NMR Spectroscopy - .NMR Spectroscopy N.M.R. = Nuclear Magnetic Resonance Basic Principles Spectroscopic

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  • NMR Spectroscopy

    MRI

    Drug design

    Structural biologyMetabonomics

    Food quality

    Applications

  • NMR Spectroscopy

    N.M.R. = Nuclear Magnetic Resonance

    Basic Principles

    Spectroscopic technique, thus relies on the interaction between material and electromagnetic radiation

    The nuclei of all atoms possess a nuclear quantum number, I. (I 0, always multiples of .)

    Only nuclei with spin number (I) >0 can absorb/emit electromagnetic radiation.

    Even atomic mass & number: I = 0 (12C, 16O)

    Even atomic mass & odd number: I = whole integer (14N, 2H, 10B)

    Odd atomic mass: I = half integer (1H, 13C, 15N, 31P)

    The spinning nuclei possess angular momentum, P, and charge, and so an associated magnetic moment, .

    = x P

    Where is the gyromagnetic ratio

  • NMR Spectroscopy

    The spin states of the nucleus are quantified:

    I, (I - 1), (I - 2), , -I

    Basic Principles

    B0

    I= (e.g. 1H)

    Ener

    gy

    B0=0

    B0>0

    E=h =h B0/2

  • NMR SpectroscopyBasic Principles

    Bo

    In the ground state all nuclear spins are disordered, and there is no energy difference between them. They are degenerate.

    Since they have a magnetic moment, when we apply a strong external magnetic field (Bo), they orient either against or with it:There is always a small excess of nuclei (population excess) aligned with the field than pointing against it.

  • NMR SpectroscopyBasic Principles

    Bo=0

    Bo>0

    E=h 0=h B0/2

    0 is the Larmor Frequency

    0= B0, angular velocity

    B0 z

    y

    x

  • NMR SpectroscopyBasic Principles

    Each level has a different population (N), and the difference between the two is related to the energy difference by the Boltzmman distribution:

    N /N = e E/kT

    E for 1H at 400 MHz (B0 = 9.5 T) is 3.8 x 10-5 Kcal/mol

    N /N =1.000064

    The surplus population is small (especially when compared to UV or IR).

    That renders NMR a rather insensitive technique!

  • NMR SpectroscopyThe electromagnetic spectrum

    1022

    1020

    1018

    1016

    1014

    1012

    1010

    108

    106

    -rays

    X-rays

    Mossbauer

    electronic ultraviolet

    visible

    infrared

    microwave

    radiofrequency

    vibrational

    rotational

    NMR

    600

    500

    400

    300

    200

    100

    1H 19F

    31P

    13C

    10

    8

    6

    4

    2

    0

    aldehydic

    aromatic

    olefinic

    acetylenic

    aliphatic

    /Hz

    /MHz

    /ppm

  • NMR SpectroscopyThe Vector Model

    y

    x

    y

    x

    M0

    y

    x

    y

    x

  • NMR SpectroscopyNMR excitation

    Mo z

    y

    i

    B1

    Transmitter coil (x)

    x

    Bo

    B1 = C * cos ( ot)

    y

    x

    y

    x

    +0

    -0

    B1 is an oscillating magnetic field

  • NMR SpectroscopyLaboratory vs. Rotating frame

    z

    y

    x

    M0

    +0

    -0

    Laboratory frame

    z

    y

    x

    M0

    +0

    -20

    Rotating frame

    B1

  • NMR SpectroscopyEffect on an rf pulse

    z

    y

    x

    M0

    B1

    z

    y

    x

    B1

    =1tp (degrees)

    =90

    =180

  • NMR SpectroscopyMagnetization properties

    z

    y

    x

    B1

    y

    x

    =5 Hz

    A

    y

    x

    MAy

    MAx

    x

    y

    x

    y

    x

    y

    1H=400,000,000 HzA=400,000,005 Hz

  • NMR SpectroscopyMagnetization properties

    1H=400,000,000 HzA=400,000,005 Hz

    z

    y

    x

    B1

    y

    x

    =5 Hz

    A

    y

    x

    MAy

    MAx

    detector

    IM

    t

    MAy=MA cos t

    MA

    IM

    t

    MAx=MA sin t

    MA

    t

  • NMR SpectroscopyThe Fourier Transform

    IM

    t

    time domain frequency domain

    FT

    FT

    t

    =1/ t

    time frequency

  • NMR SpectroscopyThe Fourier Transform

    IM

    time

    Signal Induction Decay (FID)

  • NMR SpectroscopyThe Fourier Transform

    FT

  • NMR SpectroscopyContinuous wave vs. pulsed NMR

    o or B

    o

    time

    o or B

    o

  • NMR SpectroscopyContinuous wave vs. pulsed NMR

    FT

    FT

    For cos( t)

    For sin( t)

    absorptive lines

    despersive lines

  • NMR SpectroscopyContinuous wave vs. pulsed NMR

    * =

    tp

    FT

    o

    A monochromatic radiofrequency pulse is a combination of a wave

    (cosine) of frequency 0 and a step function

    Since f=1/t, a pulse of 10 s

    duration excites a frequency bandwidth of 105 Hz!

