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.