Momentum distributions in time-dependent density functional theory: Product phase approximation for non-sequential double ionization in strong laser fields

We investigate the possibility to deduce momentum space properties from time-dependent density functional calculations. Electron and ion momentum distributions after double ionization of a model Helium atom in a strong few-cycle laser pulse are studied. We show that, in this case, the choice of suitable functionals for the observables is considerably more important than the choice of the correlation potential in the time-dependent Kohn-Sham equations. By comparison with the solution of the time-dependent Schroedinger equation, the insufficiency of functionals neglecting electron correlation is demonstrated. We construct a functional of the Kohn-Sham orbitals, which in principle yields the exact momentum distributions of the electrons and the ion. The product-phase approximation is introduced, which reduces the problem of approximating this functional significantly.Comment: 8 pages, 5 figures, RevTeX

Violation of the `Zero-Force Theorem' in the time-dependent Krieger-Li-Iafrate approximation

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the `Zero-Force Theorem'. By analyzing the time-dependent dipole moment of Na5 and Na9+, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the `Zero-Force Theorem' and the `Generalized-Translation Invariance' of the potential, are discussed.Comment: 5 pages, 4 figure

The generator coordinate method in time-dependent density-functional theory: memory made simple

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.Comment: 10 pages, 13 figure

Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

We apply the coupled dynamics of time-dependent density functional theory and Maxwell equations to the interaction of intense laser pulses with crystalline silicon. As a function of electromagnetic field intensity, we see several regions in the response. At the lowest intensities, the pulse is reflected and transmitted in accord with the dielectric response, and the characteristics of the energy deposition is consistent with two-photon absorption. The absorption process begins to deviate from that at laser intensities ~ 10^13 W/cm^2, where the energy deposited is of the order of 1 eV per atom. Changes in the reflectivity are seen as a function of intensity. When it passes a threshold of about 3 \times 1012 W/cm2, there is a small decrease. At higher intensities, above 2 \times 10^13 W/cm^2, the reflectivity increases strongly. This behavior can be understood qualitatively in a model treating the excited electron-hole pairs as a plasma.Comment: 27 pages; 11 figure

The correlation potential in density functional theory at the GW-level: spherical atoms

As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamically- screened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.Comment: 13 pages, 9 figure

Accurate density functional calculations on frequency-dependent hyperpolarizabilities of small molecules

In this paper we present time-dependent density functional calculations on frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules,

Non-linear phenomena in time-dependent density-functional theory: What Rabi physics can teach us

Through the exact solution of a two-electron system interacting with a monochromatic laser we prove that all adiabatic density functionals within time-dependent density-functional theory are not able to discern between resonant and non-resonant (detuned) Rabi oscillations. This is rationalized in terms of a fictitious dynamical exchange-correlation (xc) detuning of the resonance while the laser is acting. The non-linear dynamics of the Kohn-Sham system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We identify the source of this error in a contribution from the xc-functional to the non-linear equations describing the electron dynamics in an effective two-level system. The constraint of preventing the detuning introduces a new strong condition to be satisfied by approximate xc-functionals

Time-dependent density functional theory: Past, present, and future

Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope, and yields predictions for many more properties. We discuss some of the challenges involved in making accurate predictions for these properties.Comment: 12 pages, 4 figure

Quantum memory effects on the dynamics of electrons in small gold clusters

Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a 'memory term', i.e. attempts to describe temporal non-local correlations. Using the Iwamoto, Gross and Kohn exchange-correlation (XC) kernel we construct a translationally invariant memory action from which an XC potential is derived that is translationally covariant and exerts zero net force on the electrons. An efficient and stable numerical method to solve the resulting Kohn-Sham equations is presented. Using this framework, we study memory effects on electron dynamics in spherical Jellium 'gold clusters'. We find memory significantly broadens the surface plasmon absorption line, yet considerably less than measured in real gold clusters, attributed to the inadequacy of the Jellium model. Two-dimensional pump-probe spectroscopy is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail. Finally, we examine memory effects on high harmonic generation, finding memory narrows emission lines

Time-Dependent Density Functional Theory of Open Quantum Systems in the Linear-Response Regime

Time-Dependent Density Functional Theory (TDDFT) has recently been extended to describe many-body open quantum systems (OQS) evolving under non-unitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a non-interacting open Kohn-Sham system yielding the correct non-equilibrium density evolution. A pseudo-eigenvalue equation analogous to the Casida equations of usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C$^{2+}$ atom in an optical resonator interacting with a bath of photons. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on Gorling-Levy perturbation theory is calculated.Comment: 18 pages, 4 figure