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3.8 Molecular spectroscopy
3.8.1 Nuclear moments and magnetic resonance
The table includes all naturally occurring isotopes having non-zero spin
(excluding 180Ta). The magnetic moment, μ, is given in
units of the nuclear magneton
μn(eh/4πMc). The resonant frequency
of an isotope is given by
v = μH/hI
where H is the magnetic field at the nucleus,
h is Planck's constant and I is the nuclear spin (in units of
h/2π). Since
radio frequencies are among the most accurately measurable physical quantities
known, nuclear magnetic resonance (nmr) measurements should provide highly
accurate values of the nuclear moments. However, it was found that the
resonance frequency of a given isotope is dependent on the chemical nature of
the compound containing that isotope. This ‘chemical shift’ effect,
while limiting the accuracy of nuclear moment measurements, has proved to be a
most important tool for the determination of molecular structures (see section
3.8.2).
The values of the nuclear moments given are corrected
for diamagnetism, arrived at from considering values obtained by various
experimental techniques including nmr, atomic beam resonance, electron spin
resonance, optical spectroscopy and electron-nuclear double resonance (ENDOR).
For a few nuclei the moment values obtained by two different methods are
consistent and when this occurs those values are quoted but when discrepancies
exist the nmr values have been listed. See G. H. Fuller J. Phys. Chem. Ref.
Data, 1976, 5, 835, for further details.
Nuclear electric quadrupole moments are conveniently
written e. Q where e is the charge on the electron and the
parameter Q is in units of 10−28 m2 (barns).
The quadrupole moment values reported are averages of the values reported in
the literature (or derived from these), since some uncertainty attaches to the
accuracy of any particular value due to the difficulties in estimating the
electric field inhomogeneity at the nucleus arising from its molecular and
electronic environment. Only those values marked * contain any
correction for polarization shielding effects. Such corrections are difficult
to quantify and may amount to 30 per cent of the Q value for some
nuclei. Spin
 nuclei
have no quadrupole moment.
The nmr frequency values tabulated are those for an
externally applied field of 1 tesla (10 kilogauss).
The sensitivity at constant field, relative to the
proton, is calculated from the expression (7.652 x 10−3)
× μ3(I + 1)/I2. The term
assumes a comparison between an equal number of nuclei, at constant
temperature, where the longitudinal and transverse relaxation times are equal
(i.e., T1 = T2), and with an ideal induced
voltage in the receiver coil at saturation with constant source noise; and thus
is an optimum value.
The product of the relative sensitivity and the isotopic
natural abundance—also listed, and quoted as a percentage—gives the
relative receptivity of the nucleus compared with the proton, and is thus a
more useful guide to nuclear response in natural abundance nmr determinations.
For example, the relative receptivity of 13C compared with
1H is 0.0159 × 1.108 = 0.0176%.
The chemical reference standards listed in the table are
either those universally employed (e.g. (Me4Si) or
(H3PO4)) or those frequently used, or in a few instances
are the only compound of the nuclide to have been observed by nmr
techniques.
Some abbreviations used in the table are aq. for aqueous
solution, Et for ethyl, Me for methyl, neat for undiluted compound.
The sign of μ/μn and of
Q/10−28 m2 is uncertain for those nuclides
for which no sign is given.
The symbol † in the nuclide column
indicates that the isotope highlighted is radioactive.
