We present an efficient algorithm for generating semiglobal potential energy surfaces of reactive systems. The method takes as input molecular mechanics force fields for reactants and products and a quadratic expansion of the potential energy surface around a small number of geometries whose locations are determined by an iterative process. These Hessian expansions might come, for example, from ab initio electronic structure calculations, density functional theory, or semiempirical molecular orbital theory. A 2 x 2 electronic diabatic Hamiltonian matrix is constructed from these data such that, by construction, the lowest eigenvalue of this matrix provides a semiglobal approximation to the lowest electronically adiabatic potential energy surface. The theory is illustrated and tested by applications to rate constant calculations for three gas-phase test reactions, namely, the isomerization of 1,3-cis-pentadiene, OH + CH4--> H2O + CH3, and CH2Cl + CH3F --> CH3Cl + CH2F.