L ECTURE COURSE: NMR S PECTROSCOPY - UZH

1 L ECTURE course : NMR S PECTROSCOPY 1 Table of Content The physical basis of the NMR experiment 5 The Bloch equations: 8 Quantum-mechanical treatment: 9 The macroscopic view: 10 Fourier Transform NMR: 14 The interaction between the magnetization and the additonal RF (B1) field: 14 Description of the effect of the B1 field on transverse and lon-gitudinal magnetization using the Bloch equations: 16 The excitation profile of pulses: 17 Relaxation: 18 The intensity of the NMR signal: 20 Practical Aspects of NMR: The components of a NMR instrument The magnet system: 22 The probehead: 23 The shim system: 25 The lock-system: 28 The transmitter/receiver system: 28 Basic data acquisition parameter 31 Acquisition of 1D spectra 36 Calibration of pulse lengths: 36 Tuning the probehead: 38 Adjusting the bandwidth of the recorded spectrum: 39 Data processing: 40 Phase Correction 43 Zero-filling and the resolution of the spectrum46 Resolution enhancement and S/N improvement 47 Exponential multiplication: 48 Lorentz-to-Gauss transformation: 48 Sine-Bell apodization: 49 Baseline Correction 50 Linear prediction: 51 The chemical shift: 53 The diamagnetic effect: 53 The paramagnetic term: 54 Chemical shift anisotropy.

2 56 Magnetic anisotropy of neighboring bonds and ring current shifts: 57 Electric field gradients: 59 Hydrogen bonds: 59 Solvent effects: 60 Shifts due to paramagnetic species: 60 L ECTURE course : NMR S PECTROSCOPY 2 Scalar couplings: 60 Direct couplings (1J): 62 Geminal couplings (2J): 63 Vicinal couplings (3J): 63 Long-range couplings: 65 Couplings involving p electrons: 65 The number of lines due to scalar spin,spin couplings: 65 Strong coupling: 67 Relaxation: 68T1 relaxation: 68T2 relaxation: 69 The mechanisms of relaxation: 70 Other relaxation mechanisms: 72 Chemical shift anisotropy (CSA): 72 Scalar relaxation: 72 Quadrupolar relaxation: 73 Spin-rotation relaxation: 73 Interaction with unpaired electrons: 73 The motional properties: 73 The dependence of the relaxation rates on the fluctuating fields in x,y or z direction: 75 Excurs: The Lipari-Szabo model for motions: 77 The nature of the transitions: 78 Measurement of relaxation times: 80 The Nuclear Overhauser Effect (NOE): 84 Experiments to measure NOEs: 86 The steady-state NOE: 87 Extreme narrowing (hmax >0): 87 Spin-diffusion (hmax <0): 88 The transient NOE: 89 The state of the spin system and the density matrix: 90 The sign of the NOE: 92 Why only zero- and double-quantum transitions contribute to the NOE 94 Practical tips for NOE measurements: 96 Chemical or conformational exchange.

3 99 Two-site exchange: 99 Fast exchange: 101 The slow exchange limit: 102 The intermediate case: 102 Investigation of exchange processes: 103 EXSY spectroscopy : 103 Saturation transfer: 104 Determination of activation parameters: 105 L ECTURE course : NMR S PECTROSCOPY 3 The product operator formalism (POF) for description of pulse-experiments: 106RF pulses: 107 Chemical shift precession: 107 Scalar spin,spin coupling: 108A simple one-dimensional NMR experiment: 110 The effect of 180 degree pulses: 111 Coherence transfer: 112 Polarization transfer: 113 Two-Dimensional nmr spectroscopy : 118 The preparation period: 120 The evolution period: 121 The mixing period: 122 The detection period: 124 Hetcor and inverse-detection experiments: 124 Phasecycling: 125An Alternative: Pulsed Field Gradients 126 Hybrid 2D techniques: 128 Overview of 2D experiments: 129 Original references for 2D experiments: 130 Solid State nmr spectroscopy : 132 The chemical shift 132 Dipolar couplings: 135 Magic Angle Spinning (MAS) 136 Sensitivity Enhancement:136 Recoupling techniques in SS-NMR:137SS-NMR of oriented samples: 140 Labeling strategies for solid-state NMR applications : 142 L ECTURE course .

4 NMR S PECTROSCOPY 4 A PPLICATION F IELDS OF NMR S PECTROSCOPY High-resolution nmr spectroscopy Analytics"small" moleculesdetermination of the covalent structuredetermination of the purityElucidation of the 3D structure "small" moleculesdetermination of the stereochemistry: cis,trans isomerism, determination of optical purityBiopolymers up to about 20-30 kDadetermination of the 3D solution structure provided the pri-mary sequence is known! investigation of the interaction of molecules (complexes) investigation of the dynamics of proteins 1 H, 13 C or 15 N relaxation measurements 1 H, 1 H oder 1 H, 15 N NOE measurementsDetermination of the kinetics of reactions Solid-state nmr spectroscopy insoluble compounds (synthetic polymers)very large compounds (requires specific labels)determination of the structure in the solid-state (vs.)

