A full five-dimensional potential energy surface for the interaction of nitrogen molecules with the (110) surface plane of TiO2 (rutile) is generated. In a first step, ab initio SCF cluster calculations are performed for various adsorption geometries of N-2 above the TiO2(110) surface, which is described by different stoichiometric clusters, ranging in composition from Ti7O14 to Ti13O26, embedded in extended point charge fields. The N-N distance is fixed to the experimental equilibrium bond length 1.098 Angstrom. In a second step, a simple analytic form for the interaction potential is developed which contains the electrostatic interaction between the charge distribution of N-2 and the electric field above the surface, the polarization of the N-2 molecule by this field, and the Pauli repulsion between N-2 and the surface. By fitting the five parameters in the analytic expression (quadrupole moment and the two polarizability components of N-2, repulsive Lennard-Jones parameters between N and the O and Ti atoms of the surface) to the calculated ab initio interaction energies, one can represent the full five-dimensional interaction potential with a mean error of about 3 kcal/mol. The global minimum of the interaction potential is found for the vertical end-on adsorption of N-2 on a coordinately unsaturated row A titanium atom; it has an adsorption energy of -46 kJ/mol and a Ti-N distance of 2.39 Angstrom. The side-on adsorption of N-2 on the row B oxygen atoms with the N-N axis perpendicular to the row B direction is also slightly attractive with a small adsorption energy of -5.5 kJ/mol.