Numerical investigation of the validity of the Slater-Janak transition-state model in metallic systems

• According to the so-called Janak’s theorem, the eigenstates of the Kohn-Sham Hamiltonian are given by the derivative of the total energy with respect to the occupation numbers of the corresponding one-electron states. The linear dependence of the Kohn-Sham eigenvalues on the occupation numbers is often assumed in order to use the Janak’s theorem in applications, for instance, in calculations of the core-level shifts in materials by means of the Slater-Janak transition state model. In this work first-principles density-functional theory calculations using noninteger occupation numbers for different core states in 24 different random alloy systems were carried out in order to verify the assumptions of linearity. It is found that, to a first approximation, the Kohn-Sham eigenvalues show a linear behavior as a function of the occupation numbers. However, it is also found that deviations from linearity have observable effects on the core-level shifts for some systems. A way to reduce the error with minimal increase of computational efforts is suggested.

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