COURSE#1022: Biochemical Applications of NMR Spectroscopy. Basic Principles

Transcription

1 COURSE#1022: Biochemical Applications of NMR Spectroscopy Basic Principles LAST UPDATE: 1/11/2012

2 Reading Selected Readings for Basic Principles of NMR (any of the following): Evans, pp 2-13 Teng, Chapter 1, pp Cavanagh, Fairbrother, Palmer, & Skelton (1st Ed), pp 1-16 Keeler, Chapter 3 Derome, pp Macomber, Chapters 1 and 2 Online Sources Content from the following online sources were used for some slides in this presentation:

3 What is Spectroscopy? Spectroscopy is the study of the interaction of light with matter. Light refers to any sort of electromagnetic radiation, such as visible light, UV, IR, microwaves and radiowaves: -rays x-rays UV VIS IR -wave radio wavelength ( cm) Type of interaction with matter depends on the frequency ( ) or wavelength ( ) of the radiation involved: E (=h -rays/x-rays - inner shell electrons, nucleus UV/Vis - bonding electrons (valence electrons) IR - Bond length/angle/torsion vibrations NMR - Nuclear spin NOTE: = c (3x10 8 m/s) =c/ )

4 Nuclear Magnetic Resonance (NMR) spectroscopy is the absorption of radio frequencies by atomic nuclei within a sample that is placed in a magnetic field. The types of sample that can be studied are gases, liquids, solids - whole organisms! NMR spectroscopy finds applications in several areas of science and is routinely used to study chemical and biochemical structure and function using simple one-dimensional techniques and more complicated multidimensional techniques. A typical simple Fourier Transform (FT) NMR experiment involves: put sample ( g to g quantities) into a magnet excite nuclei in sample with radiofrequencies using RF probe record nmr spectrum of RF absorbed by sample takes from seconds (1D proton on mg of sample) to days/weeks (multiple dimensions) sample 1D NMR 2D NMR 3D NMR magnet RF probe nmr spectrum

5 Spin An atom is composed of particles (proton, neutron, electron) that possess certain fundamental properties like charge, mass and spin: Mass/amu Charge Spin Proton /2 Neutron /2 Electron 5.49x /2 Spin angular momentum is an intrinsically quantum mechanical property that does not have a classical analog. Spin is a fundamental property of nature like electrical charge or mass. All of these particles are spin=1/2 particles. The nucleus itself has a total spin angular momentum, I, formed by the coupling of the individual spin angular momenta of its constituent nucleons. The total nuclear spin angular momentum quantum number may therefore take values: 0, 1/2, 1, 3/2, 2, 5/2, etc.

6 Spin and Nuclear Magnetic Moment The magnetic moment is a measure of the strength of a magnetic source. Each nuclear spin has a magnetic moment which is associated with the angular momentum of the nucleus. When any charged particle is rotating, it behaves like a current loop with a magnetic moment. The nucleus has a positive charge and is spinning. This generates a small magnetic field. The nucleus therefore possesses a magnetic moment,, which is proportional to its spin, I - The constant,, is called the magnetogyric ratio and is a fundamental nuclear constant which has a different value for every type of nucleus. - h is Planks constant and has a value of x J s (in kms units).

7 Nuclear spin may be related to the nucleon composition of a nucleus in the following manner: Odd mass nuclei (i.e. those having an odd number of nucleons) have fractional spins. Examples are I = 1/2 ( 1 1H, 13 6C, 15 7N, 19 9F, 31 15P), I = 3/2 ( 11 5B) and I = 5/2 ( 17 8O ). Even mass nuclei composed of odd numbers of protons and neutrons have integral spins. Examples are I = 1 ( 2 1H, 14 7N). Even mass nuclei composed of even numbers of protons and neutrons have zero spin ( I = 0 ). Examples are 12 6C, and 16 8O. SIDENOTE: Spin 1/2 nuclei have a spherical charge distribution, and their NMR behavior is the easiest to understand. Other spin nuclei have nonspherical charge distributions (quadrupolar nuclei) and may be analyzed as prolate or oblate spinning bodies. All nuclei with non-zero spins have magnetic moments (μ), but the quadrupolar nuclei also have an electric quadrupole moment (eq). Some characteristic properties of selected nuclei are given in the following table.

