The mapping of time-dependent densities on potentials in systems of identical quantum mechanical particles is examined. This mapping is of significance ever since Runge and Gross [Phys. Rev. Lett. 52, 997 (1984)] established its uniqueness, forming the theoretical basis for time-dependent density functional theory. Beyond uniqueness there are two important issues: existence, often called v-representability, and stability. We show that v-representability for localized densities in turn-on situations is not assured and we give a simple example of nonexistence. As for stability, we discuss an inversion procedure and by computing its Lyapunov exponents we demonstrate that the mapping is unstable with respect to fluctuations in the initial state. We argue that such instabilities will plague any inversion procedure.

We extend our previous results [R. Baer et al., J. Chem. Phys. 126, 014705 (2007).] to develop a simple theory of localized surface plasmon-polariton (LSPP) dispersion on regular arrays of metal nanoparticles in the weak-field and weak-damping limits. This theory describes the energy-momentum as well as the polarization-momentum properties of LSPP waves, both of which are crucial to plasmonic device design. We then explicitly compute the dispersion relation for isotropic and anisotropic two-dimensional square lattices, and show curve crossings between all three levels as well as negative refraction where the phase and group velocities (refractive indices), or at least their projection along the main axis, have different signs. The curve crossing implies that scattering between the different polarizations, and therefore different velocities, is easy at the curve crossing momenta, so that a quick change in wave packet direction can be achieved. Time-resolved wave packet dynamics simulations demonstrate negative refraction and the easy scattering over nanometer length scales. This paper also gives some computational schemes for future applications, such as a way to include source terms and how to efficiently treat dissipative effects.

This Invited Article reports extensions of a recently developed approach to density functional theory with correct long-range behavior (R. Baer and D. Neuhauser, Phys. Rev. Lett., 2005, 94, 043002). The central quantities are a splitting functional \gamma[n] and a complementary exchange-correlation functional E_\gammaXC[n]. We give a practical method for determining the value of \gamma in molecules, assuming an approximation for E_\gammaXC is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent \gamma and an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond lengths of the molecules in the G2(1) database. The optimized values are \gamma = 0.5 a_0^-1 and w = 0.1. We then examine the performance of this slightly semi-empirical functional for a variety of molecular properties, comparing to related works and experiment. We show that this approach can be used for describing in a satisfactory manner a broad range of molecular properties, be they static or dynamic. Most satisfactory is the ability to describe valence, Rydberg and inter-molecular charge-transfer excitations.

Characterizing and localizing electronic energy degeneracies is important for describing and controlling electronic energy flow in molecules. We show, using topological phase considerations, that the Renner effect in polyatomic molecules with more than three nuclei is necessarily accompanied by 'satellite' conical intersections. In these intersections the non-adiabatic coupling term is on average half an integer. We present ab initio results on the tetra-atomic radical cation C2H+2 to demonstrate the theory.

Recently, the possibility of transporting electromagnetic energy as local-plasmon-polariton waves along arrays of silver nanoparticles was demonstrated experimentally [S. A. Maier et al., Nat. Mater. 2, 229 (2003)]. It was shown that dipole coupling facilitates phase-coherent excitation waves, which propagate while competing against decoherence effects occurring within each dot. In this article the authors study the ideal coherent shuttling in such a system, leaving decoherence for future investigation. In the weak field limit, the waves obey a Schrödinger equation, to be solved using either time-dependent wave-packet or energy resolved scattering techniques. The authors study some dynamical characteristics of these waves, emphasizing intuition and insight. Scattering from barriers, longitudinal-transverse coupling and acceleration methods are studied in detail. The authors also discuss briefly two-dimensional arrays and a simple decoherence model

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 nonlocal 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. Memory effects on nonlinear spectroscopy are studied as well: a real-time pump-probe setup is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail; and in high harmonic generation, we show that memory narrows and redshifts emission lines.

Real-time first principle simulations are presented of the D2 Coulomb explosion dynamics detonated by exposure to very intense few-cycle laser pulse. Three approximate functionals within the time-dependent density functional theory (TDDFT) functionals are examined for describing the electron dynamics, including time-dependent Hartree-Fock theory. Nuclei are treated classically with quantum corrections. The calculated results are sensitive to the underlying electronic structure theory, showing too narrow kinetic energy distribution peaked at too high kinetic energy when compared with recent experimental results (Phys. Rev. Lett. 2003, 91, 093002). Experiment also shows a low energy peak which is not seen in the present calculation. We conclude that while Ehrenfest-adiabatic-TDDFT can qualitatively account for the dynamics, it requires further development, probably beyond the adiabatic approximation, to be quantitative.

Inelastic effects arising from electron-phonon coupling in molecular Aharonov-Bohm (AB) interferometers are studied using the nonequilibrium Green's function method. Results for the magnetoconductance are compared for different values of the electron-phonon coupling strength. At low-bias voltages, the coupling to the phonons does not change the lifetime and leads mainly to scattering phase shifts of the conducting electrons. As a result of these dephasing processes, the magnetoconductance of the molecular AB interferometer becomes more sensitive to the threading magnetic flux as the electron-phonon coupling is increased, opposite to the behavior of an electric gate.

