NMR Spectroscopy - Rutgers University

1 NMR SpectroscopyMRIDrug designStructural biologyMetabonomicsFood qualityApplicationsNMR = Nuclear Magnetic ResonanceBasic PrinciplesSpectroscopic technique , thus relies on the interaction between material and electromagnetic radiationThe nuclei of all atoms possess a nuclear quantum number, I. ( I 0, always multiples of .)Only nuclei with spin number (I) >0 can absorb/emit electromagnetic atomic mass & number: I = 0 (12C, 16O)Even atomic mass & odd number: I = whole integer (14N, 2H, 10B)Odd atomic mass: I = half integer (1H, 13C, 15N, 31P) The spinning nuclei possess angular momentum, P, and charge, and so an associated magnetic moment, . = x PWhere is the gyromagnetic ratioNMR SpectroscopyThe spin states of the nucleus are quantified: I, (I - 1), (I - 2), .. , -IBasic PrinciplesB0 I= ( 1H)Energy B0=0 B0>0 E=h =h B0/2 NMR SpectroscopyBasic PrinciplesBo In the ground state all nuclear spins are disordered, and there is no energy difference between them.

2 They are they have a magnetic moment, when we apply a strong external magnetic field (Bo), they orient either against or with it:There is always a small excess of nuclei (population excess) aligned with the field than pointing against SpectroscopyBasic PrinciplesBo=0 Bo>0 E=h 0=h B0/2 0 is the Larmor Frequency 0= B0, angular velocityB0 z y x NMR SpectroscopyBasic PrinciplesEach level has a different population (N), and the difference between the two is related to the energy difference by the Boltzmman distribution:N /N = e E/kT E for 1H at 400 MHz (B0 = T) is x 10-5 Kcal/mol N /N = The surplus population is small (especially when compared to UV or IR).That renders NMR a rather insensitive technique !NMR SpectroscopyThe electromagnetic spectrum1022 1020 1018 1016 1014 1012 1010 108 106 -rays X-rays Mossbauer electronic ultraviolet visible infrared microwave radiofrequency vibrational rotational NMR 600 500 400 300 200 100 1H 19F 31P 13C 10 8 6 4 2 0 aldehydic aromatic olefinic acetylenic aliphatic /Hz /MHz /ppm NMR SpectroscopyThe Vector Modely x y x M0 y x y x NMR SpectroscopyNMR excitationMo z y i B1 Transmitter coil (x) x Bo B1 = C * cos ( ot) y x y x + 0 - 0 B1 is an oscillating magnetic field NMR SpectroscopyLaboratory vs.

3 Rotating framez y x M0 + 0 - 0 Laboratory frame z y x M0 + 0 -2 0 Rotating frame B1 NMR SpectroscopyEffect on an rf pulsez y x M0 B1 z y x B1 = 1tp (degrees) =90 =180 NMR SpectroscopyMagnetization propertiesz y x B1 y x =5 Hz A y x MAy MAx x y x y x y 1H=400,000,000 Hz A=400,000,005 HzNMR SpectroscopyMagnetization properties 1H=400,000,000 Hz A=400,000,005 Hzz y x B1 y x =5 Hz A y x MAy MAx detector IM t MAy=MA cos t MA IM t MAx=MA sin t MA t NMR SpectroscopyThe Fourier TransformIM t time domain frequency domain FT FT t =1/ t time frequency NMR SpectroscopyThe Fourier TransformIM time Signal Induction Decay (FID) NMR SpectroscopyThe Fourier TransformFT NMR SpectroscopyContinuous wave vs. pulsed NMR o or Bo time o or Bo NMR SpectroscopyContinuous wave vs. pulsed NMR FT FT For cos( t) For sin( t) absorptive lines despersive lines NMR SpectroscopyContinuous wave vs. pulsed NMR* = tp FT o A monochromatic radiofrequency pulse is a combination of a wave (cosine) of frequency 0 and a step function Since f=1/t, a pulse of 10 s duration excites a frequency bandwidth of 105 Hz!

