Résumé
Context. Thanks to the advent of Herschel and ALMA, new high-quality observations of molecules present in the circumstellar envelopes of asymptotic giant branch (AGB) stars are being reported that reveal large differences from the existing chemical models. New molecular data and more comprehensive models of the chemistry in circumstellar envelopes are now available. Aims. The aims are to determine and study the important formation and destruction pathways in the envelopes of O-rich AGB stars and to provide more reliable predictions of abundances, column densities, and radial distributions for potentially detectable species with physical conditions applicable to the envelope surrounding IK Tau. Methods. We use a large gas-phase chemical model of an AGB envelope including the effects of CO and N2 self-shielding in a spherical geometry and a newly compiled list of inner-circumstellar envelope parent species derived from detailed modeling and observations. We trace the dominant chemistry in the expanding envelope and investigate the chemistry as a probe for the physics of the AGB phase by studying variations of abundances with mass-loss rates and expansion velocities. Results. We find a pattern of daughter molecules forming from the photodissociation products of parent species with contributions from ion-neutral abstraction and dissociative recombination. The chemistry in the outer zones differs from that in traditional PDRs in that photoionization of daughter species plays a significant role. With the proper treatment of self-shielding, the N → N2 and C+→ CO transitions are shifted outward by factors of 7 and 2, respectively, compared with earlier models. An upper limit on the abundance of CH4 as a parent species of (≲2.5 × 10-6 with respect to H2) is found for IK Tau, and several potentially observable molecules with relatively simple chemical links to other parent species are determined. The assumed stellar mass-loss rate, in particular, has an impact on the calculated abundances of cations and the peak-abundance radius of both cations and neutrals: as the mass-loss rate increases, the peak abundance of cations generally decreases and the peak-abundance radius of all species moves outwards. The effects of varying the envelope expansion velocity and cosmic-ray ionization rate are not as significant. Conclusions.