  Aims. We probe the effect of turbulent diffusion on the chemistry at the
interface between a cold neutral medium (CNM) cloudlet and the warm neutral
medium (WNM). Methods. We perform moving grid, multifluid, 1D, hydrodynamical
simulations with chemistry including thermal and chemical diffusion. The
diffusion coefficients are enhanced to account for turbulent diffusion. We
post-process the steady-states of our simulations with a crude model of
radiative transfer to compute line profiles. Results. Turbulent diffusion
spreads out the transition region between the CNM and the WNM. We find that the
CNM slightly expands and heats up: its CH and H$_2$ content decreases due to
the lower density. The change of physical conditions and diffusive transport
increase the H$^+$ content in the CNM which results in increased OH and H$_2$O.
Diffusion transports some CO out of the CNM. It also brings H$_2$ into contact
with the warm gas with enhanced production of CH$^+$, H$_3^+$, OH and H$_2$O at
the interface. O lines are sensitive to the spread of the thermal profile in
the intermediate region between the CNM and the WNM. Enhanced molecular content
at the interface of the cloud broadens the molecular line profiles and helps
exciting transitions of intermediate energy. The relative molecular yield are
found higher for bigger clouds. Conclusions. Turbulent diffusion can be the
source of additional molecular production and should be included in chemical
models of the interstellar medium (ISM). It also is a good candidate for the
interpretation of observational problems such as warm H$_2$, CH$^+$ formation
and presence of H$_3^+$.
