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For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schr ̈ dinger equation, based o on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schr ̈ dinger o equations�the Kohn�Sham equations. The complication of the problem is hidden in the� unknown�time-dependent exchange and correlation potential that appears in the Kohn�Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe� Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems. Lecture Notes Collection FreeScience.info ID2183 Obtained from http://www.fhi-berlin.mpg.de/th/publications/RPP-70-357-2007.pdf http://www.freescience.info/go.php?pagename=books&id=2183

We demonstrate the capabilities of time-dependent density functional theory (TDDFT) for strong-field, short wavelength (soft X-ray) physics, as compared to a formalism based on rate equations. We find that TDDFT provides a very good description of the total and individual ionization yields for Ne and Ar atoms exposed to strong laser pulses. We assess the reliability of different adiabatic density functionals and conclude that an accurate description of long-range interactions by the exchange and correlation potential is crucial for obtaining the correct ionization yield over a wide range of intensities ($10^{13}$ -- $5 \times 10^{15}$ W/cm$^2$). Our TDDFT calculations disentangle the contribution from each ionization channel based on the Kohn-Sham wavefunctions.

Contents:Introduction; Basic formalism for electrons in time-dependent electric fields 2.1 One-to-one mapping between time-dependent potentials and time-dependent densities 2.2 Stationary-action principle 2.3 Time-dependent Kohn-Sham scheme 3 Motion of the nuclei 3.1 Quantum mechanical treatment of nuclear motion 3.2 Classical treatment of nuclear motion 4 Electrons in time-dependent electromagnetic fields 4.1 Coupling to spin 4.2 Coupling to orbital currents 5 Perturbative regime, basic equations 5.1 Time-dependent linear density response 5.2 Time-dependent higher-order response 6 The time-dependent exchange-correlation potential: Rigorous prop- erties and approximate functionals 6.1 Approximations based on the homogeneous electron gas 6.2 Time-dependent optimized effective potential 7 Applications within the perturbative regime 7.1 Photoresponse of finite and infinite Systems 7.2 Calculation of excitation energies 7.3 Van der Waals interactions 8 Applications beyond the perturbative regime: Atoms in strong femto-second laser pulses. Lecture Notes Collection FreeScience.info ID1948 Obtained from http://www.physik.fu-berlin.de/~ag-gross/articles/pdf/GDP96.pdf http://www.freescience.info/go.php?pagename=books&id=1948

Contents:Introduction; Basic formalism for electrons in time-dependent electric fields 2.1 One-to-one mapping between time-dependent potentials and time-dependent densities 2.2 Stationary-action principle 2.3 Time-dependent Kohn-Sham scheme 3 Motion of the nuclei 3.1 Quantum mechanical treatment of nuclear motion 3.2 Classical treatment of nuclear motion 4 Electrons in time-dependent electromagnetic fields 4.1 Coupling to spin 4.2 Coupling to orbital currents 5 Perturbative regime, basic equations 5.1 Time-dependent linear density response 5.2 Time-dependent higher-order response 6 The time-dependent exchange-correlation potential: Rigorous prop- erties and approximate functionals 6.1 Approximations based on the homogeneous electron gas 6.2 Time-dependent optimized effective potential 7 Applications within the perturbative regime 7.1 Photoresponse of finite and infinite Systems 7.2 Calculation of excitation energies 7.3 Van der Waals interactions 8 Applications beyond the perturbative regime: Atoms in strong femto-second laser pulses. Lecture Notes Collection FreeScience.info ID1948 Obtained from http://www.physik.fu-berlin.de/~ag-gross/articles/pdf/GDP96.pdf http://www.freescience.info/go.php?pagename=books&id=1948

In a recent Comment (arXiv:0710.0018), Maitra, Burke, and van Leeuwen (MBL) attempt to refute our criticism of the foundations of TDDFT (see Phys. Rev. A 75, 022513 (2007)). However, their arguments miss the essence of our position. This is mainly due to an ambiguity concerning the meaning of the so-called mapping derivation of time-dependent Kohn-Sham equations. We distinguish two different conceptions, referred to as potential-functional based fixed-point iteration (PF-FPI) and direct Kohn-Sham potential (DKSP) scheme, respectively. We argue that the DKSP scheme, apparently adopted by MBL, is not a density-functional method at all. The PF-FPI concept, on the other hand, while legitimately predicated on the Runge-Gross mapping theorem, is invalid because the convergence of the fixed-point iteration is not assured.

