A new approach is proposed and investigated for approximately including the effects of diffuse functions in one-particle basis sets when high accuracy is desired. The method is cost-effective for use in computing quartic force fields (QFFs), global potential energy surfaces (PESs), or other situations when a large part of the PES is needed. It is conservatively estimated that the use of this approximation leads to a computational savings of a factor of five, and it is argued that this could be significantly larger if input/output wait times are considered. It can be used when extrapolation to the one-particle basis set limit is performed, or it can be used simply to approximate the effect of diffuse functions for a larger basis set. The new approach is based on scaling the diffuse function effect for a smaller basis set to approximate the effect for a larger basis or an extrapolated energy in which larger basis set(s) are used. The scale factor is written as a function of the geometrical coordinates of the molecule and thus it includes a geometry dependence. We report results where the scale factor is a constant, includes through gradient terms, includes through second derivative terms, and includes through diagonal second and third derivative terms. The method has been tested in the calculation of accurate QFFs, equilibrium structures, and harmonic and fundamental vibrational frequencies for NH2-, OH-, H2O, and CH3OH. It is found that including up through diagonal second derivative terms leads to reliable fundamental vibrational frequencies and is cost-effective. It is also concluded that the use of a 5Z-quality basis set is essential if high accuracy is desired for these properties, even with extrapolation to the one-particle basis set limit.