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Nuclear Magnetic Resonance (NMR)

Nuclear Magnetic Resonance (NMR). 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. One of the MOST Routinely used Analytical Techniques. Common NMR Utility.

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Nuclear Magnetic Resonance (NMR)

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  1. Nuclear Magnetic Resonance (NMR) 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. One of the MOST Routinely used Analytical Techniques

  2. Common NMR Utility • Structural (chemical) elucidation • Natural product chemistry. • Synthetic organic chemistry.Analytical tool of choice of • synthetic chemists. • Study of dynamic processes • Reaction kinetics. • Study of equilibrium (chemical or structural). • Structural (three-dimensional) studies • Proteins. • DNA. Protein/DNA complexes • Polysaccharides • Drug design • Structure Activity Relationships by NMR • Medicine - MRI

  3. NMR: “fingerprint” of the compound’s chemical structure 2-phenyl-1,3-dioxep-5-ene 1H NMR spectra 13C NMR spectra

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

  5. NMR History 1937 Rabi predicts and observes nuclear magnetic resonance1946 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)

  6. Some Suggested NMR References “Basic One- and Two-Dimensional NMR Spectroscopy” Horst Friebolin “Modern NMR Techniques for Chemistry Research” Andrew E. Derome “NMR and Chemistry- an introduction to the fourier transform-multinuclear era” J. W. Akitt “Nuclear Magnetic Resonance Spectroscopy” R. K Harris “Protein NMR Spectroscopy: Principals and Practice” John Cavanagh, Arthur Palmer, Nicholas J. Skelton, Wayne Fairbrother “NMR of Proteins and Nucleic Acids” Kurt Wuthrich “Tables of Spectral Data for Structure Determination of Organic Compounds” Pretsch, Clerc, Seibl and Simon “Spectrometric Identification of Organic Compounds” Silverstein, Bassler and Morrill

  7. Some NMR Web Sites The Basics of NMR Hypertext based NMR course http://www.cis.rit.edu/htbooks/nmr/nmr-main.htm Educational NMR Software All kinds of NMR software http://www.york.ac.uk/depts/chem/services/nmr/edusoft.html NMR Knowledge Base A lot of useful NMR links http://www.spectroscopynow.com/ NMR Information Server News, Links, Conferences, Jobs http://www.spincore.com/nmrinfo/ Technical Tidbits Useful source for the art of shimming http://www.acornnmr.com/nmr_topics.htm BMRB (BioMagResBank) Database of NMR resonance assignments http://www.bmrb.wisc.edu/

  8. Basic NMR Spectrometer

  9. g-rays x-rays UV VIS IR m-wave radio 10-10 10-8 10-6 10-4 10-2 100 102 wavelength (cm) Information in a NMR Spectra 1) Energy E = hu h is Planck constant u is NMR resonance frequency ObservableNameQuantitativeInformation Peak position Chemical shifts (d) d(ppm) = uobs –uref/uref (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 curve T1 dependent Peak Shape Line width Du = 1/pT2 molecular motion peak half-height chemical exchange uncertainty principal uncertainty in energy

  10. Source of the NMR Signal • From Quantum Theroy: Nuclear Spin (Think Electron Spin) • NMR “active” Nuclear Spin (I) = ½: • 1H, 13C, 15N, 19F, 31P  biological and chemical relevance •  Odd atomic mass • 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

  11. Zeeman Effect and Nuclear Spin Quantum Number Zeeman effect: splitting of energy levels in magnetic field E= gBo • magnetogyric ratio (radians/Tesla) - unique value per nucleus 1H: 26.7519 x 107 rad T-1 s-1 Bo applied magnetic field - units:Tesla (Kg s-2 A-1) NMR frequency: n = g Bo/ 2p I: hyperfine interaction associate with magnetization due to nuclear spin quantum transitions 2I +1 possible energy levels For I =1/2: m= -1/2 & 1/2 m: magnetic quantum number

  12. NMR Spectra Terminology TMS CHCl3 7.27 0 ppm increasing d decreasing d low field high field down field up field high frequency (u) low frequency de-shielding high shielding Paramagnetic diamagnetic 600 MHz 150 MHz 92 MHz 1H 13C 2H Increasing field (Bo) Increasing frequency (u) Increasing g Increasing energy (E, consistent with UV/IR)

  13. Another Viewpoint: Magnetic Moment (Nuclear Spin) It is a vector quantity that gives the direction and magnitude (or strength) of the ‘nuclear magnet’ magnetic moment(m) = g Ih / 2p quantized by Planck’s constant (h) By convention: spin +1/2 => a - low energy state spin -1/2 => b Analogous to current moving in a loop which induces a magnetic field (right-hand rule)

  14. Bo Magnetic alignment = g h / 4p 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

  15. NMR Sensitivity The applied magnetic field causes an energy difference between aligned(a) and unaligned(b) nuclei b Low energy gap Bo > 0 DE = h n a Bo = 0 The population (N) difference can be determined from Boltzmman distribution: Na / Nb = e DE / kT TheDE for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol Very Small ! ~64 excess spins per million in lower state Na / Nb= 1.000064

  16. NMR Sensitivity • 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 strength signal (s) %g4Bo2NB1g(u)/T Na / Nb = e DE / kT DE = g hBo /2p Increase energy gap -> Increase population difference -> Increase NMR signal ≡ ≡ DE g Bo g - Intrinsic property of nucleus can not be changed. (gH/gN)3for 15N is 1000x (gH/gC)3for 13C is 64x 1H 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 !!

