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Unformatted text preview: a “normal” chemical
reaction. First, chemical reactions typically have activation energies in the range of 100
to 300 kJ/mol, whereas the energy required for conformational change is almost always
much smaller (on the order of a few to a few tens of kJ/mol). Second, with the notable
exception of constrained rotation in rings, the reaction coordinate for conformational
change is most often (but not always) well described in terms of a single recognizable
geometrical coordinate, most commonly a torsion angle. The reaction coordinate for a
normal reaction typically involves several geometrical coordinates changing in concert. 5 Interpreting Conformational Energy Profiles
The energy profile for rotation about a single bond repeats itself in 360o. In
fact, for many simple molecules, the rotation profile repeats itself in a
fraction of 360o, typically 120o or 180o. For example, the energy profile for
rotation about the carboncarbon bond in ethane repeats itself in 120o, and
full 360° rotation yields three identical energy minima and three identical
energy maxima. Any description of rotation about the carboncarbon bond in ethane must
accordingly repeat itself at 120o intervals. One possibility is a singleterm
Fourier series.
Etorsion (!) = ktorsion3 [1  cos 3 (!  !eq )] Etorsion(ω) is the energy as a function of the torsion angle, ω (HCCH dihedral
angle in the case of ethane), ωeq is the ideal torsion angle and ktorsion3 is a
parameter. A singleterm Fourier series will not suffice for most molecules,
as it will also be necessary to account for terms that repeat themselves in
intervals of 180o and 90o.
Etorsion (!) = ktorsion1 [1  cos (!  !eq )] + ktorsion2 [1  cos 2 ( !  !eq )]
+ ktorsion3 [1  cos 3 (!  !eq )] ktorsion1 and ktorsion2 are additional parameters. Here, the first (onefold) term
accounts for the difference in energy between 0° and 180° arrangements, the
second (twofold) term accounts for the difference in energy between 0°
(180°) and 90° (270°) conformers, and the third (threefold) term accounts
for the difference in energy between 0° (120o, 240o) and 60o (180o, 300o)
conformers. 6 A Fourier series truncated to any order is an orthogonal polynomial. This
means that the individual terms are linearly independent, and each may be
interpreted on its own. For example, the onefold terms in the Fourier series
for both nbutane and 1,2difluoroethane may be interpreted solely in terms
of a preference for the anti arrangements (CCCC and FCCF dihedral angles
of 180o) over syn arrangements (dihedral angles of 0o), irrespective of any
other factors that may contribute to the overall energy profiles.
E(CCCC) = 5 [1cos(CCCC)] 2 [1cos2(CCCC)] 8 [1cos3(CCCC)]
E(FCCF) = 8 [1cos(FCCF)] 7 [1cos2(FCCF)] 9 [1cos3(FCCF)] For nbutane, the anti preference likely reflects the need to minimize
crowding of methyl groups, whereas for 1,2difluoroethane it likely reflects
the need to reduce interactions of CF bond dipoles (fluorine is actually
smaller than hydrogen). A chemist might refer to these preferences as due to
steric and dipoledipole effects, respectively.
CH3 CH3 CH3 F VS. CH3
"crowded" "not crowded" F F VS. bond dipoles add F
bond dipoles cancel Even for molecules as simple as nbutane and 1,2difluoroethane, more than
one term may contribute significantly to the Fourier series (and to the
resulting conformational preferences). For example, two terms contribute
strongly to the Fourier fit for nbutane and all three terms contribute roughly
equally to the fit for 1,2difluoroethane. In such cases, examination of the
individual terms may provide the insight needed to understand a complex
energy profile. A good example is provided by the energy curve for rotation
about the CN bond in fluoromethylamine. Variation of the FCN: dihedral angle (: designates the nonbonded electron
pair) from 0 to 360o gives rise to three energy minima. The lowestenergy
7 (anti) minimum corresponds to a dihedral angle of 180o and the two
equivalent higherenergy (gauche) minima correspond to dihedral angles
around 45o and 315o. This energy curve is qualitatively similar to that for nbutane, although there
are significant quantitative differences. For one, the difference in energy
between anti and gauche conformers in fluoromethylamine is much larger
than the corresponding difference in nbutane. Also, the FCN: dihedral
angles in the gauche conformers for fluoromethylamine differ from the
idealized (staggered) values found in nbutane (~60o and ~300o). Finally, all
three terms in the Fourier series for fluoromethylamine make sizable
contributions, with the twofold term (which makes only a modest
contribution for nbutane) actually being the major contributor.
E(FCN:) = 4 [1cos(FCN:)] + 6 [1cos2(FCN:)] 5 [1cos3(FCN:)] Plots of the individual Fourier components provide clues to the overall shape
of the energy curve. onefold twofold threefold The onefold term reflects the desire to arrange the dipoles associated with
the CF bond and the lone pair su...
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This note was uploaded on 02/22/2010 for the course CHEM N/A taught by Professor Headgordon during the Spring '09 term at Berkeley.
 Spring '09
 HEADGORDON

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