8 Magnetic Properties of Some Useful Nuclei Isotope Natural Abundance (%) Spin (I) Magnetogyric Ratio (γ) 10 7 rad s -1 T -1 Absolute Sensitvity 1 H / H x H / C C / x N x N / x O O / x F / P /

9 It is important to note that the 12 C isotope of carbon and the 16 O isotope of oxygen have a spin of 0 this means that the main building blocks of organic compounds cannot be observed by NMR spectroscopy. NMR studies of organic compounds make use of the natural abundance of 13 C for carbon NMR. Isotopic labeling of compounds (eg. 13 C replaces 12 C) can be used under conditions where the natural abundance content is insufficient such as in biomolecules. Also, for most nuclides the nuclear angular momentum vector and the magnetic moment vector point in the same direction, i.e. they are parallel and have a positive magnetogyric ratio. However, in a few cases, for example 15 N and 17 O (and also the electron), they are antiparallel and have a negative magnetogyric ratio. The consequences of this condition will be considered later.

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11 Group I II IIIa IVa Va VIa VIIa VIII a VIII b VIII c IB IIB III IV V VI VII VIII Period 1 1 H 2 He 2 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 3 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 4 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 5 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 6 55 Cs 56 Ba * 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 7 87 Fr 88 Ra ** 103 Lr 104 Unq 105 Unp 106 Unh 107 Uns 108 Uno 109 Mt 110 Uun 111 Uuu 112 Uub 113 Uut 114 Uuq 115 Uup 116 Uuh 117 Uus 118 Uuo *Lanthanides * 57 La 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb **Actinides ** 89 Ac 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No Nuclear Spins 1/2 1 3/2 5/2 7/2 9/2

12 Quantization of Spin The magnitude of the spin angular momentum vector is Where = h/2 and h is Plank s constant, the unit of quantization and has a value of x J s (in kms units). This angular momentum is spacequantized: it can only adopt 2I+1 orientations with respect to an arbitrary axis (usually taken to be the z-axis). That is, the projection of I onto the z-axis is given by m is the magnetic quantum number and varies from I to I in increments of 1.

13 Spin States of I=1/2 For example, a nucleus (i.e. a proton), with I=1/2 is described as having two states defined by m=+1/2 ( spin up or state) and m=-1/2 ( spin down or state). The nuclear spin states of a hydrogen nucleus: the nuclear magnetic angular momentum vector, I makes a projection onto the z-axis of (+1/2)h/2 or (-1/2)h/2. In the absence of an applied magnetic field, these states are degenerate (have same energy).

14 Spin States of I=1 For spins with I=1 nuclei three different values for I z are allowed (m=1,0,-1): I z = +h/2 I z = 0 I z = -h/2

15 Effect of a Magnetic Field on 1H (I=1/2) In the ground state all nuclear spins are disordered, and there is no energy difference between them. They are degenerate: = h / 4 Since they have a magnetic moment, when nuclear spins are placed in a strong external magnetic field (B o ), they orient either against or with it: B o There is always a small excess of nuclei (population excess) aligned with the field than pointing against it.

16 Energy of 1H (I=1/2) in a Magnetic Field The aligned nuclei can occupy two energy states, depending on which direction they align in the magnetic field (parallel or antiparallel). The potential energy of an magnetic moment in an external field is given by: Recall that: m I =+1/2 for parallel alignment with external field m I =-1/2 for antiparallel alignment with external field The later stage represents a energetically higher configuration. Apply magnetic field B o

17 Selection Rule and Transitions Spins can undergo a transition between two energy states by the absorption of a photon. The quantum-mechanical selection rule states that only transitions with m=±1 are allowed. The energy of this photon must exactly match the energy difference between the two states. The energy, E, of a photon is related to its frequency,, by Plank's constant (h = 6.626x10-34 J s). E=h and E = h B/2 so B/2 In NMR, the quantity is called the resonance frequency or the Larmor frequency. Note: when calculating, make sure units are ok: (rad/s/t); B(T); 2 (rad/cycle)

18 100 s MHz

19 k is Boltzmann's constant, x10-23 J/Kelvin T is the temperature in Kelvin.... so we are very far getting a 13C spectrum as fast as 1H!

