First chemical reactions typically have activation

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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 carbon-carbon 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 carbon-carbon bond in ethane must accordingly repeat itself at 120o intervals. One possibility is a single-term 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 single-term 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 (one-fold) term accounts for the difference in energy between 0° and 180° arrangements, the second (two-fold) term accounts for the difference in energy between 0° (180°) and 90° (270°) conformers, and the third (three-fold) 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 one-fold terms in the Fourier series for both n-butane and 1,2-difluoroethane 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 [1-cos(CCCC)] -2 [1-cos2(CCCC)] -8 [1-cos3(CCCC)] E(FCCF) = -8 [1-cos(FCCF)] -7 [1-cos2(FCCF)] -9 [1-cos3(FCCF)] For n-butane, the anti preference likely reflects the need to minimize crowding of methyl groups, whereas for 1,2-difluoroethane 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 dipole-dipole 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 n-butane and 1,2-difluoroethane, 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 n-butane and all three terms contribute roughly equally to the fit for 1,2-difluoroethane. 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 non-bonded electron pair) from 0 to 360o gives rise to three energy minima. The lowest-energy 7 (anti) minimum corresponds to a dihedral angle of 180o and the two equivalent higher-energy (gauche) minima correspond to dihedral angles around 45o and 315o. This energy curve is qualitatively similar to that for n-butane, 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 n-butane. Also, the FCN: dihedral angles in the gauche conformers for fluoromethylamine differ from the idealized (staggered) values found in n-butane (~60o and ~300o). Finally, all three terms in the Fourier series for fluoromethylamine make sizable contributions, with the two-fold term (which makes only a modest contribution for n-butane) actually being the major contributor. E(FCN:) = -4 [1-cos(FCN:)] + 6 [1-cos2(FCN:)] -5 [1-cos3(FCN:)] Plots of the individual Fourier components provide clues to the overall shape of the energy curve. one-fold two-fold three-fold The one-fold 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 Head-gordon during the Spring '09 term at Berkeley.

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