Abundance distribution of C i (top) and C ii (bottom) as a function of CO density normalized to |$\mathrm{ H}_2$| for AGN and NoAGN models at disc radii <50 pc (left) and <100 pc (right). The top panels show a correlation between C i/H|$_2$| and CO/H|$_2$| ratios at low CO abundances (CO/H|$_2 < 10^{-6}$|⁠), with an anticorrelation at higher ratios (⁠|$> \!\! 10^{-6}$|⁠). The AGN model exhibits higher C i/H|$_2$| ratios, particularly within 50 pc, indicating enhanced C i abundance due to AGN feedback. The bottom panel reveals a steeper anticorrelation for C ii/H|$_2$| at high CO/H|$_2$| ratios, with the AGN model showing consistently higher ionized C ii abundances. The vertical dotted line indicates CO/H|$_2 = 10^{-6}$|⁠, marking shifts in correlation.