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EPR-Spektroskopie Einführung in die EPR-Spektroskopie Björn Corzilius Wintersemester 2018/2019 16.10.2018 Allgemeine Hinweise WS 2018/19 Vorlesung Dienstags 17:00-18:15 Uhr B2 Übung Dienstag 16:00-17:00 Uhr B2 2 SWS / 4 CP Modul: Einführung in die Theorie der Magnetischen Resonanz Wahlpflichtmodul in Physikalischer & Theoretischer Chemie Weitere Vorlesungen aus dem Modul: Einführung in die Festkörper-NMR Spektroskopie Einführung in die Hochauflösende NMR Spektroskopie 2 Veranstaltungen für das Modul benötigt, 3 möglich; EPR ist verpflichtend zur Anerkennung Übungen zur Vorlesung: Übungsaufgaben auf der Webseite (www.solidstateDNP.de) unter teaching Abgabe des bearbeiteten Übungsblattes in der darauf folgenden Übungsstunde Tutorin: Victoria Aladin ([email protected]) Leistungsnachweis für EPR Spektroskopie: Klausur (oder mündliche Abschlussprüfung) Anmeldung ab letzter Semesterwoche im Sekretariat bei Frau Schneider N140/Raum17 16.10.2018 1 Literatur • Allgemein • Chechik, Carter, Murphy: EPR, Oxford Chemistry Primers • Lund et al.: Principles and Applications of ESR Spectroscopy, Springer 2011 • Wertz & Bolton: ESR: Elementary Theory and Practical Applications, 1986 • Weil & Bolton: EPR: Elementary Theory and Practical Applications, 2007 • Carrington & McLachlan: Introduction to MR, Halper 1970 • Eaton, Eaton, Weber: Quantitative EPR, Springer, 2010 • Theorie • Schweiger, Jeschke: Principles of pulse electron paramagnetic resonance, Oxford Press 2001 • Slichter: Principles of Magnetic Resonance, Springer 1980 • Poole & Farach: Theorie of Magnetic Resonance, Wiley 1987 • Levitt: Spin Dynamics, Wiley 2001 • Skripte • Jeschke: Vorlesungsskript Einführung in die ESR-Spektroskopie • Buch-Kapitel • Methods in Physical Chemistry, Wiley-VCH 2007 • Haken & Wolf: Molekülphysik und Quantenchemie, Springer 1991 • Organische Radikale • Gersen, Huber: ESR Spectroscopy of Organic Radicals, 2003 • Übergangsmetalle & Lanthanoide • Abragam & Bleaney: EPR of Transition Ions, Oxford 1970 • Pilbrow: Transition Ion EPR, Clarendon 1991 • Anwendungen • Drescher & Jeschke: EPR Spectroscopy Applications in Chemistry and Biology, Springer 2012 • Misra: Multifrequency EPR: Theory and Applications, Wiley 2010 16.10.2018 2 Inhalt • Allgemeines + Historisches • Puls-EPR Methoden • Theoretische Grundlagen • Bloch-Gleichungen • Pauli'sche Spinmatrizen • Kohärenz und Relaxation • Spin-Hamilton Operator • Hyperfein-Spektroskopie • Das EPR-Spektrometer • ENDOR • Organische Radikale in Lösung • ESEEM/HYSCORE • Hyperfein-Wechselwirkung • Dipolare Spektroskopie • g-Wert • PELDOR/DEER • Organische Radikale im Festkörper • DQEPR • Anisotrope Wechselwirkungen • RIDME • Übergangsmetallkomplexe im Festkörper • Dynamische Kernpolarisation • S > 1/2 • Overhauser DNP in Flüssigkeiten • Nullfeldaufspaltung • Solid State DNP 16.10.2018 3 EPR und NMR Gemeinsame Geschichte und gemeinsame Zukunft? 