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  • Chem 325 NMR Intro


    Physical properties, chemical properties, formulas

    Shedding real light on molecular structure:

    Frequency νννν


    Wavelength λλλλ

    Frequency νννν

    Velocity c = 2.998 ×××× 108 m⋅⋅⋅⋅s-1

    λλλλ ×××× νννν = c

    Energy of a photon: E = hνννν = hc/λλλλ

    h = Planck’s constant = 6.626 ×××× 10-34 J⋅⋅⋅⋅s

    The Electromagnetic Spectrum

  • Chem 325 NMR Intro


    Emission and Absorption Spectroscopy

    Nuclear Magnetic Resonance


    Let’s go for a spin!

    Electron Spin: A Fourth Quantum Number

    The Stern-Gerlach Experiment

  • Chem 325 NMR Intro


    Nucleus: nucleons: protons, neutrons

    -these also have ‘spin’ properties: up, down

    - spins add together in a complicated way to give total nuclear spin I, characteristic of a given type of nucleus

    - some general guidelines….


    1H, 13C, 19F, 31P

    (I = ½)

    35Cl, 37Cl (I = 3/2)

    127I (I = 5/2)

    ½, 3/2, 5/2, …


    2H, 14N (I = 1)

    10B (I = 2) 1, 2, 3, …oddevenoddodd

    4He, 12C, 16O, 32S0eveneveneveneven

    Examples Total Spin

    I ZA#p#n

    The net nuclear spin gives rise to a number of spin states

    #spin states = 2I +1

    Spin states characterized by mI or Izvalues:

    For a given I value, mI = Iz = +I, I-1, I-2,..,-I+1, -I.

    e.g. for I = 0, mI = 0 (only!)

    for I = ½, ml = +½, -½

    for I = 1, ml = +1, 0, -1

    Normally all nuclear spin states are degenerate

    → same energy

    -degeneracy can be removed by application of an external magnetic field

  • Chem 325 NMR Intro


    Amount of splitting of the nuclear spin states, ∆∆∆∆E,

    is directly proportional to the applied magnetic

    field strength B0

    is directly proportional to magnetogyric ratio γγγγ of the particular nucleus type

    νγ π

    γ hBB h

    ) 2

    ( E 00 ===∆ h

    ) 2

    ( 0B π

    γ ν =

    νννν is the frequency of the EM radiation required for the transition from the lower to the upper spin states









    Frequency νννν



    strength B0



    (106 rad/Tesla ×××× sec)


    • Increasing B0 increases ∆∆∆∆E

    • Increasing B0 results in a higher frequency νννν of EM radiation required to produce the transition

    • For a given B0, different types of nuclei have different ∆∆∆∆E, thus different νννν values

    • EM radiation with νννν values in MHz range are radio waves

    • So far: allows us to identify which types of atoms our molecule has by monitoring which EM frequencies are absorbed at a given applied magnetic field strength (but limited to those nuclei with I ≠≠≠≠ 0!)


    Interaction of the nuclear magnetic moment and the

    applied field causes the rotational axis to precess about the

    field axis (z-axis) (like a toy top)

    H B0


    Precessional frequency or Larmor frequency ωωωω

    For a given field strength B0, nuclei of

    different types precess at different

    Larmor frequencies according to their

    magnetogyric ratio γγγγ values:

    ωωωω = γγγγB0

  • Chem 325 NMR Intro


    Mechanism of Absorption

    When a photon of, say, νννν = 60 MHz encounters this spinning charged system the two can couple and change the spin state

    of the proton.




    ν = ω/2ν = ω/2ν = ω/2ν = ω/2ππππ = = = = γγγγΒΒΒΒ0000/2/2/2/2ππππ


    ω∆Ε∆Ε∆Ε∆ΕThis state is called nuclear magnetic resonance, and the nucleus is said to be in resonance with the incoming radio wave

    Mechanism of Absorption

    To observe a spectroscopic transition, need a population

    difference between the two states involved.

    The energy difference corresponding to 60 MHz (∆∆∆∆E = hνννν) is 2.39 x 10-5 kJ mol-1.

