Methodology for determining the electronic thermal conductivity of   metals via direct non-equilibrium ab initio molecular dynamics
  Many physical properties of metals can be understood in terms of the free electron model, as proven by the Wiedemann-Franz law. According to this model, electronic thermal conductivity ($\kappa_{el}$) can be inferred from the Boltzmann transport equation (BTE). However, the BTE does not perform well for some complex metals, such as Cu. Moreover, the BTE cannot clearly describe the origin of the thermal energy carried by electrons or how this energy is transported in metals. The charge distribution of conduction electrons in metals is known to reflect the electrostatic potential (EP) of the ion cores. Based on this premise, we develop a new methodology for evaluating $\kappa_{el}$ by combining the free electron model and non-equilibrium ab initio molecular dynamics (NEAIMD) simulations. We demonstrate that the kinetic energy of thermally excited electrons originates from the energy of the spatial electrostatic potential oscillation (EPO), which is induced by the thermal motion of ion cores. This method directly predicts the $\kappa_{el}$ of pure metals with a high degree of accuracy. 
Sheng-Ying Yue, Xiaoliang Zhang, Stephen Stackhouse, Guangzhao Qin,   Edoardo Di Napoli, and Ming Hu
cond-mat.mtrl-sci physics.comp-ph