A theory of nuclear spin relaxation in isotropic liquids for nuclear spins interacting with electron spins, residing in other molecules (the outer-sphere relaxation), is presented. The approach, valid outside of the Redfield limit for electron spin relaxation, is an extension of the Swedish slow motion theory [Benetis et al, Mol. Phys.48, 329 (1983); Nilsson and Kowalewski, J. Magn. Reson.146, 345 (2000)] for inner-sphere relaxation. It is demonstrated that the outer-sphere relaxation rate can be expressed as an integral of a product of a translational diffusion correlation function and a function analogous to the inner-sphere spectral density. A numerical implementation of the theory is described and applied to a large number of realistic parameter sets for S=7/2 and S=1, which may correspond to Gd(III) and Ni(II) systems. It is shown that the outer-sphere contribution is relevant and should be included into the analysis of nuclear magnetic relaxation dispersion relaxation profiles, especially for slow relative translational diffusion and fast molecular tumbling.

1.
I.
Bertini
,
C.
Luchinat
, and
G.
Parigi
,
Solution NMR of Paramagnetic Molecules
(
Elsevier
,
Amsterdam
,
2001
).
2.
D.
Kruk
,
Theory of Evolution and Relaxation of Multi-Spin Systems
(
Arima
,
Bury St Edmunds
,
2007
).
3.
Advances in Inorganic Chemistry
, edited by
R.
van Eldik
and
I.
Bertini
(
Elsevier
,
Amsterdam
,
2005
), Vol.
57
.
5.
J.
Kowalewski
,
D.
Kruk
, and
G.
Parigi
,
Adv. Inorg. Chem.
57
,
41
(
2005
).
6.
E.
Belorizky
,
P. H.
Fries
,
L.
Helm
,
J.
Kowalewski
,
D.
Kruk
,
R. R.
Sharp
, and
P. -O.
Westlund
,
J. Chem. Phys.
128
,
052315
(
2008
).
7.
N.
Benetis
,
J.
Kowalewski
,
L.
Nordenskiöld
,
H.
Wennerström
, and
P. -O.
Westlund
,
Mol. Phys.
48
,
329
(
1983
).
8.
P. -O.
Westlund
,
H.
Wennerström
,
L.
Nordenskiöld
,
J.
Kowalewski
, and
N.
Benetis
,
J. Magn. Reson.
59
,
91
(
1984
).
9.
N.
Benetis
and
J.
Kowalewski
,
J. Magn. Reson.
65
,
13
(
1985
).
10.
T.
Larsson
,
P. -O.
Westlund
,
J.
Kowalewski
, and
S. H.
Koenig
,
J. Chem. Phys.
101
,
1116
(
1994
).
11.
T.
Nilsson
,
J.
Svoboda
,
P. -O.
Westlund
, and
J.
Kowalewski
,
J. Chem. Phys.
109
,
6364
(
1998
).
12.
T.
Nilsson
and
J.
Kowalewski
,
J. Magn. Reson.
146
,
345
(
2000
).
13.
A.
Abragam
,
The Principles of Nuclear Magnetism
(
Oxford University Press
,
Oxford
,
1961
).
14.
15.
H.
Pfeifer
,
Ann. Phys. (Leipzig)
8
,
1
(
1961
).
16.
L. P.
Hwang
and
J. H.
Freed
,
J. Chem. Phys.
63
,
4017
(
1975
).
17.
Y.
Ayant
,
E.
Belorizky
,
J.
Alizon
, and
J.
Gallice
,
J. Phys. (Paris)
36
,
991
(
1975
).
18.
Y.
Ayant
,
E.
Belorizky
,
P. H.
Fries
, and
J.
Rosset
,
J. Phys. (Paris)
38
,
325
(
1977
).
19.
J. H.
Freed
,
J. Chem. Phys.
68
,
4034
(
1978
).
20.
A. G.
Redfield
,
Adv. Magn. Reson.
1
,
1
(
1965
).
21.
D.
Kruk
,
T.
Nilsson
, and
J.
Kowalewski
,
Mol. Phys.
99
,
1435
(
2001
).
22.
D.
Kruk
,
T.
Nilsson
, and
J.
Kowalewski
,
Phys. Chem. Chem. Phys.
3
,
4907
(
2001
).
23.
S. M.
Abernathy
and
R. R.
Sharp
,
J. Chem. Phys.
106
,
9032
(
1997
).
24.