    Thermal energy at room temperature (298 K) is sufficient

    to appreciably populate both energy levels.

    The energy difference is small, so rapid exchange is

    occurring between the two populations, but there is

    always a net excess of protons in the lower energy state.

    Mechanism of Absorption

    From the Boltzman distribution equation we can

    calculate the population of each energy state:

    Nupper/Nlower = e -∆∆∆∆E/kT = e-hνννν/kT

    @ 298 K the ratio is 1,000,000 / 1,000,009 !

    There is an excess population of 9 nuclei in the lower energy state!


    As the applied B0 increases, exchange becomes more

    difficult and the excess increases:

    In each case, it is these few nuclei that allow us to

    observe NMR











  • Chem 325 NMR Intro


    When radio radiation is applied to a sample both

    transitions upward and downward are stimulated.

    If too much radiation is applied both states completely

    equilibrate – called saturation – no NMR signal can

    be observed.

    Two mechanisms for relaxation:

    1. spin-spin or transverse relaxation, exchange with

    other nuclear spins, characterized by time constant T2

    2. spin-lattice or longitudinal relaxation, transfer of

    energy to surroundings (heat), characterized by time

    constant T1


    • If all protons (1H nuclei!) absorbed the same

    amount of energy in a given magnetic field, not

    much information could be obtained.

    • But protons (1H nuclei!) are surrounded by

    electrons that shield them from the external field.

    • Circulating electrons create an induced magnetic

    field that opposes the external magnetic field.

    Electronic Motion

    A permanent magnet will induce a current carrying

    loop to spin:


    In the same way, electrons in orbitals will start to

    circulate when the molecule is placed in an external

    magnetic field. This circulation of electrons creates

    another magnetic field that opposes the external field.


  • Chem 325 NMR Intro



    Magnetic field ‘felt’ at the nucleus:

    BN (= Beff = Blocal) = B0 - σσσσB0 = B0(1-σσσσ)

    where σσσσ is the shielding constant

    Thus the local field is modulated by the local

    electronic or chemical environment of the nucleus.

    Known as the chemical shift.

    Shielded Nuclei

    Magnetic field strength must be increased for a shielded proton to flip at the same frequency.

    7.0459 T A small, but NOTICABLE, effect!

    Protons in a Molecule

    Depending on their chemical environment,

    protons in a molecule are shielded by different


    The Chemical Shift

    m os

    t d es

    hi el

    de d

    le as

    t de

    sh ie

    ld ed

    high fieldlow field

  • Chem 325 NMR Intro


    NMR Signals

    • The number of signals shows how many different

    kinds of protons (H atoms!) are present.

    • The location of the signals shows how shielded or

    deshielded the proton is.

    • The intensity of the signal shows the number of

    protons (H atoms!) of that type.

    The NMR Spectrometer There are two types of NMR

    spectrometer, continuous

    wave (CW) sweep and

    Fourier Transform (FT). CW

    instruments have been almost

    entirely phased out.

    RF (MHz) oscillator


    RF Detector

    Magnetic Field Strength

    Field Strength Magnet Type Frequency

    1.41T permanent 60 MHz

    2.35T electromagnet 100 MHz

    4.70T superconducting 200 MHz

    7.05T 300 MHz

    ............ ............

    21.2T 900 Mhz

    Frequency is that required to observe 1H signals

    Modern NMR

    Recall the concept of precession of the spinning nuclear magnet in the applied magnetic field:

    H B0 ω

    µ = magnetic moment

  • Chem 325 NMR Intro


    Behaviour of a collection of spinning nuclei:

    Spin population difference

    Net moment or magnetization

    Application of a second magnetic field

    B1 (magnetic field of EM radiation)

    matching Larmor frequency

    Phase coherence of spins

    Transfer of magnetization from

    z-axis to x,y-plane

    The x,y component of the magnetization is detected

    electronically as the ‘resonance’ signal

    Rather than show the magnetization vectors

    precessing about the z-axis, we will now make the

    x- and y-axes rotate about the z-axis with the

    Larmor frequency.

    Transfer from the stationary laboratory coordinate

    system to a rotating coordinate system.