Solving the ultranonlocality problem in time-dependent spin-density-functional theory

Progress in time-dependent density-functional theory

The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in Volume 55 of the Annual Review of Physical Chemistry left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Because doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis is placed on the problem of going beyond or around the TD-DFT adiabatic approximation, which limits TD-DFT calculations to nominally singly-excited states.

Time-dependent current-density-functional theory of spin-charge separation and spin drag in one-dimensional ultracold Fermi gases

Motivated by the large interest in the nonequilibrium dynamics of low-dimensional quantum many-body systems, we present a fully microscopic theoretical and numerical study of the charge and spin dynamics in a one-dimensional ultracold Fermi gas following a quench. Our approach, which is based on time-dependent current-density-functional theory, is applicable well beyond the linear-response regime and produces both spin-charge separation and spin-drag-induced broadening of the spin packets.

Spin drag and spin-charge separation in cold fermi gases

Low-energy spin and charge excitations of one-dimensional interacting fermions are completely decoupled and propagate with different velocities. These modes, however, can decay due to several possible mechanisms. In this Letter we expose a new facet of spin-charge separation: not only the speeds but also the damping rates of spin and charge excitations are different. While the propagation of long-wavelength charge excitations is essentially ballistic, spin propagation is intrinsically damped and diffusive. We suggest that cold Fermi gases trapped inside a tight atomic waveguide offer the opportunity to measure the spin-drag relaxation rate that controls the broadening of a spin packet.

Excitation energies of π-conjugated oligomers within time-dependent current-density-functional theory

We study the pi*<--pi singlet excitations of the pi-conjugated oligomers of polyacetylene, polydiacetylene, polybutatriene, polythiophene, poly(para-phenylene vinylene), and the lowest singlet excitations of the hydrogen chain. For this we used time-dependent current-density-functional theory within the Vignale-Kohn and adiabatic local density approximations. By studying the dependence of the excitation spectrum on the chain length we conclude that the reduction of the static polarizability when using the Vignale-Kohn functional has two origins. First, the excitation energies of transitions with a large transition dipole are shifted upward. Second, the character of the transition between the lowest occupied and highest unoccupied molecular orbitals and the oscillator strength of the lowest transition within the adiabatic local density approximation is transferred to higher transitions. The lowest transitions that have a considerable oscillator strength obtained with the Vignale-Kohn functional have excitation energies that are in most cases in better agreement with available reference data than the adiabatic local density approximation.

Time-dependent exchange-correlation current density functionals with memory

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e., the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the derived exchange-correlation potential will depend not only on present densities but also on the past. In order to ensure the potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn-Sham equations. The exchange-correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal exchange-correlation vector potential for the Kohn-Sham equations incorporating memory effects. We show explicitly that the net exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit).

Spin mass of an electron liquid

We show that in order to calculate correctly the spin current carried by a quasiparticle in an electron liquid one must use an effective "spin mass" m(s) that is larger than both the band mass m(b), which determines the charge current, and the quasiparticle effective mass m(*), which determines the heat capacity. We present two independent estimates of the spin mass enhancement, m(s)/m(b), in two- and three-dimensional electron liquids, based on (i) previously calculated values of the Landau parameters and (ii) a recent theory of the dynamical local field factor in the spin channel. Both methods yield a significant spin mass enhancement, which is larger in two dimensions than in three.

Excitation energies for a benchmark set of molecules obtained within time-dependent current-density functional theory using the Vignale–Kohn functional

In this article we explain how the existing linear response theory of time-dependent density-functional theory can be extended to obtain excitation energies in the framework of time-dependent current-density-functional theory. We use the Vignale-Kohn current-functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchange-correlation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The pi(*)<--pi transitions obtained with the Vignale-Kohn functional are in good agreement with experiment and other theoretical results and they are in general an improvement upon the adiabatic local density approximation. In case of the pi(*)<--n transitions the Vignale-Kohn functional fails, giving results that strongly overestimate the experimental and other theoretical results. The benchmark set also contains some other types of excitations for which no clear failures or improvements are observed.