Evaluation of picture change effects on fractional occupation number states in noble gas atoms

In the two-component relativistic density functional theory, the picture change error (PCE), which originates from insufficient transformation of operators, should be corrected. In this study, we examine the PCE in the fractional occupation number (FON) state based on the spin-free infinite-order two-component Hamiltonian. The PCE for the total and orbital energy changes is estimated with respect to the FON electrons of the highest occupied molecular orbital and 1s core orbital in noble gas atoms. PCE is significant in core orbitals in heavy elements but relatively small in light elements and valence orbitals. The delocalization error, which can be represented by the total energy deviation from the behavior of the exact energy, is overestimated by the lack of picture change correction of the two-electron operator and underestimated by that of the density operator. Corresponding to these results, the PCE influences the value of orbital energies and slope of orbital energy change to FON.