NMR SPECTRO

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    NMR Spectroscopy

    Basic NMR theory

    Lecture 1

    Jamil Saad

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    Useful Literature

    1) High-Resolution NMR Techniques in Organic Chemistry. By Timothy D.W. Claridge,Elsevier Science; 1 st edition (1999).

    2) Nuclear Magnetic Resonance. By P.J. Hore, Oxford University Press, USA; 1 st edition(1995).

    3)

    Basic One- and Two-Dimensional NMR Spectroscopy. By Horst Friebolin, Wiley-VCH;4 edition (2005).4) Online NMR course: http://www.cis.rit.edu/htbooks/nmr/inside.htm5) NMRVIEW http://www.onemoonscientic.com/nmrview/6) NMRPIPE http://spin.niddk.nih.gov/NMRPipe/

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    What is an atom?

    The smallest unit of an element.

    Has an electron cloud consisting of negatively charged electrons surrounding a densenucleus.

    The nucleus contains positively charged protons and electrically neutral neutrons.

    When the number of protons in the nucleus equals the number of electrons, the atomis electrically neutral.

    Otherwise, it is an ion and has a net positive or negative charge.

    An atom is classied according to its number of protons and neutrons: the number of protons determines the chemical element and the number of neutrons determines theisotope of that element.

    The electrons determine the chemical properties of an element, and strongly inuencean atom's magnetic properties.

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    What is nuclear magnetic resonance?

    Nuclear perturbation

    Nuclear reaction

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    Structure/imaging from molecules to animals

    10 -3?

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    Applications

    Medicine : Magnetic resonance imaging (MRI)

    a brain tumor (meningioma)

    A distinctive chemical which is generallyonly seen in meningiomas

    Structural Biology: Proteins, DNA/RNA, Protein-DNA/RNA complexes, Protein-lipid

    complexes, and Polysaccharides

    This is an example of the kind of biochemical information which can help doctors to make theirdiagnosis.

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    Chemistry : synthesis, pharmaceutical, quality control, structure, conformation, dynamics,kinetics, chemical exchange, equilibrium, molecular tumbling, etc

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    Drug design : Structure Activity Relationships (SAR)

    Petroleum industry : test water, oil, organic, inorganic composition.

    Process control : mining, polymer production, cool analysis, cosmetics..

    Food industry: drinks, solid foods, quality, contents, contamination..

    Environmental : fertilizers, pesticides, pollution, heavy metals..

    Natural product analysis : extracts, potential drug leads..

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    Ethanol proton spectrum@700 MHz

    First proton spectrum of ethanol @ 30 MHz

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    Details of the 20S proteasome structure: Quantication of dynamics andstructure (670 kilodalton)

    Nature 445, 618-622 (2007)

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    Why biomolecular NMR??

    Biological molecules such as proteins and nucleic acids can be large and complex. Theycan easily exceed 2000 atoms. Knowing their structure is critical in understanding therelationship between structure and function.

    - no crystal needed, native-like conditions: solution, (in cell) NMR- many biological samples can be difcult to crystallize. e.g., nucleic acids

    structures are affected by crystal packing

    NMR can be used to determine 3D structure and dynamics in solution! Its limitation ismolecular size. However, this is changing.

    Molecular weight: X-ray: > 200 kDa,NMR < 50-100 kDa, 900 kDa!?

    Ligand binding and molecular interactions in solution

    Characterization of dynamics and mobility (ps - days)- conformational dynamics, enzyme turnover, kinetics, folding

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    Structure determination by NMR

    4D ???

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    A conceptual blockdiagram of the FT NMR

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    Spectroscopy is the study of the interactions between light and matter as afunction of wavelength ( ).

    Light refers to any sort of electromagnetic radiation, such as visible light, UV,IR, and radiowaves.

    Depending on the frequency or wavelength of the radiation involved we will

    have different types of interactions with matter (molecules).

    10-10

    10-8

    10-6

    10-4

    10-2

    100

    102

    wavelength ( , cm)

    -rays x-rays UV VIS IR - wave radio

    wavelength and frequency are inversely proportional, so higher frequenciesmean shorter wavelength.

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    The relationship between energy and frequency:

    h = Planks constant = frequency

    E = h

    The higher the frequency, the higher the energy. In addition, depending on thefrequency and wavelength well have different interactions with matter (molecules).

    E,

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    Detects the absorption of radiofrequencies (electromagnetic radiation) by certainnuclei in a molecule.

    The nuclei of all atoms may be characterized by:a nuclear spin quantum number (I)

    Only nuclei with spin number ( I ) 0 can absorb/emit electromagnetic radiation.These have an odd mass #.

    Mass # Atomic # I Example

    Odd Even or odd 1/2, 3/2, 5/2, (1H, 13 C, 15 N, 31 P)Even Even 0 (12 C, 16 O)Even Odd 1, 2, 3 (14 N, 2H)

    Nuclear magnetic resonance (NMR) is a physical phenomenon based upon thequantum mechanical magnetic properties of an atom's nucleus.

