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Solid state NMR: why/how
and some applications from organic/bio molecules to inorganic materials
K. Takegoshi
Kyoto Univ.
NMR observables and interactions and structure and ....
Observables
Spin interactions
Lineshape
Chemical shift
Structure
600
400
200
0
-200
-400
C=
Longitudinal magnetization
Transverse Magnetization
O
Relaxation times
Orientation
M0
Dipole-dipole
Distance
M0
Dynamics
time
Magnetization-transfer rate/efficiency
Quadrupolar and others
Why solid-NMR?
★Various targets are non-solvable or interesting as a solid material.
Glass, coal, wood, fiber, polymer, ....
★In solution, molecular overall rotation does average spin interactions
that bear structural information
Let us estimate rotational correlation time τ
from molecular diffusion constant D in solution
Stokes-Einstern Eq.
D = kT/6πaη
τ = d 2 /2D
a : hydrodynamic radius
d : radius 2a
η: viscosity
For sucrose/H2 O, we have D = 0.521X10 -5cm 2 s-1, then
d = 1 nm
τ 10 -13 s
d = 10 nm
τ 10 -11 s
NMR frequency ~ 10 8Hz
All spin interactions become isotropic in solution,
so how it can be used for structural determination?
How to utilize anisotropic spin interactions ...
Chemical Shift Anisotropy (CSA)
C=O
C=O
Magnetic field
If your sample has a unique axis,
such as single crystal, liquid crystal,
oriented membrain, elongated polymer...
Naito et al., Biophysical J. 78 (2000) 2405
If your sample has no particular orientation (powder) ...
X-13C=O
X
C=
A powder pattern
Dipolar
O
CSA
C
Orientation
X-C distance
The Pake pattern
200
100
0
200
300
=O
300
100
0
Even for one C-13 with two interactions,
If you have both ．
．．
we have enough complexity
600
The lineshape depends
on the relative orientation
-100
400
200
0
-200
Chemical Shift/ppm
-400
To make it simple, Magic-Angle Spinning (MAS) ...
B0
Almost SSB-less isotropic spectrum
54.7
o
Liquid-like ... means less information!
8 kHz
Sample
4 kHz
Z
Spinning-side bands (SSB)
2 kHz
Y
X
C=O
0 kHz
(static)
C-O
Two CSA powder patterns overlapped
MAS removes anisotropy
300 250 200 150 100 50
0
Chemical Shift/ppm
-50 -100
Selective observation of a particular interaction
Dipiolar and CSA
13
X- C=O
rf irradiation to remove only CSA
600
400
200
0
-200
Chemical Shift/ppm
-400
Dipolar pattern
X-C distance
MAS to remove both
200
MAS synchronized rf irradiation
to recouple the X-C dipolar interaction
300
200
100
0
100
0
-100
For selective observation of dipolar interactions
CSA
H = δ(α，β,γ) I z1 + δ(α ，β ,γ ) I z2
Dipolar H = d(α*，β*,γ*) I z1 I z2
o
A π (180 ) pulse
Iz
-I z
One-point sampling
CSA
Dipolar
Iz
-I z
Iz
-I z
I z1 I z2
Iz
-I z
Observation of a C-C distance, any use?
:13C enriched 99.9%
a) Insertion mechanism
Ph
Ph
Rh
Rh
Ph
Ph
Ph
Ph
Ph
b) Metathesis mechanism
Ph
Ph
Rh
Rh
Ph
Ph
Ph
Rh
Ph
Observation of a C-C distance can be useful in many cases.
13
C dipolar powder pattern
Rc- c = 0.1386 ± 0.0009 nm
ref. (polyacetylene, 77K)
C- C = 0.148 nm
C=C = 0.136 nm
The mechanism is the insertion mechanism!
Hirao et al., Macromolecules 31 (1998) 3405.
How about MAS and recoupling
We would like to enjoy resolved peaks under MAS and appreciate dipolar.
