For an organic molecule to exhibit optical isomerism, it generally must possess at least one asymmetric (chiral) carbon atom, which is a carbon atom bonded to four different atoms or groups .

Let us analyze the given options:

1. 2,3-Dimethylpentane ($\text{CH}_3\text{-CH}(\text{CH}_3)\text{-C}^*\text{H}(\text{CH}_3)\text{-CH}_2\text{-CH}_3$): The carbon atom at position 3 (C3) is bonded to four different groups: a hydrogen atom ($-\text{H}$), a methyl group ($-\text{CH}_3$), an ethyl group ($-\text{CH}_2\text{CH}_3$), and an isopropyl group ($-\text{CH}(\text{CH}_3)_2$). Therefore, it is a chiral center, making the molecule optically active. Its molecular formula is $\text{C}_7\text{H}_{16}$.
2. 2,2-Dimethylbutane ($\text{CH}_3\text{-C}(\text{CH}_3)_2\text{-CH}_2\text{-CH}_3$): This molecule has the formula $\text{C}_6\text{H}_{14}$ (which does not match the given formula) and lacks a chiral center because C2 is attached to three identical methyl groups.
3. 2-Methylhexane ($\text{CH}_3\text{-CH}(\text{CH}_3)\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-CH}_3$): The carbon at position 2 is bonded to two identical methyl groups, so it does not have a chiral center and is achiral.