10.1 Principles of ESR and electron spin

Electron spin resonance spectroscopy reveals the behavior of unpaired electrons in materials. By applying magnetic fields and microwaves, we can observe energy level splits and transitions, giving us insights into molecular structures and dynamics.

The principles of ESR involve the Zeeman effect, spin-orbit coupling, and hyperfine interactions. Understanding these concepts helps us interpret ESR spectra, determine g-factors, and uncover valuable information about electronic environments in various substances.

Electron Spin and Interactions

Fundamental Concepts of Electron Spin

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• Electron spin represents an intrinsic angular momentum of electrons
• Quantum mechanical property characterized by spin quantum number s = 1/2
• Electrons can have two possible spin states: "spin-up" (+1/2) or "spin-down" (-1/2)
• Spin magnetic moment arises from the electron's spin angular momentum
• Magnitude of electron spin magnetic moment equals approximately one Bohr magneton

Zeeman Effect and Spin-Orbit Coupling

• Zeeman effect describes the splitting of energy levels in the presence of an external magnetic field
• Unpaired electrons in an atom experience energy level splitting proportional to the applied field strength
• Spin-orbit coupling results from the interaction between electron's spin and its orbital angular momentum
• Strength of spin-orbit coupling increases with atomic number
• Leads to fine structure in atomic spectra and influences the g-factor in ESR spectroscopy

Hyperfine Coupling and Nuclear Interactions

• Hyperfine coupling arises from the interaction between electron spin and nuclear spin
• Causes additional splitting of energy levels in ESR spectra
• Strength of hyperfine coupling depends on the distribution of unpaired electron density at the nucleus
• Provides information about the chemical environment and molecular structure
• Number of hyperfine lines in ESR spectrum relates to the nuclear spin quantum number of nearby nuclei

ESR Spectroscopy Principles

G-Factor and Resonance Condition

• G-factor (g) measures the magnetic moment of an electron in a specific environment
• Free electron g-factor equals approximately 2.0023
• G-factor deviates from free electron value due to spin-orbit coupling and local magnetic fields
• Resonance condition in ESR spectroscopy expressed as $hν = gμBB$
• h represents Planck's constant, ν denotes microwave frequency, μB equals Bohr magneton, and B signifies applied magnetic field strength

Selection Rules and Energy Level Transitions

• ESR transitions obey selection rules governing allowed changes in magnetic quantum numbers
• Primary selection rule for ESR: ΔmS = ±1 (change in electron spin magnetic quantum number)
• Transitions between energy levels occur when the resonance condition is met
• Absorption of microwave radiation induces transitions between spin states
• Intensity of ESR signal proportional to the population difference between energy levels

Energy Level Splitting and Spectral Features

• Applied magnetic field causes Zeeman splitting of electron spin energy levels
• Energy difference between split levels increases linearly with magnetic field strength
• ESR spectrum typically displays a single absorption line for simple systems
• Hyperfine interactions lead to additional splitting and multiple spectral lines
• Line shape and width provide information about relaxation processes and molecular motion
• Integrated intensity of ESR signal relates to the concentration of unpaired electrons in the sample