Time-dependent density functional theory (TDDFT) provides a successful approach to calculate excitation energies of atomic and molecular systems. In part I of this work we present a double-pole approximation (DPA) to the response equations of TDDFT. The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single- pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. Several critical pole separations can be identified, e.g. we find that the pole coupling can cause transitions to vanish entirely from the optical spectrum. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange- correlation kernel fxc from experimental input. This can serve as benchmark for the construction of future approximations for the kernel fxc. Reduced density matrix functional theory (RDMFT) has emerged recently as promising candidate to treat strongly correlated electronic many-body systems beyond traditional density functional theory (DFT). The research within RDMFT was so far focussed on the static theory. In this work we attempt some first steps towards a time-dependent generalization of RDMFT. In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schrödinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single- particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schrödinger equation. We consider the propagation of finite mesoscopic systems and demonstrate the limitations of such an approach. To overcome the shortcomings of a description of quantum transport in terms of finite systems we develop a time-propagation scheme for extended states which utilizes a mixed basis representation. Our discretization scheme allows to treat central device and lead regions on the same footing thus preventing artificial reflections at grid boundaries.

Jan 1, 200710 citations

Progress toward a formal functional theory of strongly correlated systems

Ting Zhang, Neil Qiang Su

We explore the hypercomplex Kohn-Sham (HCKS) formalism and develop a third exact functional theory beyond the popular Kohn-Sham density functional theory (KS-DFT) and reduced density matrix functional theory (RDMFT), called 1-HCKS. The orbitals of hierarchical correlation introduced in 1-HCKS are interesting because their occupations are neither necessarily integers, as in KS-DFT, nor overly flexible, as in RDMFT; rather, they can capture strong correlation with fractional occupations, governed by stringent constraints. This feature allows 1-HCKS to combine the advantages of KS-DFT and RDMFT in dealing with dynamic correlation and strong correlation, while eliminating the issues of computational convergence and basis set dependence encountered in RDMFT. Thus, 1-HCKS is a promising alternative for implementing DFT beyond KS-DFT, especially for the treatment of strongly correlated systems.

Physical Review ANov 2, 20237 citations