Identification and Resolution of Unphysical Multielectron Excitations in the Real-Time Time-Dependent Kohn-Sham Formulation

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.

Figure 1

(a) One-to-one correspondence between the KS and actual wave functions through the electron density (see also Supplemental Material [34]). (b) Transition dipoles from the ground state to the two lowest excited states of a $H_2$ molecule for noninteracting and interacting [exchange-correlation functional treated in the local density approximation (LDA) or generalized gradient approximation parameterized by Perdew, Burke, and Ernzerhof (PBE)] electrons. (c) One-electron and two-electron excited state occupations as functions of the ground-state occupation during Rabi oscillation. The maximum value of the one-electron excited state occupation is equal to 0.5.

Figure 2

Resonant Rabi oscillation from the (a) TDNKS and (b) TDKS approaches. The occupations of the ground state, $P_{gs}$ (green), one-electron excited state, $P_{1e}$ (purple), and two-electron excited state, $P_{2e}$ (red), are shown. Corresponding dipole moments are given in (c) and (d).

Figure 3

Rabi oscillation period vs detuning energy. (a) The analytical result [from Eq. (12); black line] is compared with numerical results from the TDNKS and TDKS approaches for noninteracting electrons. (b) Analogous numerical results for interacting electrons (no analytical solution exists).