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Rotational Echo, Adiabatic Passage,
Double Resonance (REAPDOR) NMR
Yong Ba
Department of Chemistry and Biochemistry, California State University
Los Angeles
Ba, Yong; Kao, Hsien-Ming; Grey, Clare P.; Chopin, Lamy; Gullion, Terry,Optimizing the 13C-14N REAPDOR NMR experiment: a theoretical andexperimental study, J. Magn. Reson. 133, 1, 104-114, (1998).
Dipolar Interaction
rij - i and j spin internuclear distance - orientation of i and j internuclear vector
relative to the direction of the magnetic field
Structural information analogous to that from diffraction method
No long-rang order is necessary
i
j
rij
B0( )( )jizjzi23
ij
jiij
D IIII3cos312
1
rH =
h
Spin Correlation via Dipolar Interactions
Atomic/molecularcluster
Internuclear proximity
Molecularmiscibility
15N
13C
Spin Echo Experiment
p/2x ±y t 1 t 2
I
xy
z
xy
z
t 1 t 2= 1
xy
z
p
Dipolar refocusing
SI
SEDOR (Spin Echo DOuble Resonance)
B. Herzog and E. L. Hahn, Physical Review, 103 (1956) 148.
p/2xp±y
I t 1 t 2
S
xy
z
xy
z
xy
z
t 1
Dipolar dephasing
t 2= 1
SI
Dipolar Dephasing
0 5 10 15 20 250.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Qf
Dt (Radian)
Theoretical SEDOR curve for coupled I-Sspin pairs in a solid powder
Internuclear proximity
Double Resonance NMR Experiments
SEDOR
QEDOR
REDOR
TEDOR
TRAPDOR
REAPDOR
MAS (Magic Angle Spinning)
Cos =3
3
B0
Samp
le
High resolution solid stateNMR spectra– Average of chemical shift
anisotropy & dipolarinteraction
Dipolar dephasing?
Recovery of Dipolar Dephasing
Dipolar interaction of I and S spins
MAS + rf pulses
High resolution spectrum + Dipolar dephasing
HDIS
0
( )zz
2
3
IS
SIIS
DSIcos31
rH =
h
REDOR (Rotational Echo DOuble Resonance)
T. Gullion and J. Schaefer, J. Magn. Reson. 81, 196 (1989). J. R. Garbow and T. Gullion, J. Magn. Reson. 95, 442 (1991).
CP
CP
Decoupling1H
13C (I=1/2)
15N (S=1/2)
Rotor
x y x y xy x y
0 1 2 3 4 5 6 7 8 9 10
xy x y xy x y
Tr
IzSz - IzSz
1st 2nd
= x or y
REDOR Dipolar Dephasing
Average dipolar dephasing frequencies
Phase accumulation of the I spin transverse magnetization
S pulse
D
IS
S
I S
IS
D
IS
S
m D where Dr
m D
1 1 3
2 2
4 2 2
4 2 2
= + =
=
sin sin
sin sin
h
±1
2
1
2m
REDOR Curve
Theoretical REDOR curve for coupled I-Sspin pairs in a solid powder
0 5 10 15 20 250.0
0.2
0.4
0.6
0.8
1.0
1.2
= NTrD
S/S0
RF Irradiation of Quadrupolar Nuclei
HQ >> Hrf for a solid powderSmall portion for S=1
Central transition & small portion of satellite transitions for S=n/2
HZeeman >> HQ
I=3/2
0
0
0
0 -’Q
0 +’Q
0
m=+3/2
m=+1/2
m=-1/2
m=-3/2
Zero Field Zeeman 1st Order Quadrupolar
I=1
0
0
0 -’Q
0 +’Q
m=+1
m=0
m=-1
Zero Field Zeeman 1st Order Quadrupolar
Population transfer?Quadrupolar nuclei S>1/2: 14N(1), 23Na(3/2), 27Al(5/2), for example
NMR Periodic Table
~ 110 NMR-active nuclear isotopes– 29 Spin-1/2
– 3 Spin-1
– 78 Spin-n/2
Adiabatic Population Transfer
A. J. Vega, J.Magn. Reson. 96, 50 (1992).
REAPDOR (Rotational Echo Adiabatic Passage DOuble Resonance)
T. Gullion, J. Magn. Reson. 1995, Series A 117, 326.Y. Ba, H. Kao, C. P. Grey, L. Chopin, T. Gullion, J. Magn. Reson. 1998, 133, 104.
CP
CP
Decoupling1H
I=1/2
S>1/2
Rotor
xy x y xy x y
0 1 2 3 4 5 6 7 8 9 10
xy x y xy x y
= x or y
|m> |n>
Adiabatic Population Transfer
I zm n D S= ( ) sin sin4 2 2 0
Q’( , ) is time dependent during MAS ( R)
– Zero-crossing Q’ ( )
– |m> |n>
± m
-20 -15 -10 -5 0 5 10 15 20-8
-4
0
4
8
|0>|-1>
|-1>
|+1>
|0>|+1>
Eig
en
va
lue
s/
rf
Q'/
rf
-20 -15 -10 -5 0 5 10 15 20
-10
-5
0
5
10
|+1/2>-|-1/2>
|+1/2>+|-1/2>
|-3/2>
|+3/2>
|-3/2>
|+1/2>-|-1/2>
|+3/2>|+1/2>+|-1/2>
Eig
en
va
lue
s/
rf
Q'/
rf
-20 -10 0 10 20
-30
-20
-10
0
10
20
30
|-5/2>
|+5/2>|+1/2>-|-1/2>
|+1/2>+|-1/2>
|-3/2>
|-3/2> |+3/2>
|+3/2>
|+1/2>-|-1/2>
|-5/2>
|+5/2>|+1/2>+|-1/2>
Eig
en
va
lue
s/
rf
Q'/rf
S=1 S=3/2 S=5/2
/ rf=0.3
Number of Zero Crossings
• Zero-crossings occur 2 or 4 times per rotor period• Only odd number of zero-crossings alter the spin states
• Maximum odd number of zero-crossings occur at 1/3 rotor period ofrf irradiation for a solid powder
Theoretical Calculation. =0.54.
Y. Ba, H. Kao, C. P. Grey, L. Chopin, T. Gullion, J. Magn. Reson. 1998, 133, 104.
Experimental result from 14NH2CH213COOH solid powder.
=14.5 kHz, rf=43 kHz , r=1.5 kHz & N=10.
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Quadruple
Triple
Double
Single
Odd
Non
Fra
ctio
n o
f ze
ro-c
rossin
gs
Rotor Fractions of rf Iradiation
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
RE
AP
DO
R F
rca
tio
ns
Rotor Fractions of rf Irradiation
Determination of Internuclear Distance
Y. Ba, H. Kao, C. P. Grey, L. Chopin, T. Gullion, J. Magn. Reson. 1998, 133, 104.
Theoretical and experimentalREAPDOR curves from 5% diluted14NH2CH2
13COOH solid powder.
(14N) =14.5 kHz
rf(14N) =43 kHz
QCC=1.18 MHz=0.54,
rN-C=2.49 ÅD=141 Hz.