Seite 2 Introduction to EPR Spectroscopy ● EPR allows paramagnetic species to be identified and their electronic and geometrical structures to be characterised ● Interactions with other molecules, concentrations, lifetimes and dynamics ● Solid state, solution, gas phase ● Non-destructive Nomenclature: Electron Paramagnetic Resonance (EPR) Electron Magnetic Resonance (EMR) Electron Spin Resonance (ESR) Prof. Dr. Christopher W. M. Kay 01/08/17
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Nomenclature: Electron Paramagnetic Resonance (EPR ... · 01/08/17 Prof. Dr. Christopher W. M. Kay Seite 15 Electron Zeeman Interaction The allowed energies are found using the complete
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Seite 2
Introduction to EPR Spectroscopy
● EPR allows paramagnetic species to be identified and their electronic and geometrical structures to be characterised
● Interactions with other molecules, concentrations, lifetimes and dynamics
● Solid state, solution, gas phase
● Non-destructive
Nomenclature: Electron Paramagnetic Resonance (EPR)
Electron Magnetic Resonance (EMR) Electron Spin Resonance (ESR)
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 3
Spectroscopy – Magnetic Resonance
Probing energy level structure via interaction with electromagnetic radiation.
Energy level transitions associated with absorption/emission of EM radiation.
Frequency proportional to energy level separation.
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 4
Outline – Applications of EPR
Biology & Medicine Chemistry Physics & Geology Materials Science
Photosynthesis Metallo-proteins Metallo-enzymes in vivo EPR Oximetry EPR Imaging Spin-labels Irradiation damage in DNA Irradiated food Beer Reactive Oxygen Species
Radicals in solution Short-lived paramagnetic compounds Radical pair reactions Fullerenes (C60) Photochemistry Reaction kinetics Excited states Spin trapping Catalysts Metal clusters
Organic conductors EPR Dosimetry EPR Dating EPR Microscopy Semiconductors Defects Laser-crystals Ferroelectrics Phase transitions Adsorption of gases oLEDs
Polymers Glasses High temperature superconductors Ceramics Nano-particles Photographic film Transition metal ions in Zeolites Porous Materials Coal
Literature Introduction to Magnetic Resonance Carrington & McLachlan Electron Spin Resonance Atherton The Theory of Magnetic Resonance Poole & Farach Principles of Pulse Electron Paramagnetic Resonance Schweiger and Jeschke Electron paramagnetic resonance of transition ions Abragam & Bleaney Electron Paramagnetic Resonance – Elementary Theory and Practical Applications Weil, Bolton, and Wertz Biological Magnetic Resonance Vol. 19: Distance Measurements in Biological Systems by EPR, Berliner, Eaton & Eaton
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 5
Outline – Research Papers: Materials
1. Group V donor in Silicon: Quantum control of hybrid nuclear–electronic qubits
2. Organic Spintronics: Ordering in thin films and relaxation of Cu-Phthalocyanine
3. Photo-excited Triplet states of Porphyrins: TR-EPR, ENDOR and DFT
4. Light-Activated Antimicrobial Agents: TR-EPR, 1O2 production, and DFT
5. Masers I: Pentacene in p-Terphenyl Crystals
6. Masers II: NV- Centers in Diamond
7. Singlet Fission in Thin Films of Pentacene in p-Terphenyl
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 6
Outline – Theory and Methodology
1. Principles of EPR • Unpaired Electrons and Electron Spin • Spectrometer Design: Helmholtz Coil ; Modulation ; Waveguide ; Resonators
2. Electron-Nuclear Hyperfine Coupling • The Hamiltonian for a system with one electron & one spin ½ Nucleus • High-Field Approximation • Examples of systems with single Nuclei: P@Si ; Bi@Si ; N@C60 ; Mn2+
• Example of a system with several (symmetry) equivalent nuclei: PNT • Line-shapes: Homogenous and Inhomogenous Broadening • Relaxation; spin echo experiments on P@Si and Bi@Si • Continuous-wave Electron-Nuclear Double Resonance (ENDOR) on PNT • Pulse ENDOR on Bi@Si
3. Photo-excited Triplet States • Zero-field Splitting • Time-resolved EPR
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 7
Stern–Gerlach Experiment (1922)
A beam of silver atoms splits in an inhomogeneous magnetic field due to the angular momentum or spin of the unpaired valence electron.
For electrons, the spin quantum number, S = ½. The total angular momentum of magnitude 〈S2〉 = {S(S + 1)} ½ !. (2S + 1) components of angular momentum mS ! where mS = S, (S – 1), ..., –S. Hence, there are two components, with mS = ±½.
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 8
Electron Transfer Reactions
Singlet S = 0
MS = 0
Doublet S = ½
MS = ±½
Triplet S = 1
MS = ±1, 0
Quartet S = 3/2
MS = ±3/2, ±½, 0
Quintet S = 2
MS = ±2, ±1, 0
For electrons, the spin quantum number, S = ½. The total angular momentum of magnitude 〈S2〉 = {S(S + 1)} ½ !. (2S + 1) components of angular momentum mS ! where mS = S, (S – 1), ..., –S. Hence, there are two components, with mS = ±½.
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 9
Which Elements are Important for EPR?
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite 10
Which species has an unpaired electron in its outer orbital and hence has an EPR signal?