S. M.
Abernathy
and
R. R.
Sharp
,
J. Phys. Chem. A
101
,
3692
(
1997
).
25.
R.
Sharp
,
L.
Lohr
, and
J.
Miller
,
Prog. Nucl. Magn. Reson. Spectrosc.
38
,
115
(
2001
).
26.
S.
Rast
,
E.
Belorizky
,
P. H.
Fries
, and
J. P.
Travers
,
J. Phys. Chem. B
105
,
1978
(
2001
).
27.
E.
Belorizky
,
P. H.
Fries
, and
S.
Rast
,
C.R. Acad. Sci., Ser. IIc: Chim
4
,
825
(
2001
).
28.
J. P.
Albrand
,
M. C.
Taieb
,
P. H.
Fries
, and
E.
Belorizky
,
J. Chem. Phys.
78
,
5809
(
1983
).
29.
P. H.
Fries
and
E.
Belorizky
,
J. Chem. Phys.
79
,
1166
(
1983
).
30.
P. H.
Fries
,
J.
Richardi
,
S.
Rast
, and
E.
Belorizky
,
Pure Appl. Chem.
73
,
1689
(
2001
).
31.
D.
Kruk
and
J.
Kowalewski
,
J. Chem. Phys.
117
,
1194
(
2002
).
32.
S.
Rast
,
P. H.
Fries
,
E.
Belorizky
,
A.
Borel
,
L.
Helm
, and
A. E.
Merbach
,
J. Chem. Phys.
115
,
7554
(
2001
).
33.
P. H.
Fries
,
G.
Ferrante
,
E.
Belorizky
, and
S.
Rast
,
J. Chem. Phys.
119
,
8636
(
2003
).
34.
E.
Belorizky
and
P. H.
Fries
,
Phys. Chem. Chem. Phys.
6
,
2341
(
2004
).
35.
P. H.
Fries
and
E.
Belorizky
,
J. Chem. Phys.
123
,
124510
(
2005
).
36.
P. H.
Fries
and
E.
Belorizky
,
J. Chem. Phys.
126
,
204503
(
2007
).
37.
S.
Rast
,
P. H.
Fries
, and
E.
Belorizky
,
J. Chem. Phys.
113
,
8724
(
2000
).
38.
S.
Rast
,
A.
Borel
,
L.
Helm
,
E.
Belorizky
,
P. H.
Fries
, and
A. E.
Merbach
,
J. Am. Chem. Soc.
123
,
2637
(
2001
).
39.
N.
Schaefle
and
R.
Sharp
,
J. Chem. Phys.
122
,
184501
(
2005
).
40.
R.
Sharp
,
J. Chem. Phys.
129
,
144307
(
2008
).
41.
M.
Rubinstein
,
A.
Baram
, and
Z.
Luz
,
Mol. Phys.
20
,
67
(
1971
).
42.
D.
Kruk
and
J.
Kowalewski
,
Mol. Phys.
101
,
2861
(
2003
).
43.
M.
Odelius
,
C.
Ribbing
, and
J.
Kowalewski
,
J. Chem. Phys.
103
,
1800
(
1995
).
44.
D.
Kruk
and
J.
Kowalewski
,
J. Chem. Phys.
116
,
4079
(
2002
).
45.
D.
Kruk
,
J.
Kowalewski
, and
P. -O.
Westlund
,
J. Chem. Phys.
121
,
2215
(
2004
).
46.
C.
Lanczos
,
J. Res. Natl. Bur. Stand.
49
,
33
(
1952
).
47.
T.
Nilsson
,
G.
Parigi
, and
J.
Kowalewski
,
J. Phys. Chem. A
106
,
4476
(
2002
).
48.
R. R.
Sharp
,
J. Chem. Phys.
98
,
6092
(
1993
).
49.
I.
Bertini
,
C.
Luchinat
, and
J.
Kowalewski
,
J. Magn. Reson.
62
,
235
(
1985
).
50.
C. S.
Bonnet
,
P. H.
Fries
,
A.
Gadelle
,
S.
Gambarelli
, and
P.
Delangle
,
J. Am. Chem. Soc.
130
,
10401
(
2008
).
51.
J.
Kowalewski
,
A.
Egorov
,
D.
Kruk
,
A.
Laaksonen
,
S.
Nikkhou Aski
,
G.
Parigi
, and
P. -O.
Westlund
,
J. Magn. Reson.
195
,
103
(
2008
).
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