Step 1: Understanding the Question:
We need to identify the functional group from the given options that is responsible for producing a negative resonance effect ($(-)\mathrm{R}$ effect).
Step 2: Key Formula or Approach:
The resonance effect ($\mathrm{R}$ effect) describes the redistribution of electron density in a conjugated system via $\pi$-bond delocalization:
• $(+)\mathrm{R}$ effect (Electron-donating): Occurs when an atom directly attached to the conjugated system possesses a lone pair of electrons available for donation into the ring or chain.
• $(-)\mathrm{R}$ effect (Electron-withdrawing): Occurs when the substituent contains electronegative atoms linked by multiple bonds ($\mathrm{C=O}$, $\mathrm{-C\equiv N}$, $-\mathrm{NO_2}$), drawing electron density away from the conjugated system towards itself.
Step 3: Detailed Explanation:
Let's examine the structural electron distribution of each option:
• $-\mathrm{COOR}$ (Ester group): Contains a strongly polarized carbonyl group ($\mathrm{C=O}$). The $\pi$-electrons can be pulled up towards the highly electronegative carbonyl oxygen atom, withdrawing $\pi$-electron density from any adjacent conjugated system through resonance. This defines a classic $(-)\mathrm{R}$ effect.
• $-\mathrm{OR}$ (Alkoxy group): The oxygen atom has two lone pairs directly adjacent to the bond axis, allowing it to donate electron density into a conjugated system via resonance ($(+)\mathrm{R}$ effect).
• $-\mathrm{OH}$ (Hydroxyl group): Possesses lone pairs on the oxygen atom that participate in conjugation by electron donation ($(+)\mathrm{R}$ effect).
• $-\mathrm{NHR}$ (Alkylamino group): The nitrogen atom bears a lone pair of electrons that is readily donated into a conjugated pathway ($(+)\mathrm{R}$ effect).
Therefore, only the $-\mathrm{COOR}$ group functions as a resonance electron-withdrawing group.
Step 4: Final Answer:
The group responsible for the $(-)\mathrm{R}$ effect is $-\mathrm{COOR}$, which matches option (A).