AMO-dance · Strong Field Dynamics of Atoms and Molecules: History-dependent Functionals and Exact Kohn-Sham Potentials of the Time-dependent (multi-component) Density Functional Theory

Strong Field Dynamics of Atoms and Molecules: History-dependent Functionals and Exact Kohn-Sham Potentials of the Time-dependent (multi-component) Density Functional Theory

The AMO-dance project aimed at four major objectives: 1)Deriving and establishing robust non-empirical Time-Dependent Density Functional Theory (TDDFT) functionals beyond the adiabatic approximation; 2)Using the developed functional to study strong field dynamics of many electron systems; 3)Developing a new algorithm for obtaining the exact potentials of the KS equations in Multi-Component TDDFT (MC-TDDFT); 4)Investigation of the exact KS-potentials of the MC-TDDFT for molecular (model) systems. These objectives are of great importance in the field of quantum dynamics and in particular in describing the light-matter interaction atoms and molecules. This is due to the fact that the interaction between atoms and molecules with ultra-short laser pulses with intensities comparable to the typical atomic and molecular binding forces gives rise to a variety of nonlinear phenomena that require a non-perturbative theoretical description due to their nonlinear nature. In case of atoms, the major challenge is to treat an interacting many-electron problem that is driven out of equilibrium by an external ultrashort intense pulse. The case of molecules is yet more difficult, due to the involvement of the additional nuclear degrees of freedom. In general, one needs to resort to a direct solution of the time-dependent Schrödinger equation (TDSE) that becomes computationally prohibitively expensive as soon as one deals with more than a few degrees of freedom. Theoretically, the time-dependent density functional theory (TDDFT) lends itself as one of the most promising approaches to describe atoms and molecules exposed to ultra-short and strong laser pulses, given its unprecedented balance between accuracy and numerical feasibility. However, the accuracy of TDDFT depends on the approximation used for the exchange-correlation (xc) potential that is a functional of the entire history of the density and on the initial state , and inclusion of this “memory-dependence” necessitates non-locality in space. Almost all calculations today neglect the memory-dependence. Notorious failures of the usual approximations for a wide range of phenomena, in particular in strange-field dynamics, have frustrated the effort for TDDFT to be used reliably as a simple black-box tool.

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