An error was found in one of the beta functions of the Vanderbilt-like pseudopotential used for titanium within the PBE approximation. We repeated the calculations using the correct Ti pseudopotential, and found only small variations in the results. Moreover, all the conclusions of our work remain unchanged.In particular: ͑i͒ the bulk equilibrium parameters of rutile and anatase do not change, anatase is still found to be more stable than rutile, and the difference in cohesive energy between the two phases is still 0.10 eV/TiO 2 ; ͑ii͒ the parameters describing the relaxation of the various surfaces are the same; ͑iii͒ the surface formation energies E sur f , calculated with the correct pseudopotential, are reported in Table I. These values are systematically smaller than the previously published ones by ϳ0.06 J/m 2 , so that the relative stability of different surfaces is not significantly affected.As already outlined in the paper, it is difficult to establish the absolute accuracy of our calculated values of E sur f , nevertheless we expect the error to be systematic to all the surfaces studied. Since the conclusions of our paper were based on the analysis of the relative values of E sur f for different surfaces, they are not affected by this error.We thank Paolo Giannozzi for pointing out the error in the pseudopotential.

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A semiempirical addition of dispersive forces to conventional density functionals (DFT-D) has been implemented into a pseudopotential plane-wave code. Test calculations on the benzene dimer reproduced the results obtained by using localized basis set, provided that the latter are corrected for the basis set superposition error. By applying the DFT-D/plane-wave approach a substantial agreement with experiments is found for the structure and energetics of polyethylene and graphite, two typical solids that are badly described by standard local and semilocal density functionals.

The adsorption of formic acid and sodium formate on the stoichiometric anatase (101) surface has been studied by means of density functional calculations with a slab geometry. On the clean surface, the most stable adsorption structure for HCOOH is a molecular monodentate configuration, hydrogen bonded to a surface bridging oxygen, while for HCOONa a dissociated bridging bidentate geometry is preferred. The bidentate chelating structure is energetically unstable for both the acid and the salt. On the hydrated surface, both HCOOH and HCOONa preferentially form an inner-sphere adsorption complex. HCOOH maintains a monodentate coordination, but, due to the interaction with a nearby water molecule, it becomes dissociated, while HCOONa again prefers a bridging bidentate structure. The energies for adsorption from an aqueous solution are estimated to be 0.30 and 0.79 eV for HCOOH and HCOONa, respectively.

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