CSA
H = δ(α，β,γ) I z1 + δ(α ，β ,γ ) I z2
Dipolar H = d(α*，β*,γ*) I z1 I z2
MAS
CSA δ(α，β,γ)
δisotropic
d
0
Let us examine how MAS works.
Alas, all gone!
How dipolar becomes 0 by MAS
Z
Dipolar H = d(α*，β*,γ*) I z1 I z2
β
X
B//Z
B//X d ∝ 3 sin 2 β cos 2α- 1
X
Y
α
dZ ∝ 3 cos 2 β - 1
B//Y
dY ∝ 3 sin 2 β sin 2α- 1
MAS averaging
Z
dx + dY+ dz = 0
o
120
Y
X
H = d(α*，β*,γ*) I z1 I z2
MAS
H (t) = d(t) I z1 I z2
t = 1 rotational period
∫
d(t) dt = 0
t=0
Dipolar recoupling under MAS
rf irradiation applied synchronously
H (t) = d(t) I z1 I z2
to modulate the spin part
t
t
t = 1 cycle
∫
t=0
H (t) dt = 0
t = 1 cycle
∫
t=0
H (t) dt ≠ 0
13
15
Modulatory resonance (MORE) for C- N recoupling
(a) conventional CPMAS
13
15
C
N
CP
(b) MORE experimental
+
-
+
-
+
Sinusoidal amplitude modulation
(c) MORE simulation
800
400
C-N dipolar powder pattern
0
Hz
- 400
- 800
[2- 13 C,15 N] glycine
K. Takegoshi, et al., Chem. Phys. Lett., 260 (1996) 331.
OK for a single pair, but for a multi-spin system ....
If you want to determine a local structure, you must determine several distances....
Strategy for a multispin system ....
Decoupling by MAS
Broadband resoupling
Selective recoupling
Uniform
Labeling
by 13C / 15N
Uniform
Decoupling
by MAS
Selective
Recoupling
by R2TR
G
180
o
o
180
o
I
-76
I
144
1
179
2
160
I
I
G
o
o
o
165
o
170
o
o
I
-70
I
153o
I
I
1
2
o
178
170
o
J. Biomol. NMR, 17 (2000) 111.
For broadband, we measure polarization-transfer rate
flip-flop exchange
Broadband recoupling under MAS
1
H
13
C
CP
Decouple
Decouple
recoupling
t1
t2
Distance precision
is not very good
but enough for
many pursposes
High resolution
Magnetization
transfer between
recoupled spins
High resolution
Application of broadband recoupling under MAS
Amyloid-β fibrils is related to
Altzheimer's disease.
13
These depositions are
composed of amyloid-β
peptides of 40- and 42-residues.
Aggrigative ability of
these peptides relate to
the 3D structures.
Val2-β↓
Val1-β↓ Val2-γ↓
Val1-γ↓
Lys-β↓
Asp1-α↓ Asp1-β↓
Ala-β↓
Lys-α↓ Asp2-β↓
Lys-γ↓
Asp2-α↓
Lys-ε↓
Lysδ↓
Val1,2-α↓
↓Ala
-α
Ala-CO↓
↓Lys-CO
Val1,2-CO
↓
Asp1-γ↓
Asp2-γ↓
184
180
13
Assignment of C signals of C-labeled 21-24
aa by DARR with the mixing time of 20ms
176
172
168
60
40
20
The Irie's model of amyloid- (Italian)
42
39 or 40
32
24
20
β-sheet
β-sheet
β-sheet
15
40
21
60
Y. Masuda, et al.,
Bioorg. Med. Chem. Lett. 18 (2008) 3206;
Boiosci. Biomtech. BioChem. 72 (2008) 2170;
Chem.BioChem,. 10 (2009) 287.
184
180
176
172
Chemical Shift/ppm
168
60
40
Chemical Shift/ppm
20
The turn structure of Aβ42 at 21-24 residues
DARR (mixing time=1 s)
Lys
40
30
160
160
120
80
40
40
Ala
Chemical Shift/ppm
120
Chemical Shift/ppm
80
20
Val
Asp
If 21-24 residue is β-sheet,
the side chains of Lys and Asp are too far.
