Chapter 15 - Molecular spectroscopy 3: magnetic resonance

  • Resonance - The condition of strong effective coupling when the frequencies of two oscillators are identical.

The effect of magnetic fields on electrons and nuclei

15.1 The energies of electrons in magnetic fields

  • Energy of a magnetic moment

   

  • Magnetogyric ratio

   

  • Larmor frequency

   

15.2 The energies of nuclei in magnetic fields

  • Nuclear g-factor - A characteristic of the nucleus.
  • Nuclear magneton - A quantity independent of the nucleus.

15.3 Magnetic resonance spectroscopy

  • Electron paramagnetic resonance (EPR)/ Electron spin resonance (ESR) - The study of molecules and ions containing unpaired electrons by observing the magnetic fields at which they come into resonance with monochromatic radiation.
  • Nuclear magnetic resonance (NMR) - The study of the properties of molecules containing magnetic nuclei by applying a magnetic field and observing the frequency of the resonant electromagnetic field.

Nuclear magnetic resonance

15.4 The NMR spectrometer

  • NMR spectrometer - Consists of the appropriate sources of radiofrequency electromagnetic radiation and a magnet that can produce a uniform, intense field.

15.5 The chemical shift

  • Chemical shift - It’s related to the difference between the resonance frequency of the nucleus in question and that of a reference standard.

   

  • Local contribution - The contribution of the electrons of the atom that contains the nucleus in question.
  • Neighboring group contribution - The contribution from the groups of atoms that form the rest of the molecule.
  • Solvent contribution - The contribution from the solvent molecules.
Local contribution

 

  • Diamagnetic contribution - It opposes the applied magnetic field and shields the nucleus in question.
  • Paramagnetic contribution - It reinforces the applied magnetic field and deshields the nucleus in question.
  • Lamb formula

   

Neighboring group contributions
  • The neighboring group contribution arises from the currents induced in nearby groups of atoms.
  • Ring current - A circulation of electrons around the ring, when it is applied perpendicular to the molecular plane.
Solvent contribution
  • A solvent can influence the local magnetic field experienced by a nucleus in a variety of ways.
  • If there are steric interactions that result in a loose but specific interaction between a solute molecule and a solvent molecule, then protons in the solute molecule may experience shielding or deshielding effects according to their location relative to the solvent molecule.

15.6 The fine structure

  • Fine structure - The splitting of resonances into individual lines.
  • Scalar coupling constant - The energy of interaction it describes is proportional to the scalar product of the two interacting spins.
  • Spin coupling constants are independent of the strength of the applied field because they do not depend on the latter for their ability to generate local fields.
  • Karplus equation

   

  • Polarization mechanism - The interaction is transmitted through the bonds.
  • Chemically equivalent nuclei - Nuclei that are related by a symmetry operation of the molecule and have the same chemical shifts.
  • Magnetically equivalent nuclei - If they are chemically equivalent and they have identical spin-spin interactions with any other magnetic nuclei in the molecule.
  • First-order spectra - The spectra that result.
  • Strongly coupled spectra - The complicated spectra that are obtained.
  • Heteronuclear spin system - Nuclei of different elements.
  • Homonuclear spin system - Nuclei are of the same element but in different environments.

15.7 Conformational conversion and exchange processes

  • Chemical exchange - The loss of fine structure in solvents able to exchange protons with the sample.

Pulse techniques in NMR

15.8 The magnetization vector

  • Magnetization - The net nuclear magnetic moment of the sample is zero.
  • Free-induction decay (FID) - The form of the signal that we can expect.

15.9 Spin relaxation

  • Spin relaxation - The return to equilibrium.
  • Spin-lattice relaxation - Caused by local magnetic fields that fluctuate at a frequency close to the resonance frequency of the transition.
  • Transverse relaxation time - The time constant that is in the randomization of the spin directions that occur exponentially.
  • Inversion recovery technique - The longitudinal relaxation time can be measured by this.
  • Spin echo - The magnetic analog of an audible echo where transverse magnetization is created by a radio frequency pulse, decays away, is reflected by a second pulse, and grows back to form an echo.
  • Refocused - It means that the spin echo has reached its maximum.

15.10 Spin decoupling

  • Dilute-spin species - It is unlikely that more than one nucleus will be found in any given small molecule.
  • Abundant-spin species - A molecule is likely to contain many of them.

15.11 The nuclear Overhauser effect

  • In the nuclear Overhauser effect (NOE), spin relaxation processes involving internuclear dipole-dipole interactions are used to transfer this population advantage to another nucleus, so that the latter's resonances are modified.

15.12 Two-dimensional NMR

  • Two-dimensional NMR - When two axes are used to display the data, with resonances belonging to different groups lying at different locations on the second axis.
  • PEMD pulse structure
    • Preparation period (P) - The spins first return to thermal equilibrium and then are excited by one or more radiofrequency pulses.
    • Evolution period (E) - During which the spins precess under the influence of their chemical shifts and spin-spin couplings
    • Mixing period (M) - In which pulses may be used to transfer information between spins.
    • Detection period (D) - During which the FID is recorded.
  • Diagonal peaks - Signals centered that lie along the diagonal F1 = F2.
  • Cross-peaks - Signals centered that owe their existence to the coupling between A and X.

15.13 Solid-state NMR

  • Principal contributions to the linewidths of solids
    • Direct magnetic dipolar interaction between nuclear spins - A nuclear magnetic moment will give rise to a local magnetic field, which points in different directions at different locations around the nucleus.
    • Anisotropy of the chemical shift - This ability depends on the orientation of the molecule relative to the applied field.
    • Magic-angle spinning (MAS) - In this technique, the sample is spun at high speed at the magic angle to the applied field.

Electron paramagnetic resonance

  • Electron paramagnetic resonance (EPR) - It is used to study radicals formed during chemical reactions or by radiation, radicals that act as probes of biological structure.

15.14 The EPR spectrometer

  • The EPR spectrum - Obtained by monitoring the microwave absorption as the field is changed.

15.15 The g-value

  • The resonance condition

   Where g is the g-value of the radical

15.16 Hyperfine structure

  • Hyperfine structure - The splitting of individual resonance lines into components.
    • It is the most important feature of the EPR spectra.
  • Spin density - The probability that an unpaired electron is on the atom.
  • McConnell equation

   

  • Hyperfine interaction - An interaction between the magnetic moments of the unpaired electron and the nuclei.