NMR Spectroscopy Part I. Origin of NMR

Nuclei in Magnetic Field Nucleus rotate about an axis -- spin Nucleus bears a charge, its spin gives rise to a magnetic field . The resulting magnetic moment is oriented along the axis of spin and is proportional to angular momentum m = g p : magnetic moment p: angular momentum g: magnetogyric ratio

Nuclei in Magnetic Field Spin Quantum Number I a characteristic property of a nucleus. May be an integer or half integer # of protons # of neutrons I even even 0 odd odd integer 1,2,3… even even half integral odd odd half integral

Nuclei in Magnetic Field Properties of nucleus with spin quantum number I 1. An angular momentum of magnitude {I(I+1)}1/2ħ 2. A component of angular momentum mIħ on an arbitrary axis where mI=I, I-1, … -I (magnetic quantum number) 3. When I>0, a magnetic moment with a constant magnitude and an orientation that is determined by the value of mI. m = g mI ħ

Nuclei in Magnetic Field In a magnetic field B (in z direction) there are 2I+1 orientations of nucleus with different energies. B0: magnetic field in z direction nL: Larmor Frequency

Nuclei in Magnetic Field For I=1/2 nucleus : mI = 1/2 and –1/2

Nuclei in Magnetic Field

Nuclei in Magnetic Field

Nuclei in Magnetic Field

Nuclei in Magnetic Field

Nuclei in Magnetic Field Distribution between two states

Nuclei in Magnetic Field

Nuclei in Magnetic Field Magnetizaton The difference in populations of the two states can be considered as a surplus in the lower energy state according to the Boltzmann distribution A net magnetization of the sample is stationary and aligned along the z axis (applied field direction)

Nuclei in Magnetic Field Two spins All spins  Sum Bulk Magnetization excess facing down Ho anti-parallel parallel

Effect of a radio frequency hn = DE H1 2. pump in energy p ap 1. equilibrium DE p ap 3. non-equilibrium hn = DE 4. release energy (detect) p ap 5. equilibrium

Effect of a radio frequency

Effect of a radio frequency

NMR Signals

Relaxation- Return to Equilibrium x,y plane z axis Transverse Longitudinal 1 1 t t 2 2 E-t/T2 1-e-t/T1 8 8 Transverse always faster!

NMR Spectroscopy Part II. Signals of NMR

Free Induction Decay (FID) FID represents the time-domain response of the spin system following application of an radio-frequency pulse. With one magnetization at w0, receiver coil would see exponentially decaying signal. This decay is due to relaxation.

Fourier Transform The Fourier transform relates the time-domain f(t) data with the frequency-domain f(w) data.

Fourier Transform

Fourier Transform

NMR line shape Lorentzian line A amplitude W half-line width

Resolution Definition For signals in frequency domain it is the deviation of the peak line-shape from standard Lorentzian peak. For time domain signal, it is the deviation of FID from exponential decay. Resolution of NMR peaks is represented by the half-height width in Hz.

Resolution

Resolution-digital resolution

Resolution Measurement half-height width: 10~15% solution of 0-dichlorobenzene (ODCB) in acetone Line-shape: Chloroform in acetone

Resolution Factors affect resolution Relaxation process of the observed nucleus Stability of B0 (shimming and deuterium locking) Probe (sample coil should be very close to the sample) Sample properties and its conditions

Sensitivity Definition signal to noise-ratio A : height of the chosen peak Npp : peak to peak noise

Sensitivity Measurement 1H 0.1% ethyl benzene in deuterochloroform 13C ASTM, mixture of 60% by volume deuterobenzene and dioxan or 10% ethyl benzene in chloroform 31P 1% trimehylphosphite in deuterobenzene 15N 90% dimethylformamide in deutero-dimethyl- sulphoxide 19F 0.1% trifluoroethanol in deuteroacetone 2H, 17O tap water

Sensitivity Factors affect sensitivity Probe: tuning, matching, size Dynamic range and ADC resolution Solubility of the sample in the chosen solvent

Spectral Parameters Chemical Shift Spin-spin Coupling Caused by the magnetic shielding of the nuclei by their surroundings. d-values give the position of the signal relative to a reference compound signal. Spin-spin Coupling The interaction between neighboring nuclear dipoles leads to a fine structure. The strength of this interaction is defined as spin-spin coupling constant J. Intensity of the signal

Chemical Shift Origin of chemical shift s shielding constant Chemically non-equivalent nuclei are shielded to different extents and give separate resonance signals in the spectrum

