On the contributions of the internal modes of molecules to the Debye-Waller factors

A method is described which allows one to estimate the contributions of the internal modes of a molecule to the Debye-Waller factors of the individual atoms. The contributions obtained are the average of the isotropic mean-square amplitudes over all atoms in the molecule having the same mass. For evaluating the contributions one needs to know only the frequencies of the internal modes of the molecule, as determined from infrared and Raman data, but not the force constants. Furthermore, a rough formula is derived which allows one to estimate the contributions of the internal modes to the vibrations of a given atom only from the number of the atoms in the molecule and from the mass of the respective atom. Numerical results are presented for the structures of benzene, naphthalene, and anthracene.