General symmetry principles for rotor-synchronized pulse sequences in magic-angle spinning solid-state nuclear magnetic resonance are presented. The theory of symmetry-based pulse sequences using π pulse elements is presented for the first time. The symmetry theory is extended to the case of generalized Hartmann–Hahn sequences, in which rotor-synchronized rf irradiation is applied simultaneously to two isotopic spin species. The symmetry principles lead to heteronuclear selection rules. The symmetry theory is used to design pulse sequences which implement heteronuclear dipolar recoupling at the same time as decoupling homonuclear spin–spin interactions, and which also suppress chemical shift anisotropies. A number of specific pulse sequences based on these principles are listed. Experimental demonstrations are given of heteronuclear two-dimensional correlation spectroscopy, heteronuclear multiple-quantum spectroscopy, and the estimation of internuclear dipolar couplings.

1.
T. G.
Oas
,
R. G.
Griffin
, and
M. H.
Levitt
,
J. Chem. Phys.
89
,
692
(
1988
).
2.
M. H.
Levitt
,
T. G.
Oas
, and
R. G.
Griffin
,
Isr. J. Chem.
28
,
271
(
1988
).
3.
T.
Gullion
and
J.
Schaefer
,
J. Magn. Reson.
81
,
196
(
1989
).
4.
T.
Gullion
and
J.
Schaefer
,
Adv. Magn. Reson.
13
,
57
(
1989
).
5.
M. H.
Levitt
,
D. P.
Raleigh
,
F.
Creuzet
, and
R. G.
Griffin
,
J. Chem. Phys.
90
,
6347
(
1990
).
6.
R.
Tycko
and
G.
Dabbagh
,
J. Am. Chem. Soc.
113
,
9444
(
1991
).
7.
D. M.
Gregory
,
D. J.
Mitchell
,
J. A.
Stringer
,
S.
Kiihne
,
J. C.
Shiels
,
J.
Callahan
,
M. A.
Metha
, and
G. P.
Drobny
,
Chem. Phys. Lett.
246
,
654
(
1995
).
8.
M.
Baldus
,
M.
Tomaselli
,
B.
Meier
, and
R. R.
Ernst
,
Chem. Phys. Lett.
230
,
329
(
1994
).
9.
M.
Baldus
and
B. H.
Meier
,
J. Magn. Reson.
128
,
172
(
1997
).
10.
N. C.
Nielsen
,
H.
Bildsøe
,
H. J.
Jakobsen
, and
M. H.
Levitt
,
J. Chem. Phys.
101
,
1805
(
1994
).
11.
Y. K.
Lee
,
N. D.
Kurur
,
M.
Helmle
,
O. G.
Johannessen
,
N. C.
Nielsen
, and
M. H.
Levitt
,
Chem. Phys. Lett.
242
,
304
(
1995
).
12.
C. M.
Rienstra
,
M. E.
Hatcher
,
L. J.
Mueller
,
B.
Sun
,
S. W.
Fesik
, and
R. G.
Griffin
,
J. Am. Chem. Soc.
120
,
10602
(
1998
).
13.
M.
Hohwy
,
H. J.
Jakobsen
,
M.
Edén
,
M. H.
Levitt
, and
N. C.
Nielsen
,
J. Chem. Phys.
108
,
2686
(
1998
).
14.
M.
Hohwy
,
C. M.
Rienstra
,
C. P.
Jaroniec
, and
R. G.
Griffin
,
J. Chem. Phys.
110
,
7983
(
1999
).
15.
M.
Helmle
,
Y. K.
Lee
,
P. J. E.
Verdegem
,
X.
Feng
,
T.
Karlsson
,
J.
Lugtenburg
,
H. J. M.
de Groot
, and
M. H.
Levitt
,
J. Magn. Reson.
140
,
379
(
1999
).
16.
K.
Nomura
,
K.
Takegoshi
,
T.
Terao
,
K.
Uchida
, and
M.
Kainosho
,
J. Am. Chem. Soc.
121
,
4064
(
1999
).
17.
M.
Carravetta
,
M.
Edén
,
X.
Zhao
,
A.
Brinkmann
, and
M. H.
Levitt
,
Chem. Phys. Lett.
321
,
205
(
2000
).
18.
