Nuclear Magnetic Resonance Lecture Date: February 11th, 2008 Nuclear Magnetic Resonance  Reading for NMR: – Chapter 19 of Skoog, et al – Handout: “What SSNMR can offer to organic chemists”  Nuclear Magnetic Resonance (NMR) – Nuclear spin transitions, in the 5-900 MHz range – Magnetic resonance imaging (MRI) The Electromagnetic Spectrum  NMR, MRI  EPR/ESR What is NMR?  NMR is an experiment in which the resonance frequencies of nuclear magnetic systems are investigated  NMR always employs some form of magnetic field (usually a strong externally applied field B0)  NMR is a form of both absorption and emission spectroscopy, in which resonant radiation is absorbed by an ensemble of nuclei in a sample, a process causing detectable emissions via a magnetically induced electromotive force A Abragam, The Principles of Nuclear Magnetism, 1961, Oxford: Clarendon Press Things that can be learned from NMR data…  Covalent chemical structure (“2D structure”) – Which atoms/functional groups are present in a molecule – How the atoms are connected (covalently bonded)  3D Structure – Conformation – Stereochemistry  Molecular motion  Chemical dynamics and exchange  Diffusion rate  3D Distribution of NMR spins in a medium – an image! – (Better known as MRI)  Plus many more things of interest to chemists… History of NMR  1920-1930: physics begins to grasp the        concepts of electron and nuclear spin 1936: C J Gorter (Netherlands) attempts to study 1H and 7Li NMR with a resonance method, but fails because of relaxation 1945-6: E M Purcell (Harvard) and F Bloch (Stanford) observe 1H NMR in kg of parafin at 30 MHz and in water at MHz, respectively 1952: Nobel Prize in Physics to Purcell and Bloch 1957: P C Lauterbur and Holm independently record 13C spectra 1991: Nobel Prize in Chemistry to R R Ernst (ETH) for FT and 2D NMR 2002: Nobel Prize in Chemistry to K Wuthrich 2003: Nobel Prize in Medicine to P C Lauterbur and P Mansfield for MRI P C Lauterbur E M Purcell F Bloch R R Ernst Photographs from www.nobelprize.org Nuclear Magnetism  A nuclear electromagnet is created by the nucleons (protons and neutrons) inside the atomic nucleus  This little electromagnet has a magnetic moment (J T-1) – The magnetic moment is proportional to the current flow through the “nuclear loop” N  The nucleus looks like a dipole to a distant charge center From http://education.jlab.org S Basic NMR Theory  In a strong applied magnetic field (B0), certain atomic nuclei will align or oppose this field  This alignment is caused by the magnetic moments of the nuclei, which themselves are caused by the internal structure of the nucleus Two nuclear properties stand out: – – Spin (1/2 for 1H, 13C, etc…) Gyromagnetic ratio  An excess of alignments is found in the lower energy state (determined by a Boltzmann distribution)  At room temperature, this excess is very small, typically only part per trillion! Nuclear Spin  In a classical sense the bulk nuclear magnetization is observed to “precess” at the Larmor frequency (usually several hundred MHz): B0  B0 2    B0 0  angular (rad/s) linear (Hz, cycles/s)  The constant  is the magnetogyric ratio Elements Accessible by NMR White = only spin ½ Pink = spin or greater (quadrupolar) Yellow = spin ½ or greater Figure from UCSB MRL website Pulsed vs Continuous-Wave NMR  NMR effects are most commonly detected by resonant radio-frequency experiments  Continuous-wave NMR: frequency is swept over a range (e.g several kilohertz), absorption of RF by sample is monitored – Historically first method for NMR – Poor sensitivity – Still used in lock circuits  Pulsed NMR – short pulses (at a specific frequency) are applied to the sample, and the response is monitored – Much more flexible (pulse sequences followed from this…) – Short pulses can excited a range of frequencies NMR Theory: The Rotating Frame  The magnetization precesses at the Larmor frequency, the RF field(s)  oscillate at or near this same frequency The “rotating frame” rotates at this frequency, simplifies the picture for analysis and understanding z z eye y x Frame rotating at the Larmor frequency (hundreds of MHz) Frame is now still Spin Systems  The reason NMR is so applicable to structural problems is that the governing interactions can be separated and treated individually – Experimentally, this results in spectral simplification (in that transitions are not hopelessly entangled) and