We introduce a new class of exchange-correlation potentials for a static and time-dependent Density Functional Theory of strongly correlated systems in 3D. The potentials are obtained via Dynamical Mean Field Theory and, for strong enough interactions, exhibit a discontinuity at half filling density, a signature of the Mott transition. For time-dependent perturbations, the dynamics is described in the adiabatic local density approximation. Results from the new scheme compare very favorably to exact ones in clusters. As an application, we study Bloch oscillations in the 3D Hubbard model.

This paper provides a pedagogical in troduction to TDDFT . With that in mind, they present, in section 2, a quite detailed proof of the Runge-Gross theorem, i.e. the time-dependent generalization of the Hohenberg-Kohn theorem, and the corresponding Kohn-Sham construction. These constitute the mathematical foundations of TDDFT. Several approximate exchange-correlation (xc) functionals are then reviewed. Section 3 is concerned with linear-response theory, and with its main ingredient, the xc kernel. The calculation of excitation energies is treated in the following section. After giving a brief overlook of the competing density-functional methods to calculate excitations, they present some results obtained from the full solution of the Kohn-Sham scheme, and from linear-response theory. Section 5 is devoted to the problem of atoms and molecules in strong laser fields. Both high-harmonic generation and ionization are discussed. Finally, the last section is reserved to some concluding remarks. Lecture Notes Collection FreeScience.info ID1451 Obtained from http://www.physik.fu-berlin.de/~ag-gross/articles/pdf/MG03.pdf http://www.freescience.info/go.php?pagename=books&id=1451

The optical absorption spectrum of the three most stable isomers of the Ag11 system was calculated using the time-dependent density functional theory, with the generalized gradient approximation for the exchange and correlation potential, and a relativistic pseudopotential parametrization for the modelling of the ion-electron interaction. The computational scheme is based on a real space code, where the photoabsorption spectrum is calculated by using the formalism developed by Casida. The significantly different spectra of the three isomers permit the identification of the ground-state configuration predominantly present in the laboratory beams in base to a comparison between the calculated photoabsorption spectrum of the most stable configuration of Ag11 and the measured spectra of medium-size silver clusters trapped in noble gas Ar and Ne matrices at different temperatures. This assignment is confirmed by the fact that this isomer has the lowest calculated energy.

Homologous classes of Polycyclic Aromatic Hydrocarbons (PAHs) in their crystalline state are among the most promising materials for organic opto-electronics. Following previous works on oligoacenes we present a systematic comparative study of the electronic, optical, and transport properties of oligoacenes, phenacenes, circumacenes, and oligorylenes. Using density functional theory (DFT) and time-dependent DFT we computed: (i) electron affinities and first ionization energies; (ii) quasiparticle correction to the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap; (iii) molecular reorganization energies; (iv) electronic absorption spectra of neutral and $\pm1$ charged systems. The excitonic effects are estimated by comparing the optical gap and the quasiparticle corrected HOMO-LUMO energy gap. For each molecular property computed, general trends as a function of molecular size and charge state are discussed. Overall, we find that circumacenes have the best transport properties, displaying a steeper decrease of the molecular reorganization energy at increasing sizes, while oligorylenes are much more efficient in absorbing low-energy photons in comparison to the other classes.

We demonstrate that the zero-temperature conductance of the Anderson model can be calculated within the Landauer formalism combined with static density functional theory (DFT). The proposed approximate functional is based on finite-temperature DFT and yields the exact Kohn-Sham potential at the particle-hole symmetric point. Furthermore, in the limit of zero temperature it correctly exhibits a derivative discontinuity which is shown to be essential to reproduce the conductance plateau. On the other hand, at the Kondo temperature the exact Kohn-Sham conductance overestimates the real one by an order of magnitude. To understand the failure of DFT we resort to its time-dependent version and conclude that the suppression of the Kondo resonance with increasing temperature must be attibuted to dynamical exchange-correlation corrections.