Nuclear spins, moments and resonant
frequencies
|
Nuclide |
I |
μ /μN |
Q/10−28
m2 |
v/MHz |
Relative
sensitivity
|
% Natural
abundance
|
Chemical shift
reference standard
|
|
|
|
|
|
|
|
|
|
|
|
|
0n† |
 |
−1.913 12 |
|
— |
29.167 |
0.322 |
— |
— |
|
1H |
|
+2.792 78 |
|
— |
42.575 9 |
1.000 |
99.985 |
Me4Si |
|
2H |
1 |
+0.857 39 |
+ |
0.002 73 |
6.535 7 |
0.009 65 |
0.015 |
— |
|
3H† |
|
+2.978 77 |
|
— |
45.412 9 |
1.210 |
— |
Me4Si-tritiated |
|
3He |
|
−2.127 6
|
|
— |
32.433 8 |
0.442 |
1.3 × 10− 4 |
— |
|
6Li |
1 |
+0.822 03 |
– |
0.000 8 |
6.265 5 |
0.008 50 |
7.42 |
Li+aq. |
|
7Li |
|
+3.256 36 |
– |
0.045 |
16.546 5 |
0.293 |
92.58 |
Li+aq. |
|
9Be |
|
−1.177 45 |
+ |
0.052 |
5.982 7 |
0.013 9 |
100 |
Be2+aq. |
|
10B |
3 |
−1.800 6
|
+ |
0.085* |
4.575 4 |
0.019 9 |
19.58 |
Et2O.BF3 or
BH4− |
|
11B |
|
+2.688 5 |
+ |
0.041* |
13.660 1 |
0.165 |
80.42 |
Et2O.BF3 or
BH4− |
|
13C |
|
+0.702 4 |
|
— |
10.705 4 |
0.015 9 |
1.108 |
Me4Si |
|
14N |
1 |
+1.403 57 |
+ |
0.016 |
3.075 6 |
0.001 01 |
99.63 |
MeNO2 or
NO3− |
|
15N |
|
−0.283 1
|
|
— |
4.315 8 |
0.001 04 |
0.37 |
MeNO2 or
NO3− |
|
17O |
 |
−1.893 7 |
− |
0.026* |
5.771 9 |
0.029 1 |
0.037 |
H2O |
|
19F |
|
+2.627 27 |
|
— |
40.061 3 |
0.833 |
100 |
CCl3F |
|
21Ne |
|
−0.661 76 |
+ |
0.09 |
3.361 1 |
0.002 50 |
0.257 |
— |
|
23Na |
|
+2.217 40 |
+ |
0.10* |
11.262 1 |
0.082 5 |
100 |
Na+aq. |
|
25Mg |
|
−0.855 4
|
+ |
0.22 |
2.605 4 |
0.002 67 |
10.13 |
Mg2+ aq. |
|
27Al |
|
+3.641 3 |
+ |
0.149* |
11.094 0 |
0.206 |
100 |
[Al(H2O)6]3+ |
|
29Si |
|
−0.555 26 |
|
— |
8.457 8 |
0.007 84 |
4.70 |
Me4Si |
|
31P |
|
+1.130 5 |
|
— |
17.235 0 |
0.066 3 |
100 |
85%
H3PO4 |
|
33S |
|
+0.643 5 |
− |
0.064 |
3.265 4 |
0.002 26 |
0.76 |
CS2 or
SO42− |
|
35Cl |
|
+0.821 81 |
− |
0.10* |
4.171 7 |
0.004 7 |
75.53 |
Cl–aq. |
|
36Cl† |
2 |
+1.285 3 |
− |
0.021* |
4.893 1 |
0.012 1 |
— |
— |
|
37Cl |
|
+0.684 07 |
− |
0.079* |
3.472 |
0.002 71 |
24.47 |
Cl−aq. |
|
39K |
|
+0.391 47 |
+ |
0.049* |
1.986 4 |
5.08 × 10− 4 |
93.10 |
K+ aq. |
|
40K† |
4 |
−1.298 1
|
− |
0.061* |
2.470 |
0.005 21 |
0.011
8 |
— |
|
41K |
|
−0.214 87 |
+ |
0.067* |
1.090 3 |
8.40 × 10− 5 |
6.88 |
K+ aq. |
|
43Ca |
 |
−1.317 2
|
|
0.2 |
2.865 4 |