also allows for detailed manipulations (pulse sequences) to extract information  This involves separation of electronic Hamiltonian from the nuclear spin Hamiltonians  NMR is thus “simplified” in that its data can be linked back to “spin systems” Examples of spin systems: – Several 1H nuclei (i.e hydrogen) within or covalent bonds of each other – A 1H nucleus attached to a 13C nucleus NMR Theory: RF Pulses  RF pulses are used to drive the bulk magnetization to the desired position  The action of an RF pulse is determined by its frequency, amplitude,  length and phase For an on-resonant pulse, the right hand rule predicts its action z z y y x Drawing depicts a 90o pulse x Drawing depicts a 180o pulse NMR Theory: RF Pulses and Spin Echoes An RF pulse: Actually not “solid”, contains RF frequencies Two pulses: echo (delays and extra pulse) Selection Rules  Single-quantum transitions (m =   +/- 1) are allowed by angular momentum rules (which govern spins in NMR) Single-quantum states are directly detected in NMR experiments However, it is possible to excite double-quantum states (or zeroquantum, triple-quantum, etc…), let them evolve with time, then convert them back to SQ states for observation  SQ X  X   Energy levels for two coupled spins showing SQ (single quantum) transitions in green and forbidden ZQ (zero quantum) and DQ (double quantum) transitions in red NMR Theory: T1 Relaxation  T1 relaxation: longitudinal relaxation (re-establishment of Boltzmann equilibrium) by spins interacting with the “lattice” z  In practice, T1 controls how quickly FT experiments can be repeated for signal averaging y x  Measurements of T1 can provide useful data on molecular motions NMR Theory: T2 Relaxation  T2 relaxation transverse relaxation (dephasing of coherence) by spins interacting with each other z  Controls how long magnetization can be kept in the x-y plane y x  Controls the linewidth (FWHH) of the NMR signals:  /   T2* NMR Theory: The Chemical Shift  The electrons around a nucleus  shield are circulated by the big magnetic field, inducing smaller fields x Anisotropy: TPPO y z  Units – ppm:  ( ppm )  10  x   ref  PbSO4  ref  Shift-structure correlations – the  basis of NMR as an analytical tool Shift-structure correlations are available for 1H, 13C, 15N, 29Si, 31P and many other nuclei Above: the chemical shift in solids is not a single peak! Typical 1H NMR Chemical Shielding 10 Typical 13C NMR Chemical Shielding Other Nuclei: 17O NMR Note – 17O NMR requires labeling or concentrated solutions, and suffers from large solution-state linewidths (caused by quadrupolar relaxation) 11 NMR Theory: The Chemical Shift  Contributions from electronegativity and ring current effects: Correlation of H Chemical Shift and Group Electronegativity for CH 3X Compounds 4.5 Group Electronegativity 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0 1.0 2.0 3.0 Re lativ e Che mical Shift ( ) 4.0 5.0 Dailey et al., J Am Chem Soc., 77, 3977 (1955) NMR Theory: The Chemical Shift  Contributions from ring current effects  Above center of ring (z-axis): shielding  In plane of ring ( axis): deshielding Figure from http://www.chemlab.chem.usyd.edu.au/thirdyear/organic/field/nmr/ans02.htm 12 NMR J-Coupling  The J-coupling is an effect in which   nuclear magnetic dipoles couple to each other via the surrounding electrons The effect is tiny but detectable! Typical J-values – – 1J –  2-4J 2-4J HH can range from –15 to +15 Hz and depends on the number of bonds, bond angles, and torsion angles CH can range from 120 to 280 Hz, but typically is ~150 Hz in most organics CH ranges from –15 to +15 Hz and depends on effects similar to the 2-4JHH The narrow ranges that certain 1H and 13C J-coupling values fall into make spectral editing and heteronuclear correlation experiments possible!!! J-Coupling: Effects on NMR Spectra  Two basic types of coupling – Homonuclear (e.g 1H-1H) – Heteronuclear (e.g 1H-19F)  Weak coupling – Large difference in frequency   >> J  #Lines = n I +  All heteronuclear coupling is “weak”  More complex splitting patterns can be visualized using Pascal’s triangle (see text)  Strong coupling – Small difference in frequency   ~ J  Complex patterns Figure simulated in Bruker Topspin 2.0 DAISY module Inspired by S W Homans, A Dictionary of Concepts in NMR, Oxford 1989, p297 13 J-Coupling: Effects on NMR Spectra ortho  Example:  meta monofluorobenzene