We investigate the time an electronic excitation travels in a supermolecular setup using a measurement process in an open quantum-system framework. The approach is based on the stochastic Schr\"odinger equation and uses a Hamiltonian from time-dependent density functional theory (TDDFT). It treats electronic-structure properties and intermolecular coupling on the level of TDDFT, while it opens a route to the description of dissipation and relaxation via a bath operator that couples to the dipole moment of the density. Within our study, we find that in supermolecular setups small deviations of the electronic structure from the perfectly resonant case have only minor influence on the pathways of excitation-energy transfer, thus lead to similar transfer times. Yet, sizable defects cause notable slowdown of the energy spread.

We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

The coupling constant dependence is derived in time-dependent {\em current} density functional theory. The scaling relation can be used to check approximate functionals and in conjunction with the adiabatic connection formula to obtain the ground-state energy from the exchange-correlation kernel. The result for the uniform gas using the Vignale-Kohn approximation is deduced.

The role of the exchange-correlation potential and the exchange-correlation kernel in the calculation of excitation energues from time-dependent density functional theory is studied. Excitation energies of the He and Be atoms are calculated, both from the exact ground-state Kohn-Sham potential, and from two orbital-dependent approximations. These are exact exchange and self-interaction corrected local density approximation (SIC-LDA), both calculated using the Krieger-Li-Iafrate (KLI) approximation. For the exchange-correlation kernela, three adiabatic approximations were tested: The local density approximation, exact exchange, and SIC-LDA. The choice of the ground-state exchange-correlation potential has the largest impact on the absolute position of most excitation energies. In particular, orbital-dependent approximate potentials result in a uniform shift of the transition energies to the Rydberg states.

We present an extension of the density-functional theory (DFT) formalism for lattice gases to systems with internal degrees of freedom. In order to test approximations commonly used in DFT approaches, we investigate the statics and dynamics of occupation (density) profiles in the one-dimensional Potts model. In particular, by taking the exact functional for this model we can directly evaluate the quality of the local equilibrium approximation used in time-dependent density-functional theory (TDFT). Excellent agreement is found in comparison with Monte Carlo simulations. Finally, principal limitations of TDFT are demonstrated.

A robust and efficient frequency dependent and non-local exchange-correlation $f_{xc}(r,r';\omega)$ is derived by imposing time-dependent density-functional theory (TDDFT) to reproduce the many-body diagrammatic expansion of the Bethe-Salpeter polarization function. As an illustration, we compute the optical spectra of LiF, \sio and diamond and the finite momentum transfer energy-loss spectrum of LiF. The TDDFT results reproduce extremely well the excitonic effects embodied in the Bethe-Salpeter approach, both for strongly bound and resonant excitons. We provide a working expression for $f_{xc}$ that is fast to evaluate and easy to implement.

Recent advances in laser technology allow us to follow electronic motion at its natural time-scale with ultra-fast time resolution, leading the way towards attosecond physics experiments of extreme precision. In this work, we assess the use of tailored pumps in order to enhance (or reduce) some given features of the probe absorption (for example, absorption in the visible range of otherwise transparent samples). This type of manipulation of the system response could be helpful for its full characterization, since it would allow us to visualize transitions that are dark when using unshaped pulses. In order to investigate these possibilities, we perform first a theoretical analysis of the non-equilibrium response function in this context, aided by one simple numerical model of the Hydrogen atom. Then, we proceed to investigate the feasibility of using time-dependent density-functional theory as a means to implement, theoretically, this absorption-optimization idea, for more complex atoms or molecules. We conclude that the proposed idea could in principle be brought to the laboratory: tailored pump pulses can excite systems into light-absorbing states. However, we also highlight the severe numerical and theoretical difficulties posed by the problem: large-scale non-equilibrium quantum dynamics are cumbersome, even with TDDFT, and the shortcomings of state-of-the-art TDDFT functionals may still be serious for these out-of-equilibrium situations.