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    = P

    is the gyromagnetic ratio , and it depends on the nature of each nuclei(constant for any given nuclei).

    The spinning nuclei possess angular momentum (P).Charge and motion of this charge gives rise to magnetic moment ( )

    Different nuclei have different magnetic moments.

    Vector quantities: They both have magnitude and direction

    The spin states of the nucleus ( m) are quantized :magnetic quantum number ( m) = I , ( I - 1), ( I - 2), , - I

    For 1H, 13 C, 15 N, 31 P (biologically relevant nuclei with I = 1 /2):

    m = 1 /2, - 1 /2This means that only two states (energy levels) can be taken by these nuclei.

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    For a particular nuclei, the magnetic moment ():

    = I h / 2

    The energy of a spin in a magnetic field ( E) will depend on a static magnetic fieldcalled Bo , and .

    E = - . BoBo

    Tesla (T)

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    When the Bo field is applied, spins have two possible energy limits (1/2, -1/2). Inone we are in favor of the field, and in the other one we are against it:

    Bo Bo

    E = - h Bo / 4

    The larger the Bo , the larger the energy difference.

    The energy difference of the two levels, and , is:

    E = - . Bo

    E = h B o / 2

    E = h Bo / 4

    E for 1Hs at Bo = 9.4 T is 4 x 10 -5 Kcal / mol.

    Magnetic energy and populations

    m = 1/2

    m = -1/2

    E2E1

    BB1 B2

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    KB = Boltzman constant = 1.3805x10 -23 JK -1

    At equilibrium, there is excess of nuclei in the a state:

    The population ratio between the two levels depends on E, and we can apply a Boltzmman distribution .

    B o EQuantumMechanicalDescription

    N / N = e E/K BT

    N / N = e - E/K BT

    Since E is very small compared with the average energy of K BT thermal motion:

    N / N = 1 - E/K BT = 1 - ( h Bo / 2 K BT)

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    Nuclei with larger will absorb/emit more energy, and will therefore be moresensitive. Sensitivity is proportional to and N / N

    (13 C) = 6,728 rad / G

    (1H) = 26,753 rad / G

    1H is ~ 64 times more sensitivethan 13 C only due to .

    If we also take into account the natural abundance, 13 C (1.1%) ends up being6400 less sensitive than 1H.

    N / N ratio is only 1.000064 . Calculate!

    In 1000,000 spins, difference is just 64: NMR is very insensitive when comparedto UV or IR.

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    We call this Larmor precession (named after Joseph Larmor) or angular frequency, o (radians) or (Hz):

    o = - Bo (rad s -1)

    In the presence of a magnetic field two forces act on the spins: One that tries to

    align them with Bo , while the other tries to maintain their angular momentum. The net result is that the nuclei spins trace a circular path about the applied field.

    Bo = - Bo / 2 (Hz) Larmor Frequency

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    There are several magnetic fields acting on the spins. One is B o , which isconstant and generates the precession at o . The others are fluctuating due tothe molecular anisotropy and its environment, and make the spins try all thepossible orientations with respect to Bo in a certain amount of time.

    Orientations in favor of Bo will have lower magnetic energy, and will be slightlyfavored. After a certain time, a net magnetization (Mo) pointing in the directionof Bo will develop.

    z

    x

    one nucleus

    z

    xy

    many nuclei

    z

    x

    y

    Mo - net magnetizationvector allows us tolook at system as awhole

    The net magnetization vector

    Mo

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    Where does the net magnetization come from? In order to figure it out wetranslate all the spins to the origin of the coordinate system. Well see somethinglike this:

    x

    y

    z

    Bo

    Well have a slight excess of spins aligned with Bo , but at any angle with respect to Z. Thedistribution is proportional to N / N.

    If we break down the vectors in Z and , we get:

    Mo z

    y

    x Bo

    y

    y

    =

    = 0

    z z

    The net magnetization isaligned with Bo , and this iswhat we use in NMR.

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    E = h o o = Bo / 2 E = h o = h B o / 2

    Nuclear magnetic resonance occurs when the nucleus changes its spin state from to . This is driven by the absorption of a quantum of energy.

    Coming from electromagnetic radiation, whose frequency must match that of Larmor precession:

    Bo = 0Randomly oriented Bo > 0

    Highly oriented

    Bo

    N

    S

    Each nucleusbehaves like

    a bar magnet.

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    So far nothing happened. We have a tube spinning in the magnet. To seesomething we have to move the system away from equilibrium. That is, we haveto perturb its populations .

    We need the system to absorb energy. That energy will induce transitionsbetween energy levels that is to cause magnetic resonance to occur. Theenergy source is an oscillating electromagnetic radiation generated by an

    alternating current.

    Mo

    z

    y

    B1 = C * cos ( o t)

    B1

    Transmitter coil(provides rf pulse)

    x Bo