Progress in Time-Dependent Density-Functional Theory

The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s, is based upon the idea that the complicated N-electron wavefunction can be replaced with the mathematically simpler 1-electron charge density in electronic struc- ture calculations of the ground stationary state. As such, ordinary DFT is neither able to treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Begin- ning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT has grown, so too has grown our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in this series [Annu. Rev. Phys. Chem. 55: 427 (2004)] left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Since doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis will be placed upon the problem of going beyond or around the TD-DFT adiabatic approximation which limits TD-DFT calculations to nominally singly-excited states. Posted with permission from the Annual Review of Physical Chemistry, Volume 63 \c{opyright} 2012 by Annual Reviews, http://www.annualreviews.org

Alloying effects on the optical properties of Ge1−x_{1-x}Six_x nanocrystals from TDDFT and comparison with effective-medium theory

We present the optical spectra of Ge$_{1-x}$Si$_x$ alloy nanocrystals calculated with time-dependent density-functional theory in the adiabatic local-density ap proximation (TDLDA). The spectra change smoothly as a function of the compositio n $x$. On the Ge side of the composition range, the lowest excitations at the ab sorption edge are almost pure Kohn-Sham independent-particle HOMO-LUMO transitio ns, while for higher Si contents strong mixing of transitions is found. Within T DLDA the first peak is slightly higher in energy than in earlier independent-par ticle calculations. However, the absorption onset and in particular its composit ion dependence is similar to independent-particle results. Moreover, classical depolarization effects are responsible for a very strong suppression of the abs orption intensity. We show that they can be taken into account in a simpler way using Maxwell-Garnett classical effective-medium theory. Emission spectra are in vestigated by calculating the absorption of excited nanocrystals at their relaxe d geometry. The structural contribution to the Stokes shift is about 0.5 eV. Th e decomposition of the emission spectra in terms of independent-particle transit ions is similar to what is found for absorption. For the emission, very weak tra nsitions are found in Ge-rich clusters well below the strong absorption onset.Comment: submitted to Phys. Rev.

Time-dependent Kohn-Sham theory with memory

In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic local density approximation can be described in terms of viscoelastic stresses in the electron liquid. In the time domain, this leads to a velocity-dependent xc vector potential with a memory containing short- and long-range components. The resulting time-dependent Kohn-Sham formalism describes the dynamics of electronic systems including decoherence and relaxation. For the example of collective charge-density oscillations in a quantum well, we illustrate the xc memory effects, clarify the dissipation mechanism, and extract intersubband relaxation rates for weak and strong excitations.Comment: 4 pages, 4 figure

Fast computation of the Kohn-Sham susceptibility of large systems

For hybrid systems, such as molecules grafted onto solid surfaces, the calculation of linear response in time dependent density functional theory is slowed down by the need to calculate, in N^4 operations, the susceptibility of N non interacting Kohn-Sham reference electrons. We show how this susceptibility can be calculated N times faster within finite precision. By itself or in combination with previous methods, this should facilitate the calculation of TDDFT response and optical spectra of hybrid systems.Comment: submitted 25/1/200

The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges

In principle, the Luttinger-Ward Green's function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW-RPA approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green's functions) is necessary. Finally, we present some relevant numerical results for atomic systems.Comment: 3 figures and 3 tables, under review at Physical Review

Undoing static correlation: Long-range charge transfer in time-dependent density functional theory

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.Comment: 2 figure

Photoelectron spectra of anionic sodium clusters from time-dependent density-functional theory in real-time

We calculate the excitation energies of small neutral sodium clusters in the framework of time-dependent density-functional theory. In the presented calculations, we extract these energies from the power spectra of the dipole and quadrupole signals that result from a real-time and real-space propagation. For comparison with measured photoelectron spectra, we use the ionic configurations of the corresponding single-charged anions. Our calculations clearly improve on earlier results for photoelectron spectra obtained from static Kohn-Sham eigenvalues

Determination of the lowest energy structure of Ag8_8 from first-principles calculations

The ground-state electronic and structural properties, and the electronic excitations of the lowest energy isomers of the Ag$_8$ cluster are calculated using density functional theory (DFT) and time-dependent DFT (TDDFT) in real time and real space scheme, respectively. The optical spectra provided by TDDFT predict that the D$_{2d}$ dodecahedron isomer is the structural minimum of Ag$_8$ cluster. Indeed, it is borne out by the experimental findings.Comment: 4 pages, 2 figures. Accepted in Physical Review A as a brief repor