  17. NMR Sensitivity Increase in Magnet Strength is a Major Means to Increase Sensitivity But at a significant cost! ~$2,00,000 ~$4,500,000 ~$800,000

  18. NMR Frequency Range (expensive radios) g-rays x-rays UV VIS IR m-wave radio 10-10 10-8 10-6 10-4 10-2 100 102 wavelength (cm) DE = h n n = g Bo/ 2p DE = g h Bo / 2p For 1H in normal magnets (2.35 - 18.6 T), this frequency is in the 100-800 MHz range.

  19. Classical View of NMR (compared to Quantum view) Precession or Larmor frequency: w = 2pnwo = g Bo (radians) angular momentum(l) l wo m Bo Simply, the nuclei spins about its axis creating a magnetic moment m Apply a large external field (Bo) and m will precess about Bo at its Larmor (w) frequency. Maxwell: Magnetic field Moving charge ≡ Important: This is the same frequency obtained from the energy transition between quantum states

  20. Bulk magnetization (Mo) Now consider a real sample containing numerous nuclear spins: Mo%(Na - Nb) m = mxi + myj +mzk z z Mo x x y y Bo Bo Since m is precessing in the xy-plane, Mo = ∑mzk – m-zk m is quantized (a or b), Mo has a continuous number of states, bulk property.

  21. 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 x y y Bo Bo Now What? Perturbed the spin population or perform spin gymnastics Basic principal of NMR experiments

  22. An NMR Experiment To perturbed the spin population need the system to absorb energy. z Mo x B1 Bo y i Transmitter coil (y) Two ways to look at the situation: (1) quantum – absorb energy equal to difference in spin states (2) classical - perturb Mo from an excited field B1

  23. 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 z Mo B1 off… (or off-resonance) x x B1 Mxy w1 y y w1 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

  24. An NMR Experiment What Happens Next? The B1 field is turned off and Mxy continues to precess about Bo at frequency wo. z x wo Mxy y  NMR signal Receiver coil (x) FID – Free Induction Decay 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.

  25. NMR Signal Detection - FID Mxy is precessing about z-axis in the x-y plane Time (s) y y y The FID reflects the change in the magnitude of Mxy as the signal is changing relative to the receiver along the y-axis Again, it is precessing at its Larmor Frequency (wo).

  26. 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

  27. Laboratory Frame vs. Rotating Frame To simplify analysis we convert to the rotating frame. z z x x Mxy Mxy wo Bo y y Laboratory Frame Rotating Frame Simply, our axis now rotates at the Larmor Freguency (wo). In the absent of any other factors, Mxy will stay on the x-axis All further analysis will use the rotating frame.

  28. 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 ) sis the magnetic shielding of the nucleus

  29. Chemical Shift Again, consider Maxwell’s theorem that an electric current in a loop generates a magnetic field. Effectively, the electron distribution in the chemical will cause distinct local magnetic fields that will either add to or subtract from Bo HO-CH2-CH3 Beff = Bo( 1 - s ) de-shielding high shielding Shielding – local field opposes Bo Aromaticity, electronegativity and similar factors will contribute to chemical shift differences

  30. C H 3 H C S i C H 3 3 C H 3 The NMR scale (d, ppm) Bo >> Bloc -- MHz compared to Hz Comparing small changes in the context of a large number is cumbersome w - wref d = ppm (parts per million) wref 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) Tetramethyl silane (TMS) is a common reference chemical

  31. 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.

  32. Chemical Shift Trends • For protons, ~ 15 ppm: Alcohols, protons a to ketones Aromatics Amides Acids Aldehydes Olefins Aliphatic ppm 15 10 7 5 2 0 TMS

  33. Chemical Shift Trends • For carbon, ~ 220 ppm: Aromatics, conjugated alkenes C=O in ketones Aliphatic CH3, CH2, CH Olefins ppm 210 150 100 80 50 0 TMS C=O of Acids, aldehydes, esters Carbons adjacent to alcohols, ketones

  34. Predicting Chemical Shift Assignments • Numerous Experimental NMR Data has been compiled and general trends identified • Examples in Handout • See also: • “Tables of Spectral Data for Structure Determination of Organic Compounds” Pretsch, Clerc, Seibl and Simon • “Spectrometric Identification of Organic Compounds” • Silverstein, Bassler and Morrill • Spectral Databases: • Aldrich/ACD Library of FT NMR Spectra • Sadtler/Spectroscopy (UV/Vis, IR, MS, GC and NMR)