B.-J.
van Rossum
,
C. P.
de Groot
,
V.
Ladizhansky
,
S.
Vega
, and
H. J. M.
de Groot
,
J. Am. Chem. Soc.
122
,
3465
(
2000
).
19.
V.
Ladizhansky
and
S.
Vega
,
J. Chem. Phys.
112
,
7158
(
2000
).
20.
Y.
Ishii
,
T.
Terao
, and
M.
Kainosho
,
Chem. Phys. Lett.
265
,
133
(
1996
).
21.
X.
Feng
,
Y. K.
Lee
,
D.
Standström
,
M.
Edén
,
H.
Maisel
,
A.
Sebald
, and
M. H.
Levitt
,
Chem. Phys. Lett.
257
,
314
(
1996
).
22.
K.
Schmidt-Rohr
,
J. Am. Chem. Soc.
118
,
7601
(
1996
).
23.
X.
Feng
,
M.
Edén
,
A.
Brinkmann
,
H.
Luthman
,
L.
Eriksson
,
A.
Gräslund
,
O. N.
Antzutkin
, and
M. H.
Levitt
,
J. Am. Chem. Soc.
119
,
12006
(
1997
).
24.
M.
Hong
,
J. D.
Gross
, and
R. G.
Griffin
,
J. Phys. Chem. B
101
,
5869
(
1997
).
25.
P. R.
Costa
,
J. D.
Gross
,
M.
Hong
, and
R. G.
Griffin
,
Chem. Phys. Lett.
280
,
95
(
1997
).
26.
T.
Fujiwara
,
T.
Shimomura
, and
H.
Akutsu
,
J. Magn. Reson.
124
,
147
(
1997
).
27.
Y.
Ishii
,
K.
Hirao
,
T.
Terao
,
T.
Terauchi
,
M.
Oba
,
K.
Nishiyama
, and
M.
Kainosho
,
Solid State Nucl. Magn. Reson.
11
,
169
(
1998
).
28.
M.
Hohwy
,
C. P.
Jaroniec
,
B.
Reif
,
C. M.
Rienstra
, and
R. G.
Griffin
,
J. Am. Chem. Soc.
122
,
3218
(
2000
).
29.
B.
Reif
,
M.
Hohwy
,
C. P.
Jaroniec
,
C. M.
Rienstra
, and
R. G.
Griffin
,
J. Magn. Reson.
145
,
132
(
2000
).
30.
S.
Ravindranathan
,
X.
Feng
,
T.
Karlsson
,
G.
Widmalm
, and
M. H.
Levitt
,
J. Am. Chem. Soc.
122
,
1102
(
2000
).
31.
E. R.
Andrew
,
A.
Bradbury
, and
R. G.
Eades
,
Nature (London)
183
,
1802
(
1959
).
32.
I. J.
Lowe
,
Phys. Rev. Lett.
2
,
285
(
1959
).
33.
A. E.
Bennett
,
R. G.
Griffin
, and
S.
Vega
,
NMR
33
,
1
(
1994
).
34.
S.
Dusold
and
A.
Sebald
,
Annu. Rep. NMR Spectrosc.
41
,
185
(
2000
).
35.
S. R.
Hartmann
and
E. L.
Hahn
,
Phys. Rev.
128
,
2042
(
1962
).
36.
A.
Pines
,
M. G.
Gibby
, and
J. S.
Waugh
,
J. Chem. Phys.
59
,
569
(
1973
).
37.
E. O.
Stejskal
,
J.
Schaefer
, and
J. S.
Waugh
,
J. Magn. Reson.
28
,
105
(
1977
).
38.
G.
Metz
,
X.
Wu
, and
S. O.
Smith
,
J. Magn. Reson., Ser. A
110
,
219
(
1994
).
39.
M.
Lee
and
W. I.
Goldburg
,
Phys. Rev.
140
,
A1261
(
1965
).
40.
A. W.
Hing
,
S.
Vega
, and
J.
Schaefer
,
J. Magn. Reson.
96
,
205
(
1992
).
41.
T.
Gullion
,
Chem. Phys. Lett.
246
,
325
(
1995
).
42.
T.
Gullion
,
J. Magn. Reson., Ser. A
117
,
326
(
1995
).
43.
T.
