Abstract:
Long-range charge transfer excited states are notoriously badly underestimated in time-dependent density functional theory (TDDFT). We resolve how {\it exact} TDDFT captures charge transfer between open-shell species: in particular the role of the step in the ground-state potential, and the severe frequency-dependence of the exchange-correlation kernel. An expression for the latter is derived, that becomes exact in the limit that the charge-transfer excitations are well-separated from other excitations. The exchange-correlation kernel has the task of undoing the static correlation in the ground state introduced by the step, in order to accurately recover the physical charge-transfer states.

Abstract:
We investigate the accuracy and efficiency of the semiclassical Frozen Gaussian method in describing electron dynamics in real time. Model systems of two soft-Coulomb-interacting electrons are used to study correlated dynamics under non-perturbative electric fields, as well as the excitation spectrum. The results show that a recently proposed method that combines exact-exchange with semiclassical correlation to propagate the one-body density-matrix holds promise for electron dynamics in many situations that either wavefunction or density-functional methods have difficulty describing. The results also however point out challenges in such a method that need to be addressed before it can become widely applicable.

Abstract:
Many recent applications of time-dependent density functional theory begin in an initially excited state, and propagate it using an adiabatic approximation for the exchange-correlation potential. This however inserts the excited-state density into a ground-state approximation. By studying a series of model calculations, we highlight the relevance of initial-state dependence of the exact functional when starting in an excited state, and explore the errors inherent in the adiabatic approximation that neglect this dependence.

Abstract:
Time-dependent density functionals in principle depend on the initial state of the system, but this is ignored in functional approximations presently in use. For one electron it is shown there is no initial-state dependence: for any density, only one initial state produces a well-behaved potential. For two non-interacting electrons with the same spin in one-dimension, an initial potential that makes an alternative initial wavefunction evolve with the same density and current as a ground state is calculated. This potential is well-behaved and can be made arbitrarily different from the original potential.

Abstract:
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.

Abstract:
Autoionizing resonances that arise from the interaction of a bound single-excitation with the continuum can be accurately captured with the presently used approximations in time-dependent density functional theory (TDDFT), but those arising from a bound double excitation cannot. In the former case, we explain how an adiabatic kernel, which has no frequency-dependence, can yet generate the strongly frequency-dependent resonant structures in the interacting response function, not present in the Kohn-Sham response function. In the case of the bound double-excitation, we explain that a strongly frequency-dependent kernel is needed, and derive one for the vicinity of a resonance of the latter type, as an {\it a posteriori} correction to the usual adiabatic approximations in TDDFT. Our approximation becomes exact for an isolated resonance in the limit of weak interaction, where one discrete state interacts with one continuum. We derive a "Fano TDDFT kernel" that reproduces the Fano lineshape within the TDDFT formalism, and also a dressed kernel, that operates on top of an adiabatic approximation. We illustrate our results on a simple model system.

Abstract:
Adiabatic time-dependent density functional theory fails for excitations of a heteroatomic molecule composed of two open-shell fragments at large separation. Strong frequency-dependence of the exchange-correlation kernel is necessary for both local and charge-transfer excitations. The root of this is static correlation created by the step in the exact Kohn-Sham ground-state potential between the two fragments. An approximate non-empirical kernel is derived for excited molecular dissociation curves at large separation. Our result is also relevant for the usual local and semi-local approximations for the ground-state potential, as static correlation there arises from the coalescence of the highest occupied and lowest unoccupied orbital energies as the molecule dissociates.

Abstract:
We explore an asymmetric two-fermion Hubbard dimer to test the accuracy of the adiabatic approximation of time-dependent density functional theory in modelling time-resolved charge transfer. We show that the model shares essential features of a ground state long-range molecule in real-space, and by applying a resonant field we show that the model also reproduces essential traits of the CT dynamics. The simplicity of the model allows us to propagate with an "adiabatically-exact" approximation, i.e. one that uses the exact ground-state exchange-correlation functional, and compare with the exact propagation. This allows us to study the impact of the time-dependent charge-transfer step feature in the exact correlation potential of real molecules on the resulting dynamics. Tuning the parameters of the dimer allows a study both of charge-transfer between open-shell fragments and between closed-shell fragments. We find that the adiabatically-exact functional is unable to properly transfer charge, even in situations where the adiabatically-exact resonance frequency is remarkably close to the exact resonance, and we analyze why.

Abstract:
We propose a novel approach to the problem of polarizabilities and dissociation in electric fields from the static limit of the Vignale-Kohn (VK) functional. We consider the response to the purely scalar part of the VK response potential.This potential has ground-state properties that notably improve over the full VK response density and over usual (semi-)local functionals. The correct qualitative behavior of our potentials means that it is expected to work well for polarizabilities in cases such as the H$_2$ chain, and it will also correctly dissociate open-shell fragments in a field.

Abstract:
The response of an extended periodic system to a homogeneous field (of wave-vector $q=0$) cannot be obtained from a $q=0$ time-dependent density functional theory (TDDFT) calculation, because the Runge-Gross theorem does not apply. Time-dependent {\em current}-density functional theory is needed and demonstrates that one key ingredient missing from TDDFT is the macroscopic current. In the low-frequency limit, in certain cases, density polarization functional theory is recovered and a formally exact expression for the polarization functional is given.