  • NMR SpectroscopyContinuous wave vs. pulsed NMR

    E t ~ h or t ~1

  • NMR SpectroscopySingle-channel signal detection

    z

    y

    x +

    FT

    + -

    0

  • NMR SpectroscopyQuadrature detection

    z

    y

    x +

    My Mx

    My Mx

  • NMR SpectroscopyQuadrature detection

    y

    x +

    sin

    cos

    + - Hz

    0

    + Hz 0

  • NMR SpectroscopyThe Chemical Shift

    The NMR frequency of a nucleus in a molecule is mainly determined by its gyromagnetic ratio and the strength of the magnetic field B

    The exact value of depends, however, on the position of the nucleus in the molecule or more precisely on the local electron distribution

    this effect is called the chemical shift

  • NMR SpectroscopyThe Chemical Shift

    Nuclei, however, in molecules are never isolated from other particles that are charged and are in motion (electrons!).

    Thus, the field actually felt by a nucleus is slightly different from that of the applied external magnetic field!!

    E=h =h B/2

  • NMR SpectroscopyThe Chemical Shift

    E=h =h Be /2

    Beff, is given by B0-B = B0-B0 =B0(1- )

    and is the chemical shift

    = B0(1- )

    2

    = ( - ref)

    ref

    106 106 ( ref- )

  • NMR SpectroscopyThe Chemical Shift

    750 MHz 1H spectrum of a small protein

    amide protons

    aromatic ring

    protonsmethyleneprotons

    methylprotons

    shielding

    magnetic field

    frequency

  • NMR SpectroscopyThe Chemical Shift

  • NMR SpectroscopyThe Chemical Shift

  • NMR SpectroscopyNuclear Shielding

    diamagnetic contribution

    paramagnetic contribution

    neighbor anisotropy effect

    ring-current effect

    electric field effect

    solvent effect

    = dia + para + nb + rc + ef + solv

  • NMR SpectroscopyNuclear Shielding - diamagnetic contribution

    The external field B0 causes the electrons to circulate within their orbitals

    B0

    B

    h B0 h B0(1- )

    The higher is the electron density close to the nucleus, the larger the protection is!

  • NMR SpectroscopyNuclear Shielding - diamagnetic contribution

    Depends on the electronegativity

    CH3X

  • NMR SpectroscopyNuclear Shielding - paramagnetic contribution

    The external field B0 mixes the wavefunction of the ground state with that of the excited state

    The induced current generates a magnetic field that enhances the external field and deshields the nucleus

    HOMO

    LUMO B

    0

    p = 1 1

    R3

  • NMR SpectroscopyChemical shift range

    Local diamagnetic and paramagnetic currents make only modest contributions to 1H shielding!

    1H; ~10 ppm

    13C; ~200 ppm

    19F; ~300 ppm

    31P; ~500 ppm

  • NMR SpectroscopyChemical Shift Anisotropy

    Nuclear shielding, , is a tensor.

    The distribution of the electrons about the nucleus is non-sperical- thus, the magnitude of the shielding depends on the relative orientation of the nucleus with respect to the static field.

    In isotropic cases: = ( 11 + 22 + 33)

    In static cases, e.g. solid state

  • NMR SpectroscopyNuclear Shielding - neighboring group

    A

    B

    par < per

    B0

    B

    par > per

    -

    -

    + +

    +

    +

    - -

    A

  • NMR SpectroscopyNuclear Shielding - neighboring group

    -

    +

    +

    C C -

    +

    -

    -

    + C C par < per

    par > per

    0 1 2 3 4 5 6 7 ppm

    C2H4 C2H2 C2H6

  • NMR SpectroscopyNuclear Shielding - ring-current effect

    More pronounced in aromatic rings due to the electron clouds

    Bo

    e- -2.99

    9.28

  • NMR SpectroscopyNuclear Shielding - hydrogen bonding

    CH3 CH2 OH

    0 2 4 6 ppm

    [EtOH] in CCl4

    1M

    0.1M

    0.01M

    0.001M

    Hydrogen bonding causes deshielding due to electron density decrease at the proton site

  • NMR SpectroscopySpin-spin (scalar) coupling

    HF (1H-19F)

    H F

    JHF JHF

  • NMR SpectroscopySpin-spin (scalar) coupling

    HF (1H-19F)

    Bo

    19F

    19F

    1H

    1H

    Nuclear moment

    Magnetic polarization

    of the electron

    H F

    H F

    H F

    H F

    H

    H

    E=h JAX

    mA m

    X

    where m is the magnetic quantum number

    JAX

    is the spin-spin coupling constant

  • NMR SpectroscopySpin-spin (scalar) coupling

    AMX AX