Molecular counterparts to atomic jets have been detected within 1000 AU of young stars. Reproducing them is a challenge for proposed ejection models. We explore whether molecules may survive in an MHD disk wind invoked to reproduce the kinematics and tentative rotation signatures of atomic jets in T Tauri stars. The coupled ionization, chemical and thermal evolution along dusty flow streamlines is computed for a prescribed MHD disk wind solution, using a method developed for magnetized shocks in the interstellar medium. Irradiation by wind-attenuated coronal X-rays and FUV photons from accretion hot spots is included, with self-shielding of H2 and CO. Disk accretion rates of 5e-6, 1e-6 and 1e-7 solar masses per year are considered, representative of low-mass young protostars (Class 0), evolved protostars (Class I) and very active T Tauri stars (Class II). The disk wind has an onion-like thermo-chemical structure, with streamlines launched from larger radii having lower temperature and ionisation, and higher H2 abundance. The coupling between charged and neutral fluids is sufficient to eject molecules from the disk out to 9 AU. The launch radius beyond which most H2 survives moves outward with evolutionary stage. CO survives in the Class 0 but is significantly photodissociated in the Class I/II. Balance between ambipolar heating and molecular cooling establishes an asymptotic temperature 700-3000 K, with cooler jets at earlier protostellar stages. Endothermic formation of H2O is efficient with abundances up to 1e-4, while CH+ and SH+ can exceed 1e-6 in the Class I/II winds. A centrifugal MHD disk wind launched from beyond 0.2-1 AU can produce molecular jets/winds up to speeds 100 km/s in young low-mass stars. The model predicts a high ratio H2/CO and an increase of molecular launch radius, temperature, and flow width as the source evolves, in agreement with current observed trends.
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