The table below shows the relative intensities of the lines according to unpaired electrons interacting with multiple equivalent nuclei. We can observe that increasing number of nucleuses leads to the complexity of the spectrum, and spectral density depends on the number of nuclei as equation shown below:.
The g factor is not necessarily isotropic and needs to be treated as a tensor g. For a free electron, g factor is close to 2. If electrons are in the atom, g factor is no longer 2, spin orbit coupling will shift g factor from 2. If the atom are placed at an electrostatic field of other atoms, the orbital energy level will also shift, and the g factor becomes anisotropic.
The anisotropies lead to line broadening in isotropic ESR spectra. The Electron-Zeeman interaction depends on the absolute orientation of the molecule with respect to the external magnetic field. Anisotropic is very important for free electrons in non-symmetric orbitals p,d.
Alpha and beta is the angle between magnetic field with respect to principle axis of g tensor. The excess population of lower state over upper state for a single spin system is very small as we can calculate from the following example. The process of this energy releasing is called spin relaxation process, of which there are two types, known as spin—lattice relaxation and spin—spin relaxation.
The energy is dissipated within the lattice as vibrational, rotational or translational energy. Rapid dissipation of energy short T 1e is essential if the population difference of the spin states is to be maintained. Slow spin-lattice relaxation, which is of frequent occurence in systems containing free radicals, especially at low temperatures, can cause saturation of the spin system.
This means that the population difference of the upper and lower spin states approaches zero, and EPR signal ceases. Spin-spin relaxation or Cross relaxation, by which energy exchange happens between electrons in a higher energy spin state and nearby electrons or magnetic nuclei in a lower energy state, without transfering to the lattice. The spin—spin relaxation can be characterized by spin-spin relaxation time T 2e.
In some cases, the EPR lines are broadened beyond detection. When a spin system is weakly coupled to the lattice, the system tends to have a long T 1e and electrons do not have time to return to the ground state, as a result the population difference of the two levels tends to approach zero and the intensity of the EPR signal decreases.
This effect, known as saturation, can be avoided by exposing the sample to low intensity microwave radiation. Systems with shorter T 1e are more difficult to saturate. Although EPR is limited to investigation of compounds and materials with unpaired electrons, it is undoubtedly the most direct and useful spectroscopic method for probing the properties of these specific systems.
Another advantage is that sample preparation is simple and EPR does not cause destruction or activation in the sample. By probing the fundamental splitting of energy levels of spins with regard to their orientation in an external magnetic field, interactions between paramagnetic spin systems and their local environments can be detected. EPR spectra is highly sensitive to the local electonic structure, oxidation state and the proximity of magnetic nuclei to the system in question.
Historical Development of EPR In , the line splitting in optical spectra in a static magnetic field was first found by a Dutch physicist Zeeman. While both spectroscopies deal with the interaction of electromagnetic radiation with magnetic moments of particles, there are many differences between the two spectroscopies: EPR focuses on the interactions between an external magnetic field and the unpaired electrons of whatever system it is localized to, as opposed to the nuclei of individual atoms.
The electromagnetic radiation used in NMR typically is confined to the radio frequency range between and MHz, whereas EPR is typically performed using microwaves in the 3 - GHz range.
In EPR, the frequency is typically held constant, while the magnetic field strength is varied. This is the reverse of how NMR experiments are typically performed, where the magnetic field is held constant while the radio frequency is varied. Due to the short relaxation times of electron spins in comparison to nuclei, EPR experiments must often be performed at very low temperatures, often below 10 K, and sometimes as low as 2 K. This typically requires the use of liquid helium as a coolant.
Origin of the EPR Signal An electron is a negatively charged particle with certain mass, it mainly has two kinds of movements. Sensitivity At the thermal equilibrium and external applied magnetic field, the spin population is split between the two Zeeman levels Figure 1 according to the Maxwell—Boltzmann law.