0.006 40 |
0.145 |
Ca2+aq. |
|
45Sc |
|
+4.755 9 |
− |
0.22 |
10.343 4 |
0.301 |
100 |
Sc(ClO4)3aq. |
|
47Ti |
|
−0.788 46 |
+ |
0.29 |
2.399 7 |
0.002 09 |
7.28 |
TiF62− /48%HFaq. |
|
49Ti |
|
−1.104 14 |
+ |
0.24 |
2.400 4 |
0.003 76 |
5.51 |
TiF62− /48%HFaq. |
|
50V |
6 |
+3.347 0 |
|
— |
4.245 0 |
0.055 5 |
0.24 |
— |
|
51V |
|
+5.148 5 |
− |
0.05 |
11.192 2 |
0.382 |
99.76 |
VOCl3 neat |
|
53Cr |
|
−0.474 4
|
+ |
0.03 |
2.406 3 |
9.03 × 10− 4 |
9.55 |
CrO42− |
|
55Mn |
|
+3.468 0 |
+ |
0.55 |
10.501 0 |
0.175 |
100 |
KMnO4aq. |
|
57Fe |
|
+0.090 24 |
|
— |
1.375 8 |
3.37 × 10− 5 |
2.19 |
Fe(CO)5 |
|
59Co |
|
+4.616 3 |
+ |
0.40 |
10.072 |
0.277 |
100 |
[Co(CN)6]3−
aq. |
|
61Ni |
|
−0.749 8
|
+ |
0.16* |
3.804 8 |
0.003 57 |
1.19 |
Ni(CO)4 neat |
|
63Cu |
|
+2.222 6 |
− |
0.211* |
11.284 7 |
0.093 1 |
69.09 |
[Cu(CN)4]3−
|
|
65Cu |
|
+2.384 9 |
− |
0.195* |
12.089 0 |
0.114 |
30.91 |
[Cu(CN)4]3−
|
|
67Zn |
|
+0.875 6 |
+ |
0.15 |
2.661 8 |
0.002 85 |
4.11 |
Zn2 + aq. |
|
69Ga |
|
+2.016 1 |
+ |
0.178 |
10.218 8 |
0.069 1 |
60.40 |
[Ga(H2O)6]3+ |
|
71Ga |
|
+2.561 7 |
+ |
0.112 |
12.984 0 |
0.142 |
39.60 |
[Ga(H2O)6]3+ |
|
73Ge |
 |
−0.879 18 |
− |
0.18 |
1.485 2 |
0.001 40 |
7.76 |
GeCl4 neat |
|
75As |
|
+1.439
|
+ |
0.29 |
7.291 9 |
0.025 1 |
100 |
KAsF6 |
|
77Se |
|
+0.532 5 |
|
— |
8.128 4 |
0.006 93 |
7.58 |
Me2Se |
|
79Br |
|
+2.105 5 |
+ |
0.37* |
10.667 0 |
0.078 6 |
50.54 |
Br−aq. |
|
81Br |
|
+2.269 6 |
+ |
0.31* |
11.498 0 |
0.098 5 |
49.46 |
Br−aq. |
|
83Kr |
|
−0.970 3 |
+ |
0.26 |
1.638 3 |
0.001 88 |
11.55 |
— |
|
85Rb |
|
+1.352 7 |
+ |
0.26* |
4.110 8 |
0.010 5 |
72.15 |
Rb+aq. |
|
87Rb |
|
+2.750 6 |
+ |
0.13* |
13.931 3 |
0.175 |
27.85 |
Rb+aq. |
|
87Sr |
|
−1.093 |
+ |
0.36 |
1.845 1 |
0.026 9 |
7.02 |
Sr2+aq. |
|
89Y |
|
−0.137 33 |
|
— |
2.086 0 |
1.18 × 10− 4 |
100 |
Y(NO3)3aq. |
|
91Zr |
|
−1.302 84 |
|
— |
3.972 5 |
0.009 48 |
11.23 |
— |
|
93Nb |
|
+6.167 |
− |
0.22 |
10.406 8 |
0.482 |
100 |
NbF6−/48%HFaq. |
|
95Mo |
|
−0.913 5 |
|
0.12 |
2.773 8 |
0.003 23 |
15.72 |
MoO42− |
|
97Mo |
|
−0.932 7 |
|
1.1 |
2.832 1 |
0.003 43 |
9.46 |
MoO42− |
|
99Tc† |
|
+5.681 |
+ |
0.3 |
9.583 2 |
0.376 |
— |
TcO4– aq. |
|
99Ru |
|
−0.643 0 |
|