16.10.2018 4 1896: Zeeman-Effekt Natrium D-Linien Anomaler Zeeman-Effekt (Spin noch unbekannt) Pieter Zeeman *1865 (Zonnemaire, NL) †1943 (Amsterdam, NL) Niederländischer Physiker 1902 Nobelpreis für Physik Professor in Leiden und Amsterdam 16.10.2018 5 Spin-Aufspaltung im starken Magnetfeld 16.10.2018 6 1922: Stern–Gerlach-Experiment Otto Stern Walter Gerlach *1888 (Sohrau, Ober-Schlesien) *1889 (Biebrich) †1969 (Berkeley, Kalifornien) †1979 (München) Habilitierte 1915 in Frankfurt Ab 1920 an Goethe-Uni Ab 1921 Privatdozent (Extraordinarius Professor) 1943 Nobelpreis für Physik 16.10.2018 7 Stern–Gerlach-Experiment 16.10.2018 8 Stern–Gerlach-Experiment dB /dz ohne 0 mit Magnetfeldgradient Magnetfeld- Erwartung Beobachtung gradient 16.10.2018 9 1925: Postulation des Eigendrehimpulses George Uhlenbeck Hendrik Kramers Samuel Goudsmit Magnetisches Spin-Moment → Quantenmechanisches Modell gµB des Spins durch Pauli und Dirac µS = S 16.10.2018 10 Die quantenmechanische Rotation ˆ HEψϕJ( ) = JJ ψϕ( ) ===ψϕJJ( 02) ψϕ( π) Randbedingungen: ∂∂ψϕ( ) ψϕ( ) JJ= ∂∂ϕϕ Ansonsten ϕ=02ϕπ= destruktive Interferenz! 16.10.2018 11 Symmetrie im 2D-Raum (ohne Spin!) Identität erreicht nach Winkel: φ = 2π φ = π φ = 2/3π Erlaubte Rotationsquantenzahlen: J = 0, 1, 2, 3, … J = 0, 2, 4, 6, … J = 0, 3, 6, 9, … 16.10.2018 12 Rotation mit Spin ortho-Wasserstoff para-Wasserstoff i1 = 1/2 i2 = 1/2 i1 = 1/2 i2 = 1/2 I = 1 I = 0 drei mögliche Spin-Wellenfunktionen: eine mögliche Spin-Wellenfunktionen: |αα> |ββ> (|αβ>+|βα>)/21/2 (|αβ>−|βα>)/21/2 Erlaubte Rotationsquantenzahlen: J = 1, 3, 5, 7, … J = 0, 2, 4, 6, … 16.10.2018 13 Der Spin — Rotationssymmetrie Spin-0 Spin-1 Spin-2 Spin-3 Spin-4 Spin-5 — 360° 180° 120° 90° 72° Bosonen Fermionen Spin-1/2 720° Möbius-Band 16.10.2018 14 Die Richtungsquantelung der Rotation Spin-Quantenzahl S Spin-Drehimpuls S= SS( +1) magnetische Spin-Quantenzahl mS =−−+{ SS, 1, , S − 1, S} z-Komponente des Spin-Drehimpulses Se⋅=zz S = m S halbzahlige S: Kramers-Systeme ganzzahlige S: nicht-Kramers-Systeme 16.10.2018 15 Spin-Moment: Elektronenspin vs. Kernspin B0 mI = +1/2 mS = –1/2 Proton I = 1/2 γn = 42.6 MHz/T Elektron S = 1/2 γe = –28.8 GHz/T mI = –1/2 qi γ ii= g 2mi mS = +1/2 −e geBµ γ ee=g = − 2me e gnnµ γ nn=g = 2mp 16.10.2018 16 Wechselwirkung Dipol–Feld Drehmoment potentielle Energie MB=µm × EBmm= −µ 16.10.2018 17 Zeeman-Aufspaltung E( mS) = g eBµ mB S0 ω∆E g µ = = eBB 2π hh0 16.10.2018 18 Rabi’s 1. MR-Experiment: Aufbau Blende Blende Blende Blende Homogenes Gradientenfeld Gradientenfeld Magnetfeld Molekular- strahl RF senkrecht zu B0 Detektor Spin-Übergänge in einem Spin-selektierten Molekularstrahl 16.10.2018 19 1938: Rabi-Experiment Isidor Isaac Rabi *1898 (Rymanów, Galizien) †1988 (New York) Professor an Columbia University 1944 Nobelpreis für Physik Erstes NMR-Experiment (7Li, 0.2 T, 3.5 MHz) 16.10.2018 20 Rabi-Oszillationen 90° Puls 180° Puls Grundlage der (gepulsten) Magnetresonanz 16.10.2018 21 1944: Zavoisky-Experiment Yevgeny Zavoisky *1907 (Mogilyov-Podolsk) †1976 (Moskau) Sovietischer Physiker Wissenschaftler in Kazan Detektion der EPR-Induktion 16.10.2018 22 1946: Detektion der Kerninduktion Felix Bloch Edward Mills Purcell *1905 (Zürich) *1912 (Taylorville, Illinois) †1983 (Zürich) †1997 (Cambridge, Massachusetts) Professor in Stanford und Berkeley Professor an MIT und Harvard 1952 Nobelpreis für Physik Erste Detektion der NMR 