Gullion
and
C. H.
Pennington
,
Chem. Phys. Lett.
290
,
88
(
1998
).
44.
K.
Takegoshi
,
K.
Takeda
, and
T.
Terao
,
Chem. Phys. Lett.
89
,
331
(
1996
).
45.
R.
Fu
,
S. A.
Smith
, and
G.
Bodenhausen
,
Chem. Phys. Lett.
272
,
361
(
1997
).
46.
C. P.
Jaroniec
,
B. A.
Tounge
,
C. M.
Rienstra
,
J.
Herzfeld
, and
R. G.
Griffin
,
J. Magn. Reson.
146
,
132
(
2000
).
47.
U.
Haeberlen
and
J. S.
Waugh
,
Phys. Rev.
175
,
453
(
1968
).
48.
J. C. C.
Chan
,
Chem. Phys. Lett.
335
,
289
(
2001
).
49.
P.
Mansfield
,
M. J.
Orchard
,
D. C.
Stalker
, and
K. H. B.
Richards
,
Phys. Rev. B
7
,
90
(
1973
).
50.
W. K.
Rhim
,
D. D.
Elleman
, and
R. W.
Vaughan
,
J. Chem. Phys.
59
,
3740
(
1973
).
51.
D. P.
Burum
and
W. K.
Rhim
,
J. Chem. Phys.
71
,
944
(
1979
).
52.
D. P.
Burum
,
M.
Linder
, and
R. R.
Ernst
,
J. Magn. Reson.
44
,
173
(
1981
).
53.
A.
Bielecki
,
A. C.
Kolbert
, and
M. H.
Levitt
,
Chem. Phys. Lett.
155
,
341
(
1989
).
54.
E.
Vinogradov
,
P. K.
Madhu
, and
S.
Vega
,
Chem. Phys. Lett.
314
,
443
(
1999
).
55.
M.
Edén
and
M. H.
Levitt
,
J. Chem. Phys.
111
,
1511
(
1999
).
56.
A.
Brinkmann
,
M.
Edén
, and
M. H.
Levitt
,
J. Chem. Phys.
112
,
8539
(
2000
).
57.
A. S. D.
Heindrichs
,
H.
Geen
,
C.
Giordani
, and
J. J.
Titman
,
Chem. Phys. Lett.
335
,
89
(
2001
).
58.
E. H.
Hardy
,
R.
Verel
, and
B. H.
Meier
,
J. Magn. Reson.
148
,
459
(
2001
).
59.
A. E.
Bennett
,
J. H.
Ok
, and
R. G.
Griffin
,
J. Chem. Phys.
96
,
8624
(
1992
).
60.
A. E.
Bennett
,
C. M.
Rienstra
,
M.
Auger
,
K. V.
Lakshmi
, and
R. G.
Griffin
,
J. Chem. Phys.
103
,
6951
(
1995
).
61.
M. H.
Levitt
,
J. Magn. Reson.
126
,
164
(
1997
).
62.
M. H.
Levitt
and
O. G.
Johannessen
,
J. Magn. Reson.
142
,
190
(
2000
).
63.
M. H.
Levitt
,
R.
Freeman
, and
T.
Frenkiel
,
Adv. Magn. Reson.
11
,
47
(
1983
).
64.
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
65.
W.
Magnus
,
Commun. Pure Appl. Math.
7
,
649
(
1954
).
66.
We employ an indexing of the Magnus expansion starting at one. The older literature on average Hamiltonian uses indices which are one less than those given here.
67.
T.
Gullion
,
D. B.
Baker
, and
M. S.
Conradi
,
J. Magn. Reson.
89
,
479
(
1990
).
68.
X. Zhao, M. Edén, and M. H. Levitt (to be published).
69.
M.
Bak
,
J. T.
Rasmussen
, and
N. C.
Nielsen
,
J. Magn. Reson.
147
,
296
(
2000
).
70.
A. S. D.
Heindrichs
,
H.
Geen
, and
J. J.
Titman
,
J. Magn. Reson.
147
,
68
(
2000
).
71.
M. H. Levitt, in Encyclopedia of Nuclear Magnetic Resonance, edited by D. M. Grant and R. K. Harris (Wiley, Chichester, England, 1996), Vol. 2, pp. 1396–1411.
