Context : Tens of light hydrides and small molecules have now been detected over several hundreds sightlines sampling the diffuse interstellar medium ( ISM ) in both the Solar neighbourhood and the inner Galactic disk .

Aims : These new data confirm the limitations of the traditional chemical pathways driven by the UV photons and the cosmic rays ( CR ) and the need for additional energy sources , such as turbulent dissipation , to open highly endoenergetic formation routes .
The goal of the present paper is to further investigate the link between specific species and the properties of the turbulent cascade in particular its space-time intermittency .

Methods : We have analysed ten different atomic and molecular species in the framework of the updated model of turbulent dissipation regions ( TDR ) .
We study the influence on the abundances of these species of parameters specific to chemistry ( density , UV field , and CR ionisation rate ) and those linked to turbulence ( the average turbulent dissipation rate , the dissipation timescale , and the ion-neutral velocity drift in the regions of dissipation ) .

Results : The most sensitive tracers of turbulent dissipation are the abundances of CH ^ { + } and SH ^ { + } , and the column densities of the J = 3 , 4 , 5 rotational levels of H _ { 2 } .
The abundances of CO , HCO ^ { + } , and the intensity of the 158 \mu m [ CII ] emission line are significantly enhanced by turbulent dissipation .
The vast diversity of chemical pathways allows the independent determinations of free parameters never estimated before : an upper limit to the average turbulent dissipation rate , { \overline { \varepsilon } } \lesssim 10 ^ { -23 } { erg } { cm } ^ { -3 } { s } ^ { -1 } for n _ { H } =20 { cm } ^ { -3 } , from the CH ^ { + } abundance ; an upper limit to the ion-neutral velocity drift , \upsilon _ { in } \lesssim 3.5 km s ^ { -1 } , from the SH ^ { + } to CH ^ { + } abundance ratio ; and a range of dissipation timescales , 100 \lesssim \tau _ { V } \lesssim 1000 yr , from the CO to HCO ^ { + } abundance ratio .
For the first time , we reproduce the large abundances of CO observed on diffuse lines of sight , and we show that CO may be abundant even in regions with UV-shieldings as low as 5 \times 10 ^ { -3 } mag .
The best range of parameters also reproduces the abundance ratios of OH , C _ { 2 } H , and H _ { 2 } O to HCO ^ { + } and are consistent with the known properties of the turbulent cascade in the Galactic diffuse ISM .

Conclusions : Our results disclose an unexpected link between the dissipation of turbulence and the emergence of molecular richness in the diffuse ISM .
Some species , such as CH ^ { + } or SH ^ { + } , turn out to be unique tracers of the energy trail in the ISM .
In spite of some degeneracy , the properties of the turbulent cascade , down to dissipation , can be captured through specific molecular abundances .