The Herschel/HIFI absorption spectroscopy surveys reveal the unexpected molecular richness of the Galactic diffuse ISM, even in gas of very low average H2 molecular fraction. In particular, two hydrides, CH+ and SH+ with highly endoergic formation routes have abundances that challenge models of UV-driven chemistry. The intermittent dissipation of turbulence appears as a plausible additional source of energy for the diffuse ISM chemistry. We present recent results of the so-called models of Turbulent Dissipation Regions (TDR). The abundances of many of the molecules observed in the diffuse ISM, including CO that is used as a tracer of the molecular cloud mass, may be understood in the framework of the TDR models.
