Singlet nuclear relaxation in liquids

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1 Singlet nuclear relaxation in liquids Malcolm Levitt Southampton University UK 1

2 Nuclear singlet states Basic principles what are singlets and triplets? why are singlets long-lived? singlets and triplets in asymmetric molecules isolation of nuclear singlets field-cycling spin-locking singlet relaxation molecular geometry/dynamics paramagnetic relaxation magnetization to singlet conversion storing magnetization for 30 minutes in a liquid working with systems close to magnetic equivalence multiple singlet states 2

3 Two spins-1/2 in equivalent sites T 0 = 1 2 T 1 T +1 = ββ ( αβ + βα ) = αα S 0 = 1 2 Singlet: I = 0 ( αβ βα ) Triplet: I = 1 3

4 Spin-lattice relaxation: T 1 T 1 T 0 S 0 T +1 42

5 Spin-lattice relaxation: T 1 T 1 T 0 S 0 T +1 42

6 Singlet-triplet relaxation: T S T 1 T 0 S 0 T +1 52

7 Singlet-triplet relaxation: T S T 1 T 0 S 0 T +1 52

8 Principles of singlet NMR Singlet states are NMR-silent Chemical shift differences induce singlet-triplet transitions Chemical shift differences may be suppressed by field-cycling spin locking 6

9 Singlet NMR Spectroscopy 7

10 Chemical inequivalence Singlet (I=0) Triplet (I=1) 8

11 Chemical inequivalence Singlet (I=0) Triplet (I=1) 8

12 Chemical inequivalence chemical shift difference Singlet (I=0) Triplet (I=1) 8

13 Isolating the singlet state: field-cycling chemical shift difference Singlet (I=0) Triplet (I=1) 9

14 Isolating the singlet state: field-cycling Singlet (I=0) Triplet (I=1) 9

15 Isolating the singlet state: high-field spin locking chemical shift difference Singlet (I=0) Triplet (I=1) 10

16 Isolating the singlet state: high-field spin locking Singlet (I=0) Triplet (I=1) 10

17 Singlet NMR : key points Pairs of spins-1/2 form singlet and triplet states Singlet-triplet interconversion is often very slow, since it is not induced by many strong relaxation mechanisms, such as the intra-pair DD coupling The singlet state cannot be observed directly Chemical inequivalence provides access to the singlet state In a high magnetic field, singlet-triplet interconversion is suppressed by a spin-locking field 11

18 singlet NMR field cycling high-field singlet NMR singlet preparation methodology ELF spectroscopy spin locking methodology isotropic signal filtering J- synchronized spin echoes low-field spectroscopy.. low-field magnetization storage hyperpolarization, in vivo NMR.. paramagnetic relaxation singlet relaxation dipole-dipole relaxation molecular geometry and dynamics.. multiple singlet states high-field singlet NMR without spin locking 12

19 High-field singlet NMR: Pulse Sequence Singlet Preparation Singlet Spin-locking Singlet Detection Carravetta et al. JACS 126, (2004) 13

20 High-field singlet decay 0.4 signal 0 T 1 = 7.7 s spin lock duration / sec T S = 141 s Carravetta et al. JACS 126, (2004) 14

21 High-field singlet decay T 1 = 1.4 s spin lock duration / sec T S = 51 s Tayler et al., J. Am. Chem. Soc. 132, (2010). 15

22 Singlet relaxation paramagnetic singlet relaxation crosscorrelation out-of-pair DD CSA 16

23 Singlet relaxation and molecular geometry/dynamics How does T S depend on the locations of other nuclei? How does T S depend on molecular dynamics? Michael Tayler, Sabrina Marie, A. Ganesan, Levitt (2009) 17

24 Geometry dependence of TS / T1 Dependence of TS / T1 on the location of a third proton Short range Long range ~ r8 18

25 Torsional angle dependence possible positions of third proton 19

26 -d1-tyrosine 20

27 -d1-tyrosine 20

28 Torsional angle dependence of T S slow ring flips fast ring flips α-d 1 -Tyrosine experimental: T S /T 1 =6.0 21

29 ring-d5-phenylalanine 22

30 ring-d5-phenylalanine 22

31 Singlet relaxation including J-couplings 23

32 Singlet relaxation and molecular geometry/dynamics T S is sensitive to the locations of neighbouring protons T S -1 is anisotropic in space with a ~r -8 characteristic at long range Results on α-d 1 -tyrosine in agreement with a rigid ring on the molecular rotational timescale, with a torsional angle around 90. Treatment is also possible in the presence of out-of-pair J-couplings, but this requires a technically difficult Liouvillian eigenvalue analysis 24