Nuclear Hyperfine Structure According to the figure 1, we should observe one spectra line in a paramagnetic molecule, but in reality, we usually observe more than one split line. The Fermi contact interaction happens in s orbital when electron density is not zero. Thus nuclear hyperfine spectra not only includes the interaction of nuclei and their positions in the molecule but also the extent to which part or all of the molecule is free to reorientate itself according to the direction of the applied magnetic field.
Isotropic Hyperfine Interaction In the case of one unpaired electron, the spin hamiltonian can be written as below for the isotropc part of nuclear hyperfine interaction. Figure 2: DPPH.
Spin Relaxation Mechanisms The excess population of lower state over upper state for a single spin system is very small as we can calculate from the following example. Spin-lattice relaxation this implies interaction between the species with unpaired electrons, known as "spin system" and the surrounding molecules, known as "lattice".
Spin-spin relaxation Spin-spin relaxation or Cross relaxation, by which energy exchange happens between electrons in a higher energy spin state and nearby electrons or magnetic nuclei in a lower energy state, without transfering to the lattice.
Parting Thoughts Although EPR is limited to investigation of compounds and materials with unpaired electrons, it is undoubtedly the most direct and useful spectroscopic method for probing the properties of these specific systems. References Abragam, A.
Poole, C. The interaction between the external magnetic field and the nuclear magnetic moment is given as follows:. This indicates the quantum number of magnetic spin, m I. Nuclear magnetic resonance transition. The nuclear magnetic resonance transition occurs between two energy levels. The transition between the two energy levels constitutes the resonance condition. Nuclear magnetic resonance stays on two important interactions.
The first one is the chemical shift and the other is the spin-spin coupling. A third interaction can also be mentioned. This is the exchange interaction. Thus, we can list three important interactions in NMR as follows:. However, the third influence is not taken into consideration.
So, we will focus on two interactions. The effective Hamiltonian expression for NMR consists of the sum of the nuclear Zeeman Hamiltonian and the nuclear spin-spin interaction Hamiltonian terms:. The electrons surrounding the nucleus of a molecular system show a spherical distribution. The external magnetic field applied on the system creates polarity in the electron distribution in the spherical structure.
That is, a current flows through the molecule. This current induces a magnetic field by induction where the core is located. This field is called the internal magnetic field Figure 2. The internal magnetic field is opposite to the external magnetic field. The total magnetic field seen by the nucleus is different from the external magnetic field. This brings about a shift in the resonance frequency of the nucleus.
This is called the chemical shift. That is, the electron-nucleus interaction originating from the magnetic field created by moving charges is the chemical shift Figure 3.
Internal magnetic field and external magnetic field orientation. The chemical shift. The internal magnetic field is connected to the external magnetic field Eq. Its scale is parts per million ppm. Contrary to the dipole-dipole interaction, it is a new type of interaction that is not dependent on the orientation of the molecule. It is the indirect spin-spin interaction period that occurs through the electrons that form chemical bonds in the molecule.
In other words, the interaction of a nucleus with another nucleus through an electron cloud is a spin-spin coupling. The energy of the spin-spin coupling is given as. J is the spin-spin coupling coefficient. Figure 4 shows a spin-spin coupling example and Figure 5 shows an NMR spectrum example. A spin-spin coupling example. An example of an NMR spectrum.
EPR deals with substance that contains unpaired electrons. These substances are free radicals, triplet excited states, and most transition metal and rare earth species. Among the parameters found in the EPR experiments are the g-factor, the hyperfine structure constant hf , the nuclear quadrupole coupling constant, and the zero-field splitting constant.
However, mostly the g -factor and the hyperfine structure constant are among the more studied parameters. For EPR analysis, the sample is placed in a strong magnetic field. The applied electromagnetic radiation is in the microwave area. STDB is a resource for scientists to aid in the identification of free radicals. It is intended as a resource for those looking to use software in their own research. It is also a forum for discussion of software issues. This software is provided free of charge to the ESR research community with the understanding that any resulting reports, either internally or externally distributed, explicitly acknowledge this contribution.
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