C-fractionation has been studied from a theoretical point of view with different models of time-dependent chemistry, including both isotope-selective photodissociation and low-temperature isotopic exchange reactions. Recent chemical models predict that the latter may lead to a depletion of $^{13}$C in nitrile-bearing species, with $^{12}$C/$^{13}$C ratios two times higher than the elemental abundance ratio of 68 in the local ISM. Since the carbon isotopic ratio is commonly used to evaluate the $^{14}$N/$^{15}$N ratios with the double-isotope method, it is important to study C-fractionation in detail to avoid incorrect assumptions. In this work we implemented a gas-grain chemical model with new isotopic exchange reactions and investigated their introduction in the context of dense and cold molecular gas. In particular, we investigated the $^{12}$C/$^{13}$C ratios of HNC, HCN, and CN using a grid of models, with temperatures and densities ranging from 10 to 50 K and 2$times$10$^{3}$ to 2$times$10$^{7}$ cm$^{-3}$, respectively. We suggest a possible $^{13}$C exchange through the $^{13}$C + C$_{3}$ $rightarrow$ $^{12}$C +$^{13}$CC$_{2}$ reaction, which does not result in dilution, but rather in $^{13}$C enhancement, for molecules formed starting from atomic carbon. This effect is efficient in a range of time between the formation of CO and its freeze-out on grains. Furthermore, we show that the $^{12}$C/$^{13}$C ratios of nitriles are predicted to be a factor 0.8-1.9 different from the local value of 68 for massive star-forming regions. This result also affects the $^{14}$N/$^{15}$N ratio: a value of 330 obtained with the double-isotope method is predicted to be 260-1150, depending on the physical conditions. Finally, we studied the $^{12}$C/$^{13}$C ratios by varying the cosmic-ray ionization rate: the ratios increase with it because of secondary photons and cosmic-ray reactions.
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