4 NMR SpectroscopyContinuous wave vs. pulsed NMR E t ~ h or t ~1 NMR SpectroscopySingle-channel signal detectionz y x + FT + - 0 NMR SpectroscopyQuadrature detectionz y x + My Mx My Mx NMR SpectroscopyQuadrature detectiony x + sin cos + - Hz 0 + Hz 0 NMR SpectroscopyThe Chemical ShiftThe NMR frequency of a nucleus in a molecule is mainly determined by its gyromagnetic ratio and the strength of the magnetic field BThe exact value of depends, however, on the position of the nucleus in the molecule or more precisely on the local electron distribution this effect is called the chemical shiftNMR SpectroscopyThe Chemical ShiftNuclei, however, in molecules are never isolated from other particles that are charged and are in motion (electrons!). Thus, the field actually felt by a nucleus is slightly different from that of the applied external magnetic field!! E=h =h B/2 NMR SpectroscopyThe Chemical Shift E=h =h Be /2 Beff, is given by B0-B = B0-B0 =B0(1- ) and is the chemical shift = B0(1- ) 2 = ( - ref) ref 106 106 ( ref- ) NMR SpectroscopyThe Chemical Shift750 MHz 1H spectrum of a small protein amide protonsaromatic ring protonsmethyleneprotonsmethylprotonsshie lding magnetic field frequency NMR SpectroscopyThe Chemical ShiftNMR SpectroscopyThe Chemical ShiftNMR SpectroscopyNuclear Shieldingdiamagnetic contributionparamagnetic contributionneighbor anisotropy effectring-current effectelectric field effectsolvent effect = dia + para + nb + rc + ef + solvNMR SpectroscopyNuclear Shielding - diamagnetic contributionThe external field B0 causes the electrons to circulate within their orbitalsB0 B h B0 h B0(1- ) The higher is the electron density close to the nucleus, the larger the protection is!

5 NMR SpectroscopyNuclear Shielding - diamagnetic contributionDepends on the electronegativityCH3 XNMR SpectroscopyNuclear Shielding - paramagnetic contributionThe external field B0 mixes the wavefunction of the ground state with that of the excited stateThe induced current generates a magnetic field that enhances the external field and deshields the nucleusHOMO LUMO B0 p = 1 1 R3 NMR SpectroscopyChemical shift rangeLocal diamagnetic and paramagnetic currents make only modest contributions to 1H shielding!1H; ~10 ppm 13C; ~200 ppm 19F; ~300 ppm 31P; ~500 ppm NMR SpectroscopyChemical Shift AnisotropyNuclear shielding, , is a distribution of the electrons about the nucleus is non-sperical- thus, the magnitude of the shielding depends on the relative orientation of the nucleus with respect to the static isotropic cases: = ( 11 + 22 + 33)In static cases, solid stateNMR SpectroscopyNuclear Shielding - neighboring groupA B par < per B0 B par > per - - + + + + - - A NMR SpectroscopyNuclear Shielding - neighboring group- + + C C - + - - + C C par < per par > per 0 1 2 3 4 5 6 7 ppm C2H4 C2H2 C2H6 NMR SpectroscopyNuclear Shielding - ring-current effectMore pronounced in aromatic rings due to the electron cloudsBo e- NMR SpectroscopyNuclear Shielding - hydrogen bondingCH3 CH2 OH 0 2 4 6 ppm [EtOH] in CCl4 1M Hydrogen bonding causes deshielding due to electron density decrease at the proton siteNMR SpectroscopySpin-spin (scalar) couplingHF (1H-19F)H F JHF JHF NMR SpectroscopySpin-spin (scalar) couplingHF (1H-19F)

