  We resolve a fundamental issue associated with the conventional Kohn-Sham
formulation of real-time time-dependent density functional theory. We show that
unphysical multielectron excitations, generated during time propagation of the
Kohn-Sham equations due to fixation of the total number of Kohn-Sham orbitals
and their occupations, result in incorrect electron density and, therefore,
wrong predictions of physical properties. A new formulation is proposed in that
the number of Kohn-Sham orbitals and their occupations are updated on the fly,
the unphysical multielectron excitations are removed, and the correct electron
density is determined. The correctness of the new formulation is demonstrated
by simulations of Rabi oscillation, as analytical results are available for
comparison in the case of noninteracting electrons.