Affecting the current through a molecular or nanoscale junction is usually done by a combination of bias and gate voltages. Magnetic fields are less studied because nanodevices can capture only low values of the magnetic flux. We review recent work done with the aim of finding the conditions for magnetic fields to significantly affect the conductance of such junctions. The basic idea is to create narrow tunneling resonances through a molecular ring-like structure that are highly sensitive to the magnetic field. We describe a computational method that allows us to examine atomistic models of such systems and discuss several specific examples of plausible systems, such as the quantum corral, carbon nanotubes, and polycyclic aromatic hydrocarbon molecules. A unique property of the magnetic field, namely, its ability to split degenerate levels on the ring, is shown to allow prototypes of interesting new nanoscale devices, such as the three-terminal parallel logic gate.

Near-field scanning microscopy and nonlinear spectroscopy on a molecular scale involve weakly interacting subsystems that dynamically exchange electrons and electromagnetic energy. The theoretical description of such processes requires unified approach to the electron-near-field dynamics. By considering electronic structure and dynamics of two distant clusters or atoms we show that adiabatic local spin-density approximation (ALSDA) fails to describe (even qualitatively) essential details of electron dynamics in weakly interacting systems. A recently developed functional addresses these ailments within a time-dependent setting. With this method we study the spectroscopy of a composite system, namely, two weakly coupled metallic clusters. The near-field (dipole-dipole) coupling and electron transfer display an interesting interplay, producing exponential sensitivity of emission yield to the intercomponent distance.

We examine the effects of self-repulsion on the predictions of charge distribution in biased molecular junctions by the local density functional theory methods. This is done using a functional with explicit long-range exchange term effects [R. Baer, D. Neuhauser, Phys. Rev. Lett. 94 (2005) 043002]. We discuss in detail the new density functional, pointing out some of the remaining difficulties in the theory. We find that in weakly coupled junctions (the typical molecular electronics case) local-density functionals fail to describe correctly the charge distribution in the intermediate bias regime. (c) 2006 Elsevier B.V. All rights reserved.

Dynamics of glycine chemisorbed on the surface of a silicon cluster is studied for a process that involves single-photon ionization, followed by recombination with the electron after a selected time delay. The process is studied by “on-the-fly” molecular dynamics simulations, using the semiempirical parametric method number 3 (PM3) potential energy surface. The system is taken to be in the ground state prior to photoionization, and time delays from 5 to 50 fs before the recombination are considered. The time evolution is computed over 10 ps. The main findings are (1) the positive charge after ionization is initially mostly distributed on the silicon cluster. (2) After ionization the major structural changes are on the silicon cluster. These include Si–Si bond breaking and formation and hydrogen transfer between different silicon atoms. (3) The transient ionization event gives rise to dynamical behavior that depends sensitively on the ion state lifetime. Subsequent to 45 fs evolution in the charged state, the glycine molecule starts to rotate on the silicon cluster. Implications of the results to various processes that are induced by transient transition to a charged state are discussed. These include inelastic tunneling in molecular devices, photochemistry on conducting surfaces, and electron-molecule scattering.

An iterative approach for calculating the frequency domain linear response of molecular systems within time-dependent density-functional theory is presented. The method completely avoids computing the exchange-correlation kernel which is typically the most expensive step for large systems. In particular, virtual orbitals are not needed. This approach may be useful for treating the response of large systems. We give an outline of the theory and a demonstration on a jellium model of an elliptic gold cluster. A detailed theory is appended discussing the computation of conductance and ac impedance of molecular junctions under bias.

Today, most application of time-dependent density functional theory (TDDFT) use adiabatic exchange- correlation (XC) potentials that do not take into account non-local temporal effects. Incorporating such "memory" terms into XC potentials is complicated by the constraint that the derived force and torque densities must integrate to zero at every instance. This requirement can be met by deriving the potentials from an XC action that is Galilean in-variant (GI). We develop a class of simple but flexible forms for an action that respect these constraints. The basic idea is to formulate the action in terms of the Eularian-Lagrangian transformation (ELT) metric tensor, which is itself GI. The general form of the XC potentials in this class is then derived and the linear response limit is derived as well.

We demonstrate the physical principles for the construction of a nanometer-sized magnetoresistance device based on the Aharonov-Bohm effect [Phys. Rev. 115, 485 (1959)]. The proposed device is made of a short single-walled carbon nanotube (SWCNT) placed on a substrate and coupled to a tip/contacts. We consider conductance due to the motion of electrons along the circumference of the tube (as opposed to the motion parallel to its axis). We find that the circumference conductance is sensitive to magnetic fields threading the SWCNT due to the Aharonov-Bohm effect, and show that by retracting the tip/contacts, so that the coupling to the SWCNT is reduced, very high sensitivity to the threading magnetic field develops. This is due to the formation of a narrow resonance through which the tunneling current flows. Using a bias potential the resonance can be shifted to low magnetic fields, allowing the control of conductance with magnetic fields of the order of 1 T.

An ab initio method is developed for variational grand-canonical molecular electronic structure of open systems based on the Gibbs–Peierls–Boguliobov inequality. We describe the theory and a practical method for performing the calculations within standard quantum chemistry codes using Gaussian basis sets. The computational effort scales similarly to the ground-state Hartree–Fock method. The quality of the approximation is studied on a hydrogen molecule by comparing to the exact Gibbs free energy, computed using full configuration-interaction calculations. We find the approximation quite accurate, with errors similar to those of the Hartree–Fock method for ground-state zero-temperature calculations. A further demonstration is given of the temperature effects on the bending potential curve for water. Some future directions and applications of the method are discussed. Several appendices give the mathematical and algorithmic details of the method.