Electron Spin Resonance Spectroscopy

ESR Spectra- Principle-Hyperfine Splitting and structure- g-factor - Factors affecting g-value - Anisotropic system- Triplet state - Kramer's degeneracy - Zero Field Splitting

1. ELECTRON SPIN RESONANCE SPECTROSCOPY Dr.P.GOVINDARAJ  Associate Professor & Head , Department of Chemistry SAIVA BHANU KSHATRIYA COLLEGE ARUPPUKOTTAI - 626101 Virudhunagar District, Tamil Nadu, India

2. ELECTRON SPIN RESONANCE SPECTRA (ESR Spectra) Definition The interaction between the electron spin energy levels of a molecule and the microwave radiation causes transition between the electron spin energy levels by the absorption of microwave radiation is called Electron Spin Resonance Spectra (ESR Spectra) Condition Molecules having unpaired electrons gives ESR Spectra. Example: Free radicals, transition metal ions and paramagnetic molecules like Nitric oxide, Oxygen etc., ESR Spectra obtained in the Microwave region: 2000-9600 MHz

3. Principle of ESR Spectra The spinning charged electron can generate spin magnetic moment μ s given by μ s = -g e μ --------(1)   Where g e ---- g-factor μ B ---- Bohr magneton = (e – charge of electron & – mass of electron) s ---- spin of the electron (½)  

4. When an electron spin having magnetic moment ( μ s ) is placed in a magnetic field B z , the interaction energy is E = - μ s B z cosθ --------(2) Where θ ---- Angle between μ s and B z Principle of ESR Spectra Substitute cosθ = and μ s = -g e μ B s in equation (2) we get   E = -(- g e μ B s ) B z = g e μ B B z   E = g e μ B B z --------(3)  

5. For an electron of spin s = ½ , the spin angular momentum quantum number will h ave values of = ± ½ and substituting the values of = ± ½ in equation in (3) we get two energy levels E -½ and E +½   Principle of ESR Spectra E -½ = - ½ g e μ B B z ---------(4) E +½ = + ½ g e μ B B z ---------(5)

6. In the absence of Magnetic field (B z = 0), the two values of will gives rise to a doubly degenerate spin energy state. If a magnetic field is applied, this degeneracy is removed by splitting the energy level as E -½ and E +½ shown in the diagram   The low energy state will have the spin magnetic moment aligned with the field and correspond to quantum number, = - ½ . The high energy state will have the spin magnetic moment opposed to the field and corresponds to the quantum number, = + ½   Principle of ESR Spectra

7. The energy of separation Δ E is obtained by subtracting equation (4) from (5) Δ E= ½ g e μ B B z – (– ½ g e μ B B z ) Δ E= ½ g e μ B B z + ½ g e μ B B z ) Since Δ E= h , equation(6) becomes     On substituting all values in the right side of the equation we get = 9530 MHz   Δ E= g e μ B B z ---------( 6) ---------( 7)   Principle of ESR Spectra

8. Since this frequency falls in the microwave region, On passing microwave radiation causes transition between the electronic spins from lower energy level to higher energy level shown in the diagram resulted ESR spectrum . Principle of ESR Spectra

9. HYPERFINE SPLITTING AND HYPERFINE STRUCTURE IN ESR SPECTRA Definition: The splitting of ESR spectra of an electron by the interactions between the magnetic spinning electron and adjacent spinning magnetic nuclei is called Hyperfine splitting and the resulted splitting ESR signals are called Hyperfine structure Number of peaks in ESR and Selection rule : In general, if a single electron interacts magnetically with “n” equivalent nuclei, the electron signal is split up into a (2nI +1) multiplet. Where n ---- No. of nuclei I ---- spin quantum number of the nucleus = ½ For H . radical , n=1 & I = ½ and No. of Signals = (2 X 1 X ½ + 1) = 2 For CH 3 . radical , n=3 & I = ½ and No. of Signals = (2 X 3 X ½ + 1) = 4 Example: The selection rule for hyperfine transition is Δ m s = ± 1 , Δ m I = 0

10. ESR spectra of free radicals in solution (or) Hyperfine structure of free radicals in solution The ESR spectra of free radicals in solution are very much useful for getting details of electron distribution and structure of the radicals The free radical must be produced in a concentration of about 10 - 13 moldm -3 for getting good ESR spectrum ESR spectrum for H . (H-atom) free radical For H . radical , S = ½ , I= ½ , m s = ± ½ and m I = ± ½ In the absence of magnetic field (B z = 0), the electron spin energy levels are degenerate In the presence of magnetic field (B z ≠ 0), the m s = -½ sublevel going down and the m s = + ½ sublevel going up (shown in the diagram)

