  We have investigated the structural and dielectric properties of
Sr$_{2}$TiO$_{4}$,the first member of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$
Ruddlesden-Popper series, within density functional theory. Motivated by recent
work in which thin films of Sr$_{2}$TiO$_{4}$ were grown by molecular beam
epitaxy (MBE) on SrTiO$_{3}$ substrates, the in-plane lattice parameter was
fixed to the theoretically optimized lattice constant of cubic SrTiO$_{3}$
(n=$\infty$), while the out-of-plane lattice parameter and the internal
structural parameters were relaxed. The fully relaxed structure was also
investigated. Density functional perturbation theory was used to calculate the
zone-center phonon frequencies, Born effective charges, and the electronic
dielectric permittivity tensor. A detailed study of the contribution of
individual infrared-active modes to the static dielectric permittivity tensor
was performed. The calculated Raman and infrared phonon frequencies were found
to be in agreement with experiment where available. Comparisons of the
calculated static dielectric permittivity with experiments on both ceramic
powders and epitaxial thin films are discussed.