6 Bo 19F 19F 1H 1H Nuclear moment Magnetic polarization of the electron H F H F H F H F H H E=h JAX mA mX where m is the magnetic quantum number JAX is the spin-spin coupling constant NMR SpectroscopySpin-spin (scalar) couplingAMX AX2 AX3 NMR SpectroscopySpin-spin (scalar) couplingStrong coupling <10|J|NMR SpectroscopySpin-spin (scalar) couplingThe principal source of scalar coupling is an indirect interaction mediated by electrons involved in chemical bondingThe magnitude of interaction is proportional to the probability of finding the electron at the nucleus (R=0)Magnitude in Hz- independent of the external magnetic fieldH3C CH3125 HzH2C CH2160 HzHC CH250 HzNMR SpectroscopySpin-spin (scalar) couplingThree-bond coupling most useful since it carries information on dihedral anglesEmpirical relationship: the Karplus relation3J = A + B cos + C cos2 NMR SpectroscopyChemical shifts on the rotating frame2 3 500 MHz 0 z y x z y x t =500 Hz NMR SpectroscopySpin couplings on the rotating frame 0 z y x t J z y x =+J/2 Hz =-J/2 Hz NMR SpectroscopyThe basic spin-echo pulse sequencex y 90 applied along x axis 180 applied along y axis delay acquisition NMR SpectroscopyEffect of spin echo on chemical shift evolutionx y 90 applied along x axis 180 applied along y axis delay acquisition z y x z y x 90x z 180y z y x A z y x y x A NMR SpectroscopyEffect of spin echo on scalar coupling evolutionx y 90 applied along x axis 180 applied along y axis delay acquisition z y x 90x z y x z y x +J/2 -J/2 180y (only 1H) z y x +J/2 -J/2 1H-X z y x NMR SpectroscopyEffect of spin echo on scalar coupling evolutionx y 90 applied along x axis 180 applied along y axis delay acquisition y x z y x 90x z y x +J/2 -J/2 180y (both 1H and X)

7 1H-X z y x -J/2 +J/2 z y x z NMR SpectroscopyWater suppression by the Jump and Return method z y x x z y 90x z y x 90-x z y x A z y x NMR SpectroscopyWater suppressionNMR SpectroscopySpin decoupling13C decouple 1H H C H H H C H C H C NMR SpectroscopyThe J-modulated spin echo13C 1H x y decouple NMR SpectroscopyThe J-modulated spin echo13C 1H x y decouple NMR SpectroscopyThe J-modulated spin echo13C 1H x y decouple If =180J degrees C: I=1 CH: I cos CH2: I cos2 CH3: I cos3 NMR SpectroscopyThe J-modulated spin echo13C 1H x y decouple =1/J 13C (ppm)NMR SpectroscopySensitivity enhancementNMR has poor sensitivity compared to other analytical techniquesThe intrinsic sensitivity depends upon the gyromagnetic ratio, A greater contributes to:a high resonant frequency- large transition energy difference- greater Boltzmann population differencehigh magnetic moment and hence a stronger signal high rate of precession which induces a greater signal in the detection coil So, the strength of NMR signal is proportional to 3 Noise increases a square-root of observed frequency}S/N 5/2 NMR SpectroscopySensitivity enhancement by polarization transferSignal sensitivity enhancement by transferring the greater population differences of high- spins onto their spin-coupled low- partners.

8 H1 H2 C2 C1 1H-13C spin pair NMR SpectroscopySensitivity enhancement by polarization transferSignal sensitivity enhancement by transferring the greater population differences of high- spins onto their spin-coupled low- partners. H1 H2 C2 C1 + C C + C C 2 2 C 2 2 C H1 H2 C2 C1 + C C + C C 2 2 +2 C 2 2 +2 C (inverted) H1 H2 C2 C1 H1 H2 C2 C1 -3:5 NMR SpectroscopySensitivity enhancement by polarization transferSignal sensitivity enhancement by transferring the greater population differences of high- spins onto their spin-coupled low- decoupled INEPT refocused INEPT refocused, decoupled INEPT NMR SpectroscopyRelaxationWhen perturbed, the nuclear spins need to relax to return to their equilibrium when the sample is put into a magnet, the Boltzmann distribution of spins among the energy levels changes due to a change in the energy of the various after applying electromagnetic radiation, which induces transitions between energy levels, the system returns to its equilibriumThis process is called relaxationNMR SpectroscopyLongitudinal Relaxation: Establishing Equilibriumz y x z x z y x z y x z x NMR SpectroscopyLongitudinal Relaxation.