Density functional theory for stationary states or ensembles is a formulation of many-body theory in terms of the particle density, rho(r). It is now a mature subject which has had many successful applications. Time-dependent density functional theory as a complete formalism is of more recent origin. A detailed description of time-dependent density-functional formalism is presented with emphasis on evolving applications. Keywords: Time-dependent density functional theory, Frequency-dependent linear response, Local field correction, Frequency-dependent local density approximation, Photoabsorption of atoms and molecules, Response of metallic surfaces.

Time-dependent density-functional theory (TDDFT) is a formally exact approach to the time-dependent electronic many-body problem which is widely used for calculating excitation energies. We present a survey of the fundamental framework, practical aspects, and applications of TDDFT. This paper is mainly intended for non-experts (students or researchers in other areas) who would like to learn about the present state of TDDFT without going too deeply into formal details.

The photoionization cross-section of several atoms (Ar, Xe, Rn, Cs) and ions (Ne-like Ar, H-like and Li-like C) of experimental interest are calculated using the time-dependent response scheme within the framework of local density functional method (DFM). The cross-sections for rare gas atoms calculated using this method agree very well with the experimental data; whereas conventional independent particle model, calculations do not. The polarization effect of the atom brought about by the incident time-varying radiation field is shown to be important in describing observed results. Unlike the independent particle model, this effect effect is treated adequately in the DFM. To study the effect plasma density and temperature on the photoionization cross-section, calculations were also done for the ions mentioned above at various densities and temperatures. For computational simplicity, a simplified model of self-consistent finite temperature DFM was used in which the long range part of the ionic potential was taken as the Debye-screened potential. These calculations were compared with the isolated ion calculations (without any plasma effect). With increasing plasma density, significant shifts of the ionization threshold as well as substantial modifications of photoionization cross-section are obtained. This points out the need for incorporating the effect of surrounding plasma in realistic modeling of atomic properties for dense plasmas.

The photoionization cross-section of several atoms (Ar, Xe, Rn, Cs) and ions (Ne-like Ar, H-like and Li-like C) of experimental interest are calculated using the time-dependent response scheme within the framework of local density functional method (DFM). The cross-sections for rare gas atoms calculated using this method agree very well with the experimental data; whereas conventional independent particle model, calculations do not. The polarization effect of the atom brought about by the incident time-varying radiation field is shown to be important in describing observed results. Unlike the independent particle model, this effect effect is treated adequately in the DFM. To study the effect plasma density and temperature on the photoionization cross-section, calculations were also done for the ions mentioned above at various densities and temperatures. For computational simplicity, a simplified model of self-consistent finite temperature DFM was used in which the long range part of the ionic potential was taken as the Debye-screened potential. These calculations were compared with the isolated ion calculations (without any plasma effect). With increasing plasma density, significant shifts of the ionization threshold as well as substantial modifications of photoionization cross-section are obtained. This points out the need for incorporating the effect of surrounding plasma in realistic modeling of atomic properties for dense plasmas.

We formulate a time-dependent density functional theory (TDDFT) in terms of the density matrix to study ultrafast phenomena in semiconductor structures. A system of equations for the density matrix components, which is equivalent to the time-dependent Kohn-Sham equation, is derived. From this we obtain a TDDFT version of the semiconductor Bloch equations, where the electronic many-body effects are taken into account in principle exactly. As an example, we study the optical response of a three-dimensional two-band insulator to an external short-time pulsed laser field. We show that the optical absorption spectrum acquires excitonic features when the exchange-correlation potential contains a $1/q^{2}$ Coulomb singularity. A qualitative comparison of the TDDFT optical absorption spectra with the corresponding results obtained within the Hartree-Fock approximation is made.

