An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

We present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)