9 Establishing EquilibriumRecovery of the z-magnetization follows exponential behavior dMz (M0-Mz) dt T1 = Mz=M0 (1-2e-t/T1) where T1 is the longitudinal relaxation time NMR SpectroscopyLongitudinal Relaxation: Measurementx x z x y z x y 180x z x y z x y 90x z x y z x y 90x NMR SpectroscopyLongitudinal Relaxation: Measurementx x NMR SpectroscopyLongitudinal Relaxation: Exponential growthMz=M0 (1-2e-t/T1) By the end of 5T1 sec, the magnetization has recovered by NMR SpectroscopyLongitudinal Relaxation: optimizing sensitivityNMR SpectroscopyLongitudinal Relaxation: optimizing sensitivityNMR SpectroscopyLongitudinal Relaxation: optimizing sensitivityoptimum pulse repetition time when using 90 Quantitative measurements and integration NMR SpectroscopyTransverse Relaxation: magnetization loss in the x-y planey x y x - + time y x - + y x - + NMR SpectroscopyTransverse Relaxation: magnetization loss in the x-y plane =1 T2*NMR SpectroscopyTransverse Relaxation: Measurementz x y z x y 90x x y z x y - + z x y z x y 180y + - NMR SpectroscopyTransverse Relaxation: MeasurementNMR SpectroscopyT1 vs T2 RelaxationT1 T2 For small molecules, T1 T2 For large molecules, T1 >> T2 Longitudinal relaxation causes loss of energy from the spins (enthalpic) Transverse relaxation occurs by mutual swapping of energy between spins (entropic) NMR SpectroscopyRelaxation mechanismsDipole-dipole Chemical shift anisotropy Two main mechanisms Nuclear spin relaxation is not a spontaneous process.

10 It requires stimulation by suitable fluctuating fields to induce the necessary spin transitions NMR SpectroscopyRelaxation mechanismsLongitudinal relaxation requires a time-dependent magnetic field fluctuating at the Larmor frequencyThe time-dependence originates in the motions of the molecule (vibration, rotation, diffusion etc)Molecules in solution tumble . This tumbling can be characterized by a rotational correlation time c c is the time needed for the rms deflection of the molecules to be ~ 1 radian (60 )NMR SpectroscopySpectral density functionRotational diffusion in solution occurs at a range of frequencies1/ c ~ rms rotational frequency (radians s-1)The probability function of finding motions at a given angular frequency can be described by the spectral density function J( )NMR SpectroscopySpectral density functionFrequency distribution of the fluctuating magnetic fields NMR SpectroscopySpectral density function: Longitudinal relaxationSpins are relaxed by local fields fluctuating at the Larmor frequency 0So, the relaxation rate (R1) will be proportional to the J( 0)Knowing the form of J( ) we can predict the dependence of the spin-lattice relaxation time (T1=1/R1) on the correlation time c for a given NMR frequency 01/T1= R1 = 2 <B2> J( 0) 0 c>>1 (large molecules), J( 0) ~ 2/ 02 c and T1 increases (R1 decreases) with increasing c ( by decreasing the temperature) 0 c=1 0 c<<1 0 c>>1 0 c=1 ,J( 0) = c= 1/ 0 and T1 is minimum (R1 maximum) 0 c<<1 (small molecules), J( 0) ~ 2 c and T1 decreases (R1 increases) with increasing c ( decreasing the temperature) NMR SpectroscopyRelaxation mechanisms: Dipole-dipoleNuclei with non-zero quantum numbers have magnetic dipoles They behave like small magnets and induce small magnetic fields that affec