Density-Matrix Coupled Time-Dependent Exchange-Correlation Functional Approximations

Density-functional approximations for exchange and correlation

Density-functional theory (DFT) is based on two pivotal theorems due to Hohenberg and Kohn [1]. The first theorem states that the ground-state density ρ(r) of a system of electrons uniquely determines the Hamiltonian and hence all properties that can be derived from it. Using mathematical language we can say that the total electronic energy of the system is a functional of the electron density,

Semiclassical Correlation in Time-Dependent Density Matrix Functional Theory

The impact of time-dependent density functional theory (TDDFT) [1, 2] on calculations of excitation spectra and response in atoms, molecules, and solids is evident in its increasing use. In such applications a weak perturbation is applied to the system beginning in its ground state, and usually the exchange-correlation (xc) effects are treated with a ground-state approximation. Generally the re...

Time-dependent density-functional and reduced density-matrix methods for few electrons: Exact versus adiabatic approximations

To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N -electron problem onto an N -dimensional single electron problem. We analyze the performance of the ...

Correlation in time-dependent density-functional theory

The exact time-dependent correlation energy in time-dependent density-functional theory is shown to sometimes become positive, which is impossible with most present TDDFT approximations. Both the correlation potential and energy can be strongly nonlocal in time. A new inequality is derived for the time-dependent exchange-correlation energy. The correlation energy appears to scale to a constant ...

Time-Dependent One-Body Reduced Density Matrix Functional Theory Adiabatic Approximations and Beyond