  We performed the non-local thermodynamic equilibrium (non-LTE) calculations
for Ti I-II with the updated model atom that includes quantum-mechanical rate
coefficients for inelastic collisions with hydrogen atoms. We have calculated
for the first time the rate coefficients for bound-bound transitions in
inelastic collisions of titanium atoms and ions with hydrogen atoms and for the
charge-exchange processes: Ti I + H <-> Ti II + H- and Ti II + H <-> Ti III +
H-. The influence of these data on non-LTE abundance determinations has been
tested for the Sun and four metal-poor stars. For Ti I and Ti II, the
application of the derived rate coefficients has led to an increase in the
departures from LTE and an increase in the titanium abundance compared to that,
obtained with approximate formulas for the rate coefficients. In metal-poor
stars, we have failed to achieve consistent non-LTE abundances from lines of
two ionization stages. The known in the literature discrepancy in the non-LTE
abundances from Ti I and Ti II lines in metal-poor stars cannot be solved by
improvement of the rates of inelastic processes in collisions with hydrogen
atoms in non-LTE calculations with classical model atmospheres.
