Density functional formalism at finite temperatures with some applications

The exchange and correlation potentials which are needed in the study of electron systems (atoms, plasmas) at finite temperatures and finite degeneracies have been calculated and presented in a parametrised form convenient for use in Thomas-Fermi, Hartree-Fock, density-functional type effective single-particle models. The exchange corrected single-particle energies and chemical potential are calculated self-consistently and in the linear approximation. The natural generalisation of the Debye-Huckel screening length is used to extract a static model valid at intermediate degeneracies. The higher-order corrections (i.e., beyond Hartree-Fock) are evaluated from the ring sum and the second-order screened contributions to the thermodynamic grand potential. The ring sum is calculated via an approximation to the polarisation function which is known to be satisfactory at 0K and exact in the Debye-Huckel limit. The numerical results show that the correlation potential at finite temperatures consists of a static contribution and a dynamic part which goes to zero at high temperatures.

Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies

Thermodynamic functions are needed for the discussion of phase transitions in gaseous and solid state plasmas. In this paper detailed numerical data for the Hartree-Fock and the Montroll-Ward (ring sum) contributions to the pressure for symmetrical multicomponent plasmas are given at any degree of degeneration. For the Montroll-Ward pressure especially also isotherms are given. There is good agreement with limiting results derived analytically.

Thermodynamic functions of Coulomb systems

A new theory based on a dielectric function and its sum rule is presented for the exchange energy and specific heat of a two-dimensional electron gas. The results are exact towards absolute zero.

D.Y. Kojima

Papers

The temperature and density dependences of the electronic specific heat