20 Classical Mechanics and the Vector Model for NMR When a nuclear magnetic moment is placed in a magnetic field B o, there are two forces acting on it: one wants to bring it towards B o and one that wants to keep it spinning. Mathematically this is described by forming the vector product between dipole moment and magnetic field: Recall that: d /dt = x B This causes it to precess around the field (like a gyroscope under the influence of gravity). The angular frequency of precession, 0, is proportional to the field, B (the same frequency derived from QM energetic considerations).

21 The NMR sample is an ensemble of many nuclear spins and we can understand much about the NMR experiment by examining the behavior of bulk magnetization, M o, resulting from the ensemble using classical mechanics. At thermal equilibrium the spins precess in the magnetic field but they have random phases- no phase coherence so that net magnetization only exists along the z-axis: This represents the situation in most real samples. However, there is an important difference between and M 0. The former is quantized and can only be in one of two states ( or ) while M 0 tells about the whole spin population.

22 The Bloch Equations The Bloch equations are a set of coupled differential equations which were originally proposed by Felix Bloch to describe the motion of the net magnetic moment, M, under different conditions. When properly integrated, the Bloch equations will yield the X, Y, and Z components of magnetization as a function of time. The full Bloch equations contain relaxation terms (to be discussed in a future class) that drive the system back to the equilibrium state (no transverse coherence by T 2 relaxation and relative population of the α/ β states according to the Boltzmann distribution by T 1 relaxation). Loss of coherence terms: d /dt = x B Re-establish Boltzman n equilibrium term:

23 In an NMR instrument, the detector is in the transverse plane perpendicular to the B o magnetic field. In order to detect the magnetization within the sample, we must tip it from the z-axis into the transverse plane. From the Bloch equations, in order to change the magnetization along the z-axis (dm z /dt) a magnetic field has to be introduced along the x- or y-axis (B x or B y,- also known as a B 1 field). Since the magnetization is precessing at the Larmor frequency, transverse magnetic fields that rotate about Z at that same frequency will create a constant torque on the spins and rotate them away from the z-axis.

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25 The longer we keep B 1 field on (called the RF pulse length ), the more we will keep tipping the magnetization:

26 Back to the beginning (can repeat over and over in a process called signalaveraging)

27 The NMR Spectrum The spectrum consists of signals that have the following properties: position or chemical shift for each type nuclei in molecule intensity which is proportional to # of nuclei of that type width which is sensitive to dynamics and size of molecule splittings or couplings which is sensitive to # of bonded nuclei So the signals within an NMR spectrum depend on the surrounding environment (i.e. structure) and dynamics of the molecule 1 H NMR spectrum of an organic compound 1 H NMR spectrum of a protein

28 Unit Variable Symbol MKSA units Ampere Current I fundamental MKSA unit Coulomb Charge Q Ampere second Farad Capacitance C Coulomb Volt -1 = Joule Volt -2 Henry Inductance L Weber Ampere -1 = Tesla meter 2 Ampere -1 Joule Energy E Newton meter = kilogram meter 2 second -2 Kelvin Temperature T fundamental MKSA unit kilogram Mass m fundamental MKSA unit meter Length L fundamental MKSA unit Newton Force F kilogram meter second -2 Ohm Resistance R Volt Ampere -1 = Volt 2 Joule -1 second -1 Pascal Pressure P Newton meter -2 second time t fundamental MKSA unit Siemens conductance G Ampere Volt -1 = Joule second Volt -2 Tesla Magnetic field B Newton Ampere -1 meter -1 = Joule Ampere -1 meter -2 = Volt second meter -2 Volt potential f Joule coulomb -1 Watt Power P Joule second -1 MKS units and Useful Constants Weber Magnetic flux Tesla meter 2 = Volt second k Boltzmann's constant x J/Kelvin h Planks constant x J s (rad/s) = 2 (s -1 ) 10 4 Gauss = 1 Telsa The earth's magnetic field in Rochester, New York is approximately 5x10-5 T. = 3 x 10 8 m/s 1 cal = 4.18 Joules