1. Ca2+
2. Cu1+ 3. Cu2+
4. Ti4+
5. Zn2+
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite Prof.Dr.ChristopherW.M.Kay 1301/08/17
Transition Metals with Unpaired Electrons
The energies of the d-orbitals are rendered non-degenerate by the presence of ligands
S = 0 S = 5/2 S = ½ S = 2
Seite 14
Electron Zeeman Interaction
The analogous quantum mechanical expression (Hamiltonian) with the magnetic field in the z direction (taking the Sz component of S):
The magnetic moment of the electron:
where is the Bohrmagneton
The interaction of the magnetic moment and an external magnetic field, B0, is given by:
For electrons S = ½, so there are two basis states with mS = ±½. These are labelled |αe⟩ and |βe⟩, and may be represented by column vectors:
Prof.Dr.ChristopherW.M.Kay01/08/17
Seite Prof.Dr.ChristopherW.M.Kay1501/08/17
Electron Zeeman Interaction
The allowed energies are found using the complete Hamiltonian in the Schrödinger equation:
In order to find the eigenvalues we need expressions for the quantum mechanical operators representing Sx, Sy and Sz. These are the Pauli spin matrices multiplied by a factor of ½:
By matrix multiplication, we can see that |αe⟩ and |βe⟩ are eigenstates of Sz. The eigenvalues are:
EPR Spectrum of a one electron system strong pitch
The Hamiltonian: HEZ = ge µβ SZ • Bo
Seite Prof.Dr.ChristopherW.M.Kay3001/08/17
Important Nuclei (I ≠ 0) for NMR/EPR
Element Isotope Spin Number of lines
Gyromagnetic ratio [ MHz / T ]
Abundance [ % ]
Electron — ½ — 176085.98 —
Hydrogen 1H ½ 2 267.51 99.985
2H 1 3 41.06 0.015
Carbon 13C ½ 2 67.26 1.11
Nitrogen 14N 1 3 19.32 99.63
15N ½ 2 –27.11 0.37
Fluorine 19F ½ 2 251.67 100
Phosphorus 31P ½ 2 108.29 100
Vanadium 51V 7/2 8 70.32 99.76
Manganese 55Mn 5/2 6 66.18 100
Iron 57Fe ½ 2 8.65 2.19
Cobalt 59Co 7/2 8 63.12 100
Nickel 61Ni 3/2 4 23.95 1.134
Copper 63Cu 3/2 4 71.07 69.1
65Cu 3/2 4 76.05 30.9
Molybdenum 95Mo 5/2 6 -17.09 15.7
97Mo 5/2 6 -17.88 9.46
Bismuth 209Bi 9/2 10 44.92 100
Seite Prof.Dr.ChristopherW.M.Kay3101/08/17
Nuclear Zeeman Interaction
The Hamiltonian: HNZ = −gN µβ IZ • Bo
Selection Rule: ΔI = ±1
Seite Prof.Dr.ChristopherW.M.Kay3201/08/17
Electron-Nuclear Hyperfine Interaction
The magnetic moments of the electron and nuclei are coupled by the Fermi contact interaction. It represents the energy of the nuclear moment in the magnetic field produced at the nucleus by electric currents associated with the "spinning" electron:
There is also a magnetic coupling between the magnetic moments of the electron and nucleus which is entirely analogous to the classical dipolar coupling between two bar magnets:
The magnetic moments of the electron and nuclei are coupled via two interactions: the isotropic Fermi contact interaction and the anisotropic dipolar coupling giving the Hamiltonian:
where
Seite Prof.Dr.ChristopherW.M.Kay3301/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Pauli Spin Matrices
Seite Prof.Dr.ChristopherW.M.Kay3401/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Direct Product Expansion is a form of matrix multiplication whereby all the elements of one matrix are multiplied by a second matrix in turn. Thus direct product expansion of an n × n matrix with an m × m matrix results in the formation of an nm × nm size matrix
Seite Prof.Dr.ChristopherW.M.Kay3501/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Seite Prof.Dr.ChristopherW.M.Kay3601/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Seite Prof.Dr.ChristopherW.M.Kay3701/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Seite Prof.Dr.ChristopherW.M.Kay3801/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Seite Prof.Dr.ChristopherW.M.Kay3901/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Hig
h-fie
ld a
ppro
xim
atio
n
Seite Prof.Dr.ChristopherW.M.Kay4001/08/17
Description of a 1 electron, 1 proton system
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Hig
h-fie
ld a
ppro
xim
atio
n
Seite Prof.Dr.ChristopherW.M.Kay4101/08/17
Silicon doped with Phosphorus @ 10 K
S = ½; mS = ±½ I = ½; mI = ±½
The Hamiltonian: H = HEZ + HNZ + HHF
Hig
h-fie
ld a
ppro
xim
atio
n
9.7GHz
Seite Prof.Dr.ChristopherW.M.Kay4201/08/17
EPR Spectrum of N@C60 @ 9 GHz
The Hamiltonian: H = HEZ + HNZ + HHF
S = 3/2 mS = 3/2, ½, –½ ,–3/2 I = 1 mI = 1, 0, –1
Seite Prof.Dr.ChristopherW.M.Kay4301/08/17
EPR Spectrum of Mn2+ @ 94 GHz
The Hamiltonian: H = HEZ + HNZ + HHF
S = ½ mS = ±½ I = 5/2 mI = ±5/2, ±3/2, ±½
Seite Prof.Dr.ChristopherW.M.Kay4401/08/17
Silicon doped with Bismuth @ 9.7 GHz
The Hamiltonian: H = HEZ + HNZ + HHF
Bi
S = ½ I = 9/2 mI = ±9/2, ±7/2, ±5/2, ±3/2, ±½ A = 1.4754 GHz
9.7GHz
Seite Prof.Dr.ChristopherW.M.Kay4501/08/17
Silicon doped with Bismuth @ 9.7 GHz
The Hamiltonian: H = HEZ + HNZ + HHF
Bi S = ½ I = 9/2 A = 1.4754 GHz
S = ½ I = ½ A = 117.1 MHz
Given that:
Hyperfine coupling ≈ gyromagnetic ratio × spin density
(1) Work out the ratio of spin density for P@Si and Bi@Si.