Repulsion minimization

Answer 6.2 Trigonal bipyramidal, as with main group AX5 species. This will be more stable (repulsions minimized) than a square pyramidal structure. 

For the relaxed boundary eonditions [s = minC O] the elastie interaction between two inclusions is repulsive minimized over 5, the interaction free energy decreases with increasing d, Fig. 12. It is interesting to analyze the free energy, F d), as a function of the contact slope 5. We consider the range 0.0 > > —0.6. When = 0, F d) increases as d increases,... 

Minimization of nonbonded overlap repulsion. None, assuming nonbonded AO overlap to be zero. Minimization of nonbonded overlap repulsion. Minimization of coulomb repulsion... 

Truncation at the first-order temi is justified when the higher-order tenns can be neglected. Wlien pe higher-order tenns small. One choice exploits the fact that a, which is the mean value of the perturbation over the reference system, provides a strict upper bound for the free energy. This is the basis of a variational approach [78, 79] in which the reference system is approximated as hard spheres, whose diameters are chosen to minimize the upper bound for the free energy. The diameter depends on the temperature as well as the density. The method was applied successfiilly to Lennard-Jones fluids, and a small correction for the softness of the repulsive part of the interaction, which differs from hard spheres, was added to improve the results. 

A range of plasticizer molecule models and a model for PVC have been generated and energy minimized to observe their most stable conformations. Such models highlight the free volume iacrease caused by the mobiHty of the plasticizer alkyl chains. More detailed models have also been produced to concentrate on the polar region of the plasticizer and its possible mode of interaction with the polymer. These show the expected repulsion between areas on the polymer and plasticizer of like charge as weU as attraction between the negative portions of the plasticizer and positive portions of the PVC. 

The case of a, -unsaturated caAonyl compounds is analogous to that of 1,3-dienes, in that stereoelectronic factors favor coplanaiity of the C=C—C=0 system. The rotamers that are important are the s-trans and s-cis conformations. Microwave data indicate that the s-trans form is the only conformation present in detectable amounts in acrolein (2-propenal). The equilibrium distribution of s-trans and s-cis conformations of a,fi-unsatuiated ketones depends on the extent of van der Waals interaction between substituents. Methyl vinyl ketone has minimal unfavorable van der Waals repulsions between substituents and exists predominantly as the s-trans conformer ... 

Figure 7.8 The structure of InCls " showing square-pyramidal (C4 ) geometry. The In-Clapex distance is significantly shorter than the In-Clbase distances and In is 59 pm above the basal plane this leads to a Clapex-In-Clbase angle of 103.9° which is very close to the theoretical value required to minimize Cl Cl repulsions whilst still retaining C4, symmetry (103.6°) calculated on the basis of a simple inverse square law for repulsion between ligands. [NEt4]2[TlCl5] is isomoiphous with [NEt4]2[InCl5] and presumably has a similar structure for the ardon.

Compare energies for both diaxial and diequatorial chair conformers of trans-2-fluoromethyIcyclohexane (X = Me). Which conformer is preferred Examine a space-filling model of each conformer. Which group is largest methyl, fluorine, or hydrogen Which is smallest Does the preferred conformer minimize steric repulsion Explain. 

Backside attack may be favored for electrostatic reasons. Examine electrostatic potential maps fox bromide + methyl bromide frontside attack and bromide + methyl bromide backside attack, transition states involving frontside and backside attack of Br (the nucleophile) onto CHsBr, respectively. Which atoms in the transition states are most electron-rich Which trajectory better minimizes electrostatic repulsion ... 

CH3I should approach the enolate from the direction that simultaneously allows its optimum overlap with the electron-donor orbital on the enolate (this is the highest-occupied molecular orbital or HOMO), and minimizes its steric repulsion with the enolate. Examine the HOMO of enolate A. Is it more heavily concentrated on the same side of the six-membered ring as the bridgehead methyl group, on the opposite side, or is it equally concentrated on the two sides A map of the HOMO on the electron density surface (a HOMO map ) provides a clearer indication, as this also provides a measure of steric requirements. Identify the direction of attack that maximizes orbital overlap and minimizes steric repulsion, and predict the major product of each reaction. Do your predictions agree with the thermodynamic preferences Repeat your analysis for enolate B, leading to product B1 nd product B2. 

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