The dynamics of a many-body system coupled to an external environment represents a fundamentally important problem. To this class of open quantum systems pertains the study of energy transport and dissipation, dephasing, quantum measurement and quantum information theory, phase transitions driven by dissipative effects, etc. Here, we discuss in detail an extension of time-dependent current-density-functional theory (TDCDFT), we named stochastic TDCDFT [Phys. Rev. Lett. {\bf 98}, 226403 (2007)], that allows the description of such problems from a microscopic point of view. We discuss the assumptions of the theory, its relation to a density matrix formalism, and the limitations of the latter in the present context. In addition, we describe a numerically convenient way to solve the corresponding equations of motion, and apply this theory to the dynamics of a 1D gas of excited bosons confined in a harmonic potential and in contact with an external bath.

We discuss the relationship between modern time-dependent density functional theory and earlier time-periodic versions, and why the criticisms in a recent paper (Chem. Phys. Lett. {\bf 433} (2006) 204) of our earlier analysis (Chem. Phys. Lett. {\bf 359} (2002) 237) are incorrect.

Owing to its numerical simplicity, a two-dimensional two-electron model atom, with each electron moving in one direction, is an ideal system to study non-perturbatively a fully correlated atom exposed to a laser field. Frequently made assumptions, such as the ``single active electron''- approach and calculational approximations, e.g. time dependent density functional theory or (semi-) classical techniques, can be tested. In this paper we examine the multiphoton short pulse-regime. We observe ``non-sequential'' ionization, i.e.\ double ionization at lower field strengths as expected from a sequential, single active electron-point of view. Since we find non-sequential ionization also in purely classical simulations, we are able to clarify the mechanism behind this effect in terms of single particle trajectories. PACS Number(s): 32.80.Rm

Quantum Optimal Control Theory (QOCT) provides the necessary tools to theoretically design driving fields capable of controlling a quantum system towards a given state or along a prescribed path in Hilbert space. This theory must be complemented with a suitable model for describing the dynamics of the quantum system. Here, we are concerned with many electron systems (atoms, molecules, quantum dots, etc) irradiated with laser pulses. The full solution of the many electron Schr{\"{o}}dinger equation is not feasible in general, and therefore, if we aim to an ab initio description, a suitable choice is time-dependent density-functional theory (TDDFT). In this work, we establish the equations that combine TDDFT with QOCT, and demonstrate their numerical feasibility with examples.

We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point question for potentials on a given time-interval. We show that the unique fixed point, i.e. the unique potential generating a given density, is reached as the limiting point of an iterative procedure. The one-to-one correspondence between densities and potentials is a straightforward result provided that the response function of the divergence of the internal forces is bounded. The existence, i.e. the v-representability of a density, can be proven as well provided that the operator norms of the response functions of the members of the iterative sequence of potentials have an upper bound. The densities under consideration have second time-derivatives that are required to satisfy a condition slightly weaker than being square-integrable. This approach avoids the usual restrictions of Taylor-expandability in time of the uniqueness theorem by Runge and Gross [Phys.Rev.Lett.52, 997 (1984)] and of the existence theorem by van Leeuwen [Phys.Rev.Lett. 82, 3863 (1999)]. Owing to its generality, the proof not only answers basic questions in density-functional theory but also has potential implications in other fields of physics.

A new parameter-free approximation for the exchange-correlation kernel $f_{\rm xc}$ of time-dependent density functional theory is proposed. This kernel is expressed as an algorithm in which the exact Dyson equation for the response as well as a further approximate condition are solved together self-consistently leading to a simple parameter-free kernel. We apply this to the calculation of optical spectra for various small bandgap (Ge, Si, GaAs, AlN, TiO$_2$, SiC), large bandgap (C, LiF, Ar, Ne) and magnetic (NiO) insulators. The calculated spectra are in very good agreement with experiment for this diverse set of materials, highlighting the universal applicability of the new kernel.

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.

