Pulse EPR spectroscopy: ENDOR, ESEEM, DEER

Transcription

1 Pulse EPR spectroscopy: ENDOR, ESEEM, DEER Penn State Bioinorganic Workshop May/June 2012 Stefan Stoll, University of Washington, Seattle References A. Schweiger, G. Jeschke, Principles of Pulse Electron Paramagnetic,Resonance, Oxford, 2001 Y. Deligiannakis, M. Louloudi, N. Hajiliadis, ESEEM spectroscopy as a tool to investigate the coordination environment of metal centers, Coord. Chem. Rev. 204, (2000) H. Thomann, M. Bernardo, Pulse Electron Nuclear Multiple Resonance Spectroscopic Methods for Metalloproteins and Metalloenzymes, Methods Enzymol. 227, (1993) 1

2 Hidden structure in cw EPR spectra cw EPR cw EPR integral cw dynamic line broadenings - lifetime - molecular motions - exchange cw static line broadenings - g, D, A anisotropies - heterogeneity - unresolved splittings pulse EPR 2

3 Information from cw EPR and pulse EPR Pulse EPR: Set of high-resolution EPR techniques to determine local structure around a spin center (metal ion, metal cluster, or radical) cw EPR: - metal center, (ligands) - strongly coupled magnetic nuclei pulse EPR: - weakly coupled magnetic nuclei ( 1 H, 14 N, 13 C, etc) - ligands in first and second ligand sphere - hydrogen bonds - distances to other spin centers other spin center magnetic nuclei within a few Å electron spins with a few nm 3

4 Information from cw EPR and pulse EPR Biochemist's view: structural cartoon EPR spectroscopist's view: system of coupled spins 1 H 1 H 14 N 14 N 14 N 1 H e 14 N 1 H 1 H 14 N 14 N 1 H e 4

5 Basics cw vs. pulse EPR Sample and spectrometer Resonators and bandwidths Pulses Spectral width Excitation width Orientation selection FIDs and Echo Deadtime Relaxation 5

6 EPR: Frequencies; cw and pulse cw (continuous-wave) EPR - low microwave power (μw-mw) - absorption spectroscopy - measures steady-state response during excitation pulse EPR - very high microwave power (W-kW) - emission spectroscopy - measures transient response after excitation 6

7 Sample quantity and positioning Sample: Basics Things to watch out for: (1) Dioxygen - oxygen-sensitive samples - dissolved dioxygen enhances relaxation - important for liquid samples - freeze/pump/thaw, or purge with Ar (2) Aggregation - due to slow freezing, solvent crystallization - enhances relaxation, shortens T m, T 1 - glassing agent (glycerol, sucrose), fast freezing Sample concentration magnetically dilute; pulse EPR: not above 1-5 mm; DEER: less than 200 μm (3) Dielectric constant - high r solvents kill mw fields in resonator - sensitivity loss - worst: liquid water (static r = 80 at 20 C) - frozen water: ( r = 3.15 at 0 C) (4) Other paramagnetic components - avoid paramagnetic impurities - run controls on buffers and reagents Measurement temperatures organic radicals K metal centers 5-20K metal clusters 2-10K 7

8 z(lab) Sample: Frozen solutions, description Frozen solution: random uniform distribution of static orientations, like a dilute powder. B 0 Lab frame: - fixed in laboratory - z long static field - x along microwave field Molecular frame - fixed in molecule - most commonly g tensor frame, or local symmetry frame Euler angles 8

9 ENDOR receiver transmitter Pulse EPR spectrometer sources mw2 pulse formers PFU high-power amplifier high-power attenuator 0-60dB mw1 PFU amplifiers phase low-noise amplifier (LNA) protection switch circulator mixer rf1 N S digitizer computer high-power amplifier resonator cryostat magnet B 0 9

10 Purpose of resonator 1. concentrate microwave B 1 field 2. separate microwave E 1 field Resonators and bandwidth Resonator Q factor and bandwidth Q = ν 0 Δν ν 0 = resonator frequency Δν = bandwidth (undercoupled) Bandwidth requirements: cw EPR: high sensitivity high Q, critically coupled pulse EPR: large bandwidth high Q + overcoupled, or low Q + critically coupled Types of resonators 1. dielectric (ring, split-ring) 2. cavity (rectangular, cylindrical) 3. loop-gap resonators 10

11 Microwave rotates spins spin arrow = - S precession nutation equilibrium non-equilibrium rotating frame: observer follows precession Resonance condition: mw frequency = precession frequency (Larmor or Zeeman frequency) hν mw = gμ B B ν mw GHz = g B mt mw frequency g factor magnetic field 1 mt = 10 G 11

