Precise solution for H-point oscillation: Mo, Na, and Fe

In the existing theory of lattice dynamics, the central roles are played by the harmonic and the quasi-harmonic approximations. In this letter, we try to derive an accurate solution for the one-dimensional oscillator, exemplified by the H-point phonon in body-centred cubic metals. This problem is formulated such that it takes the form of a one-dimensional periodic system. Mo, Na, and Fe have been chosen as prototypes and we have examined the changes of the phonon energies with temperature and pressure. We are able to reproduce, for the first time, the anomalous temperature dependence of the H-point phonon energy for Mo.