A unified strategy of two-pulse based heteronuclear decoupling for solid-state magic-angle spinning nuclear magnetic resonance is presented. The analysis presented here shows that different decoupling sequences like two-pulse phase-modulation (TPPM), X-inverse-X (XiX), and finite pulse refocused continuous wave (rCWA) are basically specific solutions of a more generalized decoupling scheme which incorporates the concept of time-modulation along with phase-modulation. A plethora of other good decoupling conditions apart from the standard, TPPM, XiX, and rCWA decoupling conditions are available from the unified decoupling approach. The importance of combined time- and phase-modulation in order to achieve the best decoupling conditions is delineated. The consequences of different indirect dipolar interactions arising from cross terms comprising of heteronuclear and homonuclear dipolar coupling terms and also those between heteronuclear dipolar coupling and chemical-shift anisotropy terms are presented in order to unfold the effects of anisotropic interactions under different decoupling conditions. Extensive numerical simulation results are corroborated with experiments on standard amino acids.

1.
A. L.
Bloom
and
J. N.
Shoolery
, “
Effects of perturbing radiofrequency fields on nuclear spin coupling
,”
Phys. Rev.
97
,
1261
-
1265
(
1955
).
2.
P.
Tekely
,
P.
Palmas
, and
D.
Canet
, “
Effect of proton spin exchange on the residual 13C MAS NMR linewidths. Phase-modulated irradiation for efficient heteronuclear decoupling in rapidly rotating solids
,”
J. Magn. Reson., Ser. A
107
,
129
-
133
(
1994
).
3.
A. E.
Bennett
,
C. M.
Rienstra
,
M.
Auger
,
K. V.
Lakshmi
, and
R. G.
Griffin
, “
Heteronuclear decoupling in rotating solids
,”
J. Chem. Phys.
103
,
6951
-
6958
(
1995
).
4.
Z. H.
Gan
and
R. R.
Ernst
, “
Frequency-and phase-modulated heteronuclear decoupling in rotating solids
,”
Solid State Nucl. Magn. Reson.
8
,
153
-
159
(
1997
).
5.
M.
Edén
and
M. H.
Levitt
, “
Pulse sequence symmetries in the nuclear magnetic resonance of spinning solids: Application to heteronuuclear decoupling
,”
J. Chem. Phys.
111
,
1511
-
1519
(
1999
).
6.
B. M.
Fung
,
A. K.
Khitrin
, and
K.
Ermolaev
, “
An improved broadband decoupling sequence for liquid crystals and solids
,”
J. Magn. Reson.
142
,
97
-
101
(
2000
).
7.
K.
Takegoshi
,
J.
Mizokami
, and
T.
Terao
, “
1H decoupling with third averaging in solid NMR
,”
Chem. Phys. Lett.
341
,
540
-
544
(
2001
).
8.
A.
Detken
,
E. H.
Hardy
,
M.
Ernst
, and
B. H.
Meier
, “
Simple and efficient decoupling in magic-angle spinning solid-state NMR
,”
Chem. Phys. Lett.
56
,
298
-
304
(
2002
).
9.
G. D.
Paëpe
,
D.
Sakellariou
,
P.
Hodgkinson
,
S.
Hediger
, and
L.
Emsley
, “
Heteronuclear decoupling in NMR of liquid crystals using continuous phase modulation
,”
Chem. Phys. Lett.
368
,
511
-
522
(
2003
).
10.
M.
Ernst
, “
Heteronuclear spin decoupling in solid-state NMR under magic-angle sample spinning
,”
J. Magn. Reson.
162
,
1
-
34
(
2003
).
11.
A. K.
Khitrin
,
T.
Fujiwara
, and
H.
Akutsu
, “
Phase-modulated heteronuclear decoupling in NMR of solids
,”
J. Magn. Reson.
162
,
46
-
53
(
2003
).
12.
P.
Hodgkinson
, “
Heteronuclear decoupling in the NMR of solids
,”
Prog. Nucl. Magn. Reson. Spectrosc.
46
,
197
-
222
(
2005
).
13.
