Overview and Context Nuclear Magnetic Resonance Summary Biophysical Chemistry: NMR Spectroscopy Nuclear Magnetism Lieven Buts Vrije Universiteit Brussel 21st October 2011 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Nuclear Magnetic Resonance Summary Outline Overview and Context 1 Practical Matters Electromagnetism Refresher Organic Chemistry Refresher Nuclear Magnetic Resonance 2 Nuclear Spin and Magnetism Practical Implications Summary 3 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Outline Overview and Context 1 Practical Matters Electromagnetism Refresher Organic Chemistry Refresher Nuclear Magnetic Resonance 2 Nuclear Spin and Magnetism Practical Implications Summary 3 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Context Functional characterisation (binding studies, enzymology, in vivo studies) Proteins (and Function and other biological dysfunction macromolecules) Structural characterisation (information about larger complexes, high-resolution structures of the components) High-resolution NMR X-ray crystallography (HNMR) (diffraction) Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Prerequisites and References This part of the course assumes basic familiarity with the theory of electromagnetism and organic chemistry. The following books are used as reference material: Nuclear Magnetic Resonance (Oxford Chemistry Primers #32), P .J. Hore, Oxford Science Publications, ISBN 0-19-855682-9 Spin Dynamics: Basics of Nuclear Magnetic Resonance (2nd edition), M.H. Levitt, Wiley, ISBN 978-0-470-51117-6 Understanding NMR Spectroscopy , J. Keeler, Wiley, ISBN 978-0-470-01786-9 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Outline Overview and Context 1 Practical Matters Electromagnetism Refresher Organic Chemistry Refresher Nuclear Magnetic Resonance 2 Nuclear Spin and Magnetism Practical Implications Summary 3 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher The Electric Field Coulomb’s law describes the force between two The deflection of an electron static charges q and q 0 : between two charged plates is a 1 qq 0 classical application of this idea: r 2 � � F = 1 r 4 πǫ 0 and leads to the concept of the electric field emanating from one charge and influencing the other: � F 1 q � r 2 � E = = 1 r 4 πǫ 0 q 0 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Magnetism The magnetic field is introduced to describe interactions between moving charges: � v × � F = q · � B Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Magnetic Dipoles (1) A magnetic dipole produces a magnetic field with a characteristic pattern of field lines, and can be describe by the following equations: B µ, x = µ 0 µ r 3 ( 3 sin ( θ ) cos ( θ )) 4 π B µ, y = 0 B µ, z = µ 0 µ r 3 ( 3 cos 2 ( θ ) − 1 ) 4 π Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Magnetic Dipoles (2) In certain positions the magnetic field vector has special properties: parallel with the dipole moment on the z axis antiparallel to the dipole moment on the x axis perpendicular to the dipole moment on a line making an angle θ = 54 . 7 ◦ (for which 3 cos 2 ( θ ) − 1 = 0 ) with the z axis. Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Magnetic Dipoles (3) The energy of a magnetic dipole in an external magnetic field is determined by their strengths and relative orientation: µ · � µ | · | � E = � B = | � B | · cos ( θ ) Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Induction and EM Waves Electric currents give rise to magnetic fields, and changing magnetic fields induce currents in conductors. An alternating current produces electromagnetic waves, in which the electric and magnetic fields evolve in a coupled way, and both become functions of position and time: � E = � r , t ); � B = � r , t ); � B ⊥ � E ( � B ( � E The most complete description of all EM phenomena is provided by the Maxwell equations. Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher Outline Overview and Context 1 Practical Matters Electromagnetism Refresher Organic Chemistry Refresher Nuclear Magnetic Resonance 2 Nuclear Spin and Magnetism Practical Implications Summary 3 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Practical Matters Nuclear Magnetic Resonance Electromagnetism Refresher Summary Organic Chemistry Refresher The Quantum Mechanical Atom The classical "solar system" model with particles following a well-defined trajectory is replaced by a probabilistic description with an inherent uncertainty principle. Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Molecular Orbitals
Overview and Context Nuclear Spin and Magnetism Nuclear Magnetic Resonance Practical Implications Summary Outline Overview and Context 1 Practical Matters Electromagnetism Refresher Organic Chemistry Refresher Nuclear Magnetic Resonance 2 Nuclear Spin and Magnetism Practical Implications Summary 3 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Nuclear Spin and Magnetism Nuclear Magnetic Resonance Practical Implications Summary Nuclear Spin Elementary particles, such as electrons, neutrons and protons, have been found to possess an intrinsic angular momentum, known as spin . Spin is a fundamental property of particles, just like their mass and charge, and cannot be intepreted in terms of an actual physical rotation. The spin angular momentum is a vector quantity � I with a � magnitude of I ( I + 1 ) � , where I is the spin quantum number of the particle. For electrons, neutrons and protons, I = 1 2 . In atomic nuclei the spins of the component protons and neutrons partially or completely compensate each other, leaving the nucleus with a relatively small spin quantum number I of 0, 1 2 , 1, 3 2 , 2, ... Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Nuclear Spin and Magnetism Nuclear Magnetic Resonance Practical Implications Summary Nuclear Magnetism The intrinsic angular momentum � I inevitably gives rise to a magnetic dipole moment � µ : µ = γ� � I in which the gyromagnetic ratio γ is a characteristic constant for each type of nucleus. Because the nuclei of different isotopes have different numbers of neutrons, they will have different spin quantum numbers and magnetogyric ratios. In NMR, isotopes are generally referred to as nuclides . Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Nuclear Spin and Magnetism Nuclear Magnetic Resonance Practical Implications Summary Biologically Relevant Nuclides γ/ 10 7 radT − 1 s − 1 Nuclide I Abundance/% 1 H 1 26.75 99.985 2 2 H 1 4.11 0.015 12 C 0 0 98.89 13 C 1 6.73 1.108 2 14 N 1 1.93 99.64 1 15 N -2.71 0.36 2 16 O 0 0 99.756 5 17 O -3.63 0.037 2 18 O 0 0 0.205 Lieven Buts Biophysical Chemistry: NMR Spectroscopy
Overview and Context Nuclear Spin and Magnetism Nuclear Magnetic Resonance Practical Implications Summary Quantisation The angular momentum, and therefore the dipole moment, are further quantised in a single direction, which is chosen to lie along the z axis by convention. The quantisation rule states that the z component of � I can only adopt values of the form I z = m � . m is the magnetic quantum number , which can adopt values between − I and I , in integer steps: m = I , I − 1 , I − 2 , ..., − I + 1 , − I 2 π , where h = 6 . 622 × 10 − 34 J . s is the Planck constant . h � = Lieven Buts Biophysical Chemistry: NMR Spectroscopy
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