This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at ??HOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The ??HOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential

Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold

Time-dependent density functional theory (TDDFT) can be viewed as an exact reformulation of time-dependent quantum mechanics, where the fundamental variable is no longer the many-body wave function but the density. This time-dependent density is determined by solving an auxiliary set of noninteracting Schrodinger equations, the Kohn-Sham equations. The nontrivial part of the many-body interaction is contained in the so-called exchange-correlation potential, for which reasonably good approximations exist. Within TDDFT two regimes can be distinguished: (a) If the external time-dependent potential is "small," the complete numerical solution of the time-dependent Kohn-Sham equations can be avoided by the use of linear response theory. This is the case, e.g., for the calculation of photoabsorption spectra. (b) For a "strong" external potential, a full solution of the time-dependent Kohn-Sham equations is in order. This situation is encountered, for instance, when matter interacts with intense laser fields. In this review we give an overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime.

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Time-Dependent Density Functional Theory

Density functional theory has been spectacularly successful in physics, chemistry, and related fields, and it keeps finding new applications. This paper gives an overview of the history of the method and its many applications since it gained wide acceptance, as well as a discussion of its likely future.

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Density functional theory: Its origins, rise to prominence, and future

Publisher Summary
Density functional theory for stationary states or ensembles is a formulation of many-body theory in terms of the particle density Time-dependent density functional theory as a complete formalism is of more recent origin, although a time-dependent version This chapter describes the linear-response limit of time-dependent density functional theory along with applications to the photo-response of atoms, molecules and metallic surfaces Beyond the regime of linear response, the description of atomic and nuclear collision processes appears to be a promising field of application where the time-dependent Kohn and Sham (KS) scheme could serve as an economical alternative to time-dependent configuration-interaction calculation So far, only a simplified version of the time-dependent KS scheme has been implemented in this context Another possible application beyond the regime of linear response is the calculation of atomic multiphoton ionization which, in the case of hydrogen, has recently been found 54i55 to exhibit chaotic behavior A full-scale numerical solution of the time-dependent Schriidinger equation for a hydrogen atom placed in strong time-dependent electric fields has recently been reported A time-dependent Hartree–Fock calculation has been achieved for the multiphoton ionization of helium For heavier atoms an analogous solution of the time dependent Kohn-Sham equations offers itself as a promising application of time-dependent density functional theory

Time-dependent density-functional theory

Quantum plasmonics is an exciting subbranch of nanoplasmonics where the laws of quantum theory are used to describe light–matter interactions on the nanoscale. Plasmonic materials allow extreme subdiffraction confinement of (quantum or classical) light to regions so small that the quantization of both light and matter may be necessary for an accurate description. State-of-the-art experiments now allow us to probe these regimes and push existing theories to the limits which opens up the possibilities of exploring the nature of many-body collective oscillations as well as developing new plasmonic devices, which use the particle quality of light and the wave quality of matter, and have a wealth of potential applications in sensing, lasing, and quantum computing. This merging of fundamental condensed matter theory with application-rich electromagnetism (and a splash of quantum optics thrown in) gives rise to a fascinating area of modern physics that is still very much in its infancy. In this review, we discuss and compare the key models and experiments used to explore how the quantum nature of electrons impacts plasmonics in the context of quantum size corrections of localized plasmons and quantum tunneling between nanoparticle dimers. We also look at some of the remarkable experiments that are revealing the quantum nature of surface plasmon polaritons.

Quantum Plasmonics

The time-dependent density-functional theory of Runge and Gross [Phys. Rev. Lett. 52, 997 (1984)] is reexamined on the basis of its limitations, and the criticisms raised by Xu and Rajagopal [Phys. Rev. A 31, 2682 (1985)] are addressed, within the imposition of natural boundary conditions of vanishing density and potential at infinity. Also, for a single-particle system characterized by an arbitrary time-dependent potential, the uniqueness of the density-to-potential mapping is established explicitly for both bound and scattering states.

Density-functional theory for time-dependent systems.

A time-dependent density-functional formalism is developed for many-electron systems subjected to external electric and magnetic fields with arbitrary time dependence. The single-particle current density is shown to determine uniquely the time-dependent scalar and vector potentials characterizing the system, and hence also the many-particle wave function. A Levy-type universal functional is defined, and practical schemes for the calculation of electron density and the current density through hydrodynamical as well as a set of single-particle Kohn-Sham-like equations are proposed. The gauge invariance of the present self-consistent formalism is also proved.

Density-functional theory of many-electron systems subjected to time-dependent electric and magnetic fields.

A class of recently discussed time-dependent classical Lagrangians possessing invariants is considered from a quantum-mechanical point of view. Quantum mechanics is introduced directly through the Feynman propagator defined as a path integral involving the classical action. It is shown, without carrying out explicit path integration, that the propagator for these time-dependent problems is related to the propagator of associated time-independent problems. The expansion of the propagator in terms of the eigenfunctions of the invariant operator and the quantum superposition principle follow naturally in our scheme. The theory is applied to obtain explicitly exact propagators for some illustrative examples.

Time-dependent invariants and the Feynman propagator

Density-functional theory of two-dimensional electron gas in a magnetic field.

For an electron gas in a uniform magnetic field, explicit expressions of the electron density, current density, and the density matrix are derived as functions of the Fermi energy and the field strength, using plane waves and the Landau energy levels. The local-density approximations for the kinetic and the exchange energy functionals for an inhomogeneous many-electron system are thereby suggested using the density quantities as basic variables. A practical scheme for the density-functional calculation involving the magnetic field in the spirit of Thomas-Fermi-Dirac theory is outlined.

Asish K. Dhara

Papers

Density-functional theory for time-dependent systems.

Density-functional theory of many-electron systems subjected to time-dependent electric and magnetic fields.

Time-dependent invariants and the Feynman propagator

Density-functional theory of two-dimensional electron gas in a magnetic field.

Local-density approximation to the energy density functionals in a magnetic field