11. Each electron sublevel interacts with nucleus of m I = + ½ and - ½ giving four sublevels designated by the value of m I . This is called hyperfine interaction. On passing microwave radiation into the H . system two transitions are possible as per the selection rule ∆m s = + 1; ∆m I = 0 resulted two ESR lines, i.e., a doublet shown in the diagram. The two ESR lines are equally intense, the spacing between them is called hyperfine coupling constant (a), expressed in tesla (or) milli tesla units. ESR spectrum for H . (H-atom) free radical

12. In the presence of magnetic field (B z ≠ 0), the electron spin energy level m s = -½ going down and the electron spin energy level m s = +½ going up (shown in the diagram) Each electron spin energy levels interacts with four nucleus spin energy levels: m I = , , , resulted eight sublevels designated by the values of m I   ESR spectrum or Hyperfine structure for . CH3 radical For . CH 3 , S = ½ , m s = + ½ and - ½ Since for a proton , I = ½ , m I values for three equivalent protons are : m I = , , , In the absence of magnetic field (B z = 0) , the electron spin energy levels (m s = ± ½ ) are degenerate  

13. On passing microwave radiation into the . CH 3 system four transition are possible as per the selection rule ∆ m s = + 1 and ∆ m I = 0 resulted four ESR lines called quartet. ESR spectrum or Hyperfine structure for . CH 3 radical

14. The position of an ESR signal is defined by the effective g-value, i.e., by Since h and (Bohr magneton) are constant, g-factor is a measure of the ration between frequency ( ) and magnetic field( ), i.e.,   g-factor in ESR spectra g =   g   

15. Factors affecting g-value For free electron and organic radicals such as the methyl radical, the g-value depends upon the spin angular momentum of the electron itself and its value was found to be 2.0023 (g e ) In the case of the transition metal ion and their complexes, g-value depends upon the spin and the orbital motion of the electron . So that, the g-value departs from the g e value. In solution, because of free rotating motion, the g-factor is isotropic, i.e., it is the average of the three g-value in the x, y and z directions. In solid state, because of restricted motion, the g-value is anisotropic, i.e., its magnitude depends upon the direction of measurement.

16. ESR of Anisotropic system Anisotropic systems in ESR is the free radicals (or) paramagnetic materials in the form of crystalline states (or) frozen solutions in which the interactions of applied magnetic field with the spin angular momentum ( ) and orbital angular momentum ( ) of the electron must be depends on the orientation of the sample. For Anisotropic systems having axial symmetry, one of these terms g ll is different from the other two g  terms. For Anisotropic systems having lower symmetries, the three terms g xx , g yy and g zz are all different.   i.e ., g-factor for anisotropic system must be directional property and represented as g xx , g yy and g zz . g zz is designated as g ll and g xx & g yy are designated as g 

17. Shapes of ESR absorption curves and first derivatives curves for anisotropic system having (a) an axis of symmetry and (b) no symmetry shown below ESR of Anisotropic system

18. ESR for Triplet state Molecules having diamagnetic ground states but which possess excited triplet states (with two unpaired electrons) which have lifetimes long enough to record ESR spectra. _________ Excited state _____ and ______ Triplet state m s = +1 m s = -1 Singlet ________ Ground state ____________ m s = 0 In the presence of a magnetic field, a triplet state splits into its three components shown in the diagram, giving two possible transition, m s = -1 → 0 and m s = 0 → +1, whose energies are identical.      

19. ESR for Triplet state

20. Kramer’s degeneracy and Zero F ield S plitting In a crystal (or) frozen sample, dipole-dipole interactions being anisotropic , the energy levels with m s = ± 1 are shifted relative to that with m s = 0 even in the absence of an applied magnetic filed. This is shown in the following diagram For a two electrons system, there are three possible spin orientations: i.e., The splitting of energy levels in anisotropic systems in the absence of applied magnetic field is called zero field is called Zero Field Splitting (ZFS ).       m s = +1 m s = -1 m s = 0

21. For a three electrons system, there are four possible spin orientations   m s = +         m s = +   m s = -   m s = -   Kramer’s degeneracy and Zero F ield S plitting

22. Kramer’s rule states that for a system having an even number of unpaired electron spins, the lowest energy state will be that with m s = 0 and all higher energy states in the even number electron system & all states for systems with an odd number of unpaired electron spin, will be doubly degeneracy i.e., m s = +1 & -1 has same energy m s = + & - has same energy m s = + & - has same energy m s = + & - has same energy .. .. This degeneracy is known as Kramer’s degeneracy   Kramer’s degeneracy and Zero F ield S plitting

23. For an even number of electron system (Two electrons) the Kramer’s degeneracy ( m s = ± 1 has same energy) is removed by an applied magnetic field, which shifts the two levels m s = -1 and m s = + 1 in opposite directions shown in the diagram. As a result, two allowed transitions ( m s = -1 → 0 and m s = 0 → + 1) occurred at different energy. Kramer’s degeneracy and Zero F ield S plitting

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