We present a technique for addressing the problem of deriving potential energy functions for the simulation of organic, polymeric, and biopolymeric systems, as well as for modeling vibrational spectroscopic properties. This method is designed to address three major objectives: deriving and comparing optimal functional forms for describing the energies of molecular deformations and interactions, developing a technique to rapidly and objectively determine reasonable force constants for intermolecular and intramolecular interactions, and determining the transferability of these potential forms and constants. The first two of these objectives are addressed in this paper, while the latter problem will be treated elsewhere. The technique uses ab initio molecular energy surfaces, which are described by the energy and its first and second derivatives with respect to coordinates. As an example, application to a small model compound (i.e., the formate anion) is given. A variety of analytical forms for the potential are tested against the data, to find which forms are best. The importance of anharmonicity and cross terms in accounting for structure and energy, as well as for dynamics, is demonstrated and a more accurate representation of the out-of-plane deformation for a trigonal center is derived from the energy surfaces. Section 1. Introduction Theoretical techniques are currently being applied to problems such as ligand binding to receptors, simulation of the structure and conformational fluctuations of flexible molecules, and the design of drugs. These techniques include molecular mechanics and dynamics simulations, Monte Carlo simulations, and vibrational normal-mode analysis (1). Such techniques ultimately will offer the possibility of understanding the complex behavior of organic molecules, polymers, biomolecules, and biomolecular complexes in terms of fundamental intermolecular and intramolecular physical forces, thus allowing an understanding of the molecular behavior of these systems at a level that is inaccessible to experimental techniques alone. However, the results of these simulations depend critically on the set of potential energy functions (i.e., force field) used. Although a great deal ofeffort has gone into the derivation offorce fields now in use (2-21), there remain many more organic and biomolecular functional groups for which adequate parameters have yet to be derived. Moreover, even the functional form required to describe molecular energy surfaces is still a subject of research (1).The derivation of the force constants and the appropriate functional forms to be used in describing the energy surfaces for biomolecular systems have been addressed previously (6,7,(9)(10)(11)(12). These studies relied for the most part on the fit of experimental properties and followed the Lifson consistentforce-field approach (3). In the crystal studies, ab initio calculations were used to obtain information about patterns of charge distribution (11), while the values of the partial charges were determined fr...