transfer calculation to convert the abundance radial distributions into brightness radial distributions which can be compared with the ALMA observations.

Chemical model: formation of carbon chains {#sec:chemical_model}
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In the chemical model, the gas is assumed to expand isotropically from an initial radius of $2\times10^{14}$ cm. We consider as parent molecules at the initial radius H$_2$, CO, C$_2$H$_2$, CH$_4$, C$_2$H$_4$, H$_2$O, N$_2$, HCN, NH$_3$, CS, H$_2$S, SiS, SiO, SiH$_4$, PH$_3$, and HCP, with abundances from [@agu2012] (2012) and a value of $4\times10^{-5}$ relative to H$_2$ for N$_2$, based on chemical equilibrium calculations and a solar elemental abundance for nitrogen. Of special interest for the formation of carbon chains in the outer envelope are the parent molecules C$_2$H$_2$ and HCN, for which the adopted abundances relative to H$_2$ are $8\times10^{-5}$ and $4\times10^{-5}$, respectively ([@fon2008] 2008). We assume that the envelope is externally illuminated by the local ultraviolet radiation field of [@dra1978] (1978). Under the assumption of a smooth envelope and adopting the $N_{\rm H}$ / $A_V$ ratio of $1.87\times10^{21}$ cm$^{-2}$ mag$^{-1}$ determined for the local interstellar medium by [@boh1978] (1978), chemical models of IRC+10216 predict that photochemistry occurs at shorter radii than indicated by interferometric observations (see, e.g., discussion in Appendix 