1952 Nobelpreis für Physik in flüssiger und fester Phase Detektion der Kerninduktion — Geburt der heutigen NMR 16.10.2018 23 Protein-Strukturparameter durch MR Short/medium-distance Long-distance 1.5 – 5 Å 10 – 100 Å One-bond couplings (through bond/space) Electron–electron couplings Connectivity/Assignments Solid-state between spin-tags + Solution (Jeschke, Prisner, …) EPR Chemical shift analysis NMR Subunit arrangement, Secondary structure elements folding, ligand binding, … Image: KcsA tetramer Endeward et al., JACS 2008 Multi-bond couplings (through space) Secondary/tertiary structure, Solid-state Paramagnetic shift analysis Solution inter-sheet/turn arrangement, … NMR + relaxation enhancement + Solid-state (Bertini, Jaroniec, …) NMR Local structure, folding, ligand binding, … Image: Cobalt MMP-12, Balayssac et al., JACS 2007 16.10.2018 24 Protein-Strukturparameter durch MR Short/medium-distance Long-distance 1.5 – 5 Å 10 – 100 Å One-bond couplings (throughNMR bond/space) leidetElectron–electronan couplings Connectivity/Assignments Solid-state between spin-tags + Solution (Jeschke, Prisner, …) EPR Chemical shift analysis geringerNMR Subunit arrangement, Secondary structure elements folding, ligand binding, … Image: KcsA tetramer Endeward et al., JACS 2008 Multi-bond couplingsEmpfindlichkeit (through space) Secondary/tertiary structure, Solid-state Paramagnetic shift analysis Solution inter-sheet/turn arrangement, … NMR + relaxation enhancement + Solid-state aufgrund (Bertini,kleiner Jaroniec, …) NMR thermischerLocal structure, folding, ligand binding, … Polarisation Image: Cobalt MMP-12, Balayssac et al., JACS 2007 16.10.2018 25 Das Empfindlichkeits-Problem Absorption Spin-Polarisation β NNαβ− γ B P = = tanh 0 Nαβ+ N2 kT Netto-Signal P ≈ 0.01 % SNR ~ N0.5 ~ P α 108-fach längere Aufnahme i.V.z. vollst. Polarisation Stimulierte Emission 16.10.2018 26 Wege zur Steigerung der Empfindlichkeit Spin-Polarisation 9.4 T 9.4 T 400 MHz − 20 K 263 GHz NNαβ γ B0 100 K P = = tanh Nαβ+ N2 kT 0.047 % 150 mK T 22.5 T – 9.4 T 950 MHz DNP! e 400 MHz 100 K 100 K B0 0.009 % 6.3 % 0.022 % 16.10.2018 27 Wege zur Steigerung der Empfindlichkeit Spin-Polarisation 9.4 T 9.4 T 400 MHz − 20 K 263 GHz NNαβ γ B0 100 K P = = tanh Nαβ+ N2 kT Polarisationsmittel 0.047 % 150 mK + MikrowellenT = DNP 22.5 T – 9.4 T 950 MHz DNP! e 400 MHz 100 K 100 K B0 0.009 % 6.3 % 0.022 % 16.10.2018 28 Dynamische Kernpolarisation • 1953 Postuliert durch Overhauser in leitfähigen Festkörpern Overhauser, Phys. Rev. 92, 411 (1953) • Overhauser Effekt im gleichen Jahr von Carver und Slichter nachgewiesen Carver and Slichter, Phys. Rev. 92, 212 (1953) • Erstmals DNP in nicht-leitenden FKs unabhängig von Jeffries, Uebersfeld und Abragam am Ende der 1950er Jeffries, Phys. Rev. 106, 164 (1957) Abraham et al., Phys. Rev. 106, 165 (1957) Erb, Motchane, and Uebersfeld, CR. Hebd. Acad. Sci. 246, 2121 (1958) Abragam and Proctor, CR. Hebd. Acad. Sci. 246, 2253 (1958). Spielwiese für Physiker während der Carver and Slichter, Phys. Rev. 92, 212 (1953) 1960er und 70er Jahre Seit 10 Jahren Renaissance im Hochfeld! 16.10.2018 29.
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