First-principles calculation of charged capacitors under open-circuit conditions using the orbital-separation approach

In a previous work [Phys. Rev. B 84, 085120 (2011)], we presented the orbital-separation approach for simulating metal/insulator/metal capacitors under bias voltage within the Kohn-Sham framework of density functional theory. A limitation mentioned in that work was that it is not straightforward to calculate the amount of free charge transferred from one electrode to the other, and thus the application of the method was limited to the closed-circuit (constant-voltage) condition. Here, we show that it is actually possible in practice to calculate the free charge by examining the change in the occupation of the Kohn-Sham eigenstates near the Fermi level. Thus it is also possible to perform open-circuit (constant-charge) simulations, and we demonstrate this on a metal/ferroelectric/metal capacitor.