A Theoretical Investigation of Time-Dependent Kohn--Sham Equations

Propagators for the time-dependent Kohn-Sham equations.

In this paper we address the problem of the numerical integration of the time-dependent Schrodinger equation i partial differential (t)phi=Hphi. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, H is in gene...

Guaranteed convergence of the Kohn-Sham equations.

A sufficiently damped iteration of the Kohn-Sham (KS) equations with the exact functional is proven to always converge to the true ground-state density, regardless of the initial density or the strength of electron correlation, for finite Coulomb systems. We numerically implement the exact functional for one-dimensional continuum systems and demonstrate convergence of the damped KS algorithm. M...

Time-dependent Kohn-Sham approach to quantum electrodynamics

We prove a generalization of the van Leeuwen theorem towards quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. We circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external fourpotential and four-curr...

Time-dependent density functional theory beyond Kohn-Sham Slater determinants.

When running time-dependent density functional theory (TDDFT) calculations for real-time simulations of non-equilibrium dynamics, the user has a choice of initial Kohn-Sham state, and typically a Slater determinant is used. We explore the impact of this choice on the exchange-correlation potential when the physical system begins in a 50 : 50 superposition of the ground and first-excited state o...

On Tensor Approximation of Green Iterations for Kohn-Sham Equations