The molecule that has minimum or no role in the formation of photochemical smog, is:

Photochemical smog is produced when primary pollutants emitted from automobile exhausts and industrial chimneys—mainly oxides of nitrogen ($$NO,\; NO_2$$) and unburnt hydrocarbons—react under the influence of sunlight. The sunlight provides energy that initiates a series of free-radical reactions in the lower atmosphere.

We have, as the core steps:

1. $$NO_2 \xrightarrow{h\nu} NO + O$$     (sunlight breaks nitrogen dioxide)

2. The nascent oxygen atom then combines with molecular oxygen:

$$O + O_2 \longrightarrow O_3$$

3. Ozone $$\left(O_3\right)$$ is highly reactive and participates in further reactions with unburnt hydrocarbons to form secondary pollutants such as peroxyacetyl nitrate (PAN), aldehydes like formaldehyde $$\left(H_2C=O\right)$$, acrolein, etc.

Thus, within a photochemical smog system:

• $$NO$$ and $$NO_2$$ act as primary precursors.
• $$O_3$$ is a key secondary oxidant that sustains the chain reactions.
• Formaldehyde $$\left(H_2C=O\right)$$ is itself a smog component produced during hydrocarbon oxidation and again feeds back into the radical cycle.

Now we examine each given option with respect to its participation:

• Option A: $$N_2$$ (molecular nitrogen) is the major constituent of air (about 78%). It is extremely stable due to the triple bond $$N\equiv N$$ (bond dissociation energy ≈ $$945\;kJ\,mol^{-1}$$). Because of this stability, $$N_2$$ does not absorb sunlight in the troposphere and does not react with the radicals generated in photochemical smog. Hence it plays virtually no role in the smog‐forming reaction network.

• Option B: $$O_3$$, as shown above, is actively formed and consumed in the smog cycle; its presence is a characteristic sign of photochemical smog.

• Option C: $$H_2C=O$$ (formaldehyde) is generated during hydrocarbon oxidation; it can photodissociate and yield free radicals that perpetuate smog formation.

• Option D: $$NO$$ is one of the primary pollutants emitted from vehicle exhausts; it initiates the radical chemistry after being oxidised to $$NO_2$$.

Comparing these roles, the only molecule that remains essentially inert and uninvolved is $$N_2$$.

Hence, the correct answer is Option A.