We construct a model atom for Ti i – ii using more than 3600 measured and predicted energy levels of Ti i and 1800 energy levels of Ti ii , and quantum mechanical photoionisation cross-sections .
Non-local thermodynamical equilibrium ( NLTE ) line formation for Ti i and Ti ii is treated through a wide range of spectral types from A to K , including metal-poor stars with [ Fe/H ] down to -2.6 dex .
NLTE leads to weakened Ti i lines and positive abundance corrections .
The magnitude of NLTE corrections is smaller compared to the literature data for FGK atmospheres .
NLTE leads to strengthened Ti ii lines and negative NLTE abundance corrections .
For the first time , we performed the NLTE calculations for Ti i – ii in the 6500 K \leq T _ { eff } \leq 13000 K range .
For four A type stars we derived in LTE an abundance discrepancy of up to 0.22 dex was obtained between Ti i and Ti ii and it vanishes in NLTE .
For other four A-B stars , with only Ti ii lines observed , NLTE leads to decrease of line-to-line scatter .
An efficiency of inelastic Ti i + H i collisions was estimated from analysis of Ti i and Ti ii lines in 17 cool stars with -2.6 \leq [ Fe/H ] \leq 0.0 .
Consistent NLTE abundances from Ti i and Ti ii were obtained applying classical Drawinian rates for the stars with log { g } \geq 4.1 , and neglecting inelastic collisions with H i for the VMP giant HD 122563 .
For the VMP turn-off stars ( [ Fe/H ] \leq - 2 and log { g } \leq 4.1 ) , we obtained the positive abundance difference Ti i – ii already in LTE and it increases in NLTE .
The accurate collisional data for Ti i and Ti ii are desired to find a clue to this problem .