Photocatalytic oxidation is used for air purification from low concentrations of organic compounds and microbiological objects. Adsorption is the first stage of photocatalytic oxidation, and adsorption constant value has direct linear influence onto the rate of oxidation at low concentration according to the Langmuir-Hinshelwood equation. The present computational investigation has been undertaken with the goal to estimate the effect of nanoparticle size in the range of 1–1.5 nm, extent of hydroxylation, surface acidity, and nanoparticle shape on adsorption of acetone over TiO2 anatase particle facets, edges, and vertices. The anatase nanoparticles were represented by three cluster models—two of cubic shape and one of decahedral shape with exposed surfaces (001), (100), and (101). Adsorption energy was calculated with density functional tight binding (DFTB) semiempirical method and varied from − 0.67 to − 25.79 kcal/mol for different sites of the clusters depending on facet types and location on a facet. Mean unweighted adsorption energy of acetone increased from − 4.49 to − 8.16 kcal/mol for (001) facet and from − 11.05 to − 12.97 kcal/mol for (100) facet when the cubic cluster size increased from 3 × 3 × 1 to 4 × 4 × 1 elementary cells. For decahedral cluster, mean adsorption energy on (001) facet was − 9.87 kcal/mol and − 14.44 kcal/mol on (101) facets. The largest adsorption energy − 25.60 and − 25.79 kcal/mol was observed on grove Ti atoms on (100) facet of the largest cubic cluster and vertex atoms in decahedral cluster, respectively. Dissociative adsorption of one and two water molecules on (001) facet increased acetone adsorption energy from − 4.02 to − 8.20 and to − 18.50 kcal/mol. A marked electronic effect on adsorption energy was observed for two adjacent sites on (001) facet with a similar structure but adsorption energy − 16.40 and − 1.40 kcal/mol. Influence of acetone adsorption on clusters’ band gap, photogenerated thermalized electron and hole location, and C=O vibration wavenumber is also reported.