The adsorption of benzotriazole--an outstanding corrosion inhibitor for copper--on Cu(111), Cu(100), Cu(110), and low coordinated defects thereon has been studied and characterized using density functional theory (DFT) calculations. We find that benzotriazole can either chemisorb in an upright geometry or physisorb with the molecular plane being nearly parallel to the surface. While the magnitude of chemisorption energy increases as passing from densely packed Cu(111) to more open surfaces and low coordinated defects, the physisorption energy is instead rather similar on all three low Miller index surfaces. It is pointed out that due to a large dipole moment of benzotriazole the dipole-dipole interactions are rather important. For perpendicular chemisorption modes the lateral repulsion is very long ranged, extending up to the nearest-neighbor distance of about 60 bohrs, whereas for parallel adsorption modes the lateral interactions are far less pronounced and the molecules experience a weak attraction at distances ≲25 bohrs. The chemisorption energies were therefore extrapolated to zero coverage by a recently developed scheme and the resulting values are -0.60, -0.73, and -0.92 eV for Cu(111), Cu(100), and Cu(110), respectively, whereas the zero-coverage physisorption energy is about -0.7 eV irrespective of the surface plane. While the more densely packed surfaces are not reactive enough to interact with the molecular π-system, the reactivity of Cu(110) appears to be at the onset of such interaction, resulting in a very stable parallel adsorption structure with an adsorption energy of -1.3 eV that is ascribed as an apparent chemisorption+physisorption mode.