50
Chemical Shift/ppm
60
180
176
172
Chemical Shift/ppm
21 Ala
NH CαH
CH3
22 Lys
23 Asp
24 Val
CO NH CαH CO NH CαH CO NH CαH
(b)
CβH
CβH
CβH
2
CγH2
Ala
Lys
CO
Asp
2
(C)
CγOOH
CδH2
CεH2 NζH2
H 3 Cγ CγH3
(a)
Val
Recent collaboration with the Paris group on Aβ42
DARR uses just X
M. Weingarth, Y. Masuda, K. Takegoshi, G. Bodenhausen, and P. Tekely,
J. Biomol. NMR, in press
Distance measurement by solid-state NMR
1) From dipolar powder patterns
2) From magnetization transfer/spin diffusion
site A
site B
3) From molecular diffusion
Photo-dimerization of solid anthracene
UV
If reaction occurs at the position
If reaction occurs at defect
where a photon is adsorbed,
sites, the dimer forms
the dimer molecule distributes
domains.
randomly.
?
Can we distinguish these?
Polarization/magnetization transfer by spin diffusion
Relax independently
No diffus ion
Short relaxation time
Slow spin diffusion
Long relaxation time
Fas t s pin diffus ion
Fast diffusion
Relax together
Relaxation and spin diffusion
Dimer
Monomer
M D = -( R D+ f D K) M D (t) + f M K M M (t)
spin diffusion
MD
MM
K
RD
M M = -( R M+ f MK) M M (t) + f D K M D (t)
RM
4
-ln((1-M(t))/2)
Lattice
R M = 1/152 s-1
R D = 1/11 s -1
f D & K : Fitting parameters
fD (t) = 1 - exp(- k d t)
kd
3.5 X 10
-4
s
-1
Pure dimer
3
After 10 min UV irr
2
Pure monomer
1
0
0
50
100 150 200 250 300
Time / s
Reaction site
Photo dimerization reaction
The maximum domain size estimated is 300 nm.
Spin-diffusion rate K/s-1
2.0
>1 s-1
1.5
1.0
Fast
0.5
0.06
Fast spin diffusion
0.04
Slow
Fast
0.02
0.0
0.5
1.0
Fraction of dimer fD
Photo-reaction takes place at defects
Takegoshi et al., Solid State NMR, 11 (1998) 189.
Domain structure can be studied by SS-NMR
For one example, glass
7.4Na2 O-24.9B 2O3 -66.3SiO2 -1.3Al2 O3
Q4
29
11.7 T
Q3
Si
I=1/2
-70
23
I=3/2
-80
Na
-90
-100 -110 -120 -130 -140 -150
+
Na(aq)
H
Li B e
Na Mg
K Ca Sc
Rb Sr Y
Cs B a La
Fr R a Ac
amorphous inorganic solids
Red : I = 1/2
Blue : I >1/2
Black : I = 0
B C N O
Al S i P S
T i V C r Mn Fe C o Ni C u Zn G a G e As S e
Zr NbMo T c R u R h P d AgC d In S n S b T e
Hf T a W R e Os Ir P t Au Hg T l P b B i P o
Ku Ha
F
Cl
Br
I
At
He
Ne
Ar
Kr
Xe
Rn
L a C e P r NdP mS mE u G d T b Dy Ho E r T mY b L u
Ac T h P a U Np P u AmC mB k C f E s FmMdNo L r
+
Na(solvated)
21.8 T
30
27
I=5/2
20
10
0
-10
-20
-30
-40
-50
four-coordinated
Al
21.8 T
90
11
80
70
60
50
40
B
30
Unlike organic molecules, we must deal with
I>1/2 nuclei in inorganic materials.
20
21.8 T
I=3/2
30
20
10
0
-1
Chemical shift / ppm
M. Murakami et al, to be publiched
For I>1/2, we must worry about the quadrupolar
interaction.....
