Current density partitioning in time-dependent current density functional theory

The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory

The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.

Time-Dependent Electronic Populations in Fragment-Based Time-Dependent Density Functional Theory

Conceiving a molecule as being composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient algorithms can be proposed to address problems in the description of chemical bond formation and breaking. We present a formally exact time-dependent density functional theory for the electronic dynamics of molecular fragments with a variable number of electrons. This new formalism is an extension of previous work [Phys. Rev. Lett. 111, 023001 (2013)]. We also introduce a stable density-inversion method that is applicable to time-dependent and ground-state density functional theories and their extensions, including those discussed in this work.

Existence, uniqueness, and construction of the density-potential mapping in time-dependent density-functional theory

In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such that a mapping from potentials to densities is defined by solving the time-dependent Schrödinger equation. We specifically discuss intricacies connected with the unboundedness of the Hamiltonian and derive the local-force equation. This equation is then used to set up an iterative sequence that determines a potential that generates a specified density via time propagation of an initial state. This fixed-point procedure needs the invertibility of a certain Sturm-Liouville problem, which we discuss for different situations. Based on these considerations we then present a discussion of the famous Runge-Gross theorem which provides a density-potential mapping for time-analytic potentials. Further we give conditions such that the general fixed-point approach is well-defined and converges under certain assumptions. Then the application of such a fixed-point procedure to lattice Hamiltonians is discussed and the numerical realization of the density-potential mapping is shown. We conclude by presenting an extension of the density-potential mapping to include vector-potentials and photons.