Lecture 7. Nuclear Magnetic Resonance (NMR)

1. Lecture 7.Nuclear Magnetic Resonance(NMR)

2. NMR is a tool that enables the user to make quantitative and structural analyses on compounds in solution or in the solid state. This tool is of great importance to organic chemistry and biochemistry.

3. Principle • NMR spectrometers provide a collection of information dealing with the interactions between the nuclei of certain atoms present in compounds. • In order to analyze the compounds with NMR, two magnetic fields are used: 1. Very high and constant static magnetic field. 2. A weaker (10,000 times weaker) oscillating magnetic field.

4. The NMR spectrum is a basic document or graph that represents signals of resonance which occurs from the absorption of specific frequencies sent by an electromagnetic source. • (insert pic of spectrumon pg.328)

5. Interactions between magnetic field and spin rotations of the nucleus • The vector quantity, spin I, is an intrinsic parameter used to explain the behavior of atoms in media where there is a preferential direction. • The application of a magnetic field creates this vector quantity, spin I, for all atoms within the field.

6. The dimensions for the spin of a nucleus (Js) are equal to the kinetic moment L of classic mechanics. • The spin of a nucleus varies due to its spin quantum number I, whose value can be zero or a positive multiple of ½.

7. An isolated nucleus with a non-zero spin number works like a small magnet with a magnetic moment µ (JT-1) such that: • µ = γ · I • The nuclear magnetic moment µ is represented by a vector co-linear to I. The direction of these vectors are the same or opposite based on the sign of γ. • (insert fig.15.2 pg.329) • An isolated nucleus with a non-zero spin number works like a small magnet with a magnetic moment µ (JT-1) such that: • µ = γ · I • The nuclear magnetic moment µ is represented by a vector co-linear to I. The direction of these vectors are the same or opposite based on the sign of γ. • (insert fig.15.2 pg.329) • An isolated nucleus with a non-zero spin number works like a small magnet with a magnetic moment µ (JT-1) such that: • µ = γ · I • The nuclear magnetic moment µ is represented by a vector co-linear to I. The direction of these vectors are the same or opposite based on the sign of γ. • (insert fig.15.2 pg.329) • An isolated nucleus with a non-zero spin number works like a small magnet with a magnetic moment µ (JT-1) such that: • µ = γ · I • The nuclear magnetic moment µ is represented by a vector co-linear to I. The direction of these vectors are the same or opposite based on the sign of γ. • (insert fig.15.2 pg.329) • An isolated nucleus with a non-zero spin number works like a small magnet with a magnetic moment µ (JT-1) such that: µ = γ · I • The nuclear magnetic moment µ is represented by a vector co-linear to I. The direction of these vectors are the same or opposite based on the sign of γ. • (insert fig.15.2 pg.329)

8. If an isolated nucleus with a non-zero spin number is submitted to a magnetic field B0 which makes an angle θ with the spin vector, an interactive coupling occurs between B0 and µ; which modifies the potential energy E of the nucleus.

9. If µz represents the projection of µ on the z-axis, which has the same orientation as B0. The resulting energy of interaction is called a Hamiltonian illustrated in the following equation: E = -µ · B0 or E = -µcos(θ)B0 or E = -µz · B0

10. Based on quantum mechanics, µz for a nucleus can only have 2I+1 different values. If a magnetic field B0 is applied to this nucleus, the potential energy E and θcan also only have 2I+1 values. • The value of µz is given by the magnetic spin number m which can have the following values in h/2π units: m = -I, -I +1, ….., I-1, I

11. By using the previous equations given, the 2I + 1 allowed energy values are given by the following relations: E = -γ · m · B0