Solid-state NMR of
O
H
O B2
O
H
O
B1
O
B1
O
H
11
10
B (I=3) and B(I=3/2)
2-


10
B B1
B2
11
B B1
B2
O
B2 O
H
O
10B:
11 B:
borax

e2qQ/h
(MHz)
1.042
5.4
0.487
2.544
B1
0.711
0.10
0.714
0.089
11
B(I=3/2)
B2
Izv. Vyssh. Uchebn. Zaved. Fiz. 29, 3 (1986)
J Chem. Phys., 38, 1912 (1963)
B1
11
Static powder
B ー NMR
10
Intensities are distributed to
B2
B(I=3)
spinning sidebands, thus leading
a smaller main peak
*
120
MAS
*
60
0
-60
-120
/ppm
20
0
Chemical shift / ppm
-20
The characteristic second-order quadrupolar
powder pattern for I=3/2 under MAS
M. Murakami, Bunseki (12) 658-663 2008.
MAS can not remove the anisotropic broadening
due to the quadrupolar interaction.
How to reduce/remove the 2nd-order quadrupolar interaction
B1
Static
I=3/2 MAS spectra (simulated)
Quadrupolar = 2 MHz
B2
MAS
Static field＝200 MHz
*
120
0
-60
-120
/ppm
−10
60
MQMAS
0
100 MHz
50 MHz
10
B1
100 50
0
-50 -100 -150 -200
20
The 2nd-order broadening
Chemical Shift/ppm
The isotropic shift
30
B2
30
Either use higher magnetic field
or do 2D-MQMAS!
20
10
0
−10
Chemical shift/ppm
M. Murakami, Bunnseki、(12) 658-663 2008.
Mesoporous B-C-N (1/3)
Mesoporous BCN prepared using graphite as a template
Sample１(MBN) ：45min@2020K
Sample 2 (MBCN)：20min@1720-1820K
11
Sample : MBCN
B MAS NMR
21.9T
Experimental
A small amount of carbon remains
At 21.9T, three distinct peaks were resolved.
11.7T
At 11.7T, the characteristic 2nd-order
site3
lineshape appears, which can be used
site1
to deduce quadrupolar coupling constants.
site2
δiso / ppm
site1
30.4
site2 18.8
Simulated
site3
40
20
0
Chemical Sift (ppm)
-20
40
20
0
Chemical Sift (ppm)
-20
M. Muramkami et al., Chem. Lett. 35 (2006) 986-987
0.94
e2Qqh-1 / MHz
3.5
2.7
η
0.4
0.2
< 0.1
0
For MBN, the site-2 and site-3 are less intense
(not shown).
Mesoporous B-C-N (2/3)
The quadrupolar coupling constants can be reproduced by using Gaussian03 (6-31G*)
The model compounds for calculation.
（● : Boron, ● : Nitrogen,
: Hydrogen)
Left: hexagonal BN-like
Right：cubic BN-like
Calculated constants and observed ones
hBN
e2Qq / h
η
cBN
calc.
ref.1
2.85
0
2.936
0
calc.
- 0.72
0.01
ref.2
< 0.05 (MHz)
0
1) Solid State NMR 12, 1-7 (1998)
2) Solid State NMR 8, 109-121 (1997)
Quadrupolar interection is nuisance but useful for structure elcidation.
Mesoporous B-C-N (3/3)
Structural determination by11B-11B 2D distance correlation
From the size of the quadrupolar couplings,
0
borons of site 1 and 2 are trigonal boron and
10.0
site3
the site-1 boron is tetragonal one.
From the 2D correlation pattern,
we postulated the pillar and wall structure shown below.
20.0
site2
This cross peak
30.0
shows site2 and 3
The wall domain (site 1)
are in close proximity
site1
30.0
20.0
10.0
0
Chemical shift / ppm
The pillar domain (site 2 and 3)
These implys that site 1 and site2&3 do not belong
to different particules. There must be
molecular contact between two groups
M.Murakami et al., Solid State NMR, 2007 (31) 193.
Acknowledgement