Data for three different cations with aryl substituents are

Question

Physical Organic Chemistry

I. Suggest reasonable mechanisms for each of the following reactions.

The starting materials are racemic, unless otherwise stated.

1.

2. 

3. 

4. 

II. The six structures beloware all found to beminima on the [C₄H₅]⁺ energy surface. The relative energies from MP2/6-311G(d,p) calculations are shown in kcal/mol. Comment on the stabilizing features that are present in each of these cations.

III. The ¹³C-NMR chemical shift of the trivalent carbon is a sensitive indicator of carbocation structure. Generally, the greater the chemical shift value, the lower the electron density at the carbon. Data for three different cations with aryl substituents are given below. How do you explain the close similarity of the trend for the first two series and the opposite trend of the third?