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Unformatted text preview: d MP2 models
with the cc-pVQZ basis set with experimental distributions. All molecules
are very small and have only two stable conformers. Aside from practical
concerns dealing with the calculations, it should be noted that reliable
experimental data are typically available only for very simple molecules.
Discussion … 30 Table P5-1: Room Temperature Boltzmann Conformer Ratios from “Limiting”
Hartree-Fock, B3LYP and MP2 Models molecule low energy/
conformer n-butane anti/gauche 85 82 72 76 1-butene skew/cis 74 66 54 59 trans/gauche 100 100 99 99 acrolein trans/cis 98 97 97 95 n-methyl formamid e cis/trans 82 83 89 92 1,3-butadiene formic acid % low-energy conformer
MP2 expt. cis/trans 100 100 100 100 1,2-difluoroethane gauche/anti 60 81 78 72 1,2-dichloroethane anti/gauche 96 94 91 86 ethanol anti/gauche 60 49 53 55 methylcyclohexane equatorial/axial 98 99 95 95 fluorocyclohexane equatorial/axial 57 62 51 57 chlorocyclohexane equatorial/axial 84 82 60 70 2-chlorotetrahydropyran axial/equatorial 98 100 100 95 31 Behavior of Practical Hartree-Fock, B3LYP and MP2 Models for
Assigning Lowest-Energy Conformation and Accounting for RoomTemperature Conformer Distributions
Except for very small molecules, Hartree-Fock, B3LYP and MP2 models
with large basis sets such as cc-pVQZ and cc-pVTZ are not currently
practical. These (and even larger) basis sets are primarily of value in
judging the limits of the underlying models. Two smaller Gaussian basis sets
will be examined, 6-311+G** and 6-31G*. The latter may be routinely
applied to molecules with weights up to 400-500 amu, while the former is
restricted to molecules with weights up to 300-400 amu.
Table P5-2 compares room-temperature conformer distributions for a
variety of molecules calculated from Hartree-Fock, B3LYP and MP2 models
with the 6-31G* and 6-311+G** basis sets with experimental distributions.
The same set of molecules used previously to uncover the limiting behavior
of the three models are examined here.
Discussion … 32 Table P5-2: Room Temperature Boltzmann Conformer Ratios from Practical
Hartree-Fock, B3LYP and MP2 Models molecule low energy/
conformer n-butane anti/gauche 84 1-butene Hartree-Fock
6-31G* 6-311+G** expt. 82 76 70 76 skew/cis 76 67 67 67 70 70 59 trans/gauche 99 100 100 100 99 99 99 acrolein trans/cis 95 97 95 98 93 98 95 n-methyl formamide cis/trans 86 86 76 84 84 88 92 formic acid cis/trans 100 100 100 100 100 100 100 1,2-difluoroethane gauche/anti 30 58 67 79 30 79 72 1,2-dichloroethane anti/gauche 96 96 95 94 96 92 86 1,3-butadiene ethanol anti/gauche 54 63 37 50 54 50 55 methylcyclohexane equatorial/axial 98 98 97 98 96 95 95 fluorocyclohexane equatorial/axial 37 54 42 58 24 54 57 chlorocyclohexane equatorial/axial 84 82 82 76 76 70 70 2-chlorotetrahydropyran axial/equatorial 99 99 100 100 99 99 95 33 Identifying the “Important” Conformer
Up to this point in the chapter, we have assumed that the “important”
conformer is the lowest-energy conformer. This is appropriate if what is of
interest is the property of a system at equilibrium or the product of a reaction
under thermodynamic control. More generally, a Boltzmann average of all
conformers needs to be constructed, although in practice conformers with
energies more than about 10 kJ/mol above the lowest-energy conformer will
not contribute significantly to the average at normal temperatures.
There are, however, situations where the important conformer will not
necessarily be the lowest-energy conformer, at least the lowest-energy
conformer of the isolated molecule. Conformational equilibrium may be
influenced by environmental factors, for example, molecules in crystalline
solids or small molecules bonded to proteins. Here, changes in conformation
from those preferred by the isolated molecule may be necessary to ensure
effective crystal packing or to reflect specific interactions with a protein. For
example, according to 6-31G* calculations, the lowest-energy conformer of
the anti breast cancer drug gleevec (shown as a tube model) is quite different
from the conformer found in the protein (ball-and spoke model). Another situation is where the “important” refers to chemical reactivity for a
process under kinetic control rather than thermodynamic control (see
discussions in Chapter P4). A simple example is provided by the DielsAlder cycloaddition of 1,3-butadiene with acrylonitrile.
CN CN As detailed earlier in the chapter, 1,3-butadiene exists primarily in a trans
conformation with the cis conformer being approximately 8 kJ/mol less
stable. This means that (at room temperature) only about 5% of butadiene
molecules will be in a cis conformation and able to react. The fact that the
34 reaction does occur is a consequence the Curtin-Hammett Principle. This
states that because energy barriers separating conformers (typically 4-30
kJ/mol) are much smaller than those for chemical reaction (typically 100200 kJ/mol), conformers reach equilibrium much more rapidly than they
react. In the case of the Diels-Alder reaction, equilibration between the
higher-energy cis conformer and the lower-energy trans conformer is much
faster and will be replenished throughout the reaction.
equilibration among conformers
"low-energy process" While it is clear that the products of kinetically-controlled reactions do not
necessarily derive from the lowest-energy conformer, the identity of the
reactive conformer is not evident. One reasonable hypothesis is that this is
the conformer which is best “poised to react”, that is, the conformer that
initially results from progression backward along the reaction coordinate
starting from the transition state.
Rates of Diels-Alder Reactions: 1,3-butadiene undergoes Diels-Alder cycloaddition
with acrylonitrile more slowly than does cyclopentadiene.
+ CN CN
+ Is this simply a consequence of the fact that, whereas the double bonds in
cyclopentadiene are properly disposed for reaction, additional energy is needed to move
from the favored trans conformer of butadiene to a cis (or nearly cis) conformer?
Alternatively, is cyclopentadiene inherently more electron rich than butadiene and,
therefore, a more reactive diene?
Use the HF/6-31G* model to establish the energy difference between the trans and
(nearly) cis conformers of 1,3-butadiene.
Use the 6-31G* model to obtain transition state geometries for Diels-Alder reactions of
both 1,3-butadiene and cyclopentadiene with acrylonitrile, and then the 6-31G* model to
obtain energies. Calculate activation energies for the two reactions using these data
(along with energies for the reactants obtained in the previous step). Is your result in
accord with the observation that the reaction with cyclopentadiene is faster? Is the 35 difference in activation energies between the two reactions of comparable magnitude to
the difference in energies between trans and (nearly) cis-1,3-butadiene?
Obtain electrostatic potential maps for cis-1,3-butadiene and cyclopentadiene, and
display side-by-side using the same color scale. Which appears to be the more reactive
diene? Explain your reasoning. Is your result consistent with the previous comparison of
activation energy conformer energy differences? Elaborate. 36...
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- Spring '09