The negative resonance effect, also called the -I effect, refers to the ability of a functional group to withdraw electron density through the p-orbitals via resonance. It is often the characteristic of groups that have atoms with high electronegativity or multiple bonds that allow for electron delocalization away from the conjugated system.

To determine which functional group shows a negative resonance effect from the options provided, let's review them one by one:

• Option A - $-\mathrm{OH}$: The hydroxyl group (-OH) is capable of donating electrons via resonance due to the lone pair of electrons on oxygen. Therefore, it has a positive resonance effect, not a negative one.


• Option B - $-\mathrm{OR}$: Similar to the hydroxyl group, alkoxides (-OR) can also donate electron density through resonance because of the lone pairs on the oxygen atom. This makes them electron-donating groups, showing a positive resonance effect.


• Option C - $-\mathrm{COOH}$: The carboxylic acid group (-COOH) contains a carbonyl group (C=O) which is highly electronegative and can withdraw electron density via resonance. The double bond between carbon and oxygen can participate in resonance, spreading the electron density away from other parts of the molecule. Thus, the carboxylic acid group shows a negative resonance effect.


• Option D - $-\mathrm{NH}_2$: The amino group (-NH₂) is an electron-donating group due to the lone pair of electrons on the nitrogen atom. It shows a positive resonance effect, similar to hydroxyl and alkoxy groups.

Given the choices, Option C - $-\mathrm{COOH}$ is the functional group that shows a negative resonance effect because of its ability to withdraw electron density through resonance with its carbonyl group which is highly electronegative and capable of delocalizing electrons.