Fast computation of the Kohn-Sham susceptibility of large systems

For hybrid systems, such as molecules grafted onto solid surfaces, the calculation of linear response in time dependent density functional theory is slowed down by the need to calculate, in N^4 operations, the susceptibility of N non interacting Kohn-Sham reference electrons. We show how this susceptibility can be calculated N times faster within finite precision. By itself or in combination with previous methods, this should facilitate the calculation of TDDFT response and optical spectra of hybrid systems.Comment: submitted 25/1/200

Rydberg transition frequencies from the Local Density Approximation

A method is given that extracts accurate Rydberg excitations from LDA density functional calculations, despite the short-ranged potential. For the case of He and Ne, the asymptotic quantum defects predicted by LDA are in less than 5% error, yielding transition frequency errors of less than 0.1eV.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

A joint time-dependent density-functional theory for excited states of electronic systems in solution

We present a novel joint time-dependent density-functional theory for the description of solute-solvent systems in time-dependent external potentials. Starting with the exact quantum-mechanical action functional for both electrons and nuclei, we systematically eliminate solvent degrees of freedom and thus arrive at coarse-grained action functionals which retain the highly accurate \emph{ab initio} description for the solute and are, in principle, exact. This procedure allows us to examine approximations underlying popular embedding theories for excited states. Finally, we introduce a novel approximate action functional for the solute-water system and compute the solvato-chromic shift of the lowest singlet excited state of formaldehyde in aqueous solution, which is in good agreement with experimental findings.Comment: 11 page

Spin gaps and spin-flip energies in density-functional theory

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is know about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single particle calculations tend to overestimate spin gaps while they underestimate charge gaps.Comment: 11 pages, 1 figure, 3 table

A new and efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be obtained from the non-symmetric block-Lanczos method. The resulting algorithm allows for the calculation of the {\em full spectrum} of a system with a computational workload which is only a few times larger than that needed for {\em static} polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with the calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.Comment: 4 pages, 2 figure

Linear Continuum Mechanics for Quantum Many-Body Systems

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.Comment: 4 pages, 1 figure, 1 tabl

Investigating interaction-induced chaos using time-dependent density functional theory

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbour level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.Comment: 8 pages, 4 figure