  35. Predicting Chemical Shift Assignments Predict the chemical shifts of: Benzene ShiftNO2 effectNH2 effectTotal Change sign since table lists as downfield shift da 7.27 0.95 -0.75 7.47 ppm dd 7.27 0.33 -0.75 6.85 ppm dc 7.27 0.17 -0.24 7.20 ppm db 7.27 0.95 -0.63 7.59 ppm From table 3-6-1 in handout: Substituent Shift relative to benzene (ppm) ortho meta para NO2 -0.95 -0.17 -0.33 NH2 0.75 0.24 0.63

  36. Predicting Chemical Shift Assignments Predict the chemical shifts of: Cb | C – C – C – C – C – C a 2 abgd • Chemical shift is determined by sum of carbon types. • From Table 3.2 in handout: • =Bs + ∑ DmAsm +gSN3 +DsN4 - empirical formula S – number of directly bonded carbons Dm – number of directly bonded carbons having M attached carbons Np – number of carbons P bonds away d2 = B2 + [1xA23+ 1xA21 ] + [1xg2] + [1xD2] d2 = 15.34 + [1X16.70 +1x0] + [1x-2.69] +[1x0.25] = 29.60 ppm

  37. 1 H 1 3 C 1 1 H H Coupling Constants Energy level of a nuclei are affected by covalently-bonded neighbors spin-states three-bond one-bond Spin-States of covalently-bonded nuclei want to be aligned. +J/4 J (Hz) bb I S ab ba -J/4 S I I S aa +J/4 The magnitude of the separation is called coupling constant (J) and has units of Hz.

  38. Coupling Constants 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. The ratios between the signal intensities within multiplets are governed by the numbers of Pascals triangle.

  39. Coupling Constants

  40. NMR Relaxation After the B1 field (pulse) is removed the system needs to “relax” back to equilibrium Mz = M0(1-exp(-t/T1)) T1 is the spin-lattice (or longitudinal) relaxation time constant. Think of T1 as bulk energy/magnetization exchange with the “solvent”. Please Note: General practice is to wait 5xT1 for the system to have fully relaxed.

  41. NMR Relaxation Related to line-shape Mx = My = M0 exp(-t/T2) (derived from Hisenberg uncertainty principal) T2 is the spin-spin (or transverse) relaxation time constant. In general: T1 T2 Think of T2 as the “randomization” of spins in the x,y-plane Please Note: Line shape is also affected by the magnetic fields homogeneity

  42. NMR Time Scale Time ScaleChem. Shift (d)Coupling Const. (J) T2 relaxation Slow k << dA- dB k << JA- JB k << 1/ T2,A- 1/ T2,B Intermediate k = dA - dB k = JA- JB k = 1/ T2,A- 1/ T2,B Fast k >> dA - dB k >> JA- JB k >> 1/ T2,A- 1/ T2,B Range (Sec-1) 0 – 1000 0 –12 1 - 20 NMR time-scale refers to the chemical shift timescale.

  43. Exchange Rates from NMR Data dobs = f1d1 + f2d2 f1 +f2 =1 k = p Dno2 /2(he - ho) k = pDno / 21/2 k = p (Dno2 -  Dne2)1/2/21/2 k = p (he-ho) • h – peak-width at half-height • – peak frequency e – with exchange o – no exchange f – mole fraction d – chemical shift

  44. 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) Increase signal-to-noise (S/N) by collecting multiple copies of FID and averaging signal. S/N r number of scans %

  45. NMR Pulse A radiofrequency pulse is a combination of a wave (cosine) of frequency wo and a step function * = tp Pulse length (time, tp) The fourier transform indicates the pulse covers a range of frequencies FT Hisenberg Uncertainty principal again: Du.Dt ~ 1/2p Shorter pulse length – larger frequency envelope Longer pulse length – selective/smaller frequency envelope Sweep Width f ~ 1/t

  46. NMR Pulse NMR pulse length or Tip angle (tp) z z qt Mo tp x x B1 Mxy y y qt = g * tp * B1 The length of time the B1 field is on => torque on bulk magnetization (B1) A measured quantity – instrument dependent.

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

  48. NMR Data Acquisition Collect Digital Data ADC – analog to digital converter 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

  49. Quadrature detection carrier • Frequency of B1 (carrier) is set to center of the spectra. • small pulse length to excite entire spectrum • minimizes folded noise carrier If carrier is at edge of spectra, then peaks are all positive or negative relative to carrier. But excite twice as much including noise How to differentiate between peaks upfield and downfield from carrier?

  50. Quadrature detection PH = 0 B F B Use two detectors 90o out of phase. w (B1) F PH = 90 PH = 0 F S Phase of Peaks are different. PH = 90 F S

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