Analytical local model potential for modeling the interaction in an atom reduces the computational effort in electronic structure calculations significantly. A new four-parameter analytical local model potential is proposed for atoms Li through Lr, and the values of four parameters are shell-independent and obtained by fitting the results of Xa method. At the same time, the energy eigenvalues, the radial wave functions and the total energies of electrons are obtained by solving the radial Schr6dinger equation with a new form of potential function by Numerov＇s numerical method. The results show that our new form of potential function is suitable for high, medium and low Z atoms. A comparison among the new potential function and other analytical potential functions shows the greater flexibility and greater accuracy of the present new potential function.
A five-parameter equation of state （EOS） is proposed to correctly incorporate the cohesive energy data in it without physically incorrect oscillations. The proposed EOS is applied to 10 selected metals. It is shown that the calculated compression curves are in good accordance with the experimental data. The values of the bulk modulus and its derivative with respect to pressure extracted from the proposed EOS remain almost unchanged while the data range used is varied.
A simple equation of state （EOS） in wide ranges of pressure and temperature is constructed within the MieGruneisen Debye framework. Instead of the popular Birch-Murnaghan and Vinet EOS, we employ a five-parameter cold energy expression to represent the static EOS term, which can correctly produce cohesive energy without any spurious oscillations in the extreme compression and expansion regions, We developed a Pade approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in the low temperature region. The anharmonic effect is taken into account by using a semi-empirical approach. Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature, and tends to ideal-gas limitation at high temperature, which is physically correct. Besides, based on this approach, the anharmonic thermal pressure can be expressed in the Griineisen form, which is convenient for applications. The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions, and the results are very satisfactory as compared with the experimental data.
