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An approach to generate anharmonic potential energy surfaces for both linear and bent XY 2 -type molecules from their equilibrium geometries, Hessians, and total atomization energies alone is presented. Two key features of the potential energy surfaces are that (a) they reproduce the harmonic behavior around the equilibrium geometries exactly and (b) they have the correct limiting behavior with respect to total bond dissociation. The potentials are constructed from two diatomic potentials, for which both the Morse or Varshni potentials are tested, and a triatomic potential, for which modified forms of the Anderson- n potential are tested. Potential energy surfaces for several linear and bent molecules are constructed from ab initio data, and the third-order derivatives of these surfaces at their equilibrium geometries are compared to the results of finite difference computations. For bent molecules, the vibrational spectra predicted by vibrational configuration interaction calculations on these surfaces are compared to experiment. A modified version of the Anderson- n potential, in combination with the Varshni potential, is demonstrated to predict vibrational frequencies associated with bond angle bending an average of 20 cm −1 below the harmonic oscillator approximation and with a fourfold reduction in the root-mean-square deviation from experiment compared to the harmonic oscillator approximation.