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420 12MAGNETIC RESONANCE
0 30 60 90 120 150 180
0
5
10
15
ϕ/○
3 J
H
H
/H
z
B = −2 Hz
B = −1 Hz
B = −0.1 Hz
Figure 12.7
(a) �e Karplus equation for 3 JHH is a linear equation in cos ϕ and cos 2ϕ,
and the experimentally determined equation for 3 JSnSn is linear in 3 JHH.
If F( f ) is linear in f , and f (x) is linear in x, it follows that F(x) is also
linear in x.�erefore 3 JSnSn is a linear equation in cos ϕ and cos 2ϕ.
(b) Substitution of theKarplus equation for 3 JHH into the expression for 3 JSnSn
gives a Karplus-type expression for the latter.
(3 JSnSn/Hz) = 78.86 × (3 JHH/Hz) + 27.84
= 78.86 × (A+ B cos ϕ + C cos 2ϕ) + 27.84
= (78.86A+ 27.84) + 78.86B cos ϕ + 78.86C cos 2ϕ
= A′ + B′ cos ϕ + C′ cos 2ϕ
Taking the values A = 7 Hz, B = −1 Hz, and C = 5 Hz from the text
gives the parameters in this new Karplus-type equation as (A′/Hz) =
78.86×(7)+27.84 = 580, (B′/Hz) = 78.86×(−1) = −78.9, and (C′/Hz) =
78.86 × (5) = 394. �us, the Karplus-type equation for the Sn–Sn cou-
plings is
(3 JSnSn/Hz) = 580 − 78.9 cos ϕ + 394 cos 2ϕ
A plot of 3 JSnSn as a function of ϕ is shown in Fig. 12.8.
(c) A staggered conformation with the SnMe3 groups trans to each other
(ϕ = 180○) is the preferred arrangement as this minimised the steric
repulsion between the bulky SnMe3 groups.
SnMe3
SnMe3
H
H
H
H