12 Rectangular pulse Pulses, excitation bandwidth Microwave pulses (typical values) frequency 9-10 GHz, GHz, 95 GHz Symbolic: short 5-20 ns medium 20 ns-200 ns π/2 flip angle long 200 ns-several μs carrier frequency t p pulse amplitude pulse length RF pulses (typical values) frequency MHz short 10 μs long 100 μs Pulse excitation bandwidth - excitation bandwidth = approx. distance between zeroes: 2/t p (for pi and pi/2 pulses) - example: 10 ns pulse 200 MHz 12

13 Basic spin dynamics: Bloch equations Magnetization M = total magnetic moment per volume Classical dynamics of magnetization in magnetic field: d M = γm B dt Precession and nutation is described by the Bloch equations: d dt M x = γ(m B) y M x T 2 d dt M y = γ(m B) x M y T 2 d dt M z = γ(m B) z M z M 0 T 1 phenomenological terms describing relaxation 13

14 Spectral width and excitation bandwidth field sweep frequency sweep For small anisotropies (organic radicals, Cu 2+, FeS, low-spin Fe 3+, Mn 2+ ), frequency spectrum is flipped field sweep. 14

15 Orientation selection Resonance frequency depends on orientation relative to field. Different orientation, different resonance frequency 15

16 FID, free induction decay spins are dephasing: they precess with different resonance frequencies pi/2 pulse dead time FID thermal equilibrium rotated by 90 degrees dephasing 16

17 Dead time τ dead time kw kw μw τ signal cannot be measured! kw kw μw Dead time: - time after pulses during which power levels are too high to open the sensitive receiver - due to 1) ringdown in cavity 2) reflections in spectrometer 3) recovery of receiver protection ns at X-band shorter at higher frequencies τ τ Consequences - short values of τ cannot be accessed - loss of broad lines - phase distortions in spectrum - spurious features in spectrum 1 kw = 1 mile 1 μw = mm 17

18 Two-pulse echo also called primary echo or Hahn echo pi/2 pulse FID pi pulse 2p echo = 2x FID thermal equilibrium rotated by 90 o precessing and dephasing dephased rotated by 180 o precessing and rephasing refocused 18

19 Three-pulse echo also called stimulated echo pi/2 pulse pi/2 pulse T pi/2 pulse 3p echo FID complex motion (approximate) thermal equilibrium rotated by 90 o precessing and dephasing dephased "stored" along -z, precessing precessing and rephasing refocused 19

20 Relaxation Relaxation constants T 1 : longitudinal relaxation (spin-lattice relaxation) T 2 : transverse relaxation (spin-spin relaxation) T m : phase memory time constant (similar to T 2 ) cw EPR - choose low mw power that avoids saturation - choose scan rates and modulation amplitudes that avoid passage effects Spectral diffusion - spin center randomly changes frequency during pulse sequence - leads to dephasing and loss of signal pulse EPR - fast relaxation prevents long pulse experiment 20

21 Theory Nuclear Zeeman interaction Hyperfine interaction Fermi contact Spin dipolar interaction Coupling regimes Nuclear spectra Quadrupole interaction Quadrupole moment Electric field gradient 21

22 Magnetic nuclei: Energy levels and frequencies Nuclear spin Hamiltonian (for one electron spin and one nuclear spin): H nuc = g n μ N B I + h S A I + h I P I B magnetic field S electron spin I nuclear spin Nuclear Zeeman interaction - magnetic interaction with external applied magnetic field (static or oscillating) Hyperfine interaction - magnetic interaction of nucleus with field due to electron spin - three contributions: 1. Fermi contact (isotropic) 2a. spin dipolar (anisotropic) 2b. orbital dipolar (anisotropic) Nuclear quadrupole interaction - electric interaction between nonspherical nucleus and inhomogeneous electric field - only for I>1/2 nuclei g n nuclear g factor A hyperfine matrix A iso isotropic coupling anisotropic coupling T P Q q K η quadrupole tensor quadrupole moment electric field gradient quadrupole constant rhombicity 22

23 Nuclear Zeeman Interaction H = g n μ N B 0 I - magnetic interaction with external applied magnetic field (static or oscillating) - scales with g n, nuclear g factor - μ N = nuclear Bohr magneton γ = g n μ N /ħ NMR: gyromagnetic ratio EPR: g n factor ν I = g n μ N B 0 /h nuclear precession frequency Nucleus Spin g n 1 H 1/ H N N 1/ C 1/ P 1/ H/ 2 H g n ratio: g n of 14 N and 15 N have opposite sign 23

