Troubleshooting Time-Dependent Density-Functional Theory for Photochemical Applications: Oxirane

The development of analytic-gradient methodology for excited states within conventional time-dependent density-functional theory (TDDFT) would seem to offer a relatively inexpensive alternative to better established quantum-chemical approaches for the modeling of photochemical reactions. However, even though TDDFT is formally exact, practical calculations involve the use of approximate functionals, in particular the TDDFT adiabatic approximation, whose use in photochemical applications must be further validated. Here, we investigate the prototypical case of the symmetric CC ring opening of oxirane. We demonstrate by direct comparison with the results of high-quality quantum Monte Carlo calculations that, far from being an approximation on TDDFT, the Tamm-Dancoff approximation (TDA) is a practical necessity for avoiding triplet instabilities and singlet near instabilities, thus helping maintain energetically reasonable excited-state potential energy surfaces during bond breaking. Other difficulties one would encounter in modeling oxirane photodynamics are pointed out but none of these is likely to prevent a qualitatively correct TDDFT/TDA description of photochemistry in this prototypical molecule.Comment: 19 pages, 17 figures, submitted to the Journal of Chemical Physic

Evaporation Prescription for Time-Dependent Density Functional Calculations

Collisions between $^{248}$Cm and $^{48}$Ca are systematically calculated by time-dependent density functional calculations with evaporation prescription. Depending on the incident energy and impact parameter, fusion, fusion-fission, and quasi-fission events are expected to appear. In this paper, the evaporation prescription is introduced, which is expected to be rather important to heavy-ion reactions producing superheavy nuclei, where the heavier total mass can be related to the higher total excitation energy.Comment: To appear in the NN2012 Proceedings in Journal of Physics: Conference Series; revised based on the referee's comment (ver. 2, 09/2012

Investigating interaction-induced chaos using time-dependent density functional theory

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbour level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.Comment: 8 pages, 4 figure

A minimal model for excitons within time-dependent density-functional theory

The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the role of the long spatial range and the frequency dependence of the xc kernel $f_{\rm xc}$ for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional Kronig-Penney model and simple approximate xc kernels, which allows us to address these questions in a transparent manner. Depending on the system, it is found that adiabatic xc kernels can produce a single bound exciton, and sometimes two bound excitons, where the long spatial range of $f_{\rm xc}$ is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.Comment: 12 pages, 11 figure

A unified approach to the density-potential mapping in a family of time-dependent density functional theories

It is shown that the density-potential mapping and the ${\cal V}$-representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schr\"odinger equation (NLSE). The derived NLSE for TDCDFT adds a link which bridges the earlier NLSE-based formulations of the time-dependent deformation functional theory (TDDefFT) and the time-dependent density functional theory (TDDFT). We establish close relations between the nonlinear many-body problems which control the existence of TDCDFT, TDDFT, and TDDefFT, and thus develop a unified point of view on the whole family of the TDDFT-like theories.Comment: RevTeX4, 15 page