R. S.
Thakur
,
N. D.
Kurur
, and
P. K.
Madhu
, “
Swept-frequency two-pulse phase modulation for heteronuclear dipolar decoupling in solid-state NMR
,”
Chem. Phys. Lett.
426
,
459
-
463
(
2006
).
14.
M.
Weingarth
,
P.
Tekely
, and
G.
Bodenhausen
, “
Efficient heteronuclear decoupling by quenching rotary resonance in solid-state NMR
,”
Chem. Phys. Lett.
466
,
247
-
251
(
2008
).
15.
J. M.
Vinther
,
A. B.
Nielsen
,
M.
Bjerring
,
E. R. H.
van Eck
,
A. P. M.
Kentgens
,
N.
Khaneja
, and
N. C.
Nielsen
, “
Refocused continuous-wave decoupling: A new approach to heteronuclear dipolar decoupling in solid-state NMR spectroscopy
,”
J. Chem. Phys.
137
,
214202
(
2012
).
16.
J. M.
Vinther
,
N.
Khaneja
, and
N. C.
Nielsen
, “
Robust and efficient 19F heteronuclear dipolar decoupling using refocused continuous-wave rf irradiation
,”
J. Magn. Reson.
226
,
88
-
92
(
2013
).
17.
V. S.
Mithu
and
P. K.
Madhu
, “
Exploring connections between phase modulated heteronuclear dipolar decoupling schemes in solid-state NMR
,”
Chem. Phys. Lett.
556
,
325
-
329
(
2013
).
18.
V.
Agarwal
,
T.
Tuherm
,
A.
Reinhold
,
J.
Past
,
A.
Samoson
,
M.
Ernst
, and
B. H.
Meier
, “
Amplitude-modulated low-power decoupling sequences for fast magic-angle spinning NMR
,”
Chem. Phys. Lett.
583
,
1
-
7
(
2013
).
19.
A.
Equbal
,
S.
Paul
,
V. S.
Mithu
,
P. K.
Madhu
, and
N. C.
Nielsen
, “
r TPPM: Towards improving solid-state NMR two-pulse phase-modulation heteronuclear dipolar decoupling sequence by refocusing
,”
J. Magn. Reson.
244
,
68
-
73
(
2014
).
20.
P. K.
Madhu
, “
Heteronuclear spin decoupling in solid-state nuclear magnetic resonance: Overview and outlook
,”
Isr. J. Chem.
54
,
25
-
38
(
2014
).
21.
A.
Equbal
,
S.
Paul
,
V. S.
Mithu
,
P. K.
Madhu
, and
N. C.
Nielsen
, “
Efficient heteronuclear decoupling in MAS solid-state NMR using non-rotor-synchronized rCW irradiation
,”
J. Magn. Reson.
246
,
104
-
109
(
2014
).
22.
J. B.
Grutzner
and
R. E.
Santini
, “
Coherent broad-band decoupling? An alternative to proton noise decoupling in carbon-13 nuclear magnetic resonance spectroscopy
,”
J. Magn. Reson.
19
,
173
-
187
(
1975
).
23.
J. S.
Waugh
, “
Theory of broadband spin decoupling
,”
J. Magn. Reson.
50
,
30
-
49
(
1982
).
24.
See supplementary material at http://dx.doi.org/10.1063/1.4919634 for experimental comparison of the decoupling optimization and peak width values for Fig. 10.
25.
M.
Bak
,
J. T.
Rasmussen
, and
N. C.
Nielsen
, “
SIMPSON: A general simulation program for solid-state NMR spectroscopy
,”
J. Magn. Reson.
147
,
296
-
330
(
2000
).
26.
Z.
Tosner
,
R.
Andersen
,
B.
Stevensson
,
M.
Edén
,
N. C.
Nielsen
, and
T.
Vosegaard
, “
Computer-intensive simulation of solid-state NMR experiments using SIMPSON
,”
J. Magn. Reson.
246
,
79
-
93
(
2014
).
27.
T. M.
Bak
,
R.
Schultz
,
T.
Vosegaard
, and
N. C.
Nielsen
, “
Specification and visualization of anisotropic interaction tensors for numerical simulation of solid-state NMR experiments on polypeptide structures
,”
J. Magn. Reson.
154
,
28
-
45
(
2002
).

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