24 Hyperfine coupling: 1. Fermi contact interaction H = h A iso S I Origin: Small, but finite probability of finding an electron at position of nucleus (s orbitals only!) one (unpaired) electron A iso = 2 3 μ 0 μ B μ N h g e g n Ψ 0 (r n ) 2 (SI units, A iso in Hz) scales* with g n spin density at position of nucleus more general A iso = 1 3 μ 0 μ B μ N h g e g n σ α β (r n ) S z 1 * possible isotope effect for 1 H/ 2 H Chemist's interpretation: spin population in atom-centered orbitals relative to 100% orbital occupancy via reference A iso Nucleus Spin A iso (100%) 1 H 1/ MHz 14 N MHz, 1538 MHz 15 N 1/ MHz, MHz 13 C 1/ MHz, 3109 MHz Reasons for non-zero A iso (1) ground-state open s shell (2) valence and core polarizations e.g 3d 2s, 3d 1s (3) configurations with open s shell better: compare to quantumchemical predictions Example: A iso ( 1 H) = 20 MHz 20/1420 = 1.4% 24

25 Hyperfine coupling: 2. Spin dipolar B 0 magnetic dipole field of nucleus H = h S T I electron spin nuclear spin magnetic dipole field of electron m e electron B n r = r n m n nucleus B e, B hf T = T T = μ 0 4πh μ Bμ N g eg n r 3 T +2T - orientation dependence - distance dependence T = dipolar hyperfine matrix eigenvalues: principal values This assumes electron is localized. In delocalized systems, integrate over electron spin density. 25

26 Combining Hyperfine and Zeeman: Local fields B 0 B 0 Zeeman field B tot total field nucleus electron B hf hyperfine field due to electron spin 26

27 Hyperfine + Zeeman: Nuclear frequencies B 0 external magnetic field total field acting on the nucleus hyperfine field line ma S I mb S B tot component of hyperfine field perpendicular to external field (nonsecular) B = A A sinθ cosθ = 3T sinθ cosθ can be neglected at high field for small hfc B hf component of hyperfine field parallel to external field (secular) A = A cos 2 θ + A sin 2 θ = A iso + T (3cos 2 θ 1) Nuclear frequencies: ν m S = (ν I + m S A) 2 +(m S B) 2 ν I = g n μ N B 0 /h m S = ±1/2 27

28 Three coupling regimes Weak coupling Intermediate coupling Strong coupling B 0 B hf B 0 B hf B 0 B hf B tot ( ) B tot ( ) matching fields B tot ( ) B tot ( ) B tot ( ) nucleus B tot ( ) u v angle between two total field vectors: sin 2 ξ = ν IB ν α ν β 2 = k k = modulation depth parameter (important in ESEEM) 28

29 Nuclear frequencies and spectra ν m S ν I + m S A ν I = g n μ B B 0 /h neglecting B term (valid for weak and strong coupling) Weak coupling regime centered at ν I, split by A ν I m S A Strong coupling regime ν I m S A centered at A/2, split by 2ν I 29

30 Nuclear spectra: Weak coupling example SAM binding to [4Fe4S] cluster in pyruvate formate-lyase activating enzyme JACS

31 Nuclear spectra: Strong coupling example [Mn 4 Ca] cluster in PSII S 2 : Mn(III,III,III,IV) 55 Mn JACS

32 + + Electric quadrupole moment of nuclei Quadrupole interaction Nuclei with spin >1/2 are nonspherical, described by an electric quadrupole moment Q. homogeneously charged ellipsoid: Q = 2 5 Z(r z 2 r 2 xy ) Q > 0: prolate nucleus (egg shaped) Q < 0: oblate nucleus (burger shaped) Inhomogeneous electric field: Orientation-dependent energy Nucleus Spin Quadrupole moment (b) 2 H N b (barn) 33 S 3/ = 100 fm 2 63 Cu 3/ O 5/ Mn 5/ Electric, not magnetic interaction!! highest energy torque lowest energy 32

33 Quadrupole interaction Electric field gradient (EFG) EFG is a 3x3 matrix V Nuclear quadrupole interaction interaction of quadrupole moment with EFG principal values Vxx Vyy Vzz 0 H = h I P I largest component rhombicity 0 1 for V eq V zz xx V V zz yy V V V zz yy xx quadrupole tensor: (1 η) 0 0 P = K 0 (1 + η) K = e2 Qq/h 4I(2I 1) = 1 sign of q ambiguous Experimental parameters: e 2 Qq/h and 33

