On the Torsional Vibrations of Long Chain Molecules

Lattice Dynamics of Simple Harmonic and Anharmonic Shell Models

“…This has not been pointed out by , although Szigeti (1959) has pointed out that higher order dipole moments make an appreciable contribution to the anharmonic potential energy.…”

“…It is true that the repulsive potential energy originates from overlap of electron distributions, but in practice a semi-empirical potential is always used and distortions of the electron cloud during lattice vibrations are not allowed for. The above model fails both in predicting many details of observed dispersion curves (Woods, Cochran, and Brockhouse 1960) and in the theory of dielectric constants (Szigeti 1949(Szigeti , 1950. Dick and Overhauser (1958) realized that the main defect of the above model was its inability to take account of the so-called "short-range polarization".…”

Dielectric Saturation in Ionic Crystals. II. Deformable Ions

“…The fourth term (diagrams (d), (e), (f), (g), and (h)) depends both on the anharmonicity and the field, and gives anharmonic contributions to the field-independent dielectric constant. This term has been evaluated by Szigeti (1959) for the quantum mechanical case and by Wilcox (1965) for the classical case, and gives rise to the observed temperature dependence of the field-independent dielectric constant. The last term (diagrams (i) and (j)) gives a contribution to the dielectric constant that is proportional to E2, i.e.…”

“…Szigeti 1959; this was also implicit in Part I) for which the macroscopic and external fields are identical. The static dielectric constant is then given by £8-£00 == -,;;(:!)…”

“…In the present paper we use a slightly different formulation of perturbation theory, in which the various terms are represented by diagrams (e.g. Cowley 1963;Parry and Turner 1964;Wilcox 1965). Some of the advantages of using diagrams are (1) they often lead to greater clarity and insight into the structure of the perturbation series, (2) they provide a systematic way of obtaining all of the terms of a given order, and (3) it is sometimes possible to sum certain classes of terms to all orders, and in this way to obtain physical approximations that cannot be readily obtained from a conventional perturbation theory.…”