Excitons are electron-hole pairs appearing below the band gap in insulators and semiconductors. They are vital to photovoltaics, but are hard to obtain with time-dependent density-functional theory (TDDFT), since most standard exchange-correlation (xc) functionals lack the proper long-range behavior. Furthermore, optical spectra of bulk solids calculated with TDDFT often lack the required resolution to distinguish discrete, weakly bound excitons from the continuum. We adapt the Casida equation formalism for molecular excitations to periodic solids, which allows us to obtain exciton binding energies directly. We calculate exciton binding energies for both small- and large-gap semiconductors and insulators, study the recently proposed bootstrap xc kernel [S. Sharma et al., Phys. Rev. Lett. 107, 186401 (2011)], and extend the formalism to triplet excitons.

Based on the time-dependent density-functional theory, we have derived a rigorous formula for the stopping power of an {\it interacting} electron gas for ions in the limit of low projectile velocities. If dynamical correlation between electrons is not taken into account, this formula recovers the corresponding stopping power of {\it noninteracting} electrons in an effective Kohn-Sham potential. The correlation effect, specifically the excitonic one in electron-hole pair excitations, however, is found to considerably enhance the stopping power for intermediately charged ions, bringing our theory into good agreement with experiment.

We present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, we implemented it in a real-space (basis-set free) code, and applied it to benchmark molecules, namely CO, H2O, and paranitroaniline (PNA). Our results are in agreement with experimental and previous theoretical studies, and fully validate our approach.

This article has been published as a chapter in "Chemical Reactivity Theory: A Density Functional View", ed. P. K. Chattaraj (CRC Press, New York, 2009), ch. 8, p. 105. In it, an overview of the relationship between time-dependent DFT and quantum hydrodynamics is presented, showing the role that Bohmian mechanics can play within the ab-initio methodology as both a numerical and an interpretative tool.

The resonant interaction of laser light with atoms is analyzed from the time-dependent density functional theory perspective using a model Helium atom which can be solved exactly. It is found that in exact-exchange approximation the time-dependent dipole shows Rabi-type oscillations of its amplitude. However, the time-dependent density itself is not well described. These seemingly contradictory findings are analyzed. The Rabi-type oscillations are found to be essentially of classical origin. The incompatibility of time-dependent density functional theory with few-level approximations for the description of resonant dynamics is discussed.

We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite element bases. Our mesh generation scheme, in which structured atomic meshes are merged to an unstructured molecular mesh, allows a highly nonuniform discretization of the space. Thus it is possible to represent the core and valence states using the same discretization scheme, i.e., no pseudopotentials or similar treatments are required. The nonuniform discretization also allows the use of large simulation cells, and therefore avoids any boundary effects.

We address a major challenge for computational materials science based on density functional theory, by showing that fundamental gaps and optical spectra of molecular solids can be predicted quantitatively and non-empirically within the framework of time-dependent density functional theory (TDDFT), using the recently-developed optimally-tuned screened range-separated hybrid (OTSRSH) approach. We provide a comprehensive benchmark for the accuracy of our approach by considering the X23 set of molecular solids and comparing results obtained from TDDFT with those obtained from many-body perturbation theory in the GW-BSE approximation. We additionally compare results obtained from dielectric screening computed within the random phase approximation to those obtained from the computationally easier many-body dispersion approach and find that this influences the fundamental gap but there is little effect on the optical spectra. We therefore believe that the method is robust and can be used for studies of molecular solids that are typically outside the reach of computationally more intensive methods.

Time-dependent density-functional response theory for molecules. Lecture Notes Collection FreeScience.info ID2122 Obtained from http://tddft.org/TDDFT2004/PracticalSessions/papers/casida_1996.ps http://www.freescience.info/go.php?pagename=books&id=2122

In a paper recently published in Phys. Rev. A [arXiv:1010.4223], Schirmer has criticized an earlier work of mine [arXiv:0803.2727], as well as the foundations of time-dependent density functional theory. In Ref.[2], I showed that the so-called "causality paradox" - i.e., the failure of the exchange-correlation potential derived from the Runge-Gross time-dependent variational principle to satisfy causality requirements - can be solved by a careful reformulation of that variational principle. Fortunately, the criticism presented in Ref.[1] is based on elementary misunderstandings of the nature of functionals, gauge transformations, and the time-dependent variational principle. In this Comment I wish to point out and clear these misunderstandings.

