Enrichment of 73Ge with the Magnetic Isotope Effect
J. Am. Chem. Soc., Vol. 120, No. 13, 1998 3229
involves a 73Ge-centered radical. Thus, the T(1-S conversion
of RPm is not blocked at B ) B1 as shown by case B of Figure
2. The δ(73Ge) value at B ) B1, therefore, becomes larger
than that at B ) 0 G. With increasing B from B1, a gradual
blocking of the T(1-S conversion starts to occur for RPm. Thus,
δ(73Ge) value starts to decrease with increasing B from B1.
Finally, the decrease in the δ value is saturated at B ) B2 ≈
2B1/2* as shown by case C of Figure 2. The magnetic field
dependence of the δ(73Ge) value due to the HFCM, therefore,
can be summarized as follows: The δ value increases with
increasing B (0 G e B e B1), attaining the maximum value at
B ) B1 (≈2B1/2). With increasing B from B1, the δ value
decreases, becoming saturated at B ) B2 (≈2B1/2*) as shown
in Figure 2a.
Figure 1. Magnetic field dependence of the relative isotope enrichment
δ(ZGe): open circles, δ(72Ge); filled circles, δ(73Ge). After photolysis
of SDS micellar solutions containing benzophenone (BP) and trieth-
ylgermane (Et3GeH) under 95% conversion in the magnetic field range
of 0-10 kG.
In the present reaction, the B1/2 value of RPn is calculated to
be 18.3 G with the reported hyperfine coupling constants (aCH
3
) 0.56 G and aCH ) 4.75 G for Et3Ge• 19 and ao ) 3.21 G, am
2
) 1.23 G, ap ) 3.64 G, and aOH ) 2.91 G for BPH• 20). On
the other hand, the hyperfine coupling constant of 73Ge of
Et3Ge• has not yet been reported, but it seems to be similar to
that of the trimethylgermyl radical which has been reported to
be 84.7 G.21 Using this value, we estimate the B1/2* value of
RPm to be 828 G. Therefore, if the blocking of the T(1-S con-
version occurs through the HFCM, the δ(73Ge) value is ex-
pected to attain the maximum value around 40 G (≈B1), but
the decrease of the δ(73Ge) value is expected to be saturated
around 1.7 kG (≈B2). In the present study, however, the
maximum δ(73Ge) value was obtained at 500 G and the decrease
of the δ value was not saturated even at 10 kG as shown in
Figure 1. Thus, the magnetic field dependence observed for
the δ value in the present reaction cannot be explained by the
HFCM.
On the other hand, according to the RM, the T(1-S con-
version through the RM occurs by the anisotropic HFCs. In
this mechanism, the T(1-S conversion rates of RPn and RPm
decrease gradually with increasing B from 0 G, but their
conversion should not be blocked at B1 and B2, respectively.
However, with increasing B from B1, the T(1-S conversion of
RPn should be almost blocked at B ) B1′ > B1 as shown by
case D of Figure 2, because the T(1-S conversion rate of RPn
becomes negligible at B ) B1′. At this stage, the T(1-S
conversion of RPm is not blocked as shown by case E of Fig-
ure 2. Thus, the δ value increases with increasing B from 0 G
to B1′ as shown in Figure 2b. At higher fields (B > B1′), a
gradual blocking of the T(1-S conversion also starts to occur
for RPm. Thus, the δ value starts to decrease with increasing
B from B1′ as shown in Figure 2b. Finally, the T(1-S
conversion of RPm is almost blocked at B ) B2′ > B2 as shown
by case F of Figure 2.
The observed δ(73,72Ge) values are plotted against the magnetic
field strength (B) in Figure 1. Here, the δ(72Ge) value shows
no appreciable change beyond the experimental error. With
increasing B from 0 to 500 G, however, the δ(73Ge) value
increases initially, attaining the maximum value of (5.3 ( 0.3)%
at 500 G. With increasing B from 500 G to 10 kG, the
δ(73Ge) value decreases gradually, becoming (1.0 ( 0.3)% at
10 kG. The magnetic field dependence of the isotope enrich-
ment of 73Ge shown in this figure is strong evidence for the
enrichment by the MIE.
The observed magnetic field dependence of the isotope en-
richment of 73Ge can be explained by the blocking of the T(1-S
conversion by external magnetic fields. Such MFEs on the
T(1-S conversion occur through the hyperfine coupling mech-
anism (HFCM)1,2,4,5 and the relaxation mechanism (RM).17
Figure 2 schematically shows the energy diagram of singlet and
triplet radical pairs and the magnetic field dependence of the
isotope enrichment (δ) expected for the T(1-S conversion
through the HFCM and RM. Here, RPn represents a radical
pair involving a nonmagnetic 70Ge, 72Ge, 74Ge, or 76Ge and RPm
that involving a magnetic 73Ge.
According to the HFCM, the half-saturation field (B1/2) of
the MFE is given as follows:18
2
B1/2 ) 2(A12 + A2 )/(A1 + A2)
(4)
The individual Ai value characterizing the radical (i ) 1, 2) is
given by
2 1/2
A ) ( I (I + 1)a )
(5)
∑
i
ij ij
ij
j
In the present study, the magnetic fields of B1′ and B2′ cannot
be calculated exactly, because the anisotropic HFCs of Et3Ge•
and BPH• have never been observed. However, the magnetic
field dependence of the isotope enrichment observed for the
present reaction can qualitatively be explained by the RM for
the following reasons: (1) Since the radical pair generated in
the present reaction involves the triethylgermyl radical, the
anisotropic HFC of 73Ge seems to be fairly large. (2) The
maximum δ(73Ge) value was obtained at 500 G which is much
larger than that (40 G) expected from the HFCM. (3) The
decrease of the δ value was not saturated even at 10 kG. Thus,
Here, aij is the isotropic hyperfine coupling constant of the jth
nuclei in radical i. In Figure 2a, the half-saturation fields of
the MFEs of RPn and RPm are represented by B1/2 and B1/2*,
respectively. At zero field, since the triplet and singlet radical
pairs are degenerate, the T-S conversions of both RPn and RPm
occur. Because the T-S conversion of RPm is much faster than
that of RPn as mentioned above, the enrichment of 73Ge is
observed for the cage product. An increase of B from 0 G to
B1 (≈2B1/2) primarily affects RPn, in which its T(1-S con-
version is induced by small aij values of protons. Therefore,
the T(1-S conversion of RPn is almost blocked at B ) B1 ≈
2B1/2 as shown by case A of Figure 2. In RPm, however, the
B1/2* value is much larger than the B1/2 value, because RPm
(19) Sakurai, H.; Mochida, K.; Kira, M. J. Am. Chem. Soc. 1975, 97,
929.
(20) Bowers, P. R.; McLauchlan, K. H.; Sealy, R. C. J. Chem. Soc.,
Perkin Trans. 2 1976, 72, 915.
(17) Hayashi, H.; Nagakura, S Bull. Chem. Soc. Jpn. 1984, 57, 322.
(18) Weller, A.; Nolting, F.; Staerk, H. Chem. Phys. Lett. 1983, 96, 24.
(21) Lloyd, R. V.; Rogers, M. T. J. Am. Chem. Soc. 1973, 95, 2459.