Context :

Aims : We model a diffuse molecular cloud present along the line of sight to the star HD 102065 .
We compare our modeling with observations to test our understanding of physical conditions and chemistry in diffuse molecular clouds .

Methods : We analyze an extensive set of spectroscopic observations which characterize the diffuse molecular cloud observed toward HD 102065 .
Absorption observations provide the extinction curve , { H _ { 2 } } , C i , { CO } , { CH } , and { CH ^ { + } } column densities and excitation .
These data are complemented by observations of { C ^ { + } } , { CO } and dust emission .
Physical conditions are determined using the Meudon PDR model of UV illuminated gas .

Results : We find that all observational results , except column densities of CH , { CH ^ { + } } and { H _ { 2 } } in its excited ( J \geq 2 ) levels , are consistent with a cloud model implying a Galactic radiation field ( G \sim 0.4 in Draine ’ s unit ) , a density of 80 { cm } ^ { -3 } and a temperature ( 60-80 K ) set by the equilibrium between heating and cooling processes .
To account for excited ( J \geq 2 ) { H _ { 2 } } levels column densities , an additional component of warm ( \sim 250 K ) and dense ( n _ { H } \geq 10 ^ { 4 } cm ^ { -3 } ) gas within 0.03 pc of the star would be required .
This solution reproduces the observations only if the ortho-to-para H _ { 2 } ratio at formation is \sim 1 .
In view of the extreme physical conditions and the unsupported requirement on the ortho-to-para ratio , we conclude that H _ { 2 } excitation is most likely to be accounted for by the presence of warm molecular gas within the diffuse cloud heated by the local dissipation of turbulent kinetic energy .
This warm H _ { 2 } is required to account for the { CH ^ { + } } column density .
It could also contribute to the CH abundance and explain the inhomogeneity of the CO abundance indicated by the comparison of absorption and emission spectra .

Conclusions :