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

With the work performed in this research project, some fundamental aspects of TDDFT for strongly correlated systems have been characterized from several perspectives, such as the role of the exchange-correlation discontinuity in metal-insulator transitions and in quantum transport, the limitations but also the merits of adiabatic approximations, the necessity to include memory and nonlocal effects, to mention a few. Furthermore, TDDFT for strongly correlated lattice models has in fact turned into an active subfield of TDDFT, with new theoretical schemes, new theorems specifically proven for lattice (TD)DFT, applications to distant areas such as ultracold atoms and Kondo physics). Several possible directions can be easily envisaged to continue research in TDDFT: introducing memory and non local effects in the XC potentials (possibly exploiting more closely the connection with Kadanoff-Baym dynamics), magnetism in strongly correlated systems, electron-phonon interactions, etc. In particular, one important aspect, mentioned in the grant proposal and not significantly developed in the period covered by the grant, is the actual implementation of TDDFT within the ab-initio SeqQuest code. This aspect was only partially dealt with during the grant period (a large amount of preliminary work was done in this respect, but no concrete implementation is available and/or in close sight), and remains a priority in the future research plans of the principal investigator. To summarize, the research carried out during the grant period has provided a solid and attractive education profile to the PhD student Alexey Kartsev. It has also showed the great potential of TDDFT in describing the nonequilibrium dynamics of strongly correlated materials, and that there are many stimulating problems to be addressed in order to further develop an important approach such as TDDFT.

It is shown that the exchange-correlation part of the action functional $A_{xc}[\rho (\vec r,t)]$ in time-dependent density functional theory , where $\rho (\vec r,t)$ is the time-dependent density, is invariant under the transformation to an accelerated frame of reference $\rho (\vec r,t) \to \rho ' (\vec r,t) = \rho (\vec r + \vec x (t),t)$, where $\vec x (t)$ is an arbitrary function of time. This invariance implies that the exchange-correlation potential in the Kohn-Sham equation transforms in the following manner: $V_{xc}[\rho '; \vec r, t] = V_{xc}[\rho; \vec r + \vec x (t),t]$. Some of the approximate formulas that have been proposed for $V_{xc}$ satisfy this exact transformation property, others do not. Those which transform in the correct manner automatically satisfy the ``harmonic potential theorem", i.e. the separation of the center of mass motion for a system of interacting particles in the presence of a harmonic external potential. A general method to generate functionals which possess the correct symmetry is proposed.

In our interest to accurately predict the photophysical properties of organic molecules that exhibit multiphoton absorption optical processes, we applied density functional theory (DFT)/time-dependent DFT (TDDFT) for the calculation of structures, and one-photon absorption (OPA), two-photon absorption (TPA) spectra, for series of relevant compounds. In our recent work TDDFT was validated regarding the exchange-correlation functional to be used for molecules that exhibit excited state charge-transfer characteristics, the application of quadratic response for TPA properties, and the inclusion of solvent effects, as applied, for example, to 4,4 `-dimethyl-amino-nitrostilbene and a donor-acceptor (DA) fluorene-based system. In this work we discuss the prediction of TPA cross-section enhancements for large porphyrin dimers.

We investigate the electronic absorption spectra of several maximally pericondensed polycyclic aromatic hydrocarbon radical cations with time dependent density functional theory calculations. We find interesting trends in the vertical excitation energies and oscillator strengths for this series containing pyrene through circumcoronene, the largest species containing more than 50 carbon atoms. We discuss the implications of these new results for the size and structure distribution of the diffuse interstellar band carriers.

Several techniques have appeared in the literatuare to solve the equations of time-dependent density functional theory. We compare the efficiency of different methods based on mesh representations of the wave function (direct and Fourier space), taking as a test case the calculation of the surface plasmon in the cluster Na_8. For smaller systems, the methods have comparable efficiency. For large systems the direct time method has a decided advantage in computer storage requirements. It is also more economical on arithmetic operations, but is not as suited for parallel computing as the methods based on a frequency representation.

