Context :

Aims : The transition between atomic and molecular hydrogen is associated with important changes in the structure of interstellar clouds , and marks the beginning of interstellar chemistry .
Most molecular ions are rapidly formed ( in ion-molecule reactions ) and destroyed ( by dissociative recombination ) in the diffuse ISM .
Because of the relatively simple networks controlling their abundances , molecular ions are usually good probes of the underlying physical conditions including for instance the fraction of gas in molecular form or the fractional ionization .
In this paper we focus on three possible probes of the molecular hydrogen column density , HCO ^ { + } , HOC ^ { + } , and CF ^ { + } .

Methods : We presented high sensitivity ALMA absorption data toward a sample of compact HII regions and bright QSOs with prominent foreground absorption , in the ground state transitions of the molecular ions HCO ^ { + } , HOC ^ { + } , and CF ^ { + } and the neutral species HCN and HNC , and from the excited state transitions of C _ { 3 } H ^ { + } ( 4-3 ) and ^ { 13 } CS ( 2-1 ) .
These data are compared with Herschel absorption spectra of the ground state transition of HF and p-H _ { 2 } O .

Results : We show that the HCO ^ { + } , HOC ^ { + } , and CF ^ { + } column densities are well correlated with each other .
HCO ^ { + } and HOC ^ { + } are tightly correlated with p-H _ { 2 } O , while they exhibit a different correlation pattern with HF depending on whether the absorbing matter is located in the Galactic disk or in the central molecular zone .
We report new detections of C _ { 3 } H ^ { + } confirming that this ion is ubiquitous in the diffuse matter , with an abundance relative to H _ { 2 } of \sim 7 \times 10 ^ { -11 } .

Conclusions : We confirm that the CF ^ { + } abundance is lower than predicted by simple chemical models and propose that the rate of the main formation reaction is lower by a factor of about 3 than usually assumed .
In the absence of CH or HF data , we recommend to use the ground state transitions of HCO ^ { + } , CCH , and HOC ^ { + } to trace diffuse molecular hydrogen , with mean abundances relative to H _ { 2 } of 3 \times 10 ^ { -9 } , 4 \times 10 ^ { -8 } and 4 \times 10 ^ { -11 } respectively , leading to sensitivity N ( { H _ { 2 } } ) / \int \tau dv of 4 \times 10 ^ { 20 } , 1.5 \times 10 ^ { 21 } , and 6 \times 10 ^ { 22 } cm ^ { -2 } / \mathrm { km~ { } s ^ { -1 } } respectively .