Isobaric heat capacity and density of liquid lead : Ab initio calculation and Bayesian approach

Isobaric heat capacity (Cp) is an essential property for characterizing the thermal behavior of liquids. This quantity is used to constrain equations of state models.

In the case of liquid lead, inconsistencies in the experimental evaluation of Cp with different measurement techniques have been observed. To address these discrepancies, we employ Quantum Molecular Dynamics (QMD) simulations to assess the theoretical Cp.

Cp is not a direct output of QMD simulations. In this study, a method is proposed. We determine the enthalpy at fixed temperature, H(T), using QMD NPT simulations. Its statistical uncertainty is determined using the bootstrap method. Subsequently, a Bayesian approach with a polynomial model is applied to H(T) with uncertainties. Cp is obtained by derivation of this polynom. Our calculations revealed that Cp remains constant (142±3 J/kg/K) between 650-2000K. A sensitivity study on Cp and density with respect to the functional, spin-orbit coupling, and pseudo PAW is currently underway. Preliminary results indicate that the calculated Cp is less sensitive to methodological choices than density.