33 Paramagnetic singlet relaxation AlaGly Mn 2+ Mn 2+ 25

34 Paramagnetic singlet relaxation Mn 2+ Mn 2+ AlaGly 25

35 Paramagnetic singlet relaxation!#)" AlaGly &'()*+,$-./%0'12'',%# 3 %),4%#!%!#(" T S -1 /s!"# $%!#'"!#&"!#%" Mn 2+ concentration slope ~ 0.3!#$"!" DD relaxn!"!#%"!#'"!#)"!#*" $" $#%" $#'" $#)"!"#!% T 1-1 /s 26

36 Paramagnetic multipole relaxation The slope and intercept of the {Γ 0, Γ 1, Γ 2 } line depends on the correlation of the paramagnetic local fields The paramagnetic local fields are highly correlated The correlation depends on the geometry and dynamics of the approach of the paramagnetic site to the spin pair 27

37 Paramagnetic multipole relaxation The slope and intercept of the {Γ 0, Γ 1, Γ 2 } line depends on the correlation of the paramagnetic local fields The paramagnetic local fields are highly correlated The correlation depends on the geometry and dynamics of the approach of the paramagnetic site to the spin pair 27

38 Paramagnetic multipole relaxation The slope and intercept of the {Γ 0, Γ 1, Γ 2 } line depends on the correlation of the paramagnetic local fields The paramagnetic local fields are highly correlated Interpretation in progress! The correlation depends on the geometry and dynamics of the approach of the paramagnetic site to the spin pair 27

39 High field singlet NMR: near-equivalence Saclay August

40 Standard pulse sequence requires a resolved chemical shift difference and/or J-coupling Saclay August

41 J-synchronized spin echo trains Saclay August

42 Magnetization to singlet polarization time Saclay August pulses 90 0 spaced by 1/(2J) delay of 1/(4J) 180 pulses spaced by 1/(2J) 31

43 Magnetization to singlet transfer triplet magnetization outer ST transitions inner ST transition Saclay August 2010 time 32

44 Magnetization to singlet transfer triplet magnetization outer ST transitions inner ST transition Saclay August 2010 time 32

45 JSET singlet NMR Saclay August

46 JSET singlet NMR Saclay August

47 Multiple singlet states Saclay August 2010 Michael Tayler & Craig Butts (Bristol) 35

48 Singlet NMR: summary long-lived nuclear singlet states exist and may be accessed in a variety of substances preparation, relaxation, and spin-locking methodologies now quite well-understood Singlet relaxation times contain information on molecular geometry and dynamics new techniques have been developed allowing singlet NMR in systems which are nearly magnetically equivalent - opening up a new class of systems 36

49 Marina Thanks Ole Marina Carravetta Peppe Giuseppe Pileio Michael Tayler Sabrina Marie, A. Ganesan Ole Johannessen Eric Hughes (Nestlé, Lausanne) Michael Funding: EPSRC-UK, Royal Society-UK 37

50 Thanks! 38

51 Thanks! 38

52 Spin dynamics in Mathematica: mpackages Saclay August 2010 completely general implementation of Hilbert and Liouville bases wide range of built-in bases, spin operators, spin superoperators, etc. routines for ensemble averaging, including powder averaging general time-dependent evolution, including arbitrary relaxation superoperators, arbitrary time-dependence, etc. relaxation superoperators may be thermalized to generate correct thermal equilibrium states analytical evaluation of spin dynamical evolution, including analytical powder averages numerical integration of LvN equation, using the state-of-the art numerical integration engine of Mathematica - no need for manual time-slicing or repeated diagonalizations/matrix multiplics. parallelization easily handled by Mathematica 39

53 NMR`SpinDynamics` In[61]:= In[55]:= Needs"NMR`SpinDynamics`" SetSpinSystem2 SetSpinSystem::set : the spin system has been set to 1, 1, 2, In[56]:= SetBasisSingletTripletBasis CheckBasis::orthonormal : State basis is orthonormal. SetBasis::set : the state basis has been set to SingletTripletBasis1, 1, 2, In[58]:= Out[58]= BasisKets ΒΑ ΑΒ, ΑΑ, 2 ΒΑ ΑΒ, ΒΒ 2 In[60]:= MatrixRepresentationopI"x" MatrixForm Saclay August 2010 Out[60]//MatrixForm=

