A model is presented to estimate the characteristic vibrational stiffness of an atomic lattice, given the pairwise interaction potential of the constituent atom. Unlike nearest-neighbor approaches (e.g., Slater or Dugdale and MacDonald), the vibrational stiffness is shown to be distinct from the bulk (i.e., volumetric) stiffness. This vibrational stiffness implies a characteristic vibrational frequency of the lattice that varies with the lattice spacing, which is used to infer the Grueneisen function of the lattice. Because non-nearest lattice neighbors are accounted for, the equations are expressed in terms of triple summations of the pairwise potential. However, an analytical fit to these triple summations has been developed. Furthermore, the analytical form calibrates to a range of cold- and shock-compression data, resulting in an analytical frequency-based equation of state (EOS) for crystalline solids. ©2000 American Institute of Physics.