— |
1.960 7 |
1.95 × 10− 4 |
12.72 |
K4[Ru(CN)6]aq. |
|
101Ru |
|
−0.720 7 |
|
— |
2.197 5 |
0.001 41 |
17.07 |
— |
|
103Rh |
|
−0.087 9 |
|
— |
1.340 1 |
3.11 × 10− 5 |
100 |
mer
[RhCl3(SMe2)3] |
|
105Pd |
|
−0.642 |
+ |
0.8 |
1.892 1 |
0.001 12 |
22.23 |
— |
|
107Ag |
|
−0.113 5 |
|
— |
1.723 0 |
6.62 × 10− 5 |
51.82 |
— |
|
109Ag |
|
−0.130 5 |
|
— |
1.980 8 |
1.01 × 10− 4 |
48.18 |
Ag+aq. |
|
111Cd |
|
−0.595 00 |
|
— |
9.028 3 |
0.009 54 |
12.75 |
CdMe2 neat |
|
113Cd |
|
−0.619 50 |
|
— |
9.444 1 |
0.010 9 |
12.26 |
CdMe2 neat |
|
113In |
|
+5.522 9 |
+ |
1.14 |
9.310 1 |
0.345 |
4.28 |
[In(H2O)6]3+ |
|
115In† |
|
+5.534 8 |
+ |
1.16 |
9.330 1 |
0.347 |
95.72 |
— |
|
115Sn |
|
−0.917 8 |
|
— |
13.922 |
0.035 0 |
0.35 |
— |
|
117Sn |
|
−0.999 9 |
|
— |
15.168 |
0.045 2 |
7.61 |
— |
|
119Sn |
|
−1.040 9 |
|
— |
15.876 8 |
0.051 8 |
8.58 |
Me4Sn |
|
121Sb |
|
+3.359 2 |
− |
0.28 |
10.188 4 |
0.160 |
57.25 |
SbCl6− |
|
123Sb |
|
+2.546 6 |
− |
0.36 |
5.517 6 |
0.045 7 |
42.75 |
SbCl6− |
|
123Te |
|
−0.735 9 |
|
— |
11.159 |
0.018 0 |
0.87 |
— |
|
125Te |
|
−0.882 4 |
|
— |
13.453 |
0.031 5 |
6.99 |
Me2Te |
|
127I |
|
+2.809 1 |
− |
0.69 |
8.518 3 |
0.093 4 |
100 |
I–aq. |
|
129I† |
|
+2.617 4 |
− |
0.48 |
5.669 4 |
0.049 6 |
— |
— |
|
129Xe |
|
−0.772 5 |
|
— |
11.776 9 |
0.021 2 |
26.44 |
XeOF4 |
|
131Xe |
|
+0.690 8 |
− |
0.12 |
3.491 1 |
0.002 76 |
21.18 |
— |
|
133Cs |
|
+2.578 8 |
− |
0.003 0* |
5.584 69 |
0.047 4 |
100 |
Cs+aq. |
|
135Ba |
|
+0.837 2 |
+ |
0.18 |
4.229 5 |
0.004 90 |
6.59 |
Ba2+aq. |
|
137Ba |
|
+0.936 5 |
+ |
0.28 |
4.731 4 |
0.006 86 |
11.32 |
Ba2+aq. |
|
138La |
5 |
+3.704 |
|
0.51* |
5.617 1 |
0.091 9 |
0.089 |
— |
|
139La |
|
+2.778 |
+ |
0.22* |
6.014 4 |
0.059 2 |
99.91 |
— |
|
141Pr |
|
+4.160 |
− |
0.058 |
13.0 |
0.293 |
100 |
— |
|
143Nd |
|
−1.063 |
− |
0.48 |
2.303 |
0.003 38 |
12.17 |
— |
|
145Nd |
|
−0.654 |
− |
0.25 |
1.414 |
7.86 × 10− 4 |
8.30 |
— |
|
147Sm |
|
−0.813 |
− |
0.18 |
1.72 |
0.001 48 |
14.97 |
— |
|
149Sm |
|
−0.670 |
+ |
0.052 |
1.39 |
7.47 × 10− 4 |
13.83 |
— |
|
151Eu |
|
+3.466 |
+ |
1.16 |
10.559 |
0.178 |
47.82 |
— |
|
153Eu |
|
+1.530 |
+ |
2.9 |
4.662 7 |
0.015 3 |
52.18 |
— |
|
155Gd |
|
−0.258 4 |
+ |