Chemical Shift

Chemical Shift d – scale or abscissa scale

Chemical Shift Shielding s CH3Br < CH2Br2 < CH3Br < TMS 90 MHz spectrum

Abscissa Scale

Chemical Shift d is dimensionless expressed as the relative shift in parts per million ( ppm ). d is independent of the magnetic field d of proton 0 ~ 13 ppm d of carbon-13 0 ~ 220 ppm d of F-19 0 ~ 800 ppm d of P-31 0 ~ 300 ppm

Chemical Shift Charge density Neighboring group Anisotropy Ring current Electric field effect Intermolecular interaction (H-bonding & solvent)

Chemical Shift – anisotropy of neighboring group c susceptibility r distance to the dipole’s center Differential shielding of HA and HB in the dipolar field of a magnetically anisotropic neighboring group

Chemical Shift – anisotropy of neighboring group d~2.88 d~9-10

Electronegative groups are "deshielding" and tend to move NMR signals from neighboring protons further "downfield" (to higher ppm values). Protons on oxygen or nitrogen have highly variable chemical shifts which are sensitive to concentration, solvent, temperature, etc. The -system of alkenes, aromatic compounds and carbonyls strongly deshield attached protons and move them "downfield" to higher ppm values.

Electronegative groups are "deshielding" and tend to move NMR signals from attached carbons further "downfield" (to higher ppm values). The -system of alkenes, aromatic compounds and carbonyls strongly deshield C nuclei and move them "downfield" to higher ppm values. Carbonyl carbons are strongly deshielded and occur at very high ppm values. Within this group, carboxylic acids and esters tend to have the smaller values, while ketones and aldehydes have values 200.

Ring Current The ring current is induced form the delocalized p electron in a magnetic field and generates an additional magnetic field. In the center of the arene ring this induced field in in the opposite direction t the external magnetic field.

Ring Current -- example

Spin-spin coupling

Spin-spin coupling

AX system

AX2 system

Spin-spin coupling

AX3 system

Multiplicity Rule Multiplicity M (number of lines in a multiplet) M = 2n I +1 n equivalent neighbor nuclei I spin number For I= ½ M = n + 1

Example AX4 system I=1; n=3 AX4

Order of Spectrum Zero order spectrum only singlet First order spectrum Dn >> J Higher order spectrum Dn ~ J

AMX system

Spin-spin coupling Hybridization of the atoms Bond angles and torsional angles Bond lengths Neighboring p-bond Effects of neighboring electron lone-pairs Substituent effect

JH-H and Chemical Structure Geminal couplings 2J (usually <0) H-C-H bond angle hybridization of the carbon atom substituents

Geminal couplings 2J bond angle

Effect of Neighboring p-electrons Geminal couplings 2J Effect of Neighboring p-electrons Substituent Effects

Vicinal couplings 3JH-H Torsional or dihedral angles Substituents HC-CH distance H-C-C bond angle

Vicinal couplings 3JH-H dihedral angles Karplus curves

Chemical Shift of amino acid http://bouman.chem.georgetown.edu/nmr/interaction/chemshf.htm

Chemical Shift Prediction Automated Protein Chemical Shift Prediction http://www.bmrb.wisc.edu:8999/shifty.html BMRB NMR-STAR Atom Table Generator for Amino Acid Chemical Shift Assignments http://www.bmrb.wisc.edu/elec_dep/gen_aa.html

http://bouman.chem.georgetown.edu/nmr/interaction/chemshf.htm

Example 1

Relaxation Time Phenomenon & Application NMR Spectroscopy Relaxation Time Phenomenon & Application

Relaxation- Return to Equilibrium x,y plane z axis Transverse Longitudinal 1 1 t t 2 2 E-t/T2 1-e-t/T1 8 8 Transverse always faster!

magnetization vector's trajectory Relaxation magnetization vector's trajectory The initial vector, Mo, evolves under the effects of T1 & T2 relaxation and from the influence of an applied rf-field. Here, the magnetization vector M(t) precesses about an effective field axis at a frequency determined by its offset. It's ends up at a "steady state" position as depicted in the lower plot of x- and y- magnetizations. http://gamma.magnet.fsu.edu/info/tour/bloch/index.html

Relaxation                       The T2 relaxation causes the horizontal (xy) magnetisation to decay. T1 relaxation re-establishes the z-magnetisation. Note that T1 relaxation is often slower than T2 relaxation.

