# Towards time-dependent current-density-functional theory in the non-linear regime

## Abstract

Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment ofmore »

- Authors:

- Université de Toulouse, UPS, Laboratoire de Physique Théorique, IRSAMC, F-31062 Toulouse Cedex (France)
- (France)
- (United Kingdom)
- Laboratoire de Physique Théorique, CNRS, IRSAMC, Université Toulouse III - Paul Sabatier and European Theoretical Spectroscopy Facility, 118 Route de Narbonne, 31062 Toulouse Cedex (France)
- Institut für Theoretische Physik, Universität Erlangen, Staudtstraße 7, D-91058 Erlangen (Germany)

- Publication Date:

- OSTI Identifier:
- 22416173

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CORRELATIONS; CURRENT DENSITY; DENSITY FUNCTIONAL METHOD; DIPOLE MOMENTS; EXCITATION; IRRADIATION; MOLECULES; NONLINEAR PROBLEMS; POTENTIALS; TIME DEPENDENCE

### Citation Formats

```
Escartín, J. M., CNRS, UMR5152, F-31062 Toulouse Cedex, Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, Vincendon, M., Dinh, P. M., Suraud, E., CNRS, UMR5152, F-31062 Toulouse Cedex, Romaniello, P., and Reinhard, P.-G.
```*Towards time-dependent current-density-functional theory in the non-linear regime*. United States: N. p., 2015.
Web. doi:10.1063/1.4913291.

```
Escartín, J. M., CNRS, UMR5152, F-31062 Toulouse Cedex, Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, Vincendon, M., Dinh, P. M., Suraud, E., CNRS, UMR5152, F-31062 Toulouse Cedex, Romaniello, P., & Reinhard, P.-G.
```*Towards time-dependent current-density-functional theory in the non-linear regime*. United States. doi:10.1063/1.4913291.

```
Escartín, J. M., CNRS, UMR5152, F-31062 Toulouse Cedex, Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, Vincendon, M., Dinh, P. M., Suraud, E., CNRS, UMR5152, F-31062 Toulouse Cedex, Romaniello, P., and Reinhard, P.-G. Sat .
"Towards time-dependent current-density-functional theory in the non-linear regime". United States.
doi:10.1063/1.4913291.
```

```
@article{osti_22416173,
```

title = {Towards time-dependent current-density-functional theory in the non-linear regime},

author = {Escartín, J. M. and CNRS, UMR5152, F-31062 Toulouse Cedex and Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE and Vincendon, M. and Dinh, P. M. and Suraud, E. and CNRS, UMR5152, F-31062 Toulouse Cedex and Romaniello, P. and Reinhard, P.-G.},

abstractNote = {Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na{sub 2}. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.},

doi = {10.1063/1.4913291},

journal = {Journal of Chemical Physics},

number = 8,

volume = 142,

place = {United States},

year = {Sat Feb 28 00:00:00 EST 2015},

month = {Sat Feb 28 00:00:00 EST 2015}

}