5 Liquid-state)determination of the dynamics in the solid-state Imaging techniques spin tomography "In vivo" nmr spectroscopy distribution of metabolites in the body L ECTURE C OURSE : NMR S PECTROSCOPY First Chapter: Physical Basis of the NMR Experiment 1. T HE PHYSICAL BASIS OF THE NMR EXPERIMENT Imagine a charge travelling circularily about an axis. This is similar to a currentthat flows through a conducting loop:Such a circular current builds up a magnetic moment whose direction is per-pendicular to the plane of the conducting loop. The faster the charge travelsthe stronger is the induced magnetic field. In other words, a magnetic dipolehas been dipoles, when placed into a magnetic field, are expected to align with thedirection of the magnetic field.

6 In the following we will look at a mechanicalequivalent represented by a compass needle that aligns within the gravita-tional field:When such a compass needle is turned away from the north-pole pointingdirection to make an angle a force acts on the needle to bring it back. For thecase of a dipole moment that has been created by a rotating charge this force isproportional to the strength of the field ( B ) and to the charge ( m ).The torque that acts to rotate the needle may be described asin which J is defined as the angular momentum which is the equivalent for rota- FIGURE 1. FIGURE 2. N Tt JrF == L ECTURE C OURSE : NMR S PECTROSCOPY First Chapter: Physical Basis of the NMR Experiment tional movements of the linear that the direction of the momentum is tangential to the direction alongwhich the particle moves.

7 The torque is formed by the vector product betweenthe radius and the momentum (see additional material) and is described by avector which is perpendicular to both radius and momentum. In fact, it is theaxis of rotation which is perpendicular to the plane. The corresponding poten-tial energy isIn contrast to the behaviour of a compass needle the nuclear spin does notexactly align with the axis of the external field: FIGURE 3. Left: linear momentum. Right: angular momentumFIGURE 4. Rotation of the nuclear momentum about its own axis (blue) and about the magnetic field axis (red).p = m vJ = r x pExcurse: Corresponding parameter for translational and rotational movementsPureTranslation (fixed direction)Pure Rotation (fixed axis)Positionx Velocityv = dx/dt =d /dtAccelerationa = dv/dt = d /dtTranslational (Rot.)

8 InertiamIForce (Torque)F T = r x FMomentump = mvJ = r x pWorkW = Int F dxW = Int T d Kinetic energyK = 1/2 mv2K = 1/2 I 2 PowerP = F vP = EpotT d0 =B LECTURE course : nmr spectroscopy First Chapter: Physical Basis of the NMR Experiment is a consequence of its rotation about its own axis. This property is calledspin. It rotates (spins) about its own axis (the blue arrow) and precesses aboutthe axis of the magnetic field B (the red arrow). The frequency of the precessionis proportional to the strength of the magnetic field: = BThe proportionality constant is called the gyromagnetic frequency is expressed in terms of a angular velocity (see additionalmaterial). It is specific for the kind of nucleus and therefore has a differentvalue for 1H,13C,19F etc.

9 The precession frequency 0 = 2 is called the Lamor frequency. In contrast to a compass needle which behaves"classically" in the way that it can adopt a continous band of energies depend-ing only on the angle it makes with the field the corresponding angle of thenuclear dipole moment is quantitized. Hence, we will later introduce the quan-tum-mechanical treatment course , we do not observe single molecules but look at an ensemble of mol-ecules (usually a huge number of identical spins belonging to different mole-cules). The sum of the dipole moments of identical spins is calledmagnetization:Excurse: The movement of a classical gyroscopeImagine a wheel fixed to a shaft. When the this gyroscope is placed with the shaft perpendicular to the ground and released it will fall down (see Fig.)

10 Below, left side). However, when the wheel spins about the axis of the shaft, the gyroscope precesses about the axis perpendicular to the ground with a fre-quency that is called the precession frequency (right side) and takes a well-defined angle with respect to the rotation axis: M ij =LECTURE course : nmr spectroscopy First Chapter: Physical Basis of the NMR Experiment The Bloch equations:The Bloch s equations describe the fate of magnetization in a magnetic have stated before that a force ( a torque) acts on a dipole moment when itis placed inside a mgnetic field such that the dipole moment will be alignedwith the direction of the static magnetic field. Mathematically this is decribedby forming the vector product between dipole moment and magnetic field (seeadd.