1.6 |
1.4 |
2.79 × 10− 4 |
14.73 |
— |
|
157Gd |
|
−0.338 8 |
+ |
1.7 |
1.9 |
5.44 × 10− 4 |
15.68 |
— |
|
159Tb |
|
−2.008 |
+ |
1.3* |
9.66 |
0.058 3 |
100 |
— |
|
161Dy |
|
−0.482 |
+ |
2.4* |
1.39 |
4.17 × 10− 4 |
18.88 |
— |
|
163Dy |
|
+0.676 |
+ |
2.5* |
1.94 |
0.001 2 |
24.97 |
— |
|
165Ho |
|
+4.12 |
+ |
2.82 |
8.73 |
0.181 |
100 |
— |
|
167Er |
|
-0.569 |
+ |
2.83 |
1.23 |
5.07 × 10− 4 |
22.94 |
— |
|
169Tm |
|
−0.230 9 |
— |
3.521 9 |
5.66 × 10− 4 |
100 |
— |
|
171Yb |
|
+0.491 8 |
— |
7.498 9 |
0.005 46 |
14.31 |
— |
|
173Yb |
|
−0.679 1 |
+ |
2.8 |
2.065 9 |
0.001 33 |
16.13 |
— |
|
175Lu |
|
+2.230 |
+ |
5.68 |
4.818 9 |
0.031 2 |
97.41 |
— |
|
176Lu† |
7 |
+3.180 |
+ |
8.0 |
3.39 |
0.037 2 |
2.59 |
— |
|
177Hf |
|
+0.790 2 |
+ |
4.5* |
1.3 |
6.38 × 10− 4 |
18.50 |
— |
|
179Hf |
|
−0.638 |
+ |
5.1* |
0.80 |
2.16 × 10− 4 |
13.75 |
— |
|
181Ta |
|
+2.35 |
+ |
3* |
5.096
3 |
0.036 |
99.988 |
TaF6− in
HF/HNO3 |
|
183W |
|
+0.116 9 |
— |
1.771 6 |
7.20 × 10− 5 |
14.40 |
WF6 neat |
|
185Re |
|
+3.172 |
+ |
2.8 |
9.585 5 |
0.133 |
37.07 |
ReO4−aq. |
|
187Re† |
|
+3.204 |
+ |
2.6 |
9.683
7 |
0.137 |
62.93 |
ReO4−aq. |
|
187Os |
|
+0.064 3 |
— |
0.980
59 |
1.22 × 10− 5 |
1.64 |
OsO4 |
|
189Os |
|
+0.656 5 |
+ |
0.8* |
3.303
4 |
0.002 34 |
16.10 |
OsO4 |
|
191Ir |
|
+0.145 4 |
+ |
1.1 |
0.731
8 |
2.53 × 10− 5 |
37.30 |
— |
|
193Ir |
|
+0.158 3 |
+ |
1.0 |
0.796
8 |
3.27 × 10− 5 |
62.70 |
— |
|
195Pt |
|
+0.600 4 |
— |
9.152
3 |
0.009 94 |
33.80 |
[Pt(CN)6]2− |
|
197Au |
|
+0.144 86 |
+ |
0.59 |
0.741
2 |
2.51 × 10− 5 |
100 |
— |
|
199Hg |
|
+0.497 8 |
— |
7.612 |
0.005 67 |
16.84 |
Me2Hg neat |
|
201Hg |
|
−0.558 30 |
+ |
0.50 |
2.810
0 |
0.001 44 |
13.22 |
Me2Hg neat |
|
203Tl |
|
+1.611 5 |
— |
24.332 |
0.187 |
29.50 |
— |
|
205Tl |
|
+1.611 6 |
— |
24.567 |
0.192 |
70.50 |
TlNO3aq. |
|
207Pb |
|
+0.584 3 |
— |
8.907
1 |
0.009 16 |
22.60 |
Me4Pb |
|
209Bi† |
|
+4.080 |
− |
0.38 |
6.841
78 |
0.137 |
100 |
— |
|
235U† |
|
−0.43 |
+ |
4.9 |
0.75 |
1.21 × 10− 4 |
0.72 |
— |
| |
|
|
|
|
|
|
|
References
(1) G. H. Fuller (1976) J. Phys. Chem. Ref. Data 5,
835.
(2) R. K. Harris and B. E. Mann (eds) (1978) NMR and the Periodic
Table, Academic Press.
J.G.E.Phillips
|