34 Quadrupole interaction: 14 N EFG depends on electron populations N x,y,z of 2p x,y,z orbitals Example: Remote nitrogen of imidazole ligand P zz N z 1 2 (N x + N y ) Townes-Dailey model Simplifications: -only one-electron contributions -no antishielding -s and p hybridization -fixed quadrupole frame 1 e 2 Qq/h = c 1 + c 2 η linear relation Valence orbitals s p x s p 2 2 x p 2 y s p 2 2 x p 2 y p 4 z cot Populations c b b a EFG components qz q 0 a (1 ) b (1 ) c qx q 0 a ( 1) b (1 ) c qy q 0 a (1 ) b (1 ) c q0 9 MHz 34

35 Quadrupole interaction: 2 H, 33 S, 17 O 2 H 33 S D 2 O: e 2 Qq/h = MHz, η = 0.12 strong hf coupling & small nq splitting mcom reductase, 33 S HYSCORE JACS O H-bonds to semiquinones κ = a b 3 r O D a = 319 khz b = 607 khz Å 3 JBC Aconitase, 17 O ENDOR J. Biol. Chem

36 Experiments Pulse field sweeps - FID-detected - echo-detected Relaxation measurements - T 1 - T 2, T m Pulse ENDOR - Mims ENDOR - Davies ENDOR ESEEM - two-pulse ESEEM - three-pulse ESEEM - HYSCORE DEER 36

37 Pulse field sweep spectra FID-detected field sweep π/2 FID π/2 integrate - works only if FID is longer than dead time - use long microwave pulse Echo-detected field sweep π echo FID two-pulse echo tau = 140 ns two-pulse echo tau = 300 ns τ τ Alexey Silakov Distortions due to tau-dependent nuclear modulation of echo amplitude 37

38 Relaxation measurements T 1 : Inversion recovery measure echo intensity as a function of t π π/2 π inverted echo t τ τ Other methods for T 1 : saturation recovery, three-pulse echo decay V t V 0 = 1 2exp ( t/t 1) T 2, T m : Two-pulse echo decay measure echo intensity as a function of π/2 π echo τ τ V t V 0 exp ( 2τ/T 2) - approximately exponential decay - phase memory, T m, rather than T 2 is obtained - best with small flip angles (avoids instantaneous diffusion) 38

39 Pulse ENDOR: Mims ENDOR Mims ENDOR: rf pulse frequency is varied π/2 π/2 π/2 echo Basics - use short hard mw pulses - acquire echo intensity as function of rf pulse frequency mw rf τ π t rf τ Spectrum - echo intensity decreases whenever rf frequency is resonant with a nuclear transition - upside-down representation Blind spots - intensity is modulated with -dependent sawtooth pattern, centered at Larmor frequency and with period 0.5/ ("Mims holes") - central hole at Larmor frequency! works best for small hyperfine couplings less than about 1/ (typically 2 H, 13 C) 39

40 Pulse ENDOR: Davies ENDOR Davies ENDOR: rf frequency is varied mw rf π t p π t rf π/2 π τ τ inverted echo Basics - based on inversion recovery - use medium/long mw pulses - acquire echo intensity as function of rf pulse frequency Spectrum - fully inverted echo is baseline - decrease in echo intensity when rf frequency is resonant with nuclear transition Blindspots - no -dependent blindspots - central hole at Larmor frequency - width proportional to 1/t p - suited for larger hf couplings - for small couplings, use long pulses (narrower central hole) 40

41 ESEEM: 1D methods Two-pulse ESEEM: is varied π/2 π primary (Hahn) echo V 2p modulation depth/amplitude V 2p τ τ τ Three-pulse ESEEM: T is varied π/2 π/2 π/2 stimulated echo V 3p modulation depth/amplitude V 3p τ T τ τ + T - modulation of echo amplitude as a function of interpulse delay(s) - modulation with nuclear resonance frequencies and their combinations - modulation due to hyperfine coupling of electron spin with surrounding nuclei - modulation depth depends on hyperfine coupling, quadrupole coupling, nuclear Zeeman 41

42 ESEEM: Mechanism (1) Electron spin flip induces nuclear precession B tot ( ) B 0 B tot ( ) sudden electron spin flip B hf ( ) B 0 stationary nuclear spin nuclear spin precession! B hf ( ) "forbidden" transition! - Electron spin flip inverts hyperfine field at nucleus. - This changes the total local field and the quantization direction of the nucleus. - The change is sudden on the timescale of the nucleus. - The nucleus will precess around the new field direction. 42

43 ESEEM: Mechanism (2) Nuclear precession modulates electron precession B tot ( ) B 0 B 0 B hf ( ) ΔB(t) precession time-dependent precession frequency! - precessing nucleus causes a time-dependent field along z felt by the electron - electron precession frequency becomes time dependent 43