Relaxation time – Bloch Equation

Relaxation time – Bloch equation

Spin-lattice Relaxation time (Longitudinal) T1 Relaxation mechanisms: 1. Dipole-Dipole interaction "through space" 2. Electric Quadrupolar Relaxation 3. Paramagnetic Relaxation 4. Scalar Relaxation 5. Chemical Shift Anisotropy Relaxation 6. Spin Rotation

Relaxation Spin-lattice relaxation converts the excess energy into translational, rotational, and vibrational energy of the surrounding atoms and molecules (the lattice). Spin-spin relaxation transfers the excess energy to other magnetic nuclei in the sample.

Longitudinal Relaxation time T1 Inversion-Recovery Experiment 180y (or x) 90y tD

T1 relaxation

Range of interaction (Hz) relevant parameters Dipolar coupling 104 - 105 - abundance of magnetically active nuclei - size of the magnetogyric ratio Quadrupolar coupling 106 - 109 - size of quadrupolar coupling constant - electric field gradient at the nucleus Paramagnetic 107 -108 concentration of paramagnetic impurities Scalar coupling 10 - 103 size of the scalar coupling constants Chemical Shift Anisotropy (CSA) 10 - 104 - size of the chemical shift anisotropy - symmetry at the nuclear site 6- Spin rotation

Spin-spin relaxation (Transverse) T2 T2 represents the lifetime of the signal in the transverse plane (XY plane) T2 is the relaxation time that is responsible for the line width. line width at half-height=1/T2

Spin-spin relaxation (Transverse) T2 Two factors contribute to the decay of transverse magnetization. molecular interactions ( lead to a pure pure T2 molecular effect) variations in Bo ( lead to an inhomogeneous T2 effect)

Spin-spin relaxation (Transverse) T2 90y 180y (or x) tD tD signal width at half-height (line-width )= (pi * T2)-1

Spin-spin relaxation (Transverse) T2

Spin-Echo Experiment

Spin-Echo experiment

MXY =MXYo e-t/T2

Carr-Purcell-Meiboom-Gill sequence

T1 and T2 In non-viscous liquids, usually T2 = T1. But some process like scalar coupling with quadrupolar nuclei, chemical exchange, interaction with a paramagnetic center, can accelerate the T2 relaxation such that T2 becomes shorter than T1.

Relaxation and correlation time For peptides in aqueous solutions the dipole-dipole spin-lattice and spin-spin relaxation process are mainly mediated by other nearby protons

Why The Interest In Dynamics? Function requires motion/kinetic energy Entropic contributions to binding events Protein Folding/Unfolding Uncertainty in NMR and crystal structures Effect on NMR experiments- spin relaxation is dependent on rate of motions  know dynamics to predict outcomes and design new experiments Quantum mechanics/prediction (masochism)

Application

Characterizing Protein Dynamics: Parameters/Timescales Relaxation

NMR Parameters That Report On Dynamics of Molecules Number of signals per atom: multiple signals for slow exchange between conformational states Linewidths: narrow = faster motion, wide = slower; dependent on MW and conformational states Exchange of NH with solvent: requires local and/or global unfolding events  slow timescales Heteronuclear relaxation measurements R1 (1/T1) spin-lattice- reports on fast motions R2 (1/T2) spin-spin- reports on fast & slow Heteronuclear NOE- reports on fast & some slow

Linewidth is Dependent on MW A B Small (Fast) Big (Slow) 1H 15N Linewidth determined by size of particle Fragments have narrower linewidths

Nuclear Overhauser Effect

Nuclear Overhauser Effect (NOE) A change in the integrated NMR absorption intensity of a nuclear spin when the NMR absorption of another spin is saturated.

Nuclear Overhauser Effect

Macromolecules or in viscous solution W0 dominant, negative NOE at i due to s Small molecules in non-viscous solution W2 dominant, positive NOE at i due to s

Nuclear Overhauser Effect Brownian motion and NOE

When 1/tc >>w0 (or tc2 w02 <<1 ) extreme narrowing limit

When 1/tc >> w0 (or tc2 w02 <<1 ) extreme narrowing limit For homo-nuclear hmax = 0.5 For hetro-nuclear hmax = 0.5 (gs/gi)

When 1/tc ~ w0 (or tc w0 ~ 1 ) M.W.~ 103 W2 and W0 effect are balanced.  max ~ 0 improvement: Change solvent ofr temperature Using rotating frame NOE

When 1/tc < w0 (or tc w0 >> 1 ) M.W. > 104 W0 dominant ,  max = -1 application Useful technique for assigning NMR spectra of protein

Nuclear Overhauser Effect & distance

citraconic acid mesaconic acid