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p5_conformations - Chapter P5 Conformations of Molecules...

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1 Chapter P5: Conformations of Molecules Introduction Up to this point in the text, we have talked about molecular structure solely in terms of bond lengths and angles, for example, the experimental structure of water in terms of two OH bonds of 0.96 Ǻ and a HOH bond angle of 104.5 o . For most molecules with four or more atoms, an additional set of variables needs to be considered. These are torsional or dihedral angles. For example, description of the geometry of hydrogen peroxide, HOOH, requires specification not only of an OO bond length, two OH bond lengths and two HOO bond angles, but also the HOOH torsional angle. O O H H The torsional or dihedral angle ABCD is defined as the angle the normal to plane made by ABC and the normal to the plane made by BCD. Variation of the HOOH dihedral angle in hydrogen peroxide over the range of 0 to 360 o reveals two equivalent energy minima around 120 o and 240 o . While hydrogen peroxide exhibits only a single unique conformational isomer or conformer , for most molecules variation in dihedral angle over the full 360 o range gives rise to more than one distinct conformer. For example, variation of the CCCC dihedral angle in n -butane from 0 to 360 o gives rise to three conformers and two distinct conformers, an anti structure (dihedral angle of 180 o ) and a pair of equivalent gauche structures (dihedral angles around 60 o and 300 o ).
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2 C H H C H H 3 C CH 3 H C H CH 3 C H H 3 C H H C CH 3 H C H H 3 C H H The average value of a property A for a molecule with more than one unique conformer follows from the Boltzmann equation . Summation is carried out over all conformers, a i is the value of the property for conformer i, n i is the number of times that it appears and W i is its Boltzmann weight. A = i a i n i W i The Boltzmann weight depends on the energy of the conformer relative to the energy of the lowest-energy conformer, Δ E i , and on the temperature, T , in K. k is the Boltzmann constant. W i = exp(- Δ E i / k T)/ j n j [exp(- Δ E j / k T) ] Distribution of Conformers for n -Butane: Obtain equilibrium geometries for both anti and gauche conformers of n -butane using the HF/6-31G* model. At what temperature does the minor conformer make up less than 1% of an equilibrium mixture? At what temperature does it make up more than 40%? Don’t forget that 360 o rotation about the central CC bond leads to two equivalent gauche conformers. Where the energy difference between conformers is small, as is the case for n -butane, the average value of a property may differ significantly from that of the lowest-energy conformer. This explains why the measured dipole moment for n -butane is finite even though the dipole moment of the lowest- energy ( anti ) conformer is zero because of symmetry.
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3 Dipole moment of n -Butane: Using the results from the previous problem, calculate the value of the dipole moment for a sample of n -butane at room temperature. To what value does the dipole moment go as the temperature is raised? Elaborate.
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