noise by applying a mathematical function to the FID. b) NMR signal is decaying by T2 as the FID is collected. Good stuff Mostly noise Sensitivity Resolution F(t) = 1 * e - ( LB * t ) – line broadening Effectively adds LB in Hz to peak Line-widths Can either increase S/N or Resolution Not Both! LB = 5.0 Hz Increase Sensitivity FT LB = -1.0 Hz Increase Resolution FT iv. Zero Filling a) Improve digital resolution by adding zero data points at end of FID 8K data 8K FID No zero-filling 8K zero-fill 16K FID 8K zero-filling v. NMR Peak Integration or Peak Area a) The relative peak intensity or peak area is proportional to the number of protons associated with the observed peak. b) Means to determine relative concentrations of multiple species present in an NMR sample. Relative peak areas = Number of protons 3 Integral trace HO-CH2-CH3 2 1 5. Exchange Rates and NMR Time Scale i. Time Scale Slow Intermediate Fast 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. Range (Sec-1) Chem. Shift (d) k << dA- dB k = dA - dB k >> dA - dB 0 – 1000 Coupling Const. (J) k << JA- JB k = JA- JB k >> JA- JB 0 –12 T2 relaxation k << 1/ T2,A- 1/ T2,B k = 1/ T2,A- 1/ T2,B k >> 1/ T2,A- 1/ T2,B 1 - 20 d) For systems in fast exchange, the observed chemical shift is the average of the individual species chemical shifts. dobs = f1d1 + f2d2 f1 +f2 =1 where: f1, f2 – mole fraction of each species d1,d2 – chemical shift of each species ii. Effects of Exchange Rates on NMR data k = p Dno2 /2(he - ho) k = p Dno / 21/2 k = p (Dno2 - Dne2)1/2/21/2 k = p (he-ho) k – exchange rate h – peak-width at half-height n – peak frequency e – with exchange o – no exchange ii. Effects of Exchange Rates on NMR data 40 Hz No exchange: With exchange: W1/ 2 = 1 1 pT2 ptex k= 1 t ex slow k = 0.1 s-1 k = 5 s-1 Increasing Exchange Rate W1/ 2 1 = pT2 k = 10 s-1 k = 20 s-1 k = 40 s-1 coalescence k = 88.8 s-1 k = 200 s-1 k = 400 s-1 k = 800 s-1 fast k = 10,000 s-1 6. Multidimensional NMR i. 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 (t1) c) more complex NMR experiments will use multiple “time-dimensiona” to obtain 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 ii. Creating Multiple Dimensions in NMR a) collect a series of FIDS incremented by a second time domain (t1) 1) evolution of a second chemical shift or coupling constant occurs during this time period b) the normal acquisition time is t2. c) Fourier transformation occurs for both t1 and t2, creating a twodimensional (2D) NMR spectra Relative appearance of each NMR spectra will be modulated by the t1 delay ii. Creating Multiple Dimensions in NMR d) During t1 time period, peak intensities are modulated at a frequency corresponding to the chemical shift of its coupled partner. e) In 2D NMR spectra, diagonal peaks are normal 1D peaks, off-diagonal or cross-peaks indicate a correlation between the two diagonal peaks Collections of FIDs with t1 modulations Fourier Transform t1 obtain 2D NMR spectra Fourier Transform t2 obtain series of NMR spectra modulated by t1 Looking down t1 axis, each point has characteristics of time domain FID Peaks along diagonal are normal 1D NMR spectra Contour map (slice at certain threshold) of 3D representation of 2D NMR spectra. (peak intensity is third dimension Cross-peaks correlate two diagonal peaks by J-coupling or NOE interactions iii. 2D NOESY NMR Spectra a) basis for solving a structure b) diagonal peaks are correlated by through-space dipole-dipole interaction (NOE) c) NOE is a relaxation factor that builds-up during the “mixing-time” (tm) d) relative magnitude of the cross-peak is related to the distance (1/r6) between the protons (≥ 5Å). 2D NOESY NMR Pulse Sequence iv. 3D & 4D NMR Spectra a) similar to 2D NMR with either three or four time domains. b) additional dimensions usually correspond to 13C & 15N chemical shifts. c) primarily used for analysis of biomolecular structures 1) disperses highly overlapped NMR spectra into 3 & 4 dimensions, simplifies analysis. d) view 3D, 4D experiments as collection of 2D spectra. e) one experiment may take 2.5 to 4 days to collect. 1) diminished resolution and sensitivity Spread peaks out by 15N chemical shift of amide N attached to NH Further spread peaks out by 13C chemical shift of C attached to CH