Nuclear Magnetic Resonance

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. 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 Taxol (natural product) NMR Structure of MMP-13 complexed to a ligand MRI images of the Human Brain

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 “Spin Dynamics – Basics of Nuclear Magnetic Resonance” M. H. Levitt “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 “Biomolecular NMR Spectroscopy” J. N. S. Evans “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 Integrated Spectral Data Base System for Organic Compounds http://www.aist.go.jp/RIODB/SDBS/menu-e.html 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. 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

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. Basic NMR Spectrometer

11. Superconducting Magnet • solenoid wound from superconducting niobium/tin or niobium/titanium wire • 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

12. Theory of NMR • 1. 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 I • 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 l

13. ii. Magnetic Moment (m) • spinning charged nucleus creates a magnetic field • 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) • magnetic moment is quantized (m) • m = I, I-1, I-2, …, -I • for common nuclei of interest: • m = +½ & -½ Magnetic moment Similar to magnetic field created by electric current flowing in a coil

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. iii. Energy Levels in a Magnetic Field • Zeeman Effect -Magnetic moments are oriented in one of two directions in magnetic field • 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 s- • Frequency of absorption:n = g Bo / 2p(observed NMR frequency) • From Boltzmann equation: Nj/No = exp(-ghBo/2pkT)

16. 2. Classical Description • Spinning particle precesses around an applied magnetic field • Angular velocity of this motion is given by: • wo = gBo • where the frequency of precession of Larmor frequency is: • n = gBo/2p • Same as quantum mechanical description

17. 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

18. z z Mo x x y y b Bo Bo Bo > 0 DE = h n a Bo Net Magnetization • 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 • 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 radio- • frequency promotes nuclear • spins from a b.

19. 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

20. 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

21. z z Mo B1 off… (or off-resonance) x x B1 Mxy w1 y y w1 b DE = h n a Absorption of RF Energy or NMR RF Pulse • Classic View: • - 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 • -- precession stops when B1 • turned off • 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 90o pulse w1 = gB1 Bo > 0 Please Note: A whole variety of pulse widths are possible, not quantized dealing with bulk magnetization

22. 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 Mxy is precessing about z-axis in the x-y plane Time (s) y y y

23. 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. NMR Probe (antenna) A magnetic field perpendicular to a circular loop will induce a current in the loop.

24. 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).

25. 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

26. 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

27. NMR Relaxation • No spontaneous reemission of photons to relax down to ground state • Probability too low  cube of the frequency • Two types of NMR relaxation processes • spin-lattice or longitudinal relaxation (T1) • 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.

28. 2) spin-spin or transverse relaxation (T2) • 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

29. 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

30. 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 !!

31. 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

32. 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

33. Chemical Shift • Small local magnetic fields (Bloc) are generated by electrons as they circulate nuclei. • Current in a circular coil generates a magnetic field • These local magnetic fields can either oppose or augment the external magnetic field • Typically oppose external magnetic field • Nuclei “see” an effective magnetic field (Beff) smaller then the external field • 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

34. 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

35. 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

36. 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.

37. 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)

38. 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)

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

40. Common Chemical Shift Ranges Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)

41. Predicting Chemical Shift Assignments • Numerous Experimental NMR Data has been compiled and general trends identified • See: • “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) Ongoing effort to predict chemical shifts from first principals (quantum mechanical description of factors contributing to chemical shifts)

42. 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 1H and 13C chemical shifts • matches sub-fragments of structure to structures in database

43. Predicting Chemical Shift Assignments How Does the Predicted Results Compare to Experimental Data? Parameter Experimental ( ppm) Predicted (ppm) D(A) 6.22 6.44 D(B) 6.53 6.44 D(C) 5.85 5.22 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

44. 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.

45. Coupling Constants • through-bond interaction that results in the splitting of a single peak into multiple peaks of various intensities • The spacing in hertz (hz) between the peaks is a constant • i. coupling constant (J) • bonding electrons convey spin states of bonded nuclei • spin states of nuclei are “coupled” • alignment of spin states of bonded nuclei affects energy of the ground (a) and excited states (b) of observed nuclei • Coupling pattern and intensity follows Pascal’s triangle 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 1 Pascal's triangle a b

46. singlet doublet triplet quartet pentet 1:1 1:2:1 1:3:3:1 1:4:6:4:1 Common NMR Splitting Patterns Multiplets consist of 2nI + 1 lines I is the nuclear spin quantum number (usually 1/2) and n is the number of neighboring spins. • Coupling Rules: • 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.

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

49. Nuclear Overhauser Effect (NOE) • Interaction between nuclear spins mediated through empty space (#5Å)  like ordinary bar magnets • Important: effect is time-averaged • Gives rise to dipolar relaxation (T1 and T2) and specially to cross-relaxation Perturb 1H spin population affects 13C spin population NOE effect

50. 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)/Io where Io is thermal equilibrium intensity irradiate N-d bb X A N N ab ba X N+d A aa Observed signals only occur from single-quantum transitions Populations and energy levels of a homonuclear AX system (large chemical shift difference)