44 ESEEM: Data processing 44

45 ENDOR vs. 1D ESEEM ENDOR Two-pulse ESEEM Three-pulse ESEEM ν α ν β k /2 k /2 ν α + ν β k 4 1 cos β k 4 1 cos α ν α ν β ν α ν β ν α ν β k /4 k /4 equal intensities T m decay (fast) sum and difference frequencies no blind spots T 1 decay (slower) no sum and difference frequencies blind spots adds to dead time 45

46 ENDOR vs. 1D ESEEM ENDOR: - maximum intensity at = 90 - mimimum intensity at = 0 ESEEM: - no intensity along principal axes - maximum intensity off-axis difficult to measure broad lines with ESEEM! only central part visible! Situations for best intensities ESEEM enhanced by nuclear state mixing; most intense in matching regime, i.e. low nuclear frequencies ENDOR enhanced by hyperfine enhancement, most intense for high nuclear frequencies 46

47 HYSCORE: t 1 and t 2 is varied π/2 π/2 π π/2 2D ESEEM: HYSCORE HYSCORE echo HYSCORE = hyperfine sublevel correlation τ t 1 t 2 τ V(t 1,t 2 ) pi pulse should be as short as possible 2D time domain (TD) 2D frequency domain (FD) 2nd quadrant 1st quadrant only 1st and 2nd quadrant are shown 3rd quadrant (identical to 1st) 4th quadrant (identical to 2nd) echo intensity as a function of t 1 and t 2 47

48 HYSCORE: Data processing TD data t 2 baseline correction t 1 baseline correction 2D windowing 2 1 2x 2x 3 4 spectrum 2D Fourier transform 2D zero filling 48

49 Weak coupling HYSCORE: Spectra Strong coupling Quadrupole splittings ν α ν α ν β ν β first quadrant ν α second quadrant ν α Powder spectra ν β ν β ν β ν α ν α ν β 49

50 HYSCORE: Blind spots Blind spots: - τ-dependent intensity factor: sin(πν 1 τ)sin(πν 2 τ) - intensity drops to zero at frequencies that are multiples of 1/τ - both dimensions, all quadrants Example: τ = 120 ns 1/τ = 8.33 MHz 3/τ 2/τ 1/τ 0 1/τ 2/τ Consequences: - peaks are missing - peaks are distorted - danger of wrong assignment Remedies: - acquire spectra with several different tau values - use blind-spot free advanced techniques 3/τ 3/τ 2/τ 1/τ 0 50

51 [FeFe] hydrogenase + model HYSCORE: Example Angew. Chem PCCP

52 ENDOR/ESEEM at higher fields and frequencies ENDOR/ESEEM frequency ranges for common isotopes Advantages - separation of isotopes - weak coupling regime for large hyperfine couplings - increased sensitivity for low-gamma nuclei - larger spin polarization - larger orientation selectivity Disadvantages - less signal for strongly anisotropic systems - less available power - longer pulses Pulse EPR power X-band 9-10 GHz 1000 W Q-band GHz 10 W W-band 95 GHz 0.4 W D-band 130 GHz W GHz W 52

53 DEER: Distances between electron spins DEER = double electron-electron resonance (also called PELDOR = pulse electron double resonance) B 0 mw2 A Dipolar coupling between two electron spins analogous to dipolar hyperfine coupling Echo modulation B mw1 ν ee = μ 0μ B 2 4πh g Ag B 1 r 3 4-pulse DEER: t is varied mw1 π/2 π two-pulse echo A = probe spin, mw1 B = pump spin, mw2 π refocused two-pulse echo mw2 τ 1 τ 2 τ π 1 τ 2 t pump spin up pump spin down 53

54 DEER: Data analysis Echo modulation Distance distribution called form factor after background correction Tikhonov regularization or least-squares fit Fourier transform estimation diagram Dipolar spectrum ν ee = 52 MHz (r/nm) 3 (g A = g B = 2.00) 54

55 DEER: Examples Iron-sulfur clusters Nitroxide spin labels PNAS unpublished 55

56 Basics Experiments Sample and spectrometer Resonators and bandwidths Pulses, excitation width Orientation selection FIDs and Echo Deadtime, Relaxation Pulse field sweeps Relaxation measurements Pulse ENDOR ESEEM/HYSCORE DEER 1 H 14 N 1 H Theory Nuclear Zeeman interaction Hyperfine interaction Coupling regimes Nuclear spectra Quadrupole interaction 1 H 1 H 14 N 14 N e 14 N 14 N 1 H 14 N 1 H e 56

57 EasySpin brown bag lunch next Friday, 12:30-1:45 easyspin.org 57