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The positions of atoms in glasses or nanocrystals deviate from those in a perfect crystal. At a distance exceeding the equilibrium value merely by 11%, the second derivative of a Lennard-Jones 6-12 potential is reduced to zero, causing the intermolecular force constant to vanish. This circumstance can explain, qualitatively, the softening and localization of phonons in disordered solids in the presence of free volume. Large density of localized, low frequency vibrations is responsible for well-known anomalies in thermal, acoustic, and spectral properties of glasses. Optical transitions in impurity centers can serve as sensitive probes for the disorder and dynamics of solids. The frequency-dependent, temperature- or pressure-induced shifts of zero-phonon lines can be expressed in terms of the first two derivatives of Lennard-Jones potentials of the ground state and the excited state. The applicability of the pair potential model is illustrated for spectral hole burning in the inhomogeneous spectra of pigments in polymer host matrices.
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