72.
P.
Caravatti
,
G.
Bodenhausen
, and
R. R.
Ernst
,
Chem. Phys. Lett.
89
,
363
(
1982
).
73.
P.
Caravatti
,
L.
Braunshweiler
, and
R. R.
Ernst
,
Chem. Phys. Lett.
100
,
305
(
1983
).
74.
J. E.
Roberts
,
S.
Vega
, and
R. G.
Griffin
,
J. Am. Chem. Soc.
106
,
2506
(
1989
).
75.
R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, 5th ed. (Clarendon, Oxford, 1988).
76.
S.
Hediger
,
B. H.
Meier
,
N. D.
Kurur
,
G.
Bodenhausen
, and
R. R.
Ernst
,
Chem. Phys. Lett.
223
,
283
(
1994
).
77.
S.
Hediger
,
B. H.
Meier
, and
R. R.
Ernst
,
Chem. Phys. Lett.
240
,
449
(
1995
).
78.
M.
Baldus
,
D. G.
Geurts
,
S.
Hediger
, and
B. H.
Meier
,
J. Magn. Reson., Ser. A
118
,
140
(
1996
).
79.
M. H. Levitt, Spin Dynamics: Basic Principles of NMR Spectroscopy (Wiley, Chichester, England, 2001).
80.
M. Carravetta, M. Edén, H. Luthman, P. J. E. Verdegem, J. Lugtenburg, A. Sebald, and M. H. Levitt (to be published).
81.
The following parameters correspond to “molecule 1” in Ref. 88 for a C13 Larmor frequency of −100.602 MHz and a N15 Larmor frequency of 40.510 MHz. A molecule-fixed frame M with a z axis along the Cα13COO internuclear vector was chosen. Cα13 site: isotropic shift ωiso/2π=0.0 Hz, shift anisotropy ωaniso/2π=1954.7 Hz, asymmetry parameter η=0.98, Euler angles ΩPM={99.4°,146.0°,138.9°}.N15 site: isotropic shift ωiso/2π=0.0 Hz. The CSA of the N15 site was neglected. The internuclear Cα1315N vector was oriented at angles ΩPM={0.0°,112.3°,117.1°}. The heteronuclear isotropic J coupling is given by J13C15N=−6.3 Hz.
82.
P.-G.
Jönsson
and
Å.
Kvick
,
Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem.
28
,
1827
(
1972
).
83.
H.
Fuess
,
D.
Hohlwein
, and
S. A.
Mason
,
Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem.
33
,
654
(
1977
).
The misprinted fractional coordinates for C(1) and H(9) given in this paper are corrected in the Cambridge Structural Database (Ref. 89).
84.
A. Brinkmann, M. Edén, and M. H. Levitt (unpublished).
85.
A.
Lesage
,
S.
Steuernagel
, and
L.
Emsley
,
J. Am. Chem. Soc.
120
,
7095
(
1998
).
86.
A.
Lesage
,
D.
Sakellariou
,
S.
Steuernagel
, and
L.
Emsley
,
J. Am. Chem. Soc.
120
,
13194
(
1998
).
87.
A.
Lesage
,
P.
Charmont
,
S.
Steuernagel
, and
L.
Emsley
,
J. Am. Chem. Soc.
122
,
9739
(
2000
).
88.
R. A.
Haberkorn
,
R. E.
Stark
,
H.
van Willigen
, and
R. G.
Griffin
,
J. Am. Chem. Soc.
103
,
2534
(
1981
).
89.
F. H.
Allen
and
O.
Kennard
,
Chem. Design Auto. News
8
,
31
(
1993
).
90.
J. L.
Markley
,
A.
Bax
,
Y.
Arata
,
C. W.
Hilbers
,
R.
Kaptein
,
B. D.
Sykes
,
P. E.
Wright
, and
K.
Wüthrich
,
Pure Appl. Chem.
70
,
117
(
1998
).
91.
V. B.
Cheng
,
H. H.
Suzukawa
, and
M.
Wolfsberg
,
J. Chem. Phys.
59
,
3992
(
1973
).
92.
R. K.
Hester
,
J. L.
Ackermann
,
V. R.
Cross
, and
J. S.
Waugh
,
Phys. Rev. Lett.
34
,
993
(
1975
).
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