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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/ high-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 Hartree-Fock B3LYP 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/ high-energy conformer n-butane anti/gauche 84 1-butene Hartree-Fock 6-31G* 6-311+G** 79 B3LYP 6-31G* 6-311+G** 79 MP2 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. chemical reaction "high-energy process" E 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 + 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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