7-Dehydrocholesterol is converted (by the action of sunlight) to vitamin \(\mathrm{D}_{3}\), which, by regulating calcium metabolism, prevents the bone disease termed rickets. A laboratory analysis of the sequence indicates that an intermediate, pre-vitamin \(D_{3}\), is the compound actually formed by the action of light. (a) Provide a mechanism for its formation. The conversion of pre-vitamin \(\mathrm{D}_{3}\) to vitamin \(\mathrm{D}_{3}\) can be 'explained" with the aid of a "no mechanism" mechanism, (b) Suggest a "mechanism" for this interconversion that lacks any of the classical intermediates of organic chemistry.

7-dehydrocholesterol is a type of cholesterol that forms pre-vitamin D3 when exposed to UV light, a process known as photochemical conversion.

The formation of pre-vitamin D3 occurs in three key steps: Step 1: The light-driven cleavage of the 9,10 bond in 7-dehydrocholesterol occurs. This step is known as photochemical cleavage and the molecule rearranges to form previtamin D3. Step 2: There's a conrotatory electrocyclic ring closure, which forms a six-membered ring. Step 3: The generated molecule undergoes a [1,7]-Hydrogen shift and fixes itself in the most stable conformation to become pre-vitamin D3.

Now, we need a mechanism that explains the conversion of pre-vitamin D3 to Vitamin D3 without the classical intermediates of organic chemistry. It might sound unusual but this happens through the process of a 'no mechanism' mechanism, which simply involves a thermally induced transformation. Step 1: Previtamin D3 is first isomerised to form vitamin D3. Step 2: This isomerisation is a slow process and does not require any enzyme. Step 3: The transformation from previtamin D3 to vitamin D3 is a temperature sensitive procedure which takes place over hours to days depending upon the temperature. In the skin, transformed Vitamin D3 is picked up by the blood stream and transported to the liver for further metabolism. While there are no detailed mechanistic steps or traditional intermediates involved in the transformation from pre-vitamin D3 to vitamin D3, it's essentially a temperature and time-dependent natural isomerisation process.