Electronic Non-Adiabatic Dynamics: memory-dependence and electron-nuclear correlation

Time-Dependent Density Functional Theory (TDDFT) is one of the most promising theoretical tools in describing the electronic dynamics. In spite of its great success calculating spectra in the linear response regime, it performs poorly in the case of the strong-field dynamics of atoms and molecules. Two main obstacles concerning the application of TDDFT to atoms and molecules in ultrashort intense laser pulses are:
i) Lack of memory dependence in the usual exchange-correlation approximations. The exact functional depends on the history of the density that is neglected in almost all of the existing approximations.
i) Lack of a proper description of the electron-ion correlation.
Towards tackling these problems, we have developed a memory-dependent functional for two-site Hubbard model that fulfils the recently proposed exact condition (Fuks et al. PRL 114, 183002 (2015)). Furthermore, by utilising the Exact-Factorization framework, we have studied the exact potential acting on the electron in charge-resonance enhanced ionization in H2+ molecule and showed that there can be significant differences between the exact potential and that used in the traditional quasistatic analyses, arising from non-adiabatic coupling to the nuclear system (Khosravi, Abedi, Maitra, PRL 115, 263002 (2015)).