  Chemical equilibrium has proven extremely useful to predict the chemical
composition of AGB atmospheres. Here we use a recently developed code and an
updated thermochemical database, including gaseous and condensed species
involving 34 elements, to compute the chemical equilibrium composition of AGB
atmospheres of M-, S-, and C-type stars. We include for the first time TixCy
clusters, with x = 1-4 and y = 1-4, and selected larger clusters ranging up to
Ti13C22, for which thermochemical data is obtained from quantum chemical
calculations. We find that in general chemical equilibrium reproduces well the
observed abundances of parent molecules in circumstellar envelopes of AGB
stars. There are however severe discrepancies, of various orders of magnitude,
for some parent molecules: HCN, CS, NH3, and SO2 in M-type stars, H2O and NH3
in S-type stars, and the hydrides H2O, NH3, SiH4, and PH3 in C-type stars.
Several molecules not yet observed in AGB atmospheres, like SiC5, SiNH, SiCl,
PS, HBO, and the metal-containing molecules MgS, CaS, CaOH, CaCl, CaF, ScO,
ZrO, VO, FeS, CoH, and NiS, are good candidates for detection with
observatories like ALMA. The first condensates predicted are carbon, TiC, and
SiC in C-rich atmospheres and Al2O3 in O-rich outflows. The most probable
gas-phase precursors of dust are acetylene, atomic carbon, and/or C3 for carbon
dust, SiC2 and Si2C for SiC dust, and atomic Al and AlOH, AlO, and Al2O for
Al2O3 dust. In the case of TiC dust, atomic Ti is probably the main supplier of
titanium. However, chemical equilibrium predicts that clusters like Ti8C12 and
Ti13C22 become the major reservoirs of titanium at the expense of atomic Ti in
the region where condensation of TiC is expected to occur, suggesting that the
assembly of large TixCy clusters could be related to the formation of the first
condensation nuclei of TiC.