Homonuclear coupling between 1H: para – ortho-coupling – meta-coupling – para-coupling  Heteronuclear coupling between 1H and 19F: – As above (ortho, meta, and para) – Observed from the 19F, appears as a doublet of triplets of triplets (ttd)  Fluorine can be decoupled from the 1H spectrum (not shown) Structural and Conformational Analysis  J-coupling is widely used (in conjunction with 2D NMR) to assemble portions of a molecule – In this case, the J-coupling is simply detected in a certain range and its magnitude is not examined closely  J-coupling is also used to study conformation and stereochemistry of organic/organometallic/biochemical systems in solution – In this case, the J-coupling is measured e.g to the nearest 0.1 Hz and analyzed more closely W A Thomas, Prog NMR Spectros., 30 (1997) 183-207 14 J-Coupling: Angle Effects  Karplus relationships – the effects of bond and torsion angles on J-coupling Bond angles, dihedral (torsion) angles, and 5bond angles  @8@ @ D D D @ < @ D D In[1]:= J q_ := 4.22Cos q In[3]:= Plot J q , q, 0, p + - 0.5Cos q + 4.5 Coupling constant (Hz) 0.5 Out[3]= …Graphics … 1.5 2.5 Dihedral angle (radians) Dipolar Coupling  The magnetic dipolar interaction between the moments of two spin-1/2 nuclei – One spin senses the other’s orientation directly through space  The dipolar coupling is simply related to the internuclear distance between the spins:   D  0 I S 8 r  The truncated (secular) dipolar Hamiltonians (relevant to NMR) have the form:   Homonuclear HD  D  cos  I z S z  I  S   I  S     Heteronuclear HD  D  cos  I z S z  15 Dipolar Coupling  Example – what’s the dipolar coupling between a 13C and a 15N nucleus 1.32 angstroms apart? The permeability constant (in kg m sec- A- ) and Planck's constant (in Joule sec): m = p ´ 10- 7; Ñ = 6.62608 ´ 10- 34 H L 2p ; The gyromagnetic ratios for 13C and 15N, in units of radians Tesla- sec- : gI = 6.728 ´ 107; @J NNN D JJ A E A gS = - 2.712 ´ 107; R r_ := gI gS Ñ m r3 2p 4p N R 1.32 ´ 10- 10 - 1331.53 The dipolar coupling is therefore 1.332 kHz The Nuclear Overhauser Effect  The idea: detect the “cross-relaxation” caused by instantaneous dipolar coupling in an NMR or EPR experiment  This was conceived by A W Overhauser, while a graduate student at UC Berkeley in 1953  Overhauser predicted that saturation of the conduction electron spin resonance in a metal, the nuclear spins would be polarized 1000 times more than normal!!! 16 The Nuclear Overhauser Effect  Dipolar coupling is a direct magnetic interaction  between the moments of two spin-1/2 nuclei The coherent effects of dipolar coupling are averaged away in solution-state NMR by rapid molecular tumbling  However, the dipolar interaction can still play a role via in solution-state NMR via dipolar crossrelaxation mechanisms, better known as the nuclear Overhauser effect (NOE) NMR Spectrometer Design  The basic idea: 17 NMR Magnets  Superconducting magnets: Resonance  The natural frequency of a inductive-capacitive circuit: r  LC  The NMR system requires a resonant circuit to detect nuclear spin transitions – this circuit is part of the probe 18 Resonant Circuits in Probes  Figure from Bruker Instruments NMR Probe Design  The NMR probe – designed to efficiently produce an inductance (~W) and detect the result (< mW) 19 NMR Electronics  NMR transmitter and receiver designs Further Reading  A E Derome, “Modern NMR Techniques for Chemistry  Research”, Pergamon 1987 P W Atkins and R S Friedman, “Molecular Quantum Mechanics, 3rd Ed.”, Oxford 1997  A Abragam, “Principles of Nuclear Magnetism”, Oxford,   1961 R R Ernst, G Bodenhausen, and A Wokaun, “Principles of Nuclear Magnetic Resonance in One and Two Dimensions”, Oxford, 1987 C P Slichter, “Principles of Nuclear Magnetic Resonance”, Springer-Verlag, 1996 20 ... Tesla- sec- : gI = 6.728 ´ 10 7; @J NNN D JJ A E A gS = - 2. 712 ´ 10 7; R r_ := gI gS Ñ m r3 2p 4p N R 1. 32 ´ 10 - 10 - 13 31. 53 The dipolar coupling is therefore 1. 332 kHz The Nuclear Overhauser Effect... 1H, 13 C, 15 N, 29Si, 31P and many other nuclei Above: the chemical shift in solids is not a single peak! Typical 1H NMR Chemical Shielding 10 Typical 13 C NMR Chemical Shielding Other Nuclei: 17 O... Oxford 19 97  A Abragam, “Principles of Nuclear Magnetism”, Oxford,   19 61 R R Ernst, G Bodenhausen, and A Wokaun, “Principles of Nuclear Magnetic Resonance in One and Two Dimensions”, Oxford, 19 87