We observe using ab initio methods that localized surface plasmon resonances in icosahedral silver nanoparticles enter the asymptotic region already between diameters of 1 and 2 nm, converging close to the classical quasistatic limit around 3.4 eV. We base the observation on time-dependent density-functional theory simulations of the icosahedral silver clusters Ag$_{55}$ (1.06 nm), Ag$_{147}$ (1.60 nm), Ag$_{309}$ (2.14 nm), and Ag$_{561}$ (2.68 nm). The simulation method combines the adiabatic GLLB-SC exchange-correlation functional with real time propagation in an atomic orbital basis set using the projector-augmented wave method. The method has been implemented for the electron structure code GPAW within the scope of this work. We obtain good agreement with experimental data and modeled results, including photoemission and plasmon resonance. Moreover, we can extrapolate the ab initio results to the classical quasistatically modeled icosahedral clusters.

We present a systematic study of the photo-absorption spectra of various Si$_{n}$H$_{m}$ clusters (n=1-10, m=1-14) using the time-dependent density functional theory (TDDFT). The method uses a real-time, real-space implementation of TDDFT involving full propagation of the time dependent Kohn-Sham equations. Our results for SiH$_{4}$ and Si$_{2}$H$_{6}$ show good agreement with the earlier calculations and experimental data. We find that for small clusters (n

We present a systematic study of the photo-absorption spectra of various Si$_{n}$H$_{m}$ clusters (n=1-10, m=1-14) using the time-dependent density functional theory (TDDFT). The method uses a real-time, real-space implementation of TDDFT involving full propagation of the time dependent Kohn-Sham equations. Our results for SiH$_{4}$ and Si$_{2}$H$_{6}$ show good agreement with the earlier calculations and experimental data. We find that for small clusters (n

First-principles calculations of the conventional and acoustic surface plasmons (CSPs and ASPs) on the (111) surfaces of Cu, Ag, and Au are presented. The effect of $s-d$ interband transitions on both types of plasmons is investigated by comparing results from the local density approximation and an orbital dependent exchange-correlation (xc) potential that improves the position and width of the $d$ bands. The plasmon dispersions calculated with the latter xc-potential agree well with electron energy loss spectroscopy (EELS) experiments. For both the CSP and ASP, the same trend of Cu$

We review the theoretical background for obtaining both quantum defects and scattering phase shifts from time-dependent density functional theory. The quantum defect on the negative energy side of the spectrum and the phase shift on the positive energy side merge continuously at E=0, allowing both to be found by the same method. We illustrate with simple one-dimensional examples: the spherical well and the delta well potential. As an example of a real system, we study in detail elastic electron scattering from the He${}^{+}$ ion. We show how the results are influenced by different approximations to the unknown components in (time-dependent) density functional theory: the ground state exchange-correlation potential and time-dependent kernel. We also revisit our previously obtained results for $e$-H scattering. Our results are remarkably accurate in may cases, but fail qualitatively in others.

The effect of nanocrystal orientation on the energy loss spectra of monoclinic hafnia (m-HfO$_2$) is measured by high resolution transmission electron microscopy (HRTEM) and valence energy loss spectroscopy (VEELS) on high quality samples. For the same momentum-transfer directions, the dielectric properties are also calculated ab initio by time-dependent density-functional theory (TDDFT). Experiments and simulations evidence anisotropy in the dielectric properties of m-HfO$_2$, most notably with the direction-dependent oscillator strength of the main bulk plasmon. The anisotropic nature of m-HfO$_2$ may contribute to the differences among VEELS spectra reported in literature. The good agreement between the complex dielectric permittivity extracted from VEELS with nanometer spatial resolution, TDDFT modeling, and past literature demonstrates that the present HRTEM-VEELS device-oriented methodology is a possible solution to the difficult nanocharacterization challenges given in the International Technology Roadmap for Semiconductors.