Using reagents no more than four carbons long, propose a synthesis of (1R,2S,4R,5S)-1,2,4,5-tetramethylcyclohexane and (1S,2R, 4R, 5S)-1,2,4,5-tetramethylcyclohexane.

Would like a way to start this...

To propose a synthesis of (1R,2S,4R,5S)-1,2,4,5-tetramethylcyclohexane and (1S,2R, 4R, 5S)-1,2,4,5-tetramethylcyclohexane, let's break it down step by step.

Step 1: Starting from a commercially available compound, such as cyclohexane, we can introduce methyl groups onto the cyclohexane ring. One common reagent to achieve this is methyl iodide (CH3I), which can react with the cyclohexane ring in the presence of a strong base like potassium hydroxide (KOH) to form 1,4-dimethylcyclohexane and 1,2-dimethylcyclohexane.

Step 2: Now we have a mixture of 1,4-dimethylcyclohexane and 1,2-dimethylcyclohexane. We need to selectively convert one of these isomers into the desired product. One way to do this is by using an oxidizing agent like potassium permanganate (KMnO4) and heat. This reaction can convert one of the methyl groups into an aldehyde group, while leaving the other methyl groups intact. Selective oxidation of the 1,4-dimethylcyclohexane could give (1R,2S,4R,5S)-1,2,4,5-tetramethylcyclohexane.

Step 3: To obtain the other enantiomer, (1S,2R, 4R, 5S)-1,2,4,5-tetramethylcyclohexane, we can start again from the mixture of 1,4-dimethylcyclohexane and 1,2-dimethylcyclohexane obtained in step 1. This time, we would selectively oxidize the other isomer, 1,2-dimethylcyclohexane, using the same conditions as in step 2. This should give us the desired enantiomer.

It's worth mentioning that this is just one possible way to approach the synthesis. There may be other reagents or reaction conditions that can achieve similar results. Additionally, the use of chiral reagents or catalysts could be considered to achieve more selective reactions and better control over the stereochemistry of the final products. The specific details of the synthesis would require further optimization and experimentation.