Storyboard:
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We seek to explain why RR,SS diasteromer is the
lowest of the four transition states involving
final ring opening (TS2) and corresponding to the
rate limiting step in the overall mechanism.
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The SS component (of RR,SS) comprises two
equatorial methyl groups. One of these exhibits a
close (attractive?) contact to the face of one aryl
ring: . Crystallographically, many examples are
known of approaches to within about 3.2Å
(measured between the ring centroid and the carbon
atom of the methyl), which matches the predicted
distance for this transition state. The other
S-methyl group of this lactide unit also approaches
the face of the other aryl ring, although here the
predicted contact is not so close (4.1Å):
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This di-equatorial arrangement also minimises
steric interactions between the two SS methyl
groups. In contrast, a RR configuration for these
methyls places them di-axial: . The difference in (total) energy between
the RRSS and RRRR diasteromers (4.0
kcal-1) quantifies the difference in the
sum of these two effects. The free energy
difference (ΔG298) of 1.4
kcal-1 agrees better with experiment. We
also note at this stage that a similar energy
difference occurs for the SSSS/SSRR pair (4.0
kcal-1 in total energy, 2.7 in
ΔG298).
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The stereochemistry of the RR lactide ring (of
RR,SS) is mediated by different interactions.
Firstly, steric repulsion between the two RR methyl
groups: . is avoided, whereas in the SS,SS isomer,
the repulsion is rather greater .
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Secondly, the RR configuration (of RR,SS) also
avoids a close contact between a methyl and an
isopropyl group: . whereas such contact cannot be avoided
with the SS configuration (of SS,SS): . These effects cumulatively amount to a
difference in the total energy of 6.2
kcal-1 (RRSS vs SSSS or RRRR vs SSRR)
and of 6.6 (RRSS vs SSSS) or 7.9 kcal-1
(RRRR vs SSRR) in ΔG298.
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In total energy, the various effects are almost
exactly additive, which means that the SS,RR isomer
is doubly disfavoured (10.2 kcal-1)
compared to the RR,SS configuration: .
The additivity is not so precise in
ΔG298 due to non-additivity in the
Rigid-Rotor-Harmonic-Oscillator approximation in
dealing with very low frequency contributions to
the entropy.
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Overall therefore, the tacticity is induced by a
possible attractive interaction between one methyl
and the face of any aryl ring, and avoidance of
repulsion between the two methyls of one lactide,
and between another methyl and one of the (four)
isopropyl substituents on one of the (two) aryl
rings.
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Total energies (Hartree)
[Corrected for ΔG298 (Hartree)]
{C-O cleaving bond length,Å} |
RRSS |
RRRR |
-2612.17812 [-2611.26219] {2.289} |
-2612.17174 [-2611.26002] {2.179} |
|
|
SSRR |
SSSS |
-2612.16180 [-2611.24743] {2.154} |
-2612.16815 [-2611.25173] {2.240} |
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