The Journal of Organic Chemistry
ARTICLE
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(28) One can estimate the force constant for bending the HCC bond
angle by carrying out successive B3LYP/6-31G(d) partial optimizations
on ethanol, in which CS symmetry is maintained, and all geometric
parameters except the HCC bond angle are allowed to vary, but the
HCC angle for the H atom anti to the oxygen is forcibly compressed in
2° increments until 30° of distortion is achieved. Fitting to a simple parabola
(Hooke’s Law) then yields a force constant of 0.0179 hartree/deg.2 An
analogous procedure yields a force constant of 0.0363 hartree/deg2 for
compressing the OCC bond angle. Using this approach thus yields a ratio of
2.02 for the bending force constants of OCC and HCC bond angles.
(29) For instance, when the methoxy group goes from a syn to an anti
orientation with respect to the carbene lone pair, the CC-OC bond
length increases from 1.409 to 1.418 Å. Similarly, a natural bond orbital
(NBO) analysis shows that the donation from the carbon (carbene) lone
pair into the C-O antibonding orbital increases from 4.2 to 10.5 kcal/mol
(B3LYP/aug-cc-pVTZ//CCSD/6-31G(d) NBO analysis).
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(30) The atomic charges were computed at B3LYP/aug-cc-pVTZ//
CCSD/6-31G(d), using Weinhold’s NPA procedure. While the carbon
in question does become less negative, as expected from the resonance
structure in Scheme 5, the migrating group does not become more negative.
Instead, it is the other carbon atom that increases in negative charge.
(31) We thank our associate editor, Professor Daniel Singleton, for
alerting us to this possibility during the review process.
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(34) For a review of this and other methods of including a simulated
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dx.doi.org/10.1021/jo1020536 |J. Org. Chem. 2011, 76, 1584–1591