54 Superoperators (1) In[66]:= SetOperatorBasisSphericalTensorOperatorBasis SetOperatorBasis::set : the operator basis has been set to SphericalTensorOperatorBasis1, 1, 2, 1, Sorted CoherenceOrder, 2 2 SphericalRank. In[63]:= BasisOperators Out[63]= I 1.I 2, I 2 2, I 1 2, I 1.I 2 z I 1 z.i 2, I 1.I 2 z I 1 z.i 2, 2, I 1.I 2 I 1.I 2 2 I 1 z.i 2 z, I 2 z, I 1 z, I 1.I 2 I 1.I 2, 3 2 I 1.I 2 I 1.I 2 4 I 1 z.i 2 z, I 2 6 2, I 1, I 1.I 2 z I 1 z.i 2, I 1.I 2 z I 1 z.i 2, I 1.I 2 2 Saclay August

55 Superoperators (1) In[68]:= SuperoperatorMatrixRepresentation CommutationSuperoperatoropI"x" MatrixForm Out[68]//MatrixForm= Saclay August

56 Spherical Tensor Operators In[72]:= SetSpinSystem4 SetSpinSystem::set : the spin system has been set to 1, 1, 2, 1, 3, 1, 4, CheckBasis::orthonormal : State basis is orthonormal. SetBasis::set : the state basis has been set to ZeemanBasis1, 1, 2, 1, 3, 1, 4, In[77]:= Out[77]= opt1, 2, 2, 0 Simplify I 1.I 2 I 1.I 2 4 I 1 z.i 2 z 2 6 In[78]:= Out[78]= opt1, 2, 3, 3, 1 Simplify I 1.I 2.I 3 I 1.I 2.I 3 I 1.I 2.I 3 4 I 1.I 2 z.i 3 z 4 I 1 z.i 2.I 3 z 4 I 1 z.i 2 z.i Saclay August 2010 In[82]:= Out[82]= 1 10 ExpressOperatoropT1, 2, 3, 3, 0, CartesianProductOperatorBasis Simplify I 1 x.i 2 x.i 3 z I 1 x.i 2 z.i 3 x I 1 y.i 2 y.i 3 z I 1 y.i 2 z.i 3 y I 1 z.i 2 x.i 3 x I 1 z.i 2 y.i 3 y 2 I 1 z.i 2 z.i 3 z 43

57 Superoperators In[85]:= SuperoperatorMatrixRepresentation DoubleCommutationSuperoperatoropT1, 2, 2, 1, opt1, 2, 2, 1 MatrixPlot Out[85]= Saclay August

58 Numerical Spin Dynamics (1) In[69]:= traj Trajectory IxST0, IyST0, IzST0, Functiont, Evaluate HzBz BELFpeak CosΩELF t, 4 Τ90ST, Background H0 IzST0; PlotEvaluateRe Throughtrajt, t, EventDurationeventsequence, 0, Frame True, PlotRange 1, Out[70]= Saclay August

59 Numerical Spin Dynamics (2) traj Trajectory eventsequence opi"x", IxST1, IyST1, IyST0, IzST0, RepeatEvent eventsequence, None, ΤJ 4, Background H0B0 Blow B Ωx opi"z", RotationSuperoperatorΠ, "x", InitialTimePoint 0 None, ΤJ 4 opi"x";, 10, PlotEvaluateRe Throughtrajt, t, 0, EventDurationeve None, ΤJ 4, Frame True, PlotRange 1.1, 1.1, RotationSuperoperatorΠ 2, 0, PlotStyle Blue, Thick, Red, Thick, Green, Yellow, RepeatEvent 1.0 None, ΤJ 4, RotationSuperoperatorΠ, "x", None, ΤJ 4 0.5, 17 ; traj Trajectory Saclay August

60 Numerical Spin Dynamics (3) eventsequence RepeatEvent None, Τ 2, Ωxnut opi"y", Τ90x, Ωxnut opi"x", Τ240x, Ωxnut opi"y", Τ90x, None, Τ 2, 10, None, ΤJ 4, Ωxnut opi"x", Τ90x, RepeatEvent None, Τ 2, Ωxnut opi"y", Τ90x, Ωxnut opi"x", Τ240x, Ωxnut opi"y", Τ90x, None, Τ 2, 16 ; traj Block$RecursionLimit 1000, Trajectory opi"x", IxST1, IyST1, IyST0, IzST0, eventsequence, Background H0B0 Blow B Ωx opi"z", InitialTimePoint 0 opi"x" ; PlotEvaluateRe Throughtrajt, t, 0, EventDurationeventsequence, Frame True, PlotRange 1.1, 1.1, PlotStyle Blue, Thick, Red, Thick, Green, Yellow, Thick, Black Saclay August