Time-dependent Functional Theory Research Articles

Excitation energies from range-separated time-dependent density and density matrix functional theory

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.

Propagators for the time-dependent Kohn-Sham equations.

In this paper we address the problem of the numerical integration of the time-dependent Schrodinger equation i partial differential (t)phi=Hphi. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, H is in general time dependent, even in the absence of an external time-dependent field. The present analysis also holds for the description of the excited state dynamics of a many-electron system under the influence of arbitrary external time-dependent electromagnetic fields. Our discussion is separated in two parts: (i) First, we look at several algorithms to approximate exp(A), where A is a time-independent operator [e.g., A=-iDeltatH(tau) for some given time tau]. In particular, polynomial expansions, projection in Krylov subspaces, and split-operator methods are investigated. (ii) We then discuss different approximations for the time-evolution operator, such as the midpoint and implicit rules, and Magnus expansions. Split-operator techniques can also be modified to approximate the full time-dependent propagator. As the Hamiltonian is time dependent, problem (ii) is not equivalent to (i). All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations.

Nonequilibrium time-dependent functional theory for coupled interacting fields.

We develop a nonequilibrium time-dependent functional theory of coupled interacting fields in terms of the Liouvillian quantum field dynamics. In this theory the expectation values of the appropriate field operators are treated as the functional variables. Thus, the formalism proposed here goes beyond the existing time-dependent density-functional method, in that we now have a mixed-state multivariable dynamical theory. A large class of condensed matter problems, with the given initial condition that the system be in thermodynamic equilibrium and subjected to time-dependent external forces, can now be examined. In particular, we formulate the self-consistent coupled equations for the electron, ion, and the electromagnetic fields. The above formalism provides a firm physical and mathematical basis for time-dependent dynamical simulation procedures such as those envisaged in the Car-Parrinello approach by replacing the fictitious Lagrangian by a precise action principle. The theory involves a certain functional representing the mutual interactions and correlations among these fields. In parallel with this, we also generalize the Baym \ensuremath{\Phi}-derivable method in many-body theory to investigate the class of problems mentioned above. This involves a functional of the exact one-particle Green functions. We compare the two methods and suggest the use of the latter in the former scheme as a way of going beyond the simple mean-field schemes. We illustrate the utility of the framework by citing a variety of illustrative examples.

A nonequilibrium time-dependent functional theory based on Liouvillean quantum field dynamics in condensed matter systems

A nonequilibrium time-dependent functional theory, for studying a condensed matter system which is initially in thermodynamic equilibrium subjected to external time-dependent fields, is constructed based on Liouvillean quantum field dynamics, by the introduction of a new superoperator in the Liouville space corresponding to the time-derivative operator in the Hilbert space. This formalism provides a rigorous justification of the self-consistent and time-dependent numerical simulation of resonant tunneling devices including their bistability. This shows the utility of the present theory in the study of open systems. The theory is further generalized to incorporate the ion motions and the electromagnetic fields. The above formalism thus provides a firm physical and mathematical basis for time-dependent simulation procedures such as those based on the Car-Parinello approach by replacing the fictitious Lagrangian used there by a precise action principle.

Time-dependent functional theory of coupled electron and electromagnetic fields in condensed-matter systems

It is shown that a time-dependent external four-vector potential ${\mathit{a}}_{\mathrm{\ensuremath{\mu}}}^{\mathrm{ext}}$(r\ensuremath{\rightarrow}t) and a conserved external four-current ${\mathit{j}}_{\mathrm{\ensuremath{\mu}}}^{\mathrm{ext}}$(r\ensuremath{\rightarrow}t), with a given fixed initial state of the combined condensed-matter--electromagnetic system, lead, respectively, to a conserved self-consistent four-current density ${\mathit{J}}_{\mathrm{\ensuremath{\mu}}}$(r\ensuremath{\rightarrow}t) and a self-consistent four-vector field ${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$(r\ensuremath{\rightarrow}t), such that a map (${\mathit{a}}_{\mathrm{\ensuremath{\mu}}}^{\mathrm{ext}}$,${\mathit{j}}_{\mathrm{\ensuremath{\mu}}}^{\mathrm{ext}}$)\ensuremath{\rightarrow}(${\mathit{J}}_{\mathrm{\ensuremath{\mu}}}$,${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$) is invertible under certain simple conditions. With this as a basis, the stationary action principle is used to derive the self-consistent equations for the electron and the electromagnetic fields appropriate for a description of the combined condensed-matter and electrodynamic systems, where real or virtual pair creation is ignored.

A time-dependent functional theory for the electron-ion system

It is shown that a time-dependent single particle potential ν e ( rt) and a time-dependent force on the ion F(lKt) with a given fixed initial state of the combined electron-ion system, leading respectively to a given ν-representable electronic density n( rt) and ionic displacement R(lKt) , are determined so that a map (ν e , F)→(n, R) is invertible. This formulation allows us to ad dress the effective self-consistent ion dynamics of the electron-ion system in contrast to existing treatments such as those based on the Car-Parrinello approach by replacing the fictitous Lagrangian introduced there by a precise action principle. Based on this, some schemes are derived to calculate the density, the displacement, etc. using the stationary action principle and some convenient choices of a suitably parametrised state vector.