Comparison of various theoretical solid-state models applied to the equation of state of beryllium

We first compare the accuracy of band-structure and model-potential methods for calculating the total energy and pressure of beryllium at normal density ${\rho }_0$. The band-structure methods are the well-known augmented-plane-wave (APW) method and the recently proposed linear-muffin-tin-orbitals (LMTO) method; their results are in reasonable agreement, the first one being slightly more accurate. On the other hand, the a priori model-potential method, as proposed by Shaw, gives poorer results. The comparison of the band-structure methods is then carried on at the density $\rho =4\mathrm{}{\rho }_0$. The LMTO method (the advantage of which is a very great computational efficiency) is shown to reproduce quite closely the volume variations of energy and pressure found in the APW calculation. Finally, the zero-temperature equation of state of beryllium in the range ${\rho }_0\le \rho \le 4{\rho }_0$ is presented. The Hugoniot curve is estimated and compared with available experimental data.