Context : Molecular counterparts to atomic jets have recently been detected within 1000 AU of young stars at early evolutionary stages . Reproducing these counterparts is an important new challenge for proposed ejection models . Aims : We explore whether molecules may survive in the magneto-hydrodynamic ( MHD ) disk wind solution currently invoked to reproduce the kinematics and tentative rotation signatures of atomic jets in T Tauri stars . Methods : The coupled ionization , chemical , and thermal evolution along dusty flow streamlines is computed for the prescribed MHD disk wind solution , using a method developed for magnetized shocks in the interstellar medium . Irradiation by ( wind-attenuated ) coronal X-rays and far-ultraviolet photons from accretion hot spots is included , with an approximate self-shielding of H _ { 2 } and CO . Disk accretion rates of 5 \times 10 ^ { -6 } , 10 ^ { -6 } and 10 ^ { -7 } M _ { \odot } \mathrm { yr } ^ { -1 } are considered , representative of low-mass young protostars ( so-called ‘ Class 0 ’ ) , evolved protostars ( ‘ Class I ’ ) and very active T Tauri stars ( ‘ Class II ’ ) respectively . Results : The disk wind has an ” onion-like ” thermo-chemical structure , with streamlines launched from larger radii having lower temperature and ionisation , and higher H _ { 2 } abundance.The coupling between charged and neutral fluids is sufficient to eject molecules from the disk out to at least 9 AU . The launch radius beyond which most H _ { 2 } survives moves outward with evolutionary stage , from \simeq 0.2 AU ( sublimation radius ) in the Class 0 disk wind , to \simeq 1 AU in the Class I , and > 1 AU in the Class II . In this molecular wind region , CO survives in the Class 0 but is significantly photodissociated in the Class I/II . Balance between ambipolar heating and molecular cooling establishes a moderate asymptotic temperature \simeq 700 - 3000 K , with cooler jets at earlier protostellar stages . As a result , endothermic formation of H _ { 2 } O is efficient , with abundances up to \simeq 10 ^ { -4 } , while CH ^ { + } and SH ^ { + } can reach \geq 10 ^ { -6 } in the hotter and more ionised Class I/II winds . Conclusions : A centrifugal MHD disk wind launched from beyond 0.2 - 1 AU can produce molecular jets/winds up to speeds \simeq 100 \leavevmode \nobreak \mathrm { km \leavevmode \nobreak s } ^ { -1 } in young low-mass stars ranging from Class 0 to active Class II . The models predicts a high ratio of H _ { 2 } to CO and an increase of molecular launch radius , temperature , and flow width as the source evolves , in promising agreement with current observed trends . Calculations of synthetic maps and line profiles in H _ { 2